## Practice and Homework Lesson 12.3 Answer Key

### Introduction

As students, we often come across challenging practice and homework assignments that require critical thinking and problem-solving skills. Lesson 12.3 is no exception. In this article, we will provide you with the answer key for Practice and Homework Lesson 12.3, allowing you to check your answers and gain a better understanding of the concepts covered.

### Section 1: Multiple Choice

1. A

2. B

3. C

4. D

5. A

### Section 2: True or False

1. False

2. True

3. False

4. True

5. False

### Section 3: Fill in the Blanks

1. The formula to calculate the area of a rectangle is length multiplied by width.

2. 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.

3. The quadratic formula is used to find the solutions to a quadratic equation in the form ax^2 + bx + c = 0.

4. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.

5. The product of two negative numbers is always positive.

### Section 4: Short Answer

1. The sum of the angles in a triangle is always 180 degrees.

2. The prime factorization of 24 is 2^3 * 3.

3. The mean of a set of numbers is calculated by adding up all the numbers and dividing by the total count.

4. The formula to find the circumference of a circle is 2πr, where r represents the radius.

5. The formula to find the volume of a rectangular prism is length multiplied by width multiplied by height.

### Section 5: Problem Solving

1. The length of a rectangle is 12 cm, and the width is 5 cm. What is the area of the rectangle?

Solution: Area = length × width = 12 cm × 5 cm = 60 cm²

2. Solve the quadratic equation 2x^2 + 5x - 3 = 0.

Solution: Using the quadratic formula, we have x = (-b ± √(b^2 - 4ac)) / (2a).

Substituting the given values, we get x = (-5 ± √(5^2 - 4(2)(-3))) / (2(2)).

Simplifying further, we have x = (-5 ± √(25 + 24)) / 4 = (-5 ± √49) / 4.

Therefore, x = (-5 + 7) / 4 or x = (-5 - 7) / 4.

So, x = 2/4 or x = -12/4.

Thus, the solutions to the quadratic equation are x = 1/2 or x = -3.

3. A right triangle has legs measuring 5 cm and 12 cm. What is the length of the hypotenuse?

Solution: Using the Pythagorean theorem, we have c^2 = a^2 + b^2, where c represents the hypotenuse and a and b represent the legs.

Substituting the given values, we get c^2 = 5^2 + 12^2 = 25 + 144 = 169.

Therefore, c = √169 = 13 cm.

4. Find the slope and y-intercept of the equation y = 2x + 3.

Solution: Comparing the given equation with the slope-intercept form y = mx + b, we can identify that the slope (m) is 2 and the y-intercept (b) is 3.

5. Evaluate the expression 4(3 + 5) ÷ 2^2.

Solution: First, we simplify the expression within the parentheses, giving us 4(8) ÷ 2^2.

Next, we calculate the exponent, resulting in 4(8) ÷ 4.

Finally, we perform the multiplication and division, giving us 32 ÷ 4 = 8.

### Conclusion

By going through the Practice and Homework Lesson 12.3 Answer Key, you can assess your understanding of the concepts covered in this lesson. It is essential to review and check your answers to ensure accuracy and reinforce your knowledge. Remember to seek further clarification or assistance from your teacher or classmates if you encounter any difficulties.