## Lesson 5.2 Answer Key

### Introduction

When it comes to education, assessments are an integral part of the learning process. They help gauge a student's understanding of a particular topic or subject. Lesson 5.2 is no exception, and having an answer key can be immensely helpful for both teachers and students. In this article, we will provide you with the answer key for Lesson 5.2, covering various topics and subtopics. Let's dive in!

### The Importance of Answer Keys

Answer keys serve as a valuable resource for students to check their understanding and identify areas where they may need further clarification. They can also be used by teachers to assess the progress of their students and provide feedback. Additionally, answer keys can be a useful tool for parents or tutors who want to support their child's learning at home.

### Answer Key for Lesson 5.2

#### Topic 1: Algebraic Equations

##### Subtopic 1: Solving Linear Equations

1. x + 5 = 10

Solution: x = 5

Explanation: To solve this equation, we need to isolate x on one side of the equation. By subtracting 5 from both sides, we find that x equals 5.

##### Subtopic 2: Factoring Quadratic Equations

1. x^2 + 5x + 6 = 0

Solution: (x + 2)(x + 3) = 0

Explanation: To factor this quadratic equation, we need to find two numbers that multiply to give 6 and add up to 5. The factors are 2 and 3, so the factored form is (x + 2)(x + 3) = 0.

#### Topic 2: Geometry

##### Subtopic 1: Area and Perimeter

1. Find the area of a rectangle with length 8 cm and width 5 cm.

Solution: Area = length x width = 8 cm x 5 cm = 40 cm^2

Explanation: The area of a rectangle is calculated by multiplying its length and width. In this case, the area is 40 square centimeters.

##### Subtopic 2: Pythagorean Theorem

1. Find the length of the hypotenuse in a right triangle with sides of length 3 cm and 4 cm.

Solution: Hypotenuse = √(3^2 + 4^2) = √(9 + 16) = √25 = 5 cm

Explanation: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. By applying this theorem, we find that the length of the hypotenuse is 5 cm.

#### Topic 3: Statistics

##### Subtopic 1: Measures of Central Tendency

1. Find the mean of the following data set: 5, 7, 8, 10, 12

Solution: Mean = (5 + 7 + 8 + 10 + 12) / 5 = 42 / 5 = 8.4

Explanation: The mean is calculated by summing up all the values in the data set and dividing it by the number of values. In this case, the mean is 8.4.

##### Subtopic 2: Probability

1. What is the probability of rolling an even number on a standard six-sided die?

Solution: There are three even numbers (2, 4, and 6) out of six possible outcomes, so the probability is 3/6 or 1/2.

Explanation: The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, there are three favorable outcomes out of six, resulting in a probability of 1/2.

### Conclusion

An answer key for Lesson 5.2 can be a valuable tool for both students and teachers alike. By providing solutions and explanations to various topics and subtopics, students can check their understanding and identify areas for improvement. Teachers can also use answer keys to assess their students' progress and provide targeted feedback. So, make the most of this answer key and enhance your learning experience!