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## Quadratic Equations: Very Difficult Problems with Solutions

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## Algebra Problems

## Basic Algebra Identities

- (a + b) 2 = a 2 + b 2 + 2ab
- (a – b) 2 = a 2 + b 2 – 2ab
- a 2 – b 2 = (a + b)(a – b)
- a 2 + b 2 = (a + b) 2 – 2ab = (a – b) 2 + 2ab
- a 3 + b 3 = (a + b)(a 2 – ab + b 2 )
- a 3 – b 3 = (a – b)(a 2 + ab + b 2 )
- (a + b) 3 = a 3 + 3ab(a + b) + b 3
- (a – b) 3 = a 3 – 3ab(a – b) – b 3

## Algebra problems With Solutions

Example 1: Solve, (x-1) 2 = [4√(x-4)] 2 Solution: x 2 -2x+1 = 16(x-4)

## Algebra Problems for Class 6

Example: Solve, 4x + 5 when, x = 3.

Now putting the value of x=3, we get;

Example: Give expressions for the following cases:

## Algebra Problems for Class 7

Example: Collect like terms and simplify the expression: 12x 2 – 9x + 5x – 4x 2 – 7x + 10.

Solution: 12x 2 – 9x + 5x – 4x 2 – 7x + 10

= (12 – 4)x 2 – 9x + 5x – 7x + 10

## Algebra Problems for Class 8

Here, students will deal with algebraic identities. See the examples.

Solution: Using the identity: (a+b) 2 = a 2 + b 2 + 2 ab, we get;

(2x+y) = (2x) 2 + y 2 + 2.2x.y = 4x 2 + y 2 + 4xy

Example: Solve (99) 2 using algebraic identity.

Solution: We can write, 99 = 100 -1

= 100 2 + 1 2 – 2 x 100 x 1 [By identity: (a -b) 2 = a 2 + b 2 – 2ab

## Algebra Word Problems

Solution: Let the number of girls be x

Question 2: The sum of two consecutive numbers is 41. What are the numbers?

Solution: Let one of the numbers be x.

Then the other number will x+1

Now, as per the given questions,

So, the first number is 20 and second number is 20+1 = 21

## Linear Algebra Problems

There are various methods For Solving the Linear Equations

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## 120 Math Word Problems To Challenge Students Grades 1 to 8

Engage and motivate your students with our adaptive, game-based learning platform!

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A jolt of creativity would help. But it doesn’t come.

There are 120 examples in total.

The list of examples is supplemented by tips to create engaging and challenging math word problems.

## 120 Math word problems, categorized by skill

Best for: 1st grade, 2nd grade

## Subtraction word problems

Best for: 1st grade, second grade

## Practice math word problems with Prodigy Math

## Multiplication word problems

Best for: 2nd grade, 3rd grade

## Division word problems

Best for: 3rd grade, 4th grade, 5th grade

## Mixed operations word problems

## Ordering and number sense word problems

33. Composing Numbers: What number is 6 tens and 10 ones?

## Fractions word problems

Best for: 3rd grade, 4th grade, 5th grade, 6th grade

## Decimals word problems

Best for: 4th grade, 5th grade

## Comparing and sequencing word problems

Best for: Kindergarten, 1st grade, 2nd grade

53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?

54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?

## Time word problems

## Money word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade

## Physical measurement word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade

## Ratios and percentages word problems

Best for: 4th grade, 5th grade, 6th grade

## Probability and data relationships word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade

## Geometry word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade

99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?

102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?

## Variables word problems

Best for: 6th grade, 7th grade, 8th grade

## How to easily make your own math word problems & word problems worksheets

- Link to Student Interests: By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
- Make Questions Topical: Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
- Include Student Names: Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
- Be Explicit: Repeating keywords distills the question, helping students focus on the core problem.
- Test Reading Comprehension: Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
- Focus on Similar Interests: Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
- Feature Red Herrings: Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.

## Final thoughts about math word problems

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## Short Answer

The differential equation is \(\frac{{dy}}{{dx}} = {x^2} + {y^2}\).

## Step by Step Solution

Step 1: define a derivative of the function..

## Step 2: Determine the differential equation for the height.

And let the rate at which the slope changes be \(y''\).

Hence, the statement describes the differential equation,

## Most popular questions for Math Textbooks

\(\frac{{dy}}{{dx}} - 2xy = {e^{{x_z}}}; y = {e^{{x^2}}}\int_0^x {{e^{t - {t^2}}}} dt\)

\(\frac{d}{{dx}}{c_1}{e^{10x}} = \_\_\_\_\_\)

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Get step-by-step solutions to your math problems Try Math Solver Type a math problem Solve Quadratic equation x2 − 4x − 5 = 0 Trigonometry 4sinθ cosθ = 2sinθ Linear equation y = 3x + 4 Arithmetic 699 ∗533 Matrix [ 2 5 3 4][ 2 −1 0 1 3 5] Simultaneous equation { 8x + 2y = 46 7x + 3y = 47 Differentiation dxd (x −5)(3x2 −2) Integration ∫ 01 xe−x2dx

Free math problem solver answers your algebra homework questions with step-by-step explanations.

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.

Symbolab, Making Math Simpler. Word Problems. Provide step-by-step solutions to math word problems. Graphing. Plot and analyze functions and equations with detailed steps. Geometry. Solve geometry problems, proofs, and draw geometric shapes.

Math Problem Solver and Calculator | Chegg.com Understand math, one step at a time Enter your problem below to see how our equation solver works Enter your math expression x2 − 2x + 1 = 3x − 5 Get Chegg Math Solver $9.95 per month (cancel anytime). See details Example math equations: Pre Algebra Algebra Pre Calculus Calculus Linear Algebra

How to solve math problems step-by-step? To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem.

Problems for 5th Grade. Multi-digit multiplication. Dividing completely. Writing expressions. Rounding whole numbers. Inequalities on a number line. Linear equation and inequality word problems. Linear equation word problems. Linear equation word problems.

Mixture Problems With Solutions Mixture problems and their solutions are presented along with their solutions. Percentages are also used to solve these types of problems. Problem 1:How many liters of 20% alcohol solution should be added to 40 liters of a 50% alcohol solution to make a 30% solution?

Unit 2: Lesson 3. Analyzing the number of solutions to linear equations. Number of solutions to equations. Worked example: number of solutions to equations. Number of solutions to equations. Creating an equation with no solutions. Creating an equation with infinitely many solutions. Number of solutions to equations challenge.

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. ... Sal solves the following word problem: You have 50 ounces of a 25% saline solution. ... If x is the required no. of liters of the 30% alcohol solution, the problem translates as follows: 30% of x (amount of ...

Problem 6 sent by Κυριάκος There is a two-digit number whose digits are the same, and has got the following property: When squared, it produces a four-digit number, whose first two digits are the same and equal to the original's minus one, and whose last two digits are the same and equal to the half of the original's.

Basic Math. Math Calculator. Step 1: Enter the expression you want to evaluate. The Math Calculator will evaluate your problem down to a final solution. You can also add, subtraction, multiply, and divide and complete any arithmetic you need. Step 2: Click the blue arrow to submit and see your result!

Algebra problems With Solutions Example 1: Solve, (x-1)2 = [4√ (x-4)]2 Solution: x 2 -2x+1 = 16 (x-4) x 2 -2x+1 = 16x-64 x 2 -18x+65 = 0 (x-13) (x-5) = 0 Hence, x = 13 and x = 5. Algebra Problems for Class 6 In class 6, students will be introduced with an algebra concept.

120 Math word problems, categorized by skill Addition word problems Best for: 1st grade, 2nd grade 1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total? 2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends.

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WebMath is designed to help you solve your math problems. Composed of forms to fill-in and then returns analysis of a problem and, when possible, provides a step-by-step solution. Covers arithmetic, algebra, geometry, calculus and statistics.

Free Math Problem Solver - MathSolve.pro Free solve math problems Although the method which one is going to use when solving a math problem depends on the exact issue in question, there are general steps and guidelines one can follow. Choose discipline Disciplines Basic Math Solve Pre-Algebra Solve Algebra Solve Trigonometry Solve Precalculus Solve

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A student can feel mathematically ready to attend College if he or she can get at least 33 out of the 36 problems correct. Sample Problems. Concept. Problem 1. Operations with Real Numbers. Problem 2. Order of Operations. Problem 3. Solving Linear Equations.

Online math solver with free step by step solutions to algebra, calculus, and other math problems. Get help on the web or with our math app.

In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation ...

In Problems 15 and 16 interpret each statement as a differential equation. On the graph of y = ϕ ( x) the rate at which the slope changes with respect to x at a point P ( x, y) is the negative of the slope of the tangent line at P ( x, y). The differential equation is d y d x = x 2 + y 2. See the step by step solution.

Even simple math problems become easier to solve when broken down into steps. From basic additions to calculus, the process of problem solving usually takes a lot of practice before answers could come easily. As problems become more complex, it becomes even more important to understand the step-by-step process by which we solve them.

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Math Problems. Studies have shown that students who practice math problems frequently have better math grades. Too often, parents and teachers think students do not have an aptitude for math when the problem actually lies in the lack of math practice.. Use our fun worksheets and resources to engage kids and help them get better at solving math problems: