Question

PLEASE HELP 4 QUESTIONS 90 POINTS

1. What are the solutions to the equation?
n^2 − 8n + 16=25

2. Solve for b.
C = b^2/25

3. Solve for t.
d = −16t^2 + 12t

4. What are the solutions to the equation?
5w^2 + 10w = 40

Answer 1

n^2 − 8n + 16=25

C = b^2/25

d = −16t^2 + 12t

5w^2 + 10w = 40

Explanation:

Answer 2

1. n^2 -8n +16 = 25

Subtract 25 from both sides

n^2 - 8n + 16 - 25 = 0

Simplify

n^2 - 8n - 9 =0

Factor

(n-9)(n+1) = 0

Solve for n

n-9 = 0, n = 9

n+1 = 0, n = -1

Solution: 9,-1

2. C = b^2/25

Multiply both sides by 25:

25c = b^2

Take square root of both sides

b = +/-√25c

Simplify:

b = 5√C, -5√C

3. d = 16t^2 +12t

subtract d from both side:

16t^2 + 12t -d =0

Use quadratic formula to solve:

t = (3 +/-√(9-4d))/8

4. 5w^2 +10w =40

Subtract 40 from both side:

5w^2 + 10w -40 = 0

Factor:

5(w-2)(w+4)=0

Divide both sides by 5:

(w-2)(w+4)=0

Solve for w:

w-2 = 0, w = 2

w+4=0, w = -4

Solution: 2,-4