Debra wants to cover a footrest in the shape of a rectangular prism with cotton fabric. The footrest is 15 inches by 7 inches by 9 inches. She has 1 square yard of fabric. Can she completely cover the footrest? Explain.

Yes, she can.

Step-by-step explanation:

We have to find the surface area of the footrest and see if it greater than or less than 1 square yard.

The surface area of a rectangular prism is given as:

A=2(wl+hl+hw)

where w = width, l = length, h = height

The footrest is 15 inches by 7 inches by 9 inches. Its surface area is:

A = 2[(7 * 15) + (9 * 15) + (9 * 7)]

A = 2[105 + 135 + 63]

A = 2 * 303 = 606 square inches

1 square inch = 0.000771605 square yards

=> 606 square inches = 606 * 0.000771605 = 0.468 square yards

Since the surface area of the prism is less than 1 square yard, she can completely cover the footrest with the fabric.

hi there!

how can i assist you?

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places