Question

evaluate the expression 2b^3 + 5 when b = 3

2b^3 + 5 = 2 (?)^3 + 5

Answer 1

the school principal is designing a square courtyard outside of the school, separated into 4 equal spaces. she wants to know the total area of the courtyard.

s = length (ft) of one side of each space

which expression shows the total area of the courtyard

4s^2
s^2 + 4
s^4 + 4
s^2

Answer 2

what is the total area if each smaller space is 5 feet on each side

Answer 3

When b = 3, the expression becomes:

2(3)^3 + 5
= 2(27) + 5
= 54 + 5
= 59

Therefore, when b = 3, the value of the expression 2b^3 + 5 is 59.

Answer 4

The total area of the courtyard can be found by calculating the area of one square space and then multiplying it by 4 since there are 4 equal spaces in the courtyard.

Area of one space = side length squared = s^2
Area of the 4 spaces = 4 * s^2 = 4s^2

Therefore, the expression that shows the total area of the courtyard is 4s^2.

Answer 5

To find the total area of the courtyard when each smaller space is 5 feet on each side, we use the expression we derived earlier:

Total area = 4s^2
Total area = 4(5)^2
Total area = 4(25)
Total area = 100 square feet

Therefore, the total area of the courtyard when each smaller space is 5 feet on each side is 100 square feet.