Middle School Math (5164) - Algebra

John spends his summer working at a retail shop. As a result, he gets a 15 percent employee discount of everything sold in the store. He decides to buy 4 pairs of pants which retail for $30 and 5 shirts which retail for $20. What is the total price he must pay after his employee discount? ($195.50) ($230) ($187) ($220)

$187

The Booster Club at Martin MS is selling spirit buttons for homecoming. The buttons cost $0.75 to make and will be sold for $2 each. How many buttons, b, must be sold to make a profit of $500? ($500 - $0.75b = $2b) ($500 = $2b - $0.75b) ($500 = $2b + $0.75b) ($500 + $2b = $0.75b)

$500 = $2b - $0.75b

If y = 3x - 2 were graphed in the xy plane, which point would fall above the graph? (-1, -6) (-1, -1) (2, 1) (1, -1)

(-1, -1)

Which ordered pair is a solution to the system of equations below? {x² - y² = 25 x² + y² + 18x + 65 = 0 ((-9, 4)) ((-7, -5)) ((-5, 0)) ((-9, 0))

(-5, 0)

Find the solution(s) to the system: y = x² - 5x + 6 y = x - 2 ((2, 4)) ((-2, -4) and (-4, -6)) ((2, 0)) ((2, 0) and (4, 2))

(2, 0) and (4, 2)

What is the solution to the system of equations below? -4x + 3y = -5 y = x - 1 ((-2, -3)) ((2, 1)) ((1, 2)) ((-4, -5))

(2, 1)

Determine the solution(s) to the system. y = x² - 5x + 8 y = 2x - 4 ((3, 2)) ((3, 2) and (4, 4)) ((3, 4)) (There is no solution.)

(3, 2) and (4, 4)

Mrs. Thompson presents the scenario to her class and asks them to use it to answer the following question: Kirsten wants to rent paddle boats for her group of friends. She will need 4 boats to fit all of her friends and the boat rental company charges $15 per hour for each boat. In addition to the hourly fee, there is a one-time membership fee of $40 to use the facilities, regardless of how many boats are rented. If Kirsten has budgeted $300 for this outing, how many hours will she and her friends enjoy on the lake? If h represents the number of hours, which of the following equations represents the scenario? (15h + 40 = 300) ((4 ⋅ 15h) + 40 = 300) ((4 ⋅ 15h) - 40 = 300) ((4 ⋅ 15h) + 40h = 300)

(4 ⋅ 15h) + 40 = 300

Before purchasing a new car, Branden wants to know his monthly payments, m. He plans to make a down payment, d, and then pay off the rest of the car in 60 months. The total cost of the car plus interest is t. Which equation can Branden use to find his monthly payment? ((d-t)/60 = m) (60/(t-d) = m) ((t-d)/60 = m) (60/(d-t) = m)

(t-d)/60 = m

Which of the following is equivalent to x² - 6x - 15 = 0? ((x + 3)² = 24) ((x - 3)² = 6) ((x - 3)² = 15) ((x - 3)² = 24)

(x - 3)² = 24

What is the y-value of the solution to the system below? x = 7/2y + 1 2x - 4y = -1 (-5/2) (-1) (1) (9/2)

-1

Which of the following values of x is a solution to the set of inequalities below? -x - 2 < 4 or -x - 2 > 8 (-7) (-12) (-10) (-6)

-12

Which of the following is not an appropriate first step when solving this equation? 6(y - 3) = 2(y - 3) + 8 (3(y - 3) = y - 3 + 4) (-2(y - 3) = 2(y - 3)) (6y - 18 = 2y - 6 + 8) (4(y - 3) = 8)

-2(y - 3) = 2(y - 3)

Which of the following equations is parallel to the line y = 5x - 2? (4 = 20y + 4x) (-20 = 4y - 20x) (-15 = 5y - 5x) (-10 = 5y + 5x)

-20 = 4y - 20x

Which of the following values of x satisfies 3x²-6x-24 > 0? (-5) (1/3) (4) (-2)

-5

Which of the following is the solution set for ∣x + 4∣ < 1? (−5 ≤ x ≤ −3) (x < -3) (-5 < x < -3) (x > -3)

-5 < x < -3

If f (x) = -x² + 3x - 2, find the value of f (4). (-6) (18) (2) (26)

-6

Which of the following is equivalent to the expression below? 2x + 4y - 3x + 6 (-x² + 4y + 6) (5x + 4y + 6) (-x + 4y + 6) (9xy)

-x + 4y + 6

Solve for x. (10x + 2)/4 = 5x - 2 (1) (-4/5) (2/5) (-1)

1

Mitchell started his weekly mathematics homework during study hall and finished 8 problems before returning home. At home, he found he took an average of 7 minutes to solve each of the remaining problems. Tawny finished only 2 problems at school but was able to solve one problem every 5 minutes at home. How many minutes did they each spend at home to finish their weekly assignment if they solved the same number of problems? (35) (140) (23) (105)

105

Which of the following is an expanded version of the expression 3 (x + 7) (4x - 2)? (12x² + 78x + 42) (90x - 42) (12x² + 90x - 42) (12x² + 78x - 42)

12x² + 78x - 42

The cost to ski at a resort is T = 85 + 5h, where T is the total cost and h is the number of hours. If Carl has $150, how many hours can he ski? (13) (325) (30) (47)

13

Find the value of f (x) = 3x² - 2x + 1 when x = -2. (9) (-7) (17) (-15)

17

A computer store sells laptops that range from $300 to $4000 and currently has 40 laptops in stock. What is the maximum number of $4000 laptops the store could have if the current inventory for laptops totals $78,600? (18) (22) (15) (20)

18

Ally and Jenny are comparing their cell phone plans. Ally pays $30 per month for her phone line and $5 for every 1GB of data used. Jenny pays $20 per month for her phone line and $10 for every 1GB of data used. If Ally's and Jenny's monthly bills are the same this month, how many GB of data did they each use? (1) (2) (3) (4)

2

Which of the following is a solution to the inequality below? -12 < 2 - 5x ≤ 7 (2.8) (-2) (-2.8) (2)

2

Use the system of equations below to answer the following question. x² + y² = 20 y = x² How many real solutions does the system have? (no real solution) (1 real solution) (2 real solutions) (infinitely many real solutions)

2 real solutions

Three of the following equations, when simplified, equal the same value. Which of the following equations, when simplified, is NOT equal to the other equations? (.25 X 100 - 40) (200 X 1/8 - 2(40 - 20)) (2(40 X .2) + 5[.4 X (1/4)]) ([20/(1/5)]-[5/(1/23)])

2(40 X .2) + 5[.4 X (1/4)]

Which four of the following lines are perpendicular to 5x - 2y = 7? Select all answers that apply. (5x + 2y = 7) (2/3x + 5/3y = 1/3) (5y = -2x + 10) (2x + 5y = 13) (y = -2/5x + 3) (-2y = -5x + 7)

2/3x + 5/3y = 1/3, 5y = -2x + 10, 2x + 5y = 13, y = -2/5x + 3

Which of the following expressions is equivalent to 9x + 24 for all values of x? (5(45x + 8)) (28 + 1/5(45x-20)) (1/5(45x + 28 - 20)) (28 + 5(45x - 20))

28 + 1/5(45x-20)

If 1/6x - 4 = 1, then x = (-18) (5/6) (30) (10)

30

Mrs. York is administering an exam consisting of 40 questions. The test is worth 100 points. Some of the questions are weighted 2 points and some are 4 points. How many 2-pt questions are on the test? (40) (30) (20) (10)

30

Estella and Manuel were hiking down from the top of a mountain toward the parking lot at the bottom. At 3:00 p.m. Estella was 1800 meters further down the mountain than Manuel. Estella hiked at a rate of 0.65 meters per second. Manuel hiked at a rate of 1.25 meters per second. At what time did Manuel catch up with Estella? (4:20) (3:30) (3:50) (4:00)

3:50

Susan is planning for volunteer day at the high school. Every person that signs up gets a free lunch for volunteering. This year, lunch includes 3 slices of pizza and a soda. If x = number of volunteers and one pizza has 8 slices, which equation can help her to determine the correct number of pizzas (n) to order? ((3x + 1)/8 = n) (3/8x = n) (3x/8 = n) (3/8 X x + 1 = n)

3x/8 = n

What is the first step in solving this equation? 3 (y + 4) - 2(3y - 1) = 10 (3y + 12 + 6y + 2 = 10) (3y + 4 − 6y − 1 = 10) (3y + 4 + 6y + 2 = 10) (3y + 12 − 6y + 2 = 10)

3y + 12 − 6y + 2 = 10

John works in sales at a car dealership. His base salary is $550 per week and he makes $900 for each car he sells. His paycheck last week was more than $4000. What is the least number of cars he could have sold? (5) (4) (6) (3)

4

Use the equation below to answer the question that follows. 4x + 8(x-3) = x+20 Which of the following is the correct value of x? (all real numbers) (4) (3) (6)

4

An airplane travels 7 times faster than a train. If the difference between the speed of the plane and the speed of the train is 420 m/h, how fast is the plane traveling? (294 m/h) (490 m/h) (70 m/h) (60 m/h)

490 m/h

Which of the following lines passes through the point (2, 3) and is parallel to 6x - 3y = 12? (4x - 2y = 2) (6x - 2y = 6) (x + 2y = 8) (2x - y = 4)

4x - 2y = 2

Which of the following equations is parallel to the line y = x/2 - 1/4? (2y + 4x = -8) (4y - 2x = 12) (4y - x = -1) (2y - 8x = -3)

4y - 2x = 12

On the way from school to the town library, Jenna rides her bike for 15 blocks and then walks the rest of the way at 13/21 block per minute. Micah follows the same route but walks the entire distance to the library at 6/7 block per minute. If they both walk for the same amount of time what is the total number of blocks between the school and the library? (54) (18) (63) (9)

54

Which of the following correctly simplifies the left side of the equation below? 3x - 4 + 6x + 5 - 4x - 2 = 16 ((3x - 4) + (6x + 5) - (4x + 2) = 16) (14x - 10 = 16) (13x - 11 = 16) (5x - 1 = 16)

5x - 1 = 16

Simplify the expression: 3x + 2(3x - 2) + 5 - 2(2x + 1) (5x + 4) (8x + 6) (13x + 11) (5x-1)

5x-1

Which of the following is equivalent to 8(8 + y + y) - 16y for all values of y? (48y) (48) (64) (64 - 8y)

64

Which of the following options shows a logical and correct first step to solving the algebraic equation given? 3(2x + 1) - 5(x + 4) = 11 (-2(3x + 5) = 11) (6x + 3 - 5x + 20 = 11) (6x + 3 - 5x - 20 = 11) (6x + 1 - 5x + 4 = 11)

6x + 3 - 5x - 20 = 11

Which equation, along with 3x + 2y = 4, creates a system of equations which has no solution? (6x + 4y = 8) (2x + 3y = 4) (6x + 4y = 12) (-2x + 3y = 6)

6x + 4y = 12

There are 110 cars that pass through the carpool lane daily. Some cars take 2 students and other cars take 3 students. If 255 students go through the carpool line, what fraction of the cars take 3 students? (1/3) (21/51) (3/5) (7/22)

7/22

Samuel has an average base metabolic rate of 80 calories per hour and uses an additional 352 calories per day walking to and from school. Sabrina uses an extra 544 calories over her base metabolic rate while on her daily bike ride. Samuel and Sabrina typically burn the same total number of calories in each 24-hour day. Using these figures, what is Sabrina's average base metabolic rate in calories per hour? (72) (1728) (112) (2272)

72

A certain hill is 30 meters high and erodes at a rate of 1/5 meter per year. A nearby hill is 25 meters high and erodes at a rate of 2/15 meter per year. In how many years will the two hills be the same height if they continue to erode at these rates? (25) (15) (75) (5)

75

A couple is planning their wedding budget. The set cost of the venue, flowers, photographer, and DJ is $4,950, and the cost per person for food and drinks is $65. Therefore, t, the total cost of the couple's wedding, can be expressed by the equation t = 65p + 4,950, where p is the number of people that attend the wedding. If the couple has a budget of $10,000 to spend on the wedding, what is the maximum number of people that can attend? (76) (78) (77) (153)

77

If f(x) = x² - 3x + 4, what is the value of f(-1)? (7) (2) (8) (0)

8

Which of the following are correct solutions to the inequality below? 2x + 5 ≥ 15 Select all answers that apply. (4) (2) (8) (5)

8, 5

Simplify the expression below: (32x + 12)/4 (8x + 12) (8x + 3) (32x + 3) (28x + 8)

8x + 3

A football team is selling raffle tickets as a fundraiser for equipment. They need at least $2000 for equipment and raffle tickets are $8.00 each. Which inequality represents the minimum number of tickets needed to be sold to reach their goal? (8x ≥ 2000) (8x ≤ 2000) (8x < 2000) (8x > 2000)

8x ≥ 2000

Which of the following sequences of steps will yield the valid solution for x to the equation -8 + 5x = 12? (Combine -8 and 5 to get -3x = 12, then divide by -3 on each side of the equation.) (Add 8 to each side of the equation, then divide by 5 on each side of the equation.) (Subtract 8 from each side of the equation, then divide by 5 on each side.) (Divide by 5 on both sides of the equation, then add 8 to each side.)

Add 8 to each side of the equation, then divide by 5 on each side of the equation.

Klaus is planning his annual garden. He wants to plant 2 carrot plants, 3 pepper plants, and 1 squash plant. If he knows the area that each plant requires to grow and wants to determine the total area his garden will require, which operation will he use last in his calculation? (subtraction) (division) (multiplication) (addition)

Addition

Using the student's work below, which property does the student still need to master? Step 1: 3x - 7 = 7x + 1 Step 2: 3x = 7x - 6 Step 3: 10x = -6 Step 4: x = -6/10 (addition property of equality) (multiplication property of equality) (transitive property) (associative property of addition)

Addition property of equality

Review the work below. Given 3(2x + 1) + 2(2x + 1) + 7 = 42 - 5x Step 1: 5(2x + 1) + 7 = 42 - 5x Step 2: 10x + 5 + 7 = 42 - 5x Step 3: 10x + 12 = 42 - 5x Step 4: 15x + 12 = 42 Step 5: 15x = 30 Step 6: x = 2 Which of the following justifies the simplification made from step 3 to step 4? (Additive property of equality) (Multiplicative inverse property) (Additive inverse property) (Multiplicative property of equality)

Additive property of equality

A travel lacrosse league requires a $200 deposit and then charges $75 a month during the season. If m is the number of months, which equation represents the cost, C, of a season? (C = 200 - 75m) (C = 125 + 75m) (C = 75 + 200m) (C = 200 + 75m)

C = 200 + 75m

A student was given the equation 3 (x² + 4) - 2 (5x² + 1) and simplified it to equal -7x² + 2. See their work below. Which of the following is the first step with an error? Step 1: 3 (x² + 4) - 2 (5x² + 1) simplified to 3x² + 4 - 2 (5x² + 1) Step 2: 3x² + 4 - 2 (5x² + 1) simplified to 3x² + 4 - 10x² - 2 Step 3: 3x² + 4 - 10x² - 2 simplified to 3x² - 10x² + 4 - 2 Step 4: 3x² - 10x² + 4 - 2 simplified to -7x² + 2 (Step 1) (Step 2) (Step 3) (Step 4)

Step 1

A student's homework answer states that 2(3x - 8) + 3(4x + 5) = 13x - 8. Which of the following is the first step with an error? Step 1: 2(3x − 8) + 3(4x + 5) = 6x − 16 + 3(4x + 5) Step 2: 6x − 16 + 3(4x + 5) = 6x − 16 + 7x + 8 Step 3: 6x − 16 + 7x + 8 = 6x + 7x − 16 + 8 Step 4: 6x + 7x − 16 + 8 = 13x − 8 (Step 1) (Step 2) (Step 3) (Step 4)

Step 2

A student simplifies the expression 4 - 3[3x - (-2 - 4y + 2x)]. In which step did the student commit the first error? Step 1: 4 - 3[3x + 2 + 4y - 2x] Step 2: 4 - 3[x + 2 + 4y] Step 3: 4 - 3x + 6 + 12y Step 4: 10 - 3x + 12y (Step 1) (Step 2) (Step 3) (Step 4)

Step 3

Which sequence of steps, when completed, will solve the equation -3y + 4 = -2? (Subtract 4 from each side and then divide both sides by -3.) (Subtract 4 from each side and then divide both sides by 3.) (Add 2 to both sides and then divide each side by -3.) (Divide both sides by -3 and then subtract 4.)

Subtract 4 from each side and then divide both sides by -3.

A first-year teacher taught his students to multiply binomials emphasizing only the FOIL method. Which of the following describes why learning other methods of binomial multiplication in addition to the FOIL method would best help students succeed when learning to multiply other polynomials? (The FOIL method works only for certain binomial multiplication problems, not for any binomial multiplication.) (The FOIL method is the most difficult method for students to learn.) (The FOIL method does not readily transfer to multiplying polynomials with more than two terms.) (Standardized test developers expect students to be able to solve problems in multiple ways.)

The FOIL method does not readily transfer to multiplying polynomials with more than two terms.

The number of tennis shoes, t, in a dorm is 12 more than 5 times the number of dress shoes. Which of the following represents the number of dress shoes in the dorm in terms of t? (d = 5t + 12) (d = (t - 12)/5) (d = (t/5) - 12) (d = 5t - 12)

d = (t - 12)/5

Which of the following is an equivalent form of the equation P = (h+v)/3? (h = 3P - v) (h = P/3 - v) (h = 3(P - v)) (h = (P - v)/3)

h = 3P - v

A toy store is running a promotion where they charge $75 for a yearly membership and $9.45 for each toy purchased throughout the year, including tax. Anyone that signs up for the promotion gets their first toy free. How much money, m, does someone spend after buying t toys and a yearly membership? (m = 9.45t + 75) (m = 75 + 9.45(t - 1)) (m = 9.45t) (m = 9.45(t - 1))

m = 75 + 9.45(t - 1)

Which of the following is the solution to 4m + 8 ≤ 10m -4? (m ≥ 2/3) (m ≤ 2) (m ≥ 6/7) (m ≥ 2)

m ≥ 2

Using the formula v = u + at, if a is equal to 6, which of the following is equivalent to t? (t = 1/6(v - u)) (t = 6/(u - v)) (t = 6(v - u)) (t = (v - 6)/u)

t = 1/6(v - u)

Solve P = 2(l + w) for w. (w = P/(2l)) (w = P - 2l) (w = (P - 2l)/2) (w = 2P - 4l)

w = (P - 2l)/2

Which expression is true for the values of x given -10x + 3 > -5x - 7? (x > 2) (x > -2) (x < 2) (x < -2)

x < 2

Which of the following describes the possible values of x in the equation x < |⅓ - ⅔| ? (x < ⅓) (x < - ⅓ and x > ⅓) (x < - ⅓) (- ⅓ < x < ⅓)

x < ⅓

What are the solutions to x² - 2x = 24? (x = -4, x = 6) (x = -2, x = 12) (x = -6, x = 4) (x = 0, x = 2)

x = -4, x = 6

Which of the following is the solution set for the system {y = 2x − 8 and y + 2 = x + 6}? (x = -6, y = -2) (x = 4, y = 0) (x = 12, y = 16) (x = -8, y = -4)

x = 12, y = 16

What are the roots of the equation y = x² - 15x + 14? (x = 14 and x = 1) (x = -14 and x = -1) (x = 7 and x = 2) (x = -15 and x = 14)

x = 14 and x = 1

Which of the following are the solutions to the equation x² - 11x + 24 = 0? (x = -8 and x = 3) (x = -8 and x = -3) (x = 3 and x = 8) (x = -3 and x = 8)

x = 3 and x = 8

Which of the following is an equivalent form of the equation a = x - y? (x = a/y) (x = a - y) (x = ay) (x = a + y)

x = a + y

Which of the following inequalities is equivalent to 6x + 1 > 4x - 5? (x > -2) (x > 2) (x > -3) (x > 3)

x > -3

Find the line parallel to the line x=-4 that goes through (2, 6). (x=2) (x=6) (y=-4x+14) (y=6)

x=2

Solve 4x - 2y > 8 for y. (y < -4 + 2x) (y < -4 - 2x) (y > -4 + 2x) (y > 4 - 2x)

y < -4 + 2x

If 3y - 13x = 67, what is y in terms of x? (y = (-67 + 13x) x 3) (y = (-13x + 67)/3) (y = (67 + 13x)/3) (y = 3(13x + 67))

y = (67 + 13x)/3

Using the formula w = 3(y + t), if t is equal to 5, which of the following is equivalent to y? (y = (w + 15)/3) (y = (w/3) - 5) (y = 3w - 5) (y = (w/3) - (15t/3))

y = (w/3) - 5

Which of the following pairs of equations result in parallel lines when graphed? (y = x + 5 and y = 4 - 2x) (y = -2x + 1 and y = x + 5) (y = -2x + 1 and y = 1/2x - 3) (y = -2x + 1 and y = 4 - 2x)

y = -2x + 1 and y = 4 - 2x

If x + y = z, which of the following is also always true? (y = x - z) (y = z ÷ x and x ≠ 0) (y = x ÷ z and z ≠ 0) (y = z - x)

y = z - x

Find the equation of the line perpendicular to y = - ¼ x +2 that goes through the point (3, -1). (y=-4x+11) (y=4x -13) (y= -¼ x - ¼) (y=4x-11)

y=4x -13

When solving an equation, Allie and Diane chose to take different approaches in their first steps. Which property ensures that they are both correct? Original equation: 5x + 3x − 2x = 4 Allie's approach: (5x + 3x) − 2x = 4 Diane's approach: 5x + (3x − 2x) = 4 (associative property of addition) (multiplication property of equality) (commutative property of addition) (addition property of equality)

Associative property of addition

Two customers are paying for a house plant that costs $6.25. Customer 1 provides the cashier with 17 quarters, 24 dimes, and 22 pennies. Customer 2 pays with 18 quarters, 5 dimes, and 19 nickels. Which of the following statements is true? (Customer 1 will receive $0.62 in change after purchasing the plant.) (Customer 2 gave the cashier more money than Customer 1.) (Customer 2 will receive $0.30 in change after purchasing the plant.) (Customer 1 does not have adequate money to pay for the house plant.)

Customer 1 will receive $0.62 in change after purchasing the plant.

A restaurant charges $7.00 for a bowl of noodles and $1.25 for each topping selected. Let D represent the total cost of a meal and let T represent the number of toppings selected. Which of the following is an equation for the total cost of a meal in dollars, D? (D = 7.00 - 1.25T) (D = 1.25 X 7.00T) (D = 1.25 + 7.00T) (D = 7.00 + 1.25T)

D = 7.00 + 1.25T

Mr. Sudu is a waiter. His total weekly earnings consist of a wage of $6 per hour plus approximately 15% in tips on his total sales for the week. One week Mr. Sudu worked 25 hours and had total sales of z dollars. Which of the following represents his total weekly earning in dollars, E, for that week? (E = 0.15z + 150) (E = 25 (0.15z + 6)) (E = 0.15 (z + 150)) (E = 6z + 25)

E = 0.15z + 150

Which of the following comparisons between equations and inequalities is NOT true? (An equation is a statement that two expressions are equal, while an inequality is a statement that two expressions are not equal.) (Equations are solved using inverse operations while inequalities cannot be solved with inverse operations.) (Equations typically have only one solution that makes the equation true, while inequalities typically have a solution set, or range of values, that make the inequality true.) (Equations contain only one possible symbol between each expression (=), while inequalities can contain four possible symbols between each expression (<, >, ≤, ≥).)

Equations are solved using inverse operations while inequalities cannot be solved with inverse operations.

Which of the following scenarios is best modeled with the inequality 6 ≤ x? (Gloria had more than 6 pairs of shoes, x.) (Usman ran up to 6 miles, x.) (Hank ate at least 6 grapes, x.) (Rachel had $6, then spent $x on a coffee.)

Hank ate at least 6 grapes, x.

Jenna wants to rent a bike. Joe's Bike Rental rents bikes for a $10 deposit and $1.00 per hour. Bobbie's Bikes rents bikes for a $15 deposit and $0.50 per hour. Assuming that Jenna rides for h hours, which of the following statements must be true? (If h ≤ 15, Joe's is the best deal.) (Joe's is always the best deal.) (If h > 5, Bobbie's is the best deal.) (If h > 10, Bobbie's is the best deal.)

If h > 10, Bobbie's is the best deal.

Tom is looking for a family photographer. Sallie's Shots charges a $50 sitting fee plus $5.00 per picture purchased. Paul's Photos charges an $85 sitting fee but charges $2.50 per picture purchased. Assuming that Tom will purchase p pictures, which of the following statements is true? (Paul is always the best deal.) (If p>14, Paul has the better deal.) (Sallie is always the best deal.) (If p<14 Paul has the better deal.)

If p>14, Paul has the better deal.

Mr. Silbaugh assesses his students' proficiency with multiplying binomials by asking his students to explain how they would find the product of (-x² + 4) and (3x + 1). Which of the following student explanations demonstrates that the student understands how to multiply binomials? (Multiply the terms in the first parentheses by the terms in the second parentheses.) (Regroup all terms using the associative property so all terms with x are together and all of the constants are together. Then, add like terms.) (Make a square and add like terms) (Multiply -x² in the first set of parentheses by both terms in the second set of parentheses, and then multiply 4 in the first set of parentheses by both terms in the second set of parentheses. Add like terms.)

Multiply -x² in the first set of parentheses by both terms in the second set of parentheses, and then multiply 4 in the first set of parentheses by both terms in the second set of parentheses. Add like terms.

The profit from local fruit stands is based on the number of peaches (p), apples (a), nectarines (n), and employees (e). The profit from two fruit stands is represented by the two equations below: According to the equations, which of the following statements is true? (The employees are paid a higher hourly wage at the second fruit stand) (The peaches cost less at the second fruit stand) (The apples cost less at the first fruit stand) (The nectarines cost more at the first fruit stand)

The employees are paid a higher hourly wage at the second fruit stand

The function below models the height (in feet), h, of an object thrown into the air, where t represents the seconds that have passed since the object was launched. h(t) = -16t² + 80t + 38 What does the number 38 represent in this function? (the initial height of the object) (the maximum speed of the object) (the maximum height of the object) (the initial speed of the object)

The initial height of the object

A teacher gives her students the following comparison problems and asks the students to solve for the variables: x + 2 = 21 + 5 5 - y = 12 - 8 58 + 7 = n - 12 Which of the following math skills is the teacher assessing? (the meaning of the equal sign) (the order in which to combine like terms that include variables) (the correct use of multiplication and division when solving equations) (the correct use of the distributive property)

The meaning of the equal sign

Jamie deposits $245 into her health club account at the beginning of the year. Each time she visits, $7 is deducted from her account. Which equation represents V, the value in her account after x visits? (V = 245x - 7) (V = 245 - 7x) (V = 7x - 245) (V = 245 + 7x)

V = 245 - 7x

For the bake sale, students sold c dozen cupcakes. It cost $0.98 to make a batch of 12 cupcakes and they charged $0.50 per cupcake. Which expression, in terms of c, represents the profit, p, made from the cupcake sales? Assume the students sold all cupcakes made. ([(12)(c) - 0.98]/0.5 = p) ([(12)(0.5) - 0.98]/c = p) ([(12)(c) - 0.98]0.5 = p) ([(12)(0.5) - 0.98]c = p)

[(12)(0.5) - 0.98]c = p

The formula for the area of a triangle is A = 1/2bh. Solve for b. (b = A/(2h)) (b = h/(2A)) (b = 2Ah) (b = (2A)/h)

b = (2A)/h