Unit 5 End-of-Unit Practice Quiz

To add fractions, convert them to a common denominator. Since 3/4 is equivalent to 6/8, adding 1/8 results in 7/8, which is the correct answer.

Subtracting 5 from both sides of the equation gives x = 7. This basic linear equation requires the use of inverse operations.

The area of a rectangle is found by multiplying its length by its width. Here, 5 multiplied by 3 equals 15, which is the correct area.

The decimal 0.75 can be written as 75/100, which simplifies to 3/4. This conversion from a decimal to a fraction shows the equivalent value.

The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 18 are 1, 2, 3, 6, 9, and 18. The largest common factor is 6, making it the correct answer.

By adding 3 to both sides, the equation becomes 2x = 10. Dividing by 2 gives x = 5, which is the correct solution.

The perimeter of a triangle is found by adding all three side lengths together: 5 + 7 + 8 = 20. This direct addition yields the correct perimeter.

Let the common factor be k so that the length is 5k and the width is 2k. Since the perimeter is 2(5k + 2k) = 14k and 14k = 28, we find k = 2 and thus the length is 10.

Using the distributive property, multiply 3 by each term inside the parentheses: 3 × 2x gives 6x and 3 × 4 gives 12. The expanded form is therefore 6x + 12.

First, expand the equation to get 4x - 8 = 12. Adding 8 to both sides results in 4x = 20, and dividing by 4 yields x = 5.

Dividing both the numerator and the denominator of 4/6 by their greatest common divisor, which is 2, simplifies the fraction to 2/3. This is the fraction in its simplest form.

The probability of complementary events always adds up to 1. Therefore, if the probability of rain is 0.3, the probability of no rain is 1 - 0.3 = 0.7.

The mean is calculated by summing the numbers and then dividing by the count. Here, (4 + 8 + 12 + 16) ÷ 4 equals 10, which is the correct mean.

According to the order of operations (PEMDAS/BODMAS), multiplication is performed before addition. This rule ensures that 3 × 2 is computed first, followed by the addition of 5.

Subtracting 2 from both sides of the equation results in x/3 = 3. Multiplying both sides by 3 gives x = 9, which is the correct answer.

The slope of a line is calculated by the change in y divided by the change in x. Here, (7 - 3) divided by (4 - 2) yields 4/2 which simplifies to 2.

Expanding the equation gives 3x + 3 - 4x + 8 = x + 10, which simplifies to -x + 11 = x + 10. Solving for x results in x = 0.5, making it the correct answer.

The area of a square is equal to the square of its side length. Taking the square root of 81 yields 9, which is the length of one side.

When two events are mutually exclusive, their probabilities can be added directly. Therefore, 0.4 + 0.5 equals 0.9, which is the correct probability that either event occurs.

First, expand the right side to get 5y - 2 = 3y + 12. Subtracting 3y from both sides results in 2y - 2 = 12 and adding 2 to both sides gives 2y = 14, so y = 7.