Felix surrounds a 12 in. by 8 in. photo with a frame that is x inches wide. Which quadratic function represents the combined area A of the picture and the frame? A. A(x) = x^2 + 20x + 96

B. A(x) = x^2 + 40x + 96

C. A(x) = 4x^2 + 20x + 96

D. A(x) = 4x^2 + 40x + 96

D: A(x) = 4x² + 40x + 96

Step-by-step explanation:

Dimensions of photo is;

Length; L = 12 inches

Width; W = 8 inches

Now, this picture is surrounded by a frame that is "x" inches wide. Thus, new dimensions are;

L_new = 12 + x + x = 2x + 12

W_new = 8 + x + x = 2x + 8

New area is;

A_new = (2x + 12) × (2x + 8)

A_new = 4x² + 24x + 16x + 96

A_new = 4x² + 40x + 96

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

asdsad

step-by-step explanation: