math exam

Which are points on the graph of y = 1.5 + ⌈x⌉? Select three options

(-4.5, -2.5) (7.9, 9.5) (1.3, 3.5)

What is the solution (a, c) to this system of linear equations? 2a - 3c = -6 a + 2c = 11

(3, 4)

What is the value of x in the equation (x + 12) = (x + 14) - 3?

-24

Samir, a carpenter, spent $300 on specialty tools to make toy horses for children. For each horse he makes, he spends $75 on supplies. He charges $125 for each horse. How many horses must Samir sell in order to break even?

6

The function f(t) represents the cost to connect to the Internet at an online gaming store. It is a function of t, the time in minutes spent on the Internet. f(t) = Which statement is true about the Internet connection cost?

Any amount of time over an hour and a half would cost $10.

Which statement is true about the end behavior of the graphed function?

As the x-values go to negative infinity, the function's values go to positive infinity.

Which graph represents the function y = 2x - 4?

C

What is the domain of the function on the graph?

all real numbers

What is the range of the function f(x) = -2|x + 1|?

all real numbers less than or equal to 0

What is the solution to the linear equation? -12 + 3b - 1 = -5 - b

b=2

The table represents a function. What is the value of f(-1)?

f(-1)=0

Which linear function represents the line given by the point-slope equation y - 2 = 4(x - 3)?

f(x) = 4x - 10

How many intersections are there of the graphs of the equations below? 1/2x + 5y = 6 3x + 30y = 36

infinitely many

When a number is added to of itself, the result is 24. The equation that models this problem is n + n = 24. What is the value n?

n=20

How many solutions does this linear system have? y = x+ 2 6x - 4y = -10

one solution: (-0.6, 1.6)

What is the solution to 4|0.5x - 2.5| = 0?

x = 5

The soccer team is conducting a fundraiser selling long-sleeved T-shirts for $14 and short-sleeved T-shirts for $10. So far the team has sold less than $200 worth of the two types of T-shirts. Which inequality best represents x, the number of long-sleeved T-shirts they have sold, and y, the number of short-sleeved T-shirts they have sold?

14x + 10y < 200

This mapping shows a functional relationship. When f(x)=4, what is the value of x?

2

Hiroto solved the equation 6 - 4|2x - 8| = -10 for one solution. His work is shown below. 6 - 4|2x - 8| = -10 -4|2x - 8| = -16 |2x - 8| = 4 2x - 8 = 4 2x = 12 x = 6 What is the other solution?

2

Elias and Niko are polishing the silver at the heritage museum. Elias could polish all the silver himself in 40 minutes. That task would take Niko 50 minutes to complete alone. Which table is filled in correctly and could be used to determine how long it would take if Elias and Niko polished the silver together?

A

The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r, where r is expressed as a decimal. What is the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years?

$80

Shannon graphed the system of equations. 7x - 4y= -8 y = x - 3 What is the closest approximate solution to the system of equations?

(-5, -6.8)

The tables represent the functions f(x) and g(x). Which input value produces the same output value for the two functions?

x = -6

Which equation is equivalent to -k + 0.03 + 1.01k = -2.45 - 1.81k?

-100k + 3 + 101k = -245 - 181k

Which sequences are arithmetic? Select three options.

-8.6, -5.0, -1.4, 2.2, 5.8, ... 5, 1, -3, -7, -11, ... -3, 3, 9, 15, 21, ...

The graph represents the data cost for monthly Internet service for a cell phone. Which function, C(x), represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month?

A

Which is the graph of linear inequality 6x + 2y > -10?

A

An electrician is hired to install a ceiling fan. She estimates that the installation will take no more than 45 minutes if the house is up to building code. If the house is not up to building code, she estimates that the installation will take longer than 120 minutes. Which graph represents the number of minutes it could take her to install the fan?

C

The potential energy, P, in a spring is represented using the formula P = kx2. Lupe uses an equivalent equation, which is solved for k, to determine the answers to her homework. Which equation should she use?

C

Which graph shows the solution to the system of linear inequalities? 2x - 3y <12 y < -3

C

A new coffee shop can hold no more than 50 seats. The owner wants at least 20 of the seats to be stools and the remaining seats to be recliners. If x is the number of stools and y is the number of recliners, which graph represents the solution to the system of inequalities? x + y ≤ 50 x ≥ 20

D

Which table represents a direct variation function?

D

Which statement is true about the graphed function f(x)?

F(x) > 0 over the intervals (-∞, -2.5) and (-0.75, 0.75).

The table shows how an elevator 500 feet above the ground is descending at a steady rate. Which equation represents the height, h(t), of the elevator in feet, as a function of t, the number of seconds during which it has been descending?

h(t) = -5t + 500

What is the inverse of the function f(x) = 4x + 8?

h(x)=1/4x-2

Gerri purchases a coupon book with discounts for her favorite coffee shop. Every coupon for the coffee shop offers the same discount. The table shows her total savings, y, based on the number of coupons, x, used from the book. What are the slope and y-intercept of the line represented by the points shown in the table?

slope: 2, y-intercept: -20

The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length in meters, l, and the possible width in meters, w, of the pool?

w ≤ l - 102l + 2w > 62

The graph represents the function where electricity usage in kilowatts per hour of a clock radio varies directly with the number of days it is plugged into the wall current. Which is a reasonable estimate of the constant of variation?

0.25 kWh per day

The inverse of the function f(x) = is shown. h(x) = 2x- What is the missing value?

20

Using a stopwatch, Tyrone determines it takes him 58.2 minutes to travel 30 miles to work. The stopwatch measures to hundredths of a minute. Going by the accuracy of the stopwatch, which is the most accurate determination for the number of feet per second Tyrone traveled on his way to work? 1 mile = 5,280 feet

45.36 feet per second

The formula for density is given by , where p is density, M is mass and V is volume. If a substance has a mass of 27.82 grams and a volume of 3.6 ml, what is the most accurate density of the substance in g/ml?

7.7

Line JK passes through points J(-3, 11) and K(1, -3). What is the equation of line JK in standard form?

7x + 2y = 1

A sequence is defined by the recursive function f(n + 1) = f(n). If f(3) = 9 , what is f(1) ?

81

Which graph represents the function g(x) = |x + 4| + 2?

A

Percy works two part-time jobs to help pay for college classes. On Monday, he works 3 hours at the library and 2 hours at the coffee cart and earns $36.50. On Tuesday, he works 2 hours at the library and 5 hours at the coffee cart and earns $50. His hourly wage at the library, x, and hourly wage at the coffee cart, y, can be determined using the system of equations below. 3x + 2y = 36.502x + 5y = 50.00 At which job does Percy earn the greater hourly wage? How much does Percy earn each hour at this job?

Percy earns a greater hourly wage of $7.50 at the library.

A function g(x) is defined as shown. g(x) = What is the value of g(4)?

12

Yesterday, Selma read 75 pages of her book. If she reads at a pace of 2 pages per minute today, which table shows only viable solutions for the total number of pages she has read, y, after x minutes have elapsed?

D

The function graphed is reflected across the x-axis to create a new function. Which is true about the domain and range of each function?

The domain stays the same, but the range changes.

Marlena created a table of values representing the height in feet, h(t), of a coconut falling to the hard ground with a height of 0 feet, collected over t seconds. Assume the coconut does not bounce. Which statement is true?

The values of h(t) when t = 4 and 5 should be 0.

Sun, a kayaker, paddles 8 miles upstream (against the current) in 2 hours. Returning to her original location, she paddles downstream (with the current) the same distance in 1 hour. The equations represent x, the paddling speed, and y, the speed of the current. 2(x - y) = ab(x + y) = 8 Which are true? Select two options.

a = 8 b = 1