Solve the problem. type the number in the box that correctly completes the sentence.

nimrod wanted to build a tower three miles high. he wants to know how far would it be from the top of his tower to a point four miles away from the base of the tower. the distance would be answer
miles.

5 miles

Step-by-step explanation:

Think of this like a triangle.  From the bottom of the tower, to the top of the tower, to the point 3 miles away, and back to the bottom of the tower.

So we already have 2 side lengths. The height of the tower, 3 miles, and the base, 4 miles.  In order to find the 3rd length, the distance from the top of the tower to the point 4 miles away from the bottom, we need to apply the formula A squared + B squared = C squared.

We have A and B,  (3 and 4) and we need C.

A squared (3 squared) is 9

B squared (4 squared) is 16

so 9 + 16 = C squared

9 + 16 = 25

C squared = 25

square root of 25 is 5

C = 5

The distance from the top of the tower to the point 4 miles away is 5.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15