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What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
The calculus section will carry out differentiation as well as definite and indefinite integration.
The matrices section contains commands for the arithmetic manipulation of matrices.
The graphs section contains commands for plotting equations and inequalities.
The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

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This tool combines the power of mathematical computation engine that excels at solving mathematical formulas with the power of artificial intelligence large language models to parse and generate natural language answers. This creates a math problem solver that's more accurate than ChatGPT, more flexible than a math calculator, and provides answers faster than a human tutor.

Problem Solver Subjects

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Math Word Problems
Pre-Algebra
Geometry Graphing
Trigonometry
Precalculus
Finite Math
Linear Algebra

Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.

Basic Math Solutions

Below are examples of basic math problems that can be solved.

Long Arithmetic
Rational Numbers
Operations with Fractions
Ratios, Proportions, Percents
Measurement, Area, and Volume
Factors, Fractions, and Exponents
Unit Conversions
Data Measurement and Statistics
Points and Line Segments

Math Word Problem Solutions

Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

Pre-Algebra Solutions

Below are examples of Pre-Algebra math problems that can be solved.

Variables, Expressions, and Integers
Simplifying and Evaluating Expressions
Solving Equations
Multi-Step Equations and Inequalities
Ratios, Proportions, and Percents
Linear Equations and Inequalities

Algebra Solutions

Below are examples of Algebra math problems that can be solved.

Algebra Concepts and Expressions
Points, Lines, and Line Segments
Simplifying Polynomials
Factoring Polynomials
Linear Equations
Absolute Value Expressions and Equations
Radical Expressions and Equations
Systems of Equations
Quadratic Equations
Inequalities
Complex Numbers and Vector Analysis
Logarithmic Expressions and Equations
Exponential Expressions and Equations
Conic Sections
Vector Spaces
3d Coordinate System
Eigenvalues and Eigenvectors
Linear Transformations
Number Sets
Analytic Geometry

Trigonometry Solutions

Below are examples of Trigonometry math problems that can be solved.

Algebra Concepts and Expressions Review
Right Triangle Trigonometry
Radian Measure and Circular Functions
Graphing Trigonometric Functions
Simplifying Trigonometric Expressions
Verifying Trigonometric Identities
Solving Trigonometric Equations
Complex Numbers
Analytic Geometry in Polar Coordinates
Exponential and Logarithmic Functions
Vector Arithmetic

Precalculus Solutions

Below are examples of Precalculus math problems that can be solved.

Operations on Functions
Rational Expressions and Equations
Polynomial and Rational Functions
Analytic Trigonometry
Sequences and Series
Analytic Geometry in Rectangular Coordinates
Limits and an Introduction to Calculus

Calculus Solutions

Below are examples of Calculus math problems that can be solved.

Evaluating Limits
Derivatives
Applications of Differentiation
Applications of Integration
Techniques of Integration
Parametric Equations and Polar Coordinates
Differential Equations

Statistics Solutions

Below are examples of Statistics problems that can be solved.

Algebra Review
Average Descriptive Statistics
Dispersion Statistics
Probability
Probability Distributions
Frequency Distribution
Normal Distributions
t-Distributions
Hypothesis Testing
Estimation and Sample Size
Correlation and Regression

Finite Math Solutions

Below are examples of Finite Math problems that can be solved.

Polynomials and Expressions
Equations and Inequalities
Linear Functions and Points
Systems of Linear Equations
Mathematics of Finance
Statistical Distributions

Linear Algebra Solutions

Below are examples of Linear Algebra math problems that can be solved.

Introduction to Matrices
Linear Independence and Combinations

Chemistry Solutions

Below are examples of Chemistry problems that can be solved.

Unit Conversion
Atomic Structure
Molecules and Compounds
Chemical Equations and Reactions
Behavior of Gases
Solutions and Concentrations

Physics Solutions

Below are examples of Physics math problems that can be solved.

Static Equilibrium
Dynamic Equilibrium
Kinematics Equations
Electricity
Thermodymanics

Geometry Graphing Solutions

Below are examples of Geometry and graphing math problems that can be solved.

Step By Step Graphing
Linear Equations and Functions
Polar Equations

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Math Input on the Wolfram|Alpha Website

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Math Solver

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UpStudy Math Solver with steps is versatile and capable of solving a wide range of mathematical problems, including pre-algebra, algebra, pre-calculus, inequalities, calculus, trigonometry, geometry, statistics and probability, and matrices. No matter the complexity of the problem, our tool aims to provide fast, clear, and step-by-step solutions.

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Play Math Games: Have fun doing math puzzles and games like Sudoku, KenKen or math riddles. These can make learning fun and improve your number skills and logical thinking.

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Discover Frequently Asked Math Questions and Their Answers

How do you write the quadratic function #y=x^2+14x+11# in vertex form?
How many points does #y=-2x^2+x-3# have in common with the vertex and where is the vertex in relation to the x axis?
How do you solve #4x^4 - 16x^2 + 15 = 0#?
How do you solve #2x^2+3x-2=0#?
How do you solve #7(x-4)^2-2=54# using any method?
How do you solve #x^2 + 5x + 6 = 0# algebraically?
How do you use factoring to solve this equation #3x^2/4=27#?
What is the vertex of # y = (1/8)(x – 5)^2 - 3#?
How do you solve #| x^2+3x-2 | =2#?
How do you solve #2x²+3x=5 # using the quadratic formula?
How do you find the derivative of #y=tan(3x)# ?
How do you differentiate #f(x)= 1/ (lnx)# using the quotient rule?
How do you differentiate #(3+sin(x))/(3x+cos(x))#?
What is the derivative of this function #sin^-1(x/4)#?
What is the derivative of this function #y=sin^-1(2x)#?
What is the derivative of this function #arcsec(x^3)#?
What is the derivative of #y=sin(tan2x)#?
How do you differentiate #cos(pi*x^2)#?
What is the derivative of #f(x)=(x^2-4)ln(x^3/3-4x)#?
What is the derivative of #y=3sin(x) - sin(3x)#?
A triangle has corners at #(5 ,1 )#, #(2 ,9 )#, and #(4 ,3 )#. What is the area of the triangle's circumscribed circle?
How can we find the area of irregular shapes?
A triangle has vertices A, B, and C. Vertex A has an angle of #pi/2 #, vertex B has an angle of #( pi)/3 #, and the triangle's area is #24 #. What is the area of the triangle's incircle?
An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(7 ,1 )# to #(8 ,5 )# and the triangle's area is #27 #, what are the possible coordinates of the triangle's third corner?
A triangle has corners at #(7 , 9 )#, #(3 ,7 )#, and #(4 ,8 )#. What is the radius of the triangle's inscribed circle?
Circle A has a center at #(2 ,3 )# and a radius of #1 #. Circle B has a center at #(0 ,-2 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?
A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 7 #. If the angle between sides A and C is #pi/4 #, what is the area of the parallelogram?
What is a quadrilateral that is not a parallelogram and not a trapezoid?
Your teacher made 8 triangles he need help to identify what type triangles they are. Help him?: 1) #12, 16, 20# 2) #15, 17, 22# 3) #6, 16, 26# 4) #12, 12, 15# 5) #5,12,13# 6) #7,24,25# 7) #8,15,17# 8) #9,40,41#
A triangle has corners A, B, and C located at #(3 ,5 )#, #(2 ,9 )#, and #(4 , 8 )#, respectively. What are the endpoints and length of the altitude going through corner C?
What is the GCF of the set #64, 16n^2, 32n#?
How do you write the reciprocal number of 5?
Jeanie has a 3/4 yard piece of ribbon. She needs one 3/8 yard piece and one 1/2 yard piece. Can she cut the piece of ribbon into the two smaller pieces? Why?
How do you find the GCF of #25k, 35j#?
How do you write 132/100 in a mixed number?
How do you evaluate the power #2^3#?
How do you simplify #(4^6)^2 #?
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DU Professor Helps Solve Famous 70-Year-Old Math Problem

Jordyn reiland.

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Assistant Professor Mandi Schaeffer Fry is the first faculty member to be published in the Annals of Mathematics since the 1880s.

University of Kaiserslautern Professor Gunter Malle, University of Denver Assistant Professor Mandi Schaeffer Fry and University of Valencia Professor Gabriel Navarro pose for a photo after announcing their theorem in Oberwolfach, Germany.

Whether it be flying trapeze, participating in competitive weightlifting or solving math problems that have confounded academics for decades, Mandi Schaeffer Fry enjoys chasing the next adventure.

Schaeffer Fry, who joined the University of Denver’s Department of Mathematics in the fall of 2023, will be the first faculty member since the 1880s to be published in the Annals of Mathematics , widely seen as the industry’s most prestigious journal.

In 2022, Schaeffer Fry helped complete a problem that dates to 1955—mathematician Richard Brauer’s Height Zero Conjecture.

“Maybe one of the most challenging parts, other than the math itself, was the knowledge of the weight that this would have on the field,” Schaeffer Fry says. “If you’re going to make an announcement like this, you have to be darn sure that it’s absolutely correct.”

Over the years, number crunchers have worked on the problem at universities across the globe, and some found partial solutions; however, the problem was not completed until now.

“Mandi’s accomplishment is exciting. Solving Brauer's Height Zero Conjecture is remarkable,” Mathematics Department Chair Alvaro Arias says.

The work is also a testament to DU’s achievement as a Research 1 (R1) institution.

Fry and her collaborators—University of Kaiserslautern Professor Gunter Malle, University of Valencia Professor Gabriel Navarro and Rutgers University Professor Pham Huu Tiep—worked around the clock over the course of three months in eight-hour shifts during the summer of 2022 to find a solution.

In April, that work was accepted for publication in the Annals of Mathematics.

'Brauer's Height Zero Conjecture (BHZ) was the first conjecture leading to the part of my field studying 'local-global' problems in the representation theory of finite groups, which seek to relate properties of groups with properties of certain nice smaller subgroups, letting us 'zoom in' on the group using just a specific prime number and simplify things," Schaeffer Fry says.

"The BHZ gives us a way to tell from the character table of a group (a table of data that encodes lots, but not all, information about the group) whether or not certain of these subgroups, called defect groups, have the commutativity property," she adds.

This paper was especially meaningful to Schaeffer Fry as she had always wanted to work with Malle, Tiep and Navarro as they have been her primary mentors. Tiep was her PhD advisor and this was the first time they had worked together since then.

Fry believes she has solidified her place in the field and knows she’ll likely never top this accomplishment, but she’s always looking for the next adventure—whether that’s in or out of the classroom.

Flying high and pumping iron

When Schaeffer Fry isn’t on DU’s campus working with students or conducting research, you can find her flying trapeze and competitive weightlifting.

Schaeffer Fry became involved in competitive weightlifting during graduate school, and, in the last year of her PhD at the University of Arizona, she defended her dissertation one day and got on a plane and competed at the national level for “university-aged” athletes—which included Olympians.

While she now lifts weights more casually, Schaeffer Fry competed last September in an over-35 competition and qualified for the USA Weightlifting Masters National Championships.

Mandi Schaeffer Fry performs a trick on the trapeze.

It was a “field trip” during a conference in Berkeley, California, in 2018 that led Fry to become enamored with flying trapeze.

In fact, she enjoyed it so much she signed up to be a member of Imperial Flyers, an amateur flying trapeze cooperative located in Westminster. Once she found out about the sport, her previous experience as a gymnast made it a natural fit.

Not only is she working on her own intermediate tricks, she’s also a “teaching assistant” at Fly Mile High, the state’s only flying trapeze and aerial fitness school.

“It’s exhilarating; it’s gotten me a bit over my fear of heights,” she says.

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Harris Chooses Walz

A guide to the career, politics and sudden stardom of gov. tim walz of minnesota, now vice president kamala harris’s running mate..

This transcript was created using speech recognition software. While it has been reviewed by human transcribers, it may contain errors. Please review the episode audio before quoting from this transcript and email [email protected] with any questions.

Hey, it’s Michael. Before we get started, I want to tell you about another show made by “The New York Times” that pairs perfectly with “The Daily.” It’s called “The Headlines.” It’s a show hosted by my colleague, Tracy Mumford, that quickly catches you up on the day’s top stories and features insights from “The Times” reporters who are covering them, all in about 10 minutes or less.

So if you like “The Daily”— and if you’re listening, I have to assume you do — I hope that means you’re going to “The Headlines” as well. You can now find “The Headlines” wherever you get your podcasts. So find it, subscribe to it, and thank you. And now, here’s today’s “Daily.”

From “The New York Times,” I’m Michael Barbaro. This is “The Daily.”

[MUSIC PLAYING]

Today, the story of how a little known Midwestern governor became Kamala Harris’s choice for a running mate. My colleague Ernesto Londoño walks us through the career, politics, and sudden stardom of Governor Tim Walz of Minnesota.

It’s Wednesday, August 7.

Ernesto, over the past few days, we watched Vice President Harris bring the final three contenders for her running mate to her house in Washington, DC, for a set of in-person interviews. And then we watched as she seemed to narrow her pool of choices down to a final two — the governor of Pennsylvania, Josh Shapiro, and the governor of Minnesota, Tim Walz. And now, of course, we know that she has made her choice. What has she told us about her campaign strategy, the way she views this race, in ultimately choosing Tim Walz?

Michael, I think what the choice tells us is that Kamala Harris was drawn to two qualities that Governor Walz brings to the table. And what’s interesting is they may seem to be in tension. For starters, here’s the ultimate everyday man, somebody who grew up in a small town in Middle America, served in the National Guard, was a high school teacher, a football coach, very plain-spoken, goes to campaign events wearing T-shirts and baseball caps, is a gun owner and very proud about it. He sort of embodies the Midwest.

And she clearly thinks that that is going to bring the kind of moderate, white, working class voters that the campaign needs in swing states to come to them, to make this feel like a balanced ticket and something that will give her enough of the crucial votes to defeat Donald Trump in the fall.

On the other hand, as governor, he passed a slew of pretty progressive legislation in the past couple of years, everything from abortion rights to gun control. So these things are likely to appeal to bread and butter Democrats.

But the question is, when voters have examined these two facets of Tim Walz, may it bring them enough enthusiasm from the base and enough undecided voters that the campaign desperately needs, or at some point, do these two aspects of him start canceling each other out?

Right. In short, you’re saying Harris is betting on a dual appeal from Walz to two essential constituencies, but the risk is that the appeal to one of them is just much, much greater than to the other.

Right. You could definitely see a scenario where voters, once they’ve examined Tim Walz’s story and legacy, may conclude that both of these candidates are quite liberal.

OK, so tell us the story of Tim Walz, a story that I think a lot of us don’t know because we really don’t know Walz all that well, and how he has come to embody these two qualities and that tension that you just described.

Michael, the origin story of Tim Walz’s political career is quite fascinating.

He and his wife were teachers in a small city south of Minneapolis. And in 2004, when George W. Bush was running for re-election, Walz took a group of his students to a political rally in his hometown. They wanted to just see the president make his case. And a strange scuffle happened when they were trying to get in.

Well, one of the kids had a John Kerry sticker on his wallet. And this is where the individual says, well, you’re not going to be allowed to enter. You’ve been deemed a threat.

Apparently, one of the students had a sticker for Bush’s rival, John Kerry, on his wallet. And security officials at the rally didn’t want to let them in.

And I said, oh, it’s OK. They’re with me. And who are you? And I said, I’m Tim Walz. I’m their teacher here, and showed them my ID. And they said, well, you two have been deemed a threat to the president. And I said, well, that’s not true. And it kind of escalated.

And this really ticked off Tim Walz. He was really upset. There was a fight and a confrontation at the rally.

At this point in time, I’m kind of nervous. I’m getting arrested. So I’m like saying, well, I’m Teacher of the Year in Mankato. And they didn’t care about that. And it was kind of a sad epiphany moment, how it felt for people to be looked right through by people. These people didn’t see me. And this is happening.

And ultimately, he sort of walks away from this moment feeling really sick of the Bush administration, the politics of the day. And he turns around and volunteers for the Kerry campaign.

And then the more interested he becomes in politics in this era, he starts looking around his congressional district, and there’s a Republican who’s held the seat for many, many years. This was a largely rural district in southern Minnesota. And there’s no reason to believe that a newcomer to politics, somebody without a donor base, could make a run for this seat and win.

But Walz signs up for this weekend boot camp, where expert campaigners train newcomers who want to run for office. And he gets really enthused by the idea that he can pull it off. So he starts raising money with the support of an army of students who become so thrilled and energized by the prospect that their nerdy and kind geography teacher is making this uphill bid for a congressional race.

So his campaign staff is basically his former students.

That’s right. And he proves to be a formidable candidate. He draws a lot of attention to his experience in the classroom and as a coach.

When I coached football, these stands held about 3,000 people. That’s a lot. It’s also the number of American soldiers who have died fighting in Iraq.

He’s a very strong advocate for pulling out of the war in Iraq.

Serving right now are kids that I taught, coached, and trained to be soldiers. They deserve a plan for Iraq to govern itself, so they can come home.

And one thing that happens in the campaign that is really surprising to people is he comes out as being in favor of same-sex marriage. Now, it’s useful to remember that this is 2006, when the vast majority of Democrats, Democrats running for most elected office, were not ready to come out in favor of same-sex marriage.

And here’s a guy who’s new to politics, who’s trying to unseat a Republican who’s held on to his seat for more than 12 years, taking what appeared to be a reckless position on something. And when he was asked about it at the time, Tim Walz told a supporter, this just happens to be what I believe in. And I’d rather lose a race that I’ve ran being true and consistent to my values than try to run as somebody I’m not.

And of course, he wins.

Yes. To everybody’s surprise, he pulled it off.

So from the get-go, he shows a kind of maverick, “politics be damned” quality, taking stands that he knows may be unpopular among the voters he’s trying to win over. But he’s got some innate political gifts that are all making it work.

Yeah, I think that first campaign showed us that Tim Walz had real political chops. He was a very effective campaigner. And people really liked him. When he was knocking on doors, when he was introducing himself to voters, they saw him as somebody who was very genuine and who was admirable.

So once he gets elected in this conservative leaning district in Minnesota, what does he actually do in Congress?

In Congress, he develops a reputation for being somebody who can work across the aisle. And this is a period where Democrats and Republicans were deeply polarized over the Iraq War. He spends a lot of his time lobbying to expand benefits for veterans, so it’s easier for them to go to college after their service, and also becomes a leading voice in the quest to repeal Don’t Ask, Don’t Tell, the policy that prohibited openly gay servicemen from serving in uniform.

And he remained really popular. He easily won re-election five times. The last time he runs for his seat happens to be 2016, when President Trump wins his district by about 15 points.

And still, voters kept Tim Walz in office.

I think it’s important to note what you just said. Walz is distinguishing himself as a Democrat who can take some pretty progressive positions, as he did in that first campaign on gay rights, as he did with Don’t Ask, Don’t Tell, and keep winning in very Trump-friendly districts of his state.

That’s right. And as he’s serving his sixth term in office, he sets his sights on the governor’s mansion and decides to run for office in 2018. He wins that race easily. And early on, during his time as governor, the eyes of the world are on Minnesota after a police officer kills George Floyd. And what we see is massive looting and protests in Minneapolis.

Right, and remind us how Governor Walz handles that violence, those protests.

Yeah, I think that’s a crucial chapter in Tim Walz’s political career and one that will come under scrutiny in the days ahead.

After George Floyd was killed on a Monday —

People are upset, and they’re tired. And being Black in Minnesota already has a stigma and a mark on your back.

— protests took root in Minneapolis.

Y’all want to sit out here and shoot off your rubber bullets and tear gas.

And they got progressively larger and more violent.

There comes a point where the mayor and the police chief in Minneapolis plead for help. They ask the governor to send in the National Guard. And crucially, that request was not immediately heeded.

This is the third precinct here. There are fires burning to the left of it at the —

And at the height of the crisis, a police precinct building was abandoned.

There’s someone climbing up the wall right now, kicking the window in, trying to climb up the wall.

Because city officials grew concerned that protesters were about to overrun it and may attack the cops inside their own turf.

[EXPLOSIONS]

And the building is set on fire.

Right, a very memorable image. I can recall it happening in real-time.

Yeah, and in the days that followed, I think there were a lot of questions of why the governor didn’t send in troops earlier and whether a more muscular, decisive response could have averted some of the destruction that spread through the city.

And how does Walz end up explaining his decision not to send in the National Guard more quickly?

The governor and his administration have said that they were really, really dealing with an unprecedented challenge. And I think there was a concern that sending in troops into this really, really tense situation could have done more to escalate rather than pacify things on the street.

But in the weeks and months that followed, there were a lot of questions about Governor Walz’s leadership. And there were critics who said, during what may have been the most challenging week of his life, we saw a governor who was indecisive and who waited too long to send in resources that ultimately allowed the city to get to a semblance of order.

Right, and it feels like this is a moment that will almost assuredly be used against him by Donald Trump and JD Vance, the Republican ticket, which has made law and order so central to their message in this campaign.

Yeah, absolutely. And here in Minnesota, that was certainly a liability for him when he ran for re-election in 2022. But voters kept him in office, and he won that race handily. And not only did he win, but Democrats managed to flip the Senate and have full control of the legislature on his watch.

And that sets in motion one of the most productive legislative sessions in Minnesota history, where Tim Walz and his allies in the House and the Senate managed to pass a trove of really progressive legislation, oftentimes on a party vote.

Tell us about some of that legislation.

Well, Minnesota becomes the first state in the wake of the Supreme Court ending the constitutional right to abortion to actually codify this right under state statute. And they did a lot more stuff. They had a huge budget surplus, and they used that, for instance, to fund meals for all school children.

They managed to pass a couple of gun control laws that were very contentious. They gave the right to undocumented immigrants to get driver’s licenses. They legalized recreational marijuana. And finally, the governor takes a pretty bold stance on this issue of gender affirming care for transgender kids and teenagers, and says that Minnesota will be a safe haven for people who want that health care.

So, Ernesto, so how should we think about that blitz of legislation and the largely progressive tone of it, given the way that Walz had campaigned and succeeded up to that moment as somebody with such broad appeal across the political spectrum?

When the governor was asked whether this had been too much too quickly in terms of progressive legislation, his answer was that these were broadly popular policies, that these are issues Democrats had campaigned on. And here, Democrats had a window of opportunity where they were in control of the governor’s mansion and control of the House, the Senate, and that when you have political capital, you spend it.

But when you start listening to Republicans in Minnesota, they say, here’s a guy who campaigned on this mantra of “One Minnesota.” That was his campaign slogan. And he sort of came into office with this promise that he would govern in a bipartisan way, reach across the aisle.

But when they had all the votes they needed to pass their policies, Republicans felt that Walz was not bothering to bring them into the fold and to pass legislation that was going to be palatable to conservatives in the state. So I think people who once regarded him as a moderate now start seeing him as somebody who, when he had the power, acted in ways that were really progressive and liberal.

So at the height of his power, Governor Walz emerges as somebody who, when given a shot at getting done what he really wants to get done with a Democratic legislature, is a pretty progressive leader, even at the risk of being somewhat at odds with his earlier image as more moderate, because in his mind, enough people in the state are behind these policies.

Yeah, and I think he assumed that he had banked enough goodwill and that people across the state liked him enough to tolerate policies they may have disagreed with. And I think it’s safe to say, among the people who cover him here regularly, there was never any real hint that Tim Walz was eyeing a run for higher office. He’s not somebody who has written the kind of political memoir that oftentimes serves as a case of what you would bring to a national ticket or to the White House. And he seems pretty happy with a state job.

So it was a huge surprise when Tim Walz starts going viral through a string of cable news appearances right after President Biden drops out of the race, and the Democrats are scrambling to put Harris at the top of the ticket. And what becomes clear is that Walz is very forcefully auditioning for the role of vice president, and Vice President. Harris starts taking him very seriously.

We’ll be right back.

So, Ernesto, tell us about this cable news audition that Governor Walz undertakes over the past few weeks and how, ultimately, it seemed to help him land this job of being Harris’s running mate.

I think Walz does something really interesting, and that is that he says that Democrats shouldn’t be talking about Trump and Vance as existential threats. He kind of makes the case that Democrats have been in this state of fear and paralysis for too long, and that it’s not serving them well. So the word he latches onto is “weird.”

Well, it’s true. These guys are just weird.

It is. It is.

And they’re running for he-man women hater’s club or something. That’s what they go at. That’s not what people are interested in.

And I think one other thing we see in Walz is somebody who’s putting himself out there as a foil to JD Vance.

That angst that JD Vance talks about in “Hillbilly Elegy,” none of my hillbilly cousins went to Yale, and none of them went on to be venture capitalists or whatever. It’s not —

I think the case he’s making is that Tim Walz is a more authentic embodiment of small town values.

What I know is, is that people like JD Vance know nothing about small town America. My town had 400 people in it, 24 kids in my graduating class. 12 were cousins. And he gets it all wrong. It’s not about hate.

And behind the scenes, people from Tim Walz’s days on Capitol Hill start calling everybody they know in the Harris campaign and the Harris orbit and saying, here’s a guy who has executive experience as governor, but also somebody who has a really impressive record from his time on Capitol Hill and somebody who could be an asset in helping a Harris administration pass tough legislation. So you should take a hard look at this guy.

Which is, of course, exactly what Harris ends up doing. And I want to talk for a moment about how Harris announces Walz as her running mate on Tuesday morning. She did it in an Instagram message. And it felt like the way she did it very much embraced this idea that you raised earlier, Ernesto, that Walz contains these two appeals, one to the Democratic base, one to the white working class.

Harris specifically cites the work that Walz did with Republicans on infrastructure and then cites his work on gun control. She mentions that he was a football coach and the founder of the high school Gay Straight Alliance. She’s straddling these two versions of Walz.

But I want to linger on the idea for a moment of Walz’s vulnerabilities, because once he becomes Harris’s running mate, Harris and Walz are going to lose a fair amount of control over how they present him to the country, because he’s going to become the subject of very fierce attacks from the Republicans in this race. So talk about that for just a moment.

Yeah, I mean, it’s important to keep in mind that Governor Walz has never endured the scrutiny of a presidential race. So the questions he’s going to be asked and the way his record is going to be looked at is going to be different and sharper. I think the Harris campaign is billing him as, first and foremost, a fighter for the middle class. And I think that certainly will have some appeal.

But I think in coming days, there’s going to be a lot of attention drawn to parts of his record that may be unpopular with many voters. For instance, giving undocumented immigrants driver’s licenses, which Governor Walz championed. It’s likely to provide fodder for an attack ad.

The very dramatic footage of Minneapolis burning in 2020 is also something that I think people will be drawn to. And there’s going to be interest in reexamining what the governor did and what he could have done differently to avert the chaos.

And on Tuesday, we saw that the Trump campaign wasted no time in trying to define Tim Walz as soft on crime, permissive on immigration policy. And they also made clear they wanted to relitigate the era of George Floyd’s killing. And specifically, they want to try to tie him to the effort at the time to defund the police, which is a movement that Walz personally never endorsed.

So the Republican attack here will be pretty simple. Walz is liberal. Harris is liberal. So, in their efforts to speak to especially white working class and rural voters in swing states, the Trump campaign is going to say this is not the ticket for that group of voters. This is the ticket of burning police precincts and gun control. And of course, that may not be fair, but that’s very likely going to be the message over the next couple of months.

Right. I think there’s going to be effort to portray him as a radical liberal who has used his small town roots to put on this sort of veneer of being a moderate and a really sort of understanding and being part of the segments of the electorate that I think are critical in this election.

I want to speak for just a moment about the person Harris did not pick when she chose Walz because many Democrats had felt that Walz was a potentially too liberal seeming running mate for a candidate, Kamala Harris, who herself comes from a blue state and is caricatured by the Republicans as liberal herself.

And the person she didn’t choose was Governor Josh Shapiro of Pennsylvania, who was seen as having a huge appeal in that particular key swing state, but also presented risks of his own of alienating parts of the Democratic base with his well-documented support for Israel and his criticism of campus protesters. How should we think about the fact that, ultimately, Harris chose Walz over Shapiro?

Yeah, I think in the final stretch of this campaign to be the vice presidential pick, we started seeing a lot of acrimony in pockets of the Democratic base, drawing attention to the fact that Governor Shapiro could be divisive on Gaza, which has really sort of split the party in recent months.

So I think at the end of the day, they made a calculation that Tim Walz would be more of a unifying figure and would be somebody who would inspire and energize enough pockets of the electorate that they need, particularly in the Midwest, to make him the stronger and more exciting pick and somebody who wouldn’t force them to go back to defending and relitigating the Biden administration’s record on Israel and on the war in Gaza.

Right, and then, on Tuesday night, we got our first glimpse of Harris and Walz together on stage for the first time at a campaign rally. I’m curious, what struck you about their debut together.

Good evening, Philadelphia.

I think everybody was watching the opening scene of this rally to see what the chemistry between these two people was going to be like. And they both seemed giddy. They were literally, at times, bouncing with enthusiasm.

Since the day that I announced my candidacy, I set out to find a partner who can help build this brighter future.

So Pennsylvania, I’m here today because I found such a leader.

Governor Tim Walz of the great state of Minnesota.

They soon got down to business. And that business was how to define Tim Waltz for voters who don’t know him well.

To those who know him best, Tim is more than a governor.

And right off the bat, we saw that Kamala Harris really highlighted a lot of pieces of his pre-political career.

To his former high school football players, he was Coach.

She repeatedly called him Coach Walz, Mr. Walz, evoking his time in the classroom, and even used his military title from his days in the Army.

To his fellow veterans, he is Sergeant Major Walz.

And then when it came time for Tim Walz to introduce himself on this massive stage —

Welcome the next vice president of the United States, Tim Walz.

— he drew a lot of attention to his small town roots.

I was born in West Point, Nebraska. I lived in Butte, a small town of 400.

He said something that he said repeatedly recently in campaign appearances, which is —

In Minnesota, we respect our neighbors and their personal choices that they make. Even if we wouldn’t make the same choice for ourselves, there’s a golden rule — mind your own damn business.

The golden rule of small towns is you mind your own damn business, which is something he said in the context of his argument that Republicans have been limiting, rather than expanding, people’s rights. But he also drew attention to the fact that he’s a gun owner.

By the way, as you heard, I was one of the best shots in Congress. But in Minnesota, we believe in the Second Amendment, but we also believe in common sense gun violence laws.

And then when it came time to draw a sharp contrast with their opponents, Tim Walz said, these guys are phonies.

Donald Trump is not fighting for you or your family. He never sat at that kitchen table like the one I grew up at, wondering how we were going to pay the bills. He sat at his country club in Mar-a-Lago, wondering how he can cut taxes for his rich friends.

He said it’s actually people like me and Kamala Harris who come from humble origins and showed what is possible in America when you hail from a working class background, and you seize opportunities that were available to you.

Thank you, Philadelphia. Thank you, Vice President. God bless America.

So when it comes to this question of Walz’s dual identities and dual appeals, what did we learn on day one of this new Democratic ticket, do you think?

I think the campaign is trying to convey that these two facets of Tim Walz’s life are not mutually exclusive, that they don’t need to be in tension. They don’t cancel each other out. They’re both part of Tim Walz’s story. And I think that’s how they’re going to present him from now until Election Day.

Ernesto, thank you very much. We appreciate it.

It’s my pleasure, Michael.

Here’s what else you need to know today. On Tuesday, Hamas said that Yahya Sinwar, one of the masterminds behind the deadly October 7 attacks on Israel, had consolidated his power over the entire organization. Until now, Sinwar had held the title of Hamas’s leader in Gaza. But with the assassination of Hamas’s top political leader by Israel last week, Hamas said that Sinwar would take on that title as well. Sinwar remains a major target of Israel and is believed to have been hiding in tunnels underneath Gaza since October 7.

And the US Department of Justice has charged a Pakistani man with ties to Iran with trying to hire a hitman to assassinate political figures in the United States. The man recently traveled to the US and was arrested in New York last month. American authorities believe that his potential targets likely included former President Trump.

Today’s episode was produced by Alex Stern, Eric Krupke, and Olivia Natt. It was edited by Lisa Chow and Patricia Willens, contains original music by Pat McCusker and Marion Lozano, and was engineered by Alyssa Moxley. Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Nick Pittman and Minnesota Public Radio.

That’s it for “The Daily.” I’m Michael Barbaro. See you tomorrow.

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Earlier this summer, few Democrats could have identified Gov. Tim Walz of Minnesota.

But, in a matter of weeks, Mr. Walz has garnered an enthusiastic following in his party, particularly among the liberals who cheer on his progressive policies. On Tuesday, Vice President Kamala Harris named him as her running mate. Ernesto Londoño, who reports for The Times from Minnesota, walks us through Mr. Walz’s career, politics and sudden stardom.

On today’s episode

Ernesto Londoño , a reporter for The Times based in Minnesota, covering news in the Midwest.

Kamala Harris and Tim Walz waving onstage in front of a “Harris Walz” sign.

Background reading

Who is Tim Walz , Kamala Harris’s running mate?

Mr. Walz has faced criticism for his response to the George Floyd protests.

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Michael Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Maddy Masiello, Isabella Anderson, Nina Lassam and Nick Pitman.

An earlier version of this episode misstated the subject that Walz’s wife taught. She taught English, not Social Studies.

How we handle corrections

Ernesto Londoño is a Times reporter based in Minnesota, covering news in the Midwest and drug use and counternarcotics policy. More about Ernesto Londoño

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