LESSON 3.3-3.5

4 divided by the sum of a number and 12

• 4 / n + 12

• 4 / 12n

• 4 / (n + 12) 

• (4 / n) + 12

Answer explanation

The question asks for 4 divided by the sum of a number (n) and 12. This is mathematically represented as 4 divided by (n + 12), which is correctly written as 4 / (n + 12). Thus, the correct choice is 4 / (n + 12).

Translate this phrase into an algebraic expression.
8 less than the product of 4 and a number
Use the variable m to represent the unknown number.

• 8 - 4m

• 8m - 4

• 8m + 4

• 4m - 8

Answer explanation

The phrase "8 less than the product of 4 and a number" translates to 4m - 8. Here, 4m represents the product of 4 and the number m, and subtracting 8 indicates '8 less than' that product.

Evaluate the expression when
x =5    and   z = 4
z²  - 2x

• 6

• 2

• 17

• 26

Answer explanation

Substituting x = 5 and z = 4 into the expression z² - 2x gives 4² - 2(5) = 16 - 10 = 6. Thus, the correct answer is 6.

Which of the expressions does NOT show the product of four and n. 

• 4n

• 4 x n

• 4(n)

• 4 ÷ n

Answer explanation

The expression '4 ÷ n' represents division, not multiplication. The other options (4n, 4 x n, and 4(n)) all correctly show the product of four and n.

2x + 5(y - 1) when x=8 and y=5

• 20

• 31

• 36

• -4

Answer explanation

Substituting x=8 and y=5 into the expression: 2(8) + 5(5 - 1) = 16 + 5(4) = 16 + 20 = 36. Thus, the correct answer is 36.

Evaluate 6ab + 2c if a = 3, b = 10, and       c = 7

• 19

• 194

• 180

• 14

Answer explanation

Substituting a=3, b=10, and c=7 into 6ab + 2c gives 6(3)(10) + 2(7) = 180 + 14 = 194. Thus, the correct answer is 194.

How many terms are in the following expression?
2x+4y+8-2

• 1

• 2

• 3

• 4

Answer explanation

The expression 2x + 4y + 8 - 2 can be simplified to 2x + 4y + 6. It contains four distinct terms: 2x, 4y, 8, and -2. Therefore, the correct answer is 4.

Identify the variables in the expression: 3x + 4y - 7

• x and y

• 3 and -7

• x and 7

• 3 and 4

Answer explanation

In the expression 3x + 4y - 7, the variables are x and y. The terms 3 and -7 are constants, while x and y represent unknown values that can change.

• 10

• 13

• 21

Answer explanation

Substituting x = 3 into the expression gives: \(\frac{1}{4}(12 \cdot 3 + 4) = \frac{1}{4}(36 + 4) = \frac{1}{4}(40) = 10\). Thus, the correct answer is 10.

What is the coefficient in the following expression: 5 + 4m

• 5

• 4

• m

• 4m

Answer explanation

In the expression 5 + 4m, the coefficient is the number that multiplies the variable m. Here, 4 is the coefficient of m, making the correct answer 4.