The population of Candyworld is 14.4 Candys per acre. Exactly 792 Candys live in
Candyworld. How many acres is Candyworld? Only enter a numerical value in the
answer blank.(5 points)

55

Step-by-step explanation:

Step 1: Density = mass/volume        

Step 2: Density = Candyworld/acres  

The number of Candys is 792, the density is 14.4, and acres is the volume. Let V represent the volume in acres.

Step 3: 14.4 = 792 Candys/V  

Step 4: (V)(14.4) = 792 Candys/V (V)  

Step 5: (14.4)(V) = 792 Candys

Step 6: V = 55 [volume is 55 acres]  Candyworld is 55 acres.

55

Step-by-step explanation:

D = M/V

D = 14.4

M = 792

V = ?

14.4 = 792/V

V (14.4) = 792/V (V)

14.4v = 792

14.4v/14.4 = 792/14.4

V = 55

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240