(( answer with a b c or d))
if x = 3 inches, what is the perimeter of the figure above?
a. (36 + 36) inches
b. (6 + 12) inches
c. 72 inches
d. (6 + 12) inches

  B. (6√2 + 12) inches

Step-by-step explanation:

The length of the kite edge at upper left is ...

  x/sin(45°) = x/(1/√2) = x√2

The length of the kite edge at upper right is ...

  x/sin(30°) = x/(1/2) = 2x

The perimeter of the kite is double the sum of the lengths of these edges:

  P = 2(x√2 +2x) = 2x(√2 +2)

For x=3 in, this is ...

  P = 2·(3 in)(√2 +2)

  P = (6√2 +12) in

The sine of an angle is the ratio of the side opposite to the hypotenuse. Here, the side opposite is x, and the hypotenuse is the kite edge of interest.

  x/hypotenuse = sin(angle)

  hypotenuse = x/sin(angle) . . . . . solve for hypotenuse

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.