Question

Help me please i reallly need it​

Answer 1

Answer:

a) A = 64(2s - 1)

b) A = 1,856 cm²

Step-by-step explanation:

Given the side of the frame, 8s, and that the border that frames the picture is 4 on either side = 8:

a) Find an expression for the area of the frame, in factored form.

A = area of the square frame

A₁ = Total area (including the picture inside the frame) = (8s)²

A₂ = Area of the picture inside the frame = 4 + 4 = (8s - 8)²

To find the area of the frame, subtract the area of the picture from the total area.

A = A₁ - A₂

A = (8s)² - (8s - 8)²

Perform the necessary exponential operations:

A = 64s²- (64s² - 64s - 64s + 64)

A = 64s²- (64s² - 128s + 64)

A = 64s²- (64s² - 128s + 64)

Distribute -1 into the parenthesis:

A = 64s²- 64s² + 128s - 64

Combine like terms:

A = 0 + 128s - 64

A = 128s - 64

Factor out 64:

A = 64(2s - 1)

The expression for the area of the frame in factored form is: A = 64(2s - 1).

b) Determine the area of the frame when s = 15cm

Using the same expression from part A:

A = 64(2s - 1)

Substitute s = 15 into the expression:

A = 64[2(15) - 1]

A = 64(30 - 1)

A = 64(29)

A = 1,856 cm²

Therefore, the area of the frame that has a side of 15 cm is: A = 1,856 cm²