Answer:
18. [tex] x = 8 [/tex]
19. [tex] c = 9 [/tex]
20. [tex] d = \sqrt{10} [/tex]
21. 83 1/3 ft
22.
a. decay
b. growth
c. decay
Step-by-step explanation:
18.
[tex] \sqrt{x + 1} + 12 + 10 = 25 [/tex]
[tex[ \sqrt{x + 1} = 3 [/tex]
Square both sides.
[tex] x + 1 = 9 [/tex]
[tex] x = 8 [/tex]
19.
[tex] a^2 + b^2 = c^2 [/tex]
[tex] (\sqrt{75})^2 + (\sqrt{6})^2 = c^2 [/tex]
[tex] 75 + 6 = c^2 [/tex]
[tex] 81 = c^2 [/tex]
[tex] c = 9 [/tex]
20.
[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
[tex] d = \sqrt{(3 - 4)^2 + (-9 - (-6))^2} [/tex]
[tex] d = \sqrt{(-1)^2 + (-3)^2} [/tex]
[tex] d = \sqrt{1 + 9} [/tex]
[tex] d = \sqrt{10} [/tex]
21.
Max: 5 ft tall; 3 ft shadow
Building: x ft tall; 50 ft shadow
5 ft is to 3 ft as x ft is to 50 ft
5/3 = x/50
3x = 250
x = 250/3
x = 83 1/3
Answer: 83 1/3 ft
22.
Exponential function:
y = a(b)^x
b is the number in parentheses raised to exponent x.
If b > 1, it is growth.
If b is between 0 and 1, it is decay.
Look at each case.
a. 0.85 is between 0 and 1: decay
b. 1.025 > 1: growth
c. 0.682 is between 0 and 1: decay
