Can someone help me?

Question

Annie is framing a photo with a length of 6 inches and a width of 4 inches. The distance from the edge of the photo to the edge of the frame is x inches. The combined area of the photo and frame is 63 square inches.

A) write a quadric function to find the distance from the edge of the photo to the edge of the frame. You must show your work to receive credit

b) what is the value of x? Must show work to receive credit

c) how wide are the photo and frame together? Must show work to receive credit

Answer 1

let 2x + 4 be the width and 2x + 6 be the length of the frame. The total area of the picture and frame is then

(2x + 4 )( 2x +6) = 63 in² so 4x² + 20x +24 = 63 and so 4x² + 20x - 39 =0 solving for x will give the distance from the edge of the photo to the edge of the frame. Using the quadratic formula x = - 20/8 ±√(400+ 624)/8 and this simplifies to x = - 20/8 ±√ 1024/8 = -20/8÷ 32/8 and x= 1.5 in The width is 2x + 4 = 3 +4 = 7in.

Answer 2

Annie is framing a photo with a length of 6 inches and a width of 4 inches. The distance from the edge of the photo to the edge of the frame is x inches. The combined area of the photo and frame is 63 square inches.

First, draw and label a picture based on the description (note: you certainly can do better than WyzAnt Answers Forum allows):

^ XXXXXXX

| L X111111X

| E X222222X

| N X333333X

| X444444X

V XXXXXXX

A) write a quadratic function to find the distance from the edge of the photo to the edge of the frame. You must show your work to receive credit

"combined area of the photo and frame is 63 square inches" = length*width = (x+6+x)*(x+4+x) = 63

(2x+6)(2x+4) = 63 [combine terms]

4x² + 8x + 12x + 24 = 63 [use F-O-I-L]

4x² + 20x - 39 = 0 [combine terms; and subtract 63 from both sides]

b) what is the value of x? Must show work to receive credit

4x² + 20x - 39 = 0

(x-1.5)(x+6.5) = 0 [either factor or use quadratic formula]

The multiplicative property of zero demands that either x=1.5, x=-6.5, or both.

-6.5 is not possible measurement

x=1.5

c) how wide are the photo and frame together? Must show work to receive credit

width of photo = 4 in; width of photo and frame together = 1.5+4+1.5 = 7 inches

Also, length of photo = 6 in; length of photo and frame together = 1.5 + 6 +1.5 = 9 inches

Check (very important):

Does width*length = 63 square inches ?

(7 inches)*(9 inches) = 63 square inches ?yes

Answer 3