Deck 18: Algebraic Equation Practice

Question 1

Find the product. (2a + 6)(10a + 1)

A) 20a² + 22a + 6
B) 20a² + 19a + 6
C) 20a² + 6a + 62
D) 20a² + 62a + 6

Answer 1

20a² + 62a + 6

Question 2

Simplify: y - (6y + 5)

A) 7y - 5
B) -5y + 5
C) -5y - 5
D) 7y + 5

Answer 2

-5y - 5

Question 3

Graph the solution to the compound inequality.

A)
B)
C)
D)

Answer 3

Question 4

Kamika works at a bakery and can prepare a birthday cake in 4 hours. It takes her 5 hours to prepare a wedding cake. If Kamika works a 40-hour week, and if she must bake more birthday cakes than wedding cakes, which graph below correctly illustrates the number of each type of cake Kamika can bake per week?

A)

B)

C)

D) None of these.

Question 5

Raphael can load a large shipping truck in 12 hours. Working together, Raphael and Jana can load the same truck in 3 hours. How long would it take Jana to load the truck by herself?

A) 3 hours
B) 5 hours
C) 6 hours
D) 4 hours

Question 6

Write the expression without negative exponents.

A)
B)
C)
D)

Question 7

Conrad builds picnic tables and porch swings which he sells at flea markets. A picnic table requires six 2 $\times$ 4's and nine 1 $\times$ 6's. A swing uses three 2 $\times$ 4's and six 1 $\times$ 6's. Conrad currently has 108 2 $\times$ 4's and 180 1 $\times$ 6's in his inventory. If tables sell for $50 and swings sell for $30, how many of each item should Conrad make in order to maximize his revenue?

A) 15 picnic tables and 10 porch swings
B) 0 picnic tables and 30 porch swings
C) 18 picnic tables and 0 porch swings
D) 12 picnic tables and 12 porch swings

Question 8

Factor. 64y³ - 125z³

A) (4y + 5z)(16y² - 20yz + 25z²)
B) (4y - 5z)(16y² + 20yz + 25z²)
C) (4y - 5z)(4y² + 20yz + 5z²)
D) (4y - 5z)(16y² - 20yz + 25z²)

Question 9

Find four consecutive integers whose sum is 226.

A) 55, 57, 59, 61
B) 56, 57, 58, 59
C) 55, 56, 57, 58
D) 54, 55, 56, 57

Question 10

If a golf ball is dropped from a tall building, the distance it has fallen in feet is given by 16t², where t is the time in seconds since the ball was dropped. How far has the ball fallen after 12 seconds?

A) 240 ft
B) 192 ft
C) 1936 ft
D) 2304 ft

Question 11

Solve the given equation. 18c² + 3c - 10 = 0

A)
B)
C)
D) -2, 3

Question 12

Simplify.

A)
B)
C)
D)

Question 13

Together, Paul and Quincy weigh 357 pounds, Quincy and Ramon weigh 348 pounds, and Paul and Ramon weigh 337 pounds. How much does each weigh individually?

A) Paul = 175 lb., Quincy = 180 lb. , Ramon = 166 lb.
B) Paul = 163 lb., Quincy = 184 lb. , Ramon = 174 lb.
C) Paul = 173 lb., Quincy = 184 lb. , Ramon = 164 lb.
D) Paul = 181 lb., Quincy = 180 lb. , Ramon = 160 lb.

Question 14

Write an equation that represents a line l that goes through (12, 5) and has a slope of .

A)
B)
C)
D)

Question 15

Simplify.

A)
B)
C)
D)

Question 16

Justin is shopping for new tires for his 4-wheel-drive truck. In addition to the price of the tires, there is a 7% sales tax plus a state-mandated $40 fee for disposing of his old tires. If Justin has determined that he will spend less than $301.08 total, then what is the price range he can spend on the tire set?

A) $244 or more
B) Less than $244
C) Less than $248
D) At least $247

Question 17

Solve the equation. Watch for extraneous solutions.

A) -5, 5
B) No solution
C) 7, -4
D) 5

Question 18

The solution set is not the empty set for which one of the following inequalities?

A)

B)

C)

D)

Question 19

Find the x- and y-intercepts of 7x - 2y = -5 and use these intercepts to graph the equation.

A)

B)

C)

D)

Question 20

Solve the absolute value inequality and graph the solution. |x - 1| $\ge$ 2

A)
B)
C)
D)

Question 21

Find the complex solutions.

A)
B)
C)
D)

Question 22

Find the inverse of the given function and include any domain restrictions. f(x) = (x - 6)²

A)
+ 6 for

B)
+ 6 for
-6
C)
- 6 for any real number x
D)
+ 6 for any real number x

Question 23

Find the midpoint and length of the line segment with the endpoints (3,2) and (13,26).

A) (9, 15), 13
B) (8, 14), 13
C) (-2, -10), 26
D) (8, 14), 26

Question 24

The owner of a hobby store bought a case of 9-volt batteries for $24.00. He marked the price up such that his profit was $1.76 per battery. After selling 12 batteries, the store owner had recovered his cost. How many 9-volt batteries are in a case?

A) 100 batteries
B) 110 batteries
C) 105 batteries
D) 95 batteries

Question 25

Find all real solutions of the given equation. (x² - x)² - 39(x² - x) - 126 = 0

A) {-7, 6}
B) {-7, 3, 6}
C) {-6, -3, 7}
D) {-6, 7}

Question 26

Solve. (z + 4)^1/3 = -4

A) {-68, 68}
B) {-60}
C) {-68}
D) {-68, -60}

Question 27

For the given polynomial, find the x-intercepts and determine the behavior of the graph of the polynomial at each x-intercept. f(x) = x³ - 10x²

A) Crosses at (10, 0) and at (-10, 0) but does not cross at (0, 0)
B) Crosses at (10, 0) but does not cross at (0, 0)
C) Crosses at (10, 0)
D) Crosses at (10, 0) and at (0, 0)

Question 28

If $700 is deposited in an account paying 9% compounded continuously, then what amount will be in the account after 5 years?

A) $1,097.82
B) $960.06
C) $2,157.15
D) $1,262.74

Question 29

Write ln(x¹⁰) - ln(x⁶) as a single logarithm.

A) ln(x⁴)
B) The logarithms cannot be combined.
C) ln(x⁶⁰)
D) ln(x¹⁶)

Question 30

If a rancher has one sheep with hoof and mouth disease in a flock of 1600, then the time in days t for n sheep to become infected is modeled by . To the nearest tenth, find the number of days it takes for one-half of the flock to contract the disease.

A) 14.8 days
B) 22.1 days
C) 15.6 days
D) 36.8 days

Question 31

Solve the inequality. Graph the solution set. x² + 10x + 21 ≥ 0

A)
B)
C)
D)

Question 32

Which choice below is the correct graph of ?

A)

B)

C)

D)

Question 33

Which of the following is the correct graph of y = x² + 1?

A)

B)

C)

D)

Question 34

In a certain country there are currently 125 million workers and 50 million retired people. The population of workers is decreasing according to the formula , where t is in years and W is in millions. The population of retired people is increasing according to the formula , where t is in years and R is in millions. In how many years will the number of workers equal the number of retired people?

A) 13.1 years
B) 14.1 years
C) 5.3 years
D) 10.8 years

Question 35

How are the graphs of and related?

A) The graph of g(x) is the same as that of f(x), but translated upward by 4 units.
B) The graph of g(x) is the same as that of f(x), but translated downward by 4 units.
C) The graph of g(x) is the same as that of f(x), but translated 4 units to the right.
D) The graph of g(x) is the same as that of f(x), but translated 4 units to the left.

Question 36

Determine all asymptotes for the graph of the given function.

A) Vertical : x = -2; Oblique:

B) Vertical : x = 2; Horizontal: x-axis.
C) Vertical : x = -2; Horizontal: x-axis.
D) Vertical : x = 2; Oblique:

Question 37

Solve 4^{-6x - 10} = 16^{-4x - 1}.

A) {5}
B) {-4}
C) {6}
D) {4}

Question 38

Find the imaginary solutions: 100x² + 160x + 100 = 0

A)

B)

C)

D)

Question 39

Find the complex solutions.

A)
B) {9i}
C) {-9i, 9i}
D) {-81i, 81i}

Question 40

Solve the given system of equations. y = x²
Y = 6

A) Ø
B) {(-6, 36), (6, 36)}
C)
D)

Question 41

Which of the following is the correct graph of ?

A)

B)

C)

D)

Question 42

Use the binomial theorem to expand the given binomial. (y + 1)³

A) y³ + y² + y + 1
B) y³ + 1
C) y³ + 3y² + 3y + 1
D) 3y³ + 3y² + 3y + 3

Question 43

Write a formula for the nth term of the given arithmetic sequence. 9, 14, 19, 24, 29, . . .

A) a_n = 5n + 4
B) a_n = 4n - 5
C) a_n = 5n - 4
D) a_n = 6n - 5

Question 44

List all terms of the finite sequence a_n = n + 4 for 1 ≤ n ≤ 5.

A) 5, 9, 13, 17, 21
B) 4, 5, 6, 7, 8
C) 5, 6, 7, 8, 9
D) 4, 8, 12, 16, 20

Question 45

Graph both equations of the system on the same coordinate axes. Use elimination to find all points of intersection. y = 1 - x²
X² + 4y² = 4

A) (-2, 0), (2, 0)

B) (0, -1),
,


C) (-2, 0), (2, 0)

D) (0, 1),
,

Question 46

Find the sum of the given infinite geometric series. 16 + 12 + 9 + ...

A) "64"
B) " $\infty$ "
C) "68"
D) "60"

Question 47

Write the standard equation for the circle with the given radius and center. Center (9, 5), radius

A) (x + 9)² + (y + 5)² = 196
B) (x - 9)² + (y - 5)² = 196
C) (x - 9)² + (y - 5)² = 14
D) (x + 9)² + (y + 5)² = 14

Question 48

Complete the rewriting of the given series using the new index as indicated. (2i + 1) =

A)
(2i + 1) =
(2j + 2)
B)
(2i + 1) =
(2j + 3)
C)
(2i + 1) =
(2j + 4)
D)
(2i + 1) =
(2j + 3)

Question 49

Find the sum of the given series.

A) -108
B) 99
C) -99
D) 108

Question 50

Write the given equation in the form y = a(x - h)² + k and identify the vertex, focus, and directrix. y = 3x² - 8x + 5

A) Vertex:
; Focus:
; Directrix:

B) Vertex:
; Focus:
; Directrix:

C) Vertex:
; Focus:
; Directrix:

D) Vertex:
; Focus:
; Directrix: