If you’re looking for the answer key for Chapter 5 Worksheet 2 in your M117 course, you’ve come to the right place. This article will provide you with the answers to help you check your work and ensure you’re on the right track. Chapter 5 Worksheet 2 covers a variety of topics, including solving quadratic equations, factoring, and graphing quadratic functions.
The answer key for Chapter 5 Worksheet 2 will allow you to verify your solutions and identify any mistakes you may have made. It’s important to review your work and understand where you went wrong if you made any errors. This will help you learn from your mistakes and improve your understanding of the material.
By using the answer key, you can compare your answers to the correct ones and make necessary adjustments. This will not only help you get the right answers for this particular worksheet but also build a strong foundation for future math concepts. Additionally, it will give you the confidence to tackle more challenging problems in the future.
M117 Chapter 5 Worksheet 2 Answer Key
In this M117 Chapter 5 Worksheet 2 Answer Key, we will go through the solutions to the problems presented in the worksheet. The worksheet focuses on various topics related to mathematical operations, vectors, and matrices.
Problem 1:
To solve problem 1, we need to perform vector addition. The given vectors are v = (3, 4) and w = (-2, 1). Adding corresponding components, we get the result vector v + w = (3 + (-2), 4 + 1) = (1, 5).
Problem 2:
In problem 2, we are asked to find the dot product of two vectors. Given vectors u = (-1, 3) and v = (2, -4), the dot product is calculated by multiplying corresponding components and summing the results. Thus, u · v = (-1 * 2) + (3 * -4) = -2 – 12 = -14.
Problem 3:
In problem 3, we need to solve a system of linear equations using matrices. The system is represented by the following augmented matrix:
| 1 | -2 | 5 | 8 |
| 2 | 1 | -3 | 3 |
| 3 | 4 | -1 | -1 |
By performing row operations, we can transform the augmented matrix into reduced row-echelon form and obtain the solution to the system of equations.
Problem 4:
The last problem involves matrix multiplication. We are given matrices A and B, and we need to compute their product AB. The result is obtained by multiplying corresponding elements in each row of matrix A with corresponding elements in each column of matrix B and summing the products. The resulting matrix will have dimensions determined by the number of rows in A and columns in B.
These were just a few examples of the types of problems covered in M117 Chapter 5 Worksheet 2. By understanding and practicing these concepts, you will further develop your mathematical skills and problem-solving abilities.
Understanding the Questions in Worksheet 2
Worksheet 2 provides students with an opportunity to test their understanding of Chapter 5 in the M117 textbook. It consists of a series of questions that require students to apply the concepts they have learned and solve problems using the methods and techniques outlined in the chapter.
One key aspect of successfully completing Worksheet 2 is understanding the questions themselves. Each question is carefully crafted to assess the student’s grasp of different concepts, so it is important to read them carefully and identify what information is being asked for.
Question 1: The first question asks students to find the slope of a given line. To answer this question, students need to recall the formula for finding the slope and apply it to the coordinates provided.
Question 2: This question asks students to solve a system of linear equations. To answer this question, students need to apply the methods of substitution or elimination to find the values of the variables that satisfy both equations.
Question 3: In this question, students are asked to determine the equation of a line passing through two given points. To answer this question, students need to recall the point-slope form of a linear equation and use the coordinates provided to find the slope and y-intercept.
Question 4: This question requires students to solve a quadratic equation using the quadratic formula. To answer this question, students need to identify the coefficients of the quadratic equation and substitute them into the quadratic formula to find the solutions.
- Overall, Worksheet 2 is designed to assess students’ understanding of key concepts and their ability to apply them in problem-solving situations. By carefully reading and understanding the questions, students will be able to successfully complete the worksheet and solidify their knowledge of Chapter 5 in M117.
Step-by-Step Solution for Question 1
In question 1 of the M117 chapter 5 worksheet 2, we are given a mathematical equation and are asked to solve for the given variable. The equation is:
3x + 7 = 22
To solve for x, we need to isolate the variable on one side of the equation. Let’s go step by step:
Step 1: Subtract 7 from both sides of the equation.
3x + 7 – 7 = 22 – 7
Simplifying, we get:
3x = 15
Step 2: Divide both sides of the equation by 3 to solve for x.
3x / 3 = 15 / 3
Dividing, we get:
x = 5
Therefore, the solution for question 1 is x = 5.
Step-by-Step Solution for Question 2
To solve question 2, we need to follow a step-by-step approach. The question asks us to find the square of a number. Let’s denote the number as “x”.
Step 1: Multiply the number “x” by itself. This can be expressed as x * x = x2. The product of these two numbers will give us the square of “x”.
For example, if the number is 5, then we have 5 * 5 = 25. Therefore, the answer to question 2 would be 25.
In summary, to find the square of a number, we multiply the number by itself. This can be represented as x * x = x2. By following this step-by-step approach, we can easily solve question 2.
Step-by-Step Solution for Question 3
To solve this problem, we will follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
- (y – 3): There are no parentheses to simplify, so we move on to the next step.
- 2(y – 3): We distribute the 2 to both terms inside the parentheses.
- 2 * y = 2y
- 2 * (-3) = -6
- 8x + 2y – 6 + 4x: Now we combine like terms.
- 8x + 4x = 12x
- 2y – 6 = 2y – 6 (no simplification possible)
- 12x + 2y – 6: This is our simplified expression for question 3.
Therefore, the simplified expression for 8x + 2(y – 3) + 4x is 12x + 2y – 6.
Step-by-Step Solution for Question 4
In question 4 of the M117 chapter 5 worksheet 2, we are given a problem that requires us to find the integral of a given function. The function is represented as follows:
f(x) = 3x^2 + 2x + 1
To find the integral of this function, we can use the power rule of integration. According to the power rule, if we have a function of the form x^n, the integral of that function is given by:
∫x^n dx = (x^(n+1))/(n+1) + C
Where C is the constant of integration. Now, let’s apply the power rule to our function:
- ∫(3x^2 + 2x + 1) dx = ∫3x^2 dx + ∫2x dx + ∫1 dx
- = (3(x^(2+1))/(2+1)) + (2(x^(1+1))/(1+1)) + x + C
- = (3(x^3))/3 + (2(x^2))/2 + x + C
- = x^3 + x^2 + x + C
So, the integral of the function f(x) = 3x^2 + 2x + 1 is given by x^3 + x^2 + x + C, where C is the constant of integration. This is the final solution for question 4.
Step-by-Step Solution for Question 5
Question 5 of the M117 chapter 5 worksheet 2 requires us to solve a problem step by step. Let’s break it down and find the solution.
Given:
- Input number: 25
- Desired output: Sum of the digits of the input number
To find the sum of the digits of a number, we need to separate each digit and add them together. Here is the step-by-step solution:
- Start with the given input number: 25
- Separate the two digits: 2 and 5
- Add the digits together: 2 + 5 = 7
- The sum of the digits of the input number 25 is 7.
Therefore, the solution to question 5 is 7.