School House

Question 1

X= 18 / 23 / 26
Y= 130 / 160 / 178

For line h, the table shows three values of x and their corresponding values of y. Line k is the result of translating line hh
h down 5 units in the xy-plane. What is the x-intercept of line k?

Answer 1

(-17/6, 0)

Question 2

x^2 - 34x + c = 0

In the given equation, c is a constant. The equation has no real solutions if c > n. What is the least possible value of n?

Answer 2

b^2 - 4ac
-34^2 - 4 (1) (c)
1156 - 4c

c > n
4c > 1156
c > 289

Question 3

The equation E(t) = 5(1.8)^t gives the estimated number of employees at a restaurant, where t is the number of years since the restaurant opened. Which of the following is the best interpretation of the number 5 in this context?

A) The estimated number of employees when the restaurant opened
B) The increase in the estimated number of employees each year
C) The number of years the restaurant has been open
D) The percent increase in the estimated number of employees each year

Answer 3

A) The estimated number of employees when the restaurant opened

Question 4

For the exponential function f, the value of f(1) is k, where k is a constant.

Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?

A) f(x) = 50(1.6)^(x+1)
B) f(x) = 80(1.6)^x
C) f(x) = 128(1.6)^(x-1)
D) f(x) = 204.8(1.6)^(x-2)

Answer 4

C) f(x) = 128(1.6)^(x-1)
128(1.6)^(1-1)
128(1.6)^0
128(1)
128

Question 5

A model estimates that at the end of each year from 2015 to 2020, the number of squirrels in a population was 150% more than the number of squirrels in the population at the end of the previous year. The model estimates that at the end of 2016, there were 180 squirrels in the population. Which of the following equations represents this model, where n is the estimated number of squirrels in the population t years after the end of 2015 and t ≤ 5?

A) n = 72(1.5)^t
B) n = 72(2.5)^t
C) n = 180(1.5)^t
D) n = 180(2.5)^t

Answer 5

A = P (1 + R) ^T
180 = P(1 + 1.5) ^t
180 = p(2.5)^t —— t = 1 / a = 180
180 = 2.5p
p = 72

B) n = 72(2.5)^t

Question 6

Line t in the xy-plane has a slope of -1/3 and passes through the point (9,10). Which equation defines line t?

A. y = 13x - 1/3
B. y = 9x + 10
C. y = -x/3 + 10
D. y = -x/3 + 13

Answer 6

D. y = -x/3 + 13

y = mx + b
y = -1/3 + b or y = -x/3 + b
10 = -9/3 + b
10 = -3 + b
13 = b

y = -x/3 + 13