Algebra, Cumulative Exam 86%

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? $60 $80 $90 $100

$80

Which ordered pair needs to be removed in order for the mapping to represent a function? (-3, -4) (-2, -1) (1, -3) (3, 7)

(-2, -1)

Shannon graphed the system of equations. 7x - 4y= -8 y = x - 3 What is the closest approximate solution to the system of equations? (-5, -7.2) (-5, -6.8) (-5, -6.2) (-5, -5.9)

(-5, -7.2)

What is the solution (a, c) to this system of linear equations? 2a - 3c = -6 a + 2c = 11 (3, -4) (3, 4)

(3, 4)

Which equation is equivalent to -k + 0.03 + 1.01k = -2.45 - 1.81k? -100k + 3 + 101k = -245 - 181k -100k + 300 + 101k = -245 - 181k -k + 3 + 101k = -245 - 181k -k + 300 + 101k = -245 - 181k

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

What is the value of x in the equation (x + 12) = (x + 14) - 3? -24 -6 0

-24

Which sequences are arithmetic? Select three options. -8.6, -5.0, -1.4, 2.2, 5.8, ... 2, -2.2, 2.42, -2.662, 2.9282, ... 5, 1, -3, -7, -11, ... -3, 3, 9, 15, 21, ... -6.2, -3.1, -1.55, -0.775, -0.3875, ...

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

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 0.50 kWh per day 2.40 kWh per day 4.00 kWh per day

0.25 kWh per day

The crew of a garbage truck takes 5 hours to empty all the bins in one neighborhood on pickup day. The city assigned a second garbage truck to this neighborhood. During their training, it took the crew from the second truck 8 hours to empty all the bins. When the two crews start working together, what part of all the garbage bins will the first garbage truck empty? 0.6 0.5 0.7 0.4

0.6

Wren recorded an outside temperature of -2°F at 8 a.m. When she checked the temperature again, it was 4°F at 12:00 p.m. If x represents the time and y represents the temperature in degrees Fahrenheit, what is the slope of the line through these two data points? -1.5 -0.5 0.5 1.5

1.5

Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each. Dance World: y = 15xToe Tappers: y = 25 + 12.5x How many classes would Gina need to take for the total cost to be the same at both dance studios? 10 15 100 150

10

A recipe calls for cup of broth. The largest volume-measuring tool that Tabitha has is a teaspoon. She knows that there are 16 tablespoons in 1 cup and 3 teaspoons in 1 tablespoon. How many teaspoons of broth should she use? teaspoons 12 teaspoons 19 teaspoons teaspoons

12 teaspoons

At a carnival, food tickets cost $2 each and ride tickets cost $3 each. A total of $1,240 was collected at the carnival. The number of food tickets sold was 10 less than twice the number of ride tickets sold. The system of equations represents x, the number of food tickets sold, and y, the number of ride tickets sold. 2x + 3y = 1240 x = 2y - 10 How many of each type of ticket were sold? 180 food tickets and 293 ride tickets 180 food tickets and 350 ride tickets 293 food tickets and 180 ride tickets 350 food tickets and 180 ride tickets

180 food tickets and 350 ride tickets

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? -6 -4 2 10

2

This mapping shows a functional relationship. When f(x)=4, what is the value of x? 0 2 3 4

2

The inverse of the function f(x) = is shown. h(x) = 2x- What is the missing value? 1 5 10 20

20

Two solutions of different concentrations of acid are mixed creating 40 mL of a solution that is 32% acid. One-quarter of the solution is made up of a 20% acid solution. The remaining three-quarters is made up of a solution of unknown concentration, c. Which equation can be used to determine c, the unknown concentration? 30c + 10(0.2) = 40(0.32) (c) + (0.2) = 40(0.32) (c)( (0.2)) = 40(0.32) 30(c)(10(0.2)) = 40(0.32)

30c + 10(0.2) = 40(0.32)

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 19.8 feet per second 19.84 feet per second 45.3 feet per second 45.36 feet per second

45.36 feet per second

Sonji has $5.25 in nickels and dimes.The coin value can be modeled by the equation , where d represents the number of dimes and n represents the number of nickels. If Sonji has 21 dimes, how many nickels does she have? 35 42 63 105

63

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 7x + 2y = 1 14x + 4y = -1 14x + 4y = 1

7x + 2y = 1

Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be? 9 feet 18 feet 30 feet 33 feet

9 feet

Which statement is true about the end behavior of the graphed function? As the x-values go to positive infinity, the function's values go to negative infinity. As the x-values go to zero, the function's values go to positive infinity. As the x-values go to negative infinity, the function's values are equal to zero. As the x-values go to negative infinity, the function's values go to positive infinity.

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

Which statement is true about the graphed function f(x)? F(x) < 0 over the intervals (-∞, -2.5) and (-0.75, 0.75). F(x) > 0 over the intervals (-∞, -2.5) and (-0.75, 0.75). F(x) < 0 over the intervals ( -2.5, -0.75) and (-0.75, ∞). F(x) > 0 over the intervals ( -2.5, -0.75) and (0.75, ∞).

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

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 $7.00 at the library. Percy earns a greater hourly wage of $7.00 at the coffee cart. Percy earns a greater hourly wage of $7.50 at the library. Percy earns a greater hourly wage of $7.50 at the coffee cart.

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

Which scenario can be represented using the inequalities below? 1.25 < x < 1.5 A container of milk costs at least $1.25 but less than $1.50. A student spends at least 1 hour 15 minutes, but no more than 1 hour 30 minutes on homework. A tip added to a restaurant bill is less than or equal to 25% or less than or equal to 50%. The point value of a test item is more than 1.25 points and less than 1.5 points.

The point value of a test item is more than 1.25 points and less than 1.5 points.

A tree company charges a delivery fee for each tree purchased in addition to the cost of the tree. The delivery fee decreases as the number of trees purchased increases. The table below represents the total cost of x trees purchased, including delivery fees. Which best describes why the function is nonlinear? The rate of change between 1 and 2 trees is different than the rate of change between 2 and 3 trees. The rate of change between 1 and 2 trees is different than the rate of change between 1 and 3 trees. The rate of change between 2 and 3 trees is different than the rate of change between 3 and 4 trees. The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

The rate of change between 2 and 3 trees is different than the rate of change between 3 and 5 trees.

Becky created a graph to represent her distance away from home one afternoon. She left home and ran to the park, met some friends and stayed at the park, and then walked back home using the same route. Which graph could Becky have created?

a

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

What is the inverse of the function f(x) = 4x + 8? h(x) = x - 2 h(x) = x + 2 h(x) = x - 2 h(x) = x + 2

a

What is the solution to -2(8x - 4) < 2x + 5? x > x < x > 6 x < 6

a

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

a

Which is the graph of linear inequality x - 2y ≥ -12?

a

Which table represents viable solutions for y = 5x, where x is the number of tickets sold for the school play and y is the amount of money collected for the tickets?

a

What is the domain of the function on the graph? all real numbers all real numbers greater than or equal to -2 all real numbers greater than or equal to -5 all real numbers greater than or equal to 0

all real numbers

What is the solution to the linear equation? -12 + 3b - 1 = -5 - b b = -2 b = -1.5 b = 1.5 b = 2

b = 2

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

Ray was in charge of filling the soccer team's water jug for practice. At the beginning of practice he filled the jug. Halfway through practice the team took a water break. After the break Ray refilled the jug so the players could have water after practice. At the end of practice Ray drained the jug. Which graph could represent the level of the water in the jug during and after practice?

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? k = 2Px2 k = Px2 k = k =

c

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

c

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

c

Which system of linear inequalities has the point (2, 1) in its solution set?

d

Which table represents a direct variation function?

d

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 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 h(t) = 5t - 500 h(t) = -5t + 500 h(t) = -5t - 500

h(t) = -5t + 500

How many intersections are there of the graphs of the equations below? x + 5y = 6 3x + 30y = 36 none one two infinitely many

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 = 18 n = 20 n = 21 n = 23

n = 20

A team is selling discount cards as a fundraiser. The table shows the number of cards sold and the remaining amount of money needed. Which word describes the slope of the line representing the data in the table? zero undefined negative positive

negative

How many solutions does this linear system have? y = x+ 2 6x - 4y = -10 one solution: (-0.6, -1.6) one solution: (-0.6, 1.6) no solution infinite number of solutions

one solution: (-0.6, 1.6)

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 slope: 2, y-intercept: 10 slope: 5, y-intercept: -20 slope: 5, y-intercept: 10

slope: 2, y-intercept: -20

What is the solution to 4|0.5x - 2.5| = 0? x = 1.25 x = 5 x = -1.25 or x = 1.25 x = -5 or x = 5

x = 5