First Semester Exam (Algebra)
Solve the equation |2m − 6 | = 10.
m = −2 or m = 8
Evaluate the expression ab2 + 2ab + a2 for a = 6 and b = 3.
126
Multiply 4x3y(3x2 − 5y).
12x5y − 20x3y2
Solve the equation.x2 − 4x + 4 = 3
2 +- square root 3
Identify the number and type of solutions for the equation x2 − 7x + 3 = 0.
2 real
Multiply (2a − 1)(a2 − 3a + 6).
2a3 − 7a2 + 15a − 6
Evaluate the expression 2qp + 5p − 3q for p = 3 and q = 5.
30
Multiply 2pq(3q − 4p).
6pq2 − 8p2q
Simplify.7i32
7
Dena bought 4 stuffed animals and 7 toy trains for $75. At the same prices, Nico bought 6 stuffed animals and 5 toy trains for $74. What is the price of a stuffed animal?
$6.50
Identify the factors of the expression x3 + 3x2 − 9x − 27.
(x − 3)(x + 3)(x + 3)
Solve the system using row reduction on a calculator:7x − 3y + 2z = 196x + 5z = 325x − 2y + 6z = 32
(2, 1, 4)
A company distributes its product by train and by truck. The cost of distributing by train can be modeled as −0.06x2 + 32x − 100, and the cost of distributing by truck can be modeled as −0.04x2 + 26x − 170, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck.
−0.02x2 + 6x + 70
Identify the vertex of the function h(x) = −2x2 + 10x + 1.
(2.5, 13.5)
Factor.14ab − 12a − 21b + 18
(2a − 3)(7b − 6)
Find the factors of f(x) given that x = 4 is a zero.f(x) = x3 + x2 − 26x + 24.
(x − 4)(x − 1)(x + 6)
Factor.2x3 + 5x2 + 6x + 15
(x2 + 3)(2x + 5)
Solve the equation.x2 + 6x = 12
-3 +- square root 21
Evaluate the expression 6−3.
1/216
Evaluate the expression 2−5.
1/32
Maximize the objective function P = 5x + 3y for the given constraints.x ≥ 0y ≥ 03x + 6y ≤ 482x + 8y ≤ 56
80
Evaluate the expression (4/9)−2.
81/16
Maximize the objective function P = 80x + 55y for the given constraints.x ≥ 0y ≥ 04x + 3y ≤ 442x + 5y ≤ 36
880
Identify the property demonstrated by the equation. 3 ∙ 2 = 2 ∙ 3
Comm. Prop. of Mult.
Solve the inequality.x2 − 3x + 4 > 8
x < −1 or x > 4
Determine the direction in which the graph of the function f(x) = x2 + x − 2 opens.
upward
Identify the solution of the inequality |4x + 4| > 8 and the graph that represents it.
x < −3 or x > 1
Solve the equation.5x2 + 200 = 0
x = +-2i /10
Identify the product in the form a + bi.(−2 + 7i)(−5 + 6i)
−32 − 47i
Simplify.−9i45
-9i
Identify the function that reflects f(x) = 2x3 − 3 across the y-axis and shifts it 4 units down.
h(x) = −2x3 − 7
Identify the solution and graph of the inequality.17 + 5m > 11m − 7
m < 4
Solve the inequality.3x + 4 > x2
−1 < x < 4
Find the degree of the polynomial 6x3 y6 + 2xy + x4 .
9
Identify the simplest polynomial function with the given zeros.−4, 3, 2
P(x) = x3 − x2 − 14x + 24
Classify the polynomial according to its degree and number of terms.5b3 + 4b2 + 4b
cubic trinomial
Identify the product in the form a + bi.(1 − 5i)(−3 + 4i)
17 + 19i
Identify the factors of the expression 128b5 − 54b2.
2b2 (4b − 3)(16b2 + 12b + 9)
Identify the simplest polynomial function that has the given zeros.−2, 4, 5
P(x) = x3 − 7x2 + 2x + 40
The profit function p(x) of a tour operator is modeled by p(x) = −2x2 + 700x − 10000, where x is the average number of tours he arranges per day. What is the range of the average number of tours he must arrange per day to earn a monthly profit of at least $50,000?
between 150 and 200; inclusive
Let f(x) = x3 + 2x2 + 7x − 11 and g(x) = 3f(x). Which of the following describes g as a function of f and gives the correct rule?
vertical stretch; g(x) = 3x3 + 6x2 + 21x − 33
Identify the difference in the form a + bi.(3 − 8i) − (4 + i)
−1 − 9i
Identify the product in the form a + bi.(−1 + i)(1 − i)
0 + 2i
Identify the expansion of the expression (p + 5q)3.
p3 + 15p2q + 75pq2 + 125q3
Multiply (p2 − 2p + 3)(p2 + 3p − 2).
p4 + p3 − 5p2 + 13p − 6
Multiply (p2 − 5p + 2)(p2 − p + 6).
p4 − 6p3 + 13p2 − 32p + 12
Evaluate the polynomial for the given value by using synthetic division.P(x) = 3x4 − x3 + 7x − 2 for x = 4 and x = −2
730; 40
Identify the roots of the equation and the multiplicities of the roots.8(x − 2)3 = 0
The root 2 has a multiplicity of 3.
Identify the quadratic function that is in standard form has zeros 4 and −7.
f(x) = x2 + 3x − 28
Identify the quadratic function that is in standard form and has zeros −11 and 6.
f(x) = x2 + 5x − 66
Identify the binomial that is a factor of the polynomial P(x) = x3 − 5x2 − 2x + 24.
x + 2
The parent function f(x) = x2 is reflected across the x-axis, vertically stretched by a factor of 5, and translated 3 units down to create g. Identify g in vertex form.
g(x) = −5x2 − 3
Let g(x) be the reflection across the x-axis of the function f(x) = 7x + 3. Identify the rule for g(x).
g(x) = −7x − 3
Let f(x) = x3 + 2x2 + 3x − 10. Identify the function g that reflects f across the y-axis.
g(x) = −x3 + 2x2 − 3x − 10
Let f(x) = x3 + 9x2 − 3x − 1. Identify the function g that reflects f across the x-axis.
g(x) = −x3 − 9x2 + 3x + 1
Let g(x) be the indicated transformation of f(x) = |2x| − 5. Compress the graph of f(x) = |2x| − 5 horizontally by a factor of 1/4 and reflect it across the x-axis. Identify the rule and graph of g(x).
g(x) = −|8x| + 5
Classify the system of equations and identify the number of solutions.4x + 2y = −86x + 3y = 9
inconsistent; none
Solve the equation |3m + 3 | = 15.
m = 4 or m = −6
John and Harry went to a stationery shop. John bought 3 pens and 8 notebooks for $20.50. Harry bought 4 pens and 5 notebooks for $16.00. Identify the cost of a pen and the cost of a notebook.
pen: $1.50; notebook: $2.00
Complete the statement.The line x = −2 is _______.
vertical
Divide using long division.(x2 + 5x + 6) ÷ (x + 3)
x + 2
Solve the inequality by using a table or graph.x2 − 6x + 8 > 35
x < −3 or x > 9
Identify the solution of the inequality |5x + 10| > 15 and the graph that represents it.
x < −5 or x > 1
Solve the inequality.x2 + 3x − 5 > 5
x < −5 or x > 2
Solve using Cramer's rule.3x + 2y = 5x + 3y = 4
x = 1, y = 1
Identify the axis of symmetry of the function f(x) = x2 − 6x + 8.
x = 3
Identify the values of x and y that make the equation 3x − 4i = 9 + (16y)i true.
x = 3, y = −1/4
Solve using Cramer's rule.2x − 5y = 6x − 3y = 4
x = −2, y = −2
Find the factors of f(x), given that x = −2 is a zero.f(x) = x3 + x2 − 14x − 24
(x + 2)(x + 3)(x − 4)
Identify the factors of the expression x4 − 120x2 − 121.
(x2 + 1)(x + 11)(x − 11)
Factor.x2y2 − 7y2 − 13x2 + 91
(x2 − 7)(y2 − 13)
Identify the factors of the expression x4 − 17x2 + 72.
(x2 − 8)(x + 3)(x − 3)
Identify the vertex of the function g(x) = x2 + 2x − 15.
(−1, −16)
Solve the system using row reduction on a calculator.2x + 3y + 6z = −2x − 2y + 4z = 163x − 5y = 8
(−4, −4, 3)
Solve the equation by factoring.2x4 + 8x3 + 8x2 = 0
-2, 0
Identify all of the real roots of x3 − 8x2 + 4x + 48 = 0.
-2, 4, 6
Simplify.3i23
-3i
Solve the equation.x2 + 8x = 17
-4 +- square root 33
Solve the equation by factoring.x3 − 16x = x2 − 16
-4, 4, 1
Identify the solution of the compound inequality x + 4 ≤ 3 or 4x > 8 and the graph that represents it.
x ≤ −1 or x > 2
Evaluate the expression 4−3.
1/64
Multiply.(3m − 5n)3
27m3 − 135m2n + 225mn2 − 125n3
Find |−3 + 6i|.
3/5
Multiply (m2 − 2m − 3)(3m + 4).
3m3 − 2m2 − 17m − 12
Identify the factors of the expression 4m4 + 108m.
4m(m + 3)(m2 − 3m + 9)
Find the degree of the polynomial 4q2 − 13q5 + 12q + 3q3 .
5
The root −2 has a multiplicity of 3.
5 ft
Find |−5 + 5i|.
5/2
Identify the solution of the inequality |5p| + 16 > 1 and the graph that represents it.
all real numbers
Classify the system of equations and identify the number of solutions.3 = 4x + y2y = 6 − 8x
consistent, dependent; infinite
Classify the system of equations and identify the number of solutions.3x + y = 412x + 4y = 16
consistent, dependent; infinite
Classify the system of equations and identify the number of solutions.5x + y = 22y = 4 − 10x
consistent, dependent; infinite
Classify the system and identify the number of solutions.3x + 5y + 4z = −112x − 4y − z = −114x + 3y − 2z = 11
consistent, independent; one
Classify the system and identify the number of solutions.3x − y + z = 4x + y − 2z = 02x − y + 2z = 3
consistent, independent; one
Classify the system and identify the number of solutions.4x + 3y − 4z = 43x + 5y + 2z = 97x + 4y − 6z = 1
consistent, independent; one
Classify the system and identify the number of solutions.x − 3y − 8z = −102x + 5y + 6z = 133x + 2y − 2z = 3
consistent; dependent; infinite
Identify the parent function for the function g(x) = (x + 1)3 based on its function rule. Then graph g and identify the transformation of the parent function that it represents.
cubic; translation left 1 unit
Identify the parent function for the function g(x) = (x − 2)3 from its function rule. Then graph g and identify what transformation of the parent function it represents.
cubic; translation right 2 units
Determine the direction in which the graph of the function g(x) = −2x2 − 2x − 15 opens.
downward
Solve the equation |2q − 8 | = 14.
q = −3 or q = 11
Identify the slope-intercept form and the graph of the line described by the equation −4x + y = −3
y = 4x − 3
Multiply (y2 − 5y + 10)(y + 3).
y3 − 2y2 − 5y + 30
Indicate whether the product is defined. If it is, give the dimensions of the product.A2 × 3 and B3 × 4; AB
yes; AB2 × 4
Indicate whether the product is defined. If it is, give the dimensions of the product.A5 × 3 and B3 × 4; AB
yes; AB5 × 4
Which of the following represents the set "all values of x greater than −4 and less than 10" in set builder notation?
{x | −4 < x < 10}
Sophie works 4 hours a day, and earns a salary of $500.00 per month. She earns $10 for every extra hour that she works. If she earned $650.00 last month, how many extra hours did Sophie work?
15
Identify the relation that is a function.
number of apples purchased to the cost of the apples
Solve the equation.3(p − 5) = 30
p = 15
Solve the equation |p + 5| = 3.
p = −8 or p = −2
Identify the relation that is a function.
professional golfers to their rankings
Solve the equation |7q| + 3 = 24.
q = 3 or q = −3
Identify the parent function for the function g(x) = x2 − 4 based on its function rule. Then graph g and identify the transformation of the parent function that it represents.
quadratic; translation down 4 units
Identify the parent function for the function g(x) = x2 − 6 from its function rule. Then graph g and identify what transformation of the parent function it represents.
quadratic; translation down 6 units
Describe the transformation from the graph of f(x) to the graph of g(x).f(x) = 2x, g(x) = −2x
reflection over the y-axis
Describe the transformation from the graph of f(x) to the graph of g(x).f(x) = 4x, g(x) = −4x
reflection over the y-axis
Identify the relation that is not a function.
weight of a person to a person's height
Solve the equation.(5x + 19) − 10 = 6x + 27 + 8x
x = -2
Identify the solution and graph of the inequality.4x + 9 < 14x − 21
x > 3
Identify the solution of the compound inequality x + 4 > 9 or 2x ≥ 14 and the graph that represents it.
x > 5
Graph the system of linear inequalities.y > −x + 3y ≤ 2x − 1Give two ordered pairs that are solutions and two that are not solutions.
(3, 2) and (5, 0) are solutions.(0, 0) and (−4, 1) are not solutions.
Graph f(x) = x3 + x2 − 4x + 2 on a calculator and estimate the correct local maximum and minimum.
6.88; −0.06
Identify the expansion of the expression (4m − 3n)3.
64m3 − 144m2n + 108mn2 − 27n3
7a2 + 3b + 6a − 2a2
5a2 + 3b + 6a
Multiply (5a − 3)(a2 − 4a + 1).
5a3 − 23a2 + 17a − 3
Simplify.−5i19
5i
Graph f(x) = x3 + 2x2 − 3x + 1 on a calculator and estimate the correct local maximum and minimum.
7.06; 0.12
Divide using long division.(x2 + 2x − 24) ÷ (x + 6)
x − 4
Identify the solution of the inequality and the graph that represents it. |2x-2|/4≤1
x ≥ −1 and x ≤ 3
Add.(28a2 − 10) + (5a2 − 2b + 6)
33a2 − 2b − 4
Factor.2w3 − 5w2 + 2w − 5
(w2 + 1)(2w − 5)
Factor.3w3 − 2w2 − 18w + 12
(w2 − 6)(3w − 2)
Find the factors of f(x) given that x = −3 is a zero.f(x) = x3 + 12x2 + 47x + 60
(x + 3)(x + 4)(x + 5)
Add.(8z4−6z3−1)+(9z4+6z−2)
17z4−6z3+6z−3
Evaluate A + 3B if possible.
not possible
Evaluate G + 2H if possible.
not possible
Identify the factors of the expression 27z3 − 125.
(3z − 5)(9z2 + 15z + 25)
The equation of a line of best fit relating the money earned e at a bake sale to the number of customers c is e = 1.1c + 19. Use the equation to predict the earnings from a bake sale with 80 customers.
$107
Corinne bought 6 bags of chips and 3 jars of dipping sauce for $25.32. At the same prices, Ginger bought 4 bags of chips and 5 jars of dipping sauce for $24.32. What is the price of one jar of dipping sauce?
$2.48
Dee bought 6 dolls and 2 toy trains for $55. At the same prices, Joy bought 4 dolls and 7 toy trains for $65. What is the price of a doll?
$7.50
The number of cars sold per month can be modeled by f(x) = 0.04x3 + 0.2x2 + 0.5x + 60, where x represents the number of months since March. Let g(x) = f(x) + 30. Which of the following gives the rule for g and the correct explanation of the meaning of the transformation in terms of monthly car sales?
0.04x3 + 0.2x2 + 0.5x + 90vertical shift 30 units up increase of 30 units per month
Identify the number and type of solutions for the equation 25x2 − 20x + 4 = 0.
1 real
Let g(x) be the transformation of f(x) = |x| such that the vertex is at (2, 5). Identify the rule for g(x) and its graph.
g(x) = |x − 2| + 5
Let g(x) be the transformation of f(x) = |x| up 3 units. Identify the rule for g(x) and its graph.
g(x) = |x| + 3
Let g(x) be the transformation of f(x) = |x| down 2 units. Identify the rule for g(x) and its graph.
g(x) = |x| − 2
Let g(x) be the indicated transformation of f(x) = |3x| + 4. Stretch the graph of f(x) = |3x| + 4 vertically by a factor of 3 and reflect it across the x-axis. Identify the rule and graph of g(x).
g(x) = −3|3x| − 12
Multiply.(m + 6)4
m4 + 24m3 + 216m2 + 864m + 1296
Identify the solution of the compound inequality−5m − 8 < 3m and 3m − 7 ≤ −m + 13.
−1 < m ≤ 5
Solve the inequality.−2x2 + 3x + 4 ≥ −1
−1 ≤ x ≤ 2.5
A company distributes its product by train and by truck. The cost of distributing by train can be modeled as −0.06x2 + 35x − 135, and the cost of distributing by truck can be modeled as −0.03x2 + 29x − 165, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck.
−0.03x2 + 6x + 30
A company distributes its product by train and by truck. The cost of distributing by train can be modeled as −0.09x2 + 36x − 110, and the cost of distributing by truck can be modeled as −0.03x2 + 23x − 155, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck.
−0.06x2 + 13x + 45
Which of the following represents the polynomial 2x − 5x3 − 10x5 + 9 in standard form and identifies the degree of the polynomial and the number of terms?
−10x5 − 5x3 + 2x + 9 degree: 5 number of terms:4
Write the polynomial 3x2 − 8x − 12x5 − 5x3 + 2x4 − 6 in standard form. Then give the leading coefficient.
−12x5 + 2x4 − 5x3 + 3x2 − 8x − 6 The leading coefficient is −12.
Solve the inequality.2x2 − 8x − 17 ≤ 7
−2 ≤ x ≤ 6
Solve the equation by factoring.3x4 − 3x3 − 18x2 = 0
−2, 0, 3
Subtract. (z4+5z2−2z)−(z2+3z4−z−6)
−2z4+4z2−z+6
Identify the sum in the form a + bi.(8 − i) + (−11 + 5i)
−3 + 4i
Use a table or graph to solve the inequality.x2 − 4x − 9 < 12
−3 < x < 7
Solve the equation by factoring.4x4 − 20x3 − 96x2 = 0
−3, 0, 8
Solve by finding all roots.x4 + 4x3 + 4x2 + 4x + 3 = 0
−3, −1, i, −i
Identify the solution of the compound inequality −3y < 12 and y − 2 ≤ 4.
−4 < y ≤ 6
Divide.(−20y4 + 10y2 − 15y) ÷ 5y
−4y3 + 2y − 3
Subtract.(−7m4−9m3+3m)−(−2m4+5m3−9m2+4m)
−5m4−14m3+9m2−m
Divide.(−20y4 + 8y2 − 12y) ÷ 4y
−5y3 + 2y − 3
Identify the difference in the form a + bi.(2 − i) − (8 − 4i)
−6 + 3i
Subtract.(2p4−4p3−4p)−(8p4−2p3−2p2−3p)
−6p4−2p3+2p2−p
Identify the sum in the form a + bi.(7 − 3i) + (−14 − 6i)
−7 − 9i
Identify all of the real roots of x3 − 7x2 − 65x + 231 = 0.
−7, 3, 11
For the function f(x) = 6x − 8, identify the values of f(0), f(1/2), and f(−2).
−8; −5; −20
Subtract.(b4−8b2+6b)−(9b4−4b3+4b2+8b)
−8b4+4b3−12b2−2b
Identify all of the real roots of x3 + 7x2 − 21x − 27 = 0.
−9, −1, 3
Which of the following represents the polynomial 11 − x3 in standard form, the degree of the polynomial, and the number of terms?
−x3 + 11 degree: 3 number of terms: 2
Corinne bought 5 bags of chips and 4 jars of dipping sauce for $21.82. At the same prices, Ginger bought 4 bags of chips and 3 jars of dipping sauce for $16.86. What is the price of one jar of dipping sauce?
$2.98
Solve the system of equations using substitution.−3x + y = −1y = 5x + 1
(-1, -4)
Solve the system of equations using elimination.2x − 3y = −56x + 4y = −2
(-1, 1)
Solve the system of equations using substitution.x − 2y = −35x + 3y = −2
(-1, 1)
Using substitution, identify the ordered pair that is not an element of the solution set of the system of equations.6x + 3y = 62x + y = 2
(-2, 0)
Solve the system using the matrix equation.x − 9y = −332x + 7y = 9
(-6, 3)
Solve the system of equations by elimination.4x − 3y − z = −5x + y + 2z = 04x + 2y + z = 3
(0, 2, −1)
Solve the system of equations by elimination.x + y + 2z = 05x − 3y − z = −55x + 2y + z = 3
(0, 2, −1)
Solve the system using the matrix equation.3x − 4y = 84x + 3y = −6
(0, −2)
Solve the system of equations by elimination.3x − y − 2z = 4x + y − z = 02x − y + 3z = 3
(1, −1, 0)
Solve the system of equations by elimination.3x − y − z = 2x + y + 2z = 42x − y + 3z = 9
(1, −1, 2)
Solve the system of equations using elimination.6x + y = 94x + 3y = −1
(2, -3)
Using substitution, identify the ordered pair that is an element of the solution set of the system of equations.3x + y = 2y − x = −6
(2, -4)
Solve the system of equations using substitution.y = 3 − 4xy = 3x − 11
(2, -5)
Using substitution, identify the ordered pair that is an element of the solution set of the system of equations.5x + 2y = 103x + y = 6
(2, 0)
Solve the system of equations using elimination.6x − 2y = 105x − 8 = 2y
(2, 1)
Identify the factors of the expression 8a3 − 125.
(2a − 5)(4a2 + 10a + 25)
Solve the system of equations using substitution.4x + 6y = 103y + x = 2
(3, −1/3)
Solve the system of equations by elimination.5x − 2y − z = 15x + y + 2z = 9−x − y + 3z = 11
(3, −2, 4)
Factor.6ab − 15a − 8b + 20
(3a − 4)(2b − 5)
Solve the system of equations using elimination.4x + y = 93x + 2y = −2
(4, -7)
Solve the system using the matrix equation.2x + 3y = 233x − 4y = −8
(4, 5)
Identify the factors of the expression 64a3 − 1.
(4a − 1)(16a2 + 4a + 1)
Identify the factors of the expression 64m3 + 27.
(4m + 3)(16m2 − 12m + 9)
Solve the system of equations using elimination.7x + 5y = 106x + 5y = 5
(5, -5)
Identify the factors of the expression x3 + 3x2 − 25x − 75.
(x + 3)(x − 5)(x + 5)
Find the factors of f(x), given that x = 4 is a zero.f(x) = x3 − 7x2 + 2x + 40.
(x − 4)(x − 5)(x + 2)
Find the factors of f(x) given that x = 5 is a zero.f(x) = x3 − 6x2 − x + 30.
(x − 5)(x − 3)(x + 2)
Identify the factors of the expression x3 − 2x2 − 4x + 8.
(x −2)(x −2)(x + 2)
Identify the factors of the expression x4 + 4x2 − 32.
(x2 + 8)(x + 2)(x − 2)
Solve the system of equations by elimination.x + 2y + z = 23x + y + 2z = −32x − 3y − z = −7
(−1, 2, −1)
Solve the system of equations by elimination.3x − y − z = −5x + y + 2z = 52x − y + 3z = 12
(−1, −2, 4)
Solve the system of equations using elimination.8x − 3y = −12x + 4y = −5
(−1/2, −1)
Identify all of the real roots of x4 − 2x2 − 3x − 2 = 0.
-1, 2
Evaluate the polynomial for the given value by using synthetic division.P(x) = x4 − x2 + 7x + 5 for x = −1 and x = 2
-2; 31
Identify the zeros of the function f(x) = x2 − 2x − 15.
-3, 5
Identify the zeros of the function f(x) = x2 − 3x.
0, 3
Solve the equation by factoring.2x4 + 12x3 + 16x2 = 0
0, −2, −4
The number of cars sold per month can be modeled by f(x) = 0.03x3 + 0.2x2 + 0.8x + 60, where x represents the number of months since April. Let g(x) = f(x) − 12. Which of the following gives the rule for g and the correct explanation of the meaning of the transformation in terms of monthly car sales?
0.03x3 + 0.2x2 + 0.8x + 48vertical shift 12 units down decrease of 12 units per month
Nancy needs to earn at least $60 per day. She gets $10 per hour as a babysitter and $20 per hour as a sales person. If she can work at most 5 hours per day, identify the system of inequalities and the corresponding graph that determine when Nancy will be able to meet her goal.
10x + 20y ≥ 60x + y ≤ 5
Find the degree of the monomial −5a7b4.
11
Evaluate the expression uv2 + 5uv + u2 for u = 3 and v = 4.
117
Graph f(x) = −x3 + 5x2 − 3x + 2 on a calculator and estimate the correct local maximum and minimum.
11; 1.52
A toy rocket is launched from a platform 29 feet above the ground at a speed of 79 feet per second. The height of the rocket in feet is given by the polynomial −16t2 + 79t + 29, where t is the time in seconds. How high will the rocket be after 3 seconds?
122 feet
Add.(8g5−9g3+7)+(4g5+6g−4)
12g5−9g3+6g+3
In an auditorium, a charity show is conducted in order to raise at least $3,000. The auditorium can accommodate up to 180 spectators. Tickets cost $12 for students and $20 for adults. Identify the system of inequalities and the corresponding graph that determine whether the charity will reach its goal. 12x + 20y ≤ 3000x + y ≤ 180
12x + 20y ≥ 3000x + y ≤ 180
Simplify −7p8(−2p). Assume all variables are non-zero.
14p9
A furniture company has 480 board ft of teak wood and can sustain up to 450 hours of labor each week. Each chair produced requires 8 ft of wood and 12 hours of labor, and each table requires 20 ft of wood and 15 hours of labor. If a chair yields a profit of $65 and a table yields a profit of $90, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit?
15 chairs; 18 tables
10% of the fruits in a basket are apples. If there are 15 apples, how many fruits are in the basket?
150
The equation of a line of best fit relating the number of cats c at an animal shelter to the number of dogs d is c = 3.5d − 20. Predict the number of cats at a shelter where there are 50 dogs.
155
A toy rocket is launched from a platform 42 feet above the ground at a speed of 91 feet per second. The height of the rocket in feet is given by the polynomial −16t2 + 91t + 42, where t is the time in seconds. How high will the rocket be after 3 seconds?
171 feet
A manufacturer makes two types of handmade fancy paper bags: type A and type B. Two designers—a cutter and a finisher—need to work on both kinds of bags. A type A bag requires 2 hours of the cutter's time and 3 hours of the finisher's time. A type B bag requires 3 hours of the cutter's time and 1 hour of the finisher's time. Each month the cutter is available for 108 hours and the finisher is available for 78 hours. The manufacturer gets a profit of $12 for each bag of type A and $9 for each bag of type B. Identify the number of bags of each type to be manufactured to obtain maximum profit.
18 bag A; 24 bag B
Graph f(x) = x3 + 3x2 − 4x + 5 on a calculator and estimate the correct local maximum and minimum.
18.13; 3.87
A toy rocket is launched from a platform 36 feet above the ground at a speed of 97 feet per second. The height of the rocket in feet is given by the polynomial −16t2 + 97t + 36, where t is the time in seconds. How high will the rocket be after 3 seconds?
183 feet
A nutritionist planning a diet for a swimmer wants him to consume 4,000 Calories and 760 grams of food daily. Calories from carbohydrates and fat will be 60% of the total Calories. There are 4, 4, and 9 Calories per gram for protein, carbohydrates, and fat, respectively. How many daily grams of fat will the diet include?
192
Evaluate the polynomial for the given value by using synthetic division.P(x) = 3x4 + x3 − 4x + 5 for x = 5 and x = −3
1985; 233
Identify the product in the form a + bi.(3 − 2i)(−4 + 7i)
2 + 29i
Skating school A charges $7 for equipment rental plus $20 per hour for lessons. Skating School B charges $25 for equipment rental plus $12 per hour for lessons. Identify the number of hours for which the equipment rental and fee for lessons is the same for both schools.
2 1/4 hours
Identify the number and type of solutions for the equation 3x2 − 5x + 19 = 0.
2 nonreal complex
Identify the sum in the form a + bi.(−3 + 2i) + (5 − 7i)
2 − 5i
Identify the zeros of the function g(x) = x2 − 6x + 8.
2, 4
Evaluate g(x) = 1.8x3 − 0.0034x + 0.5 for x = 1 and x = 2.
2.2966; 14.8932
Identify an algebraic expression that represents Jo's age y years after her 20th birthday.
20 + y
A nutritionist planning a diet for a basketball player wants him to consume 3,650 Calories and 650 grams of food daily. Calories from carbohydrates and fat will be 60% of the total Calories. There are 4, 4, and 9 Calories per gram for protein, carbohydrates, and fat, respectively. How many daily grams of fat will the diet include?
210
A nutritionist planning a diet for a rugby player wants him to consume 3,650 Calories and 650 grams of food daily. Calories from carbohydrates and fat will be 70% of the total Calories. There are 4, 4, and 9 Calories per gram for protein, carbohydrates, and fat, respectively. How many daily grams of fat will the diet include?
210
A furniture company has 400 board ft of teak wood and can sustain up to 450 hours of labor each week. Each chair produced requires 5 ft of wood and 10 hours of labor, and each table requires 20 ft of wood and 15 hours of labor. If a chair yields a profit of $45 and a table yields a profit of $80, what are the numbers of chairs and tables that should be produced each week in order to maximize the company's profit?
24 chairs; 14 tables
The number of toys sold per month can be modeled by f(x) = 2x4 + x3 + 6x + 5, where x represents the number of months since June. Let g(x) = f(x) + 7. Which of the following gives the rule for g and the correct explanation of the meaning of the transformation in terms of monthly toy sales?
2x4 + x3 + 6x + 12vertical shift 7 units up increase of 7 units per month
Lisa purchased groceries worth $34 for a party. A gallon of milk costs $2.50, a gallon of ice cream costs $7.50, and a gallon of lemonade costs $3.00. If Lisa bought 4 gallons of milk, and 2 gallons of ice cream, how many gallons of lemonade did she buy?
3
A tank's length is 4 feet longer than its width. The height is 2 feet more than the width. The volume of the tank is 105 cubic feet. What is the width of the tank?
3 ft
Solve by finding all roots.x4 − x3 + 3x2 − 9x − 54 = 0
3, −2, 3i, −3i
Susan needs to buy apples and oranges to make fruit salad. She needs 15 fruits in all. Apples cost $3 per piece, and oranges cost $2 per piece. Let m represent the number of apples. Identify an expression that represents the amount Susan spent on the fruits. Then identify the amount she spent if she bought 6 apples.
30 + m; $36
A cell phone service provider offers a plan that charges $30.35 per month and $0.05 per minute for phone calls. If a person received a bill of $45.35 last month, how many minutes of phone calls were they charged for?
300 min
Evaluate the expression (3/7)−3.
343/27
Evaluate the polynomial for the given value by using synthetic division.P(x) = 3x4 − 2x3 − 5x + 11 for x = 6 and x = −4
3437; 927
An airplane pilot is fertilizing a field. The height y in feet of the fertilizer t seconds after it is dropped is modeled by y(t) = −16t2 − 3t + 300. The horizontal distance x in feet between the fertilizer and its dropping point is modeled by x(t) = 85t. At approximately what horizontal distance from the field should the pilot start dropping the fertilizer?
360 ft
Minimize the objective function P = 5x + 8y for the given constraints.x ≥ 0y ≥ 02x + 3y ≥ 153x + 2y ≥ 15
37.5
Multiply (3a − 2)(a2 + 2a − 2).
3a3 + 4a2 − 10a + 4
Identify an expression for the height of a rectangle whose area is represented by 3x3 − x2 − 6x − 8, and whose base is represented by x − 2.
3x2 + 5x + 4
The number of toys sold per month can be modeled by f(x) = 3x4 + 2x3 + 5x + 10, where x represents the number of months since June. Let g(x) = f(x) + 3. Which of the following gives the rule for g and the correct explanation of the meaning of the transformation in terms of monthly toy sales?
3x4 + 2x3 + 5x + 13vertical shift 3 units upincrease of 3 units per month
A blueprint of a shopping complex shows the bottom edge of the roof to be 68 feet above the ground. If the roof rises to a point 122 feet above the ground over a horizontal distance of 4.5 yards, what is the slope of the roof?
4
A blueprint of a shopping complex shows the bottom edge of the roof to be 93 feet above the ground. If the roof rises to a point 171 feet above the ground over a horizontal distance of 6.5 yards, what is the slope of the roof?
4
A blueprint of an office shows the bottom edge of the roof to be 54 feet above the ground. If the roof rises to a point 120 feet above the ground over a horizontal distance of 5.5 yards, what is the slope of the roof?
4
A tank's length is 4 feet longer than its width. The height is 1 foot less than the width. The volume of the tank is 96 cubic feet. What is the width of the tank?
4 ft
Maximize the objective function P = 5x + 7y for the given constraints.x ≥ 0y ≥ 02x + 3y ≤ 185x + 2y ≤ 23
43
A manufacturer makes two types of handmade fancy paper bags: type A and type B. Two designers—a cutter and a finisher—need to work on both kinds of bags. A type A bag requires 2 hours of the cutter's time and 1 hour of the finisher's time. A type B bag requires 1 hour of the cutter's time and 2 hours of the finisher's time. Each month the cutter is available for 104 hours and the finisher is available for 76 hours. The manufacturer gets a profit of $6 on each bag of type A and $11 on each bag of type B. Identify the number of bags of each type to be manufactured to obtain maximum profit.
44 bag A; 16 bag B
A 27-foot pole casts a 25-foot shadow. At the same time, a nearby tower casts a 45-foot shadow. How tall is the tower?
48.6ft
For the function f(x) = x2 + 4, identify the values of f(0), f(1/2), and f(−1).
4; 17/4; 5
Steve spent $40 at the grocery store. He bought bottled water, soda, and sandwiches. A bottle of water costs $1.50, a bottle of soda costs $2, and a sandwich costs $3. If he bought 10 bottles of water and 5 bottles of soda, how many sandwiches did he buy?
5
Evaluate g(x) = 0.023x3 + 0.4x2 − 2.1x + 8.3 for x = 2 and x = 4.
5.884; 7.772
Divide. Simplify your answer.(15x3 −12x2 + 6x) ÷ 3x
5x2 − 4x + 2
Identify entry Q23 .
6
Steve spent $48 at the grocery store. He bought bottled water, soda, and sandwiches. A bottle of water costs $1.50, a bottle of soda costs $2, and a sandwich costs $4. If he bought 8 bottles of water and 6 bottles of soda, how many sandwiches did he buy?
6
The equation of a line of best fit relating the number of cats c at an animal shelter to the number of dogs d is c = 1.9d − 8. Predict the number of cats at a shelter where there are 40 dogs.
68
Identify the product in the form a + bi.(5 − 8i)(3 − i)
7 − 29i
A cliff diver dives into the water from an overlook. His height in feet is given by y(t) = −16t2 + 32t + 84, where t is the time in seconds. The horizontal distance in feet of the diver from the overlook is given by x(t) = 2t. What horizontal distance will the diver travel before he hits the water?
7.0 ft
Evaluate the polynomial for the given value by using synthetic division.P(x) = 3x4 + x3 − 2x + 6 for x = 7 and x = − 5
7538; 1766
Multiply 7m2(m4 + 6).
7m6 + 42m2
There are two identical oil tanks. The level of oil in Tank A is 6 ft and is drained at the rate of 0.5 ft/min. Tank B contains 10 ft of oil and is drained at the rate of 1 ft/min. After how many minutes will the level of oil in the two tanks be the same?
8 minutes
Identify the expansion of the expression (2m − 3n)3.
8m3 − 36m2n + 54mn2 − 27n3
Calvin owns a toy store. He can spend at most $200 on restocking cars and dolls. A doll costs $6.50, and a car costs $8.00. Let x represent the number of cars, and let y represent the number of dolls. Identify an inequality for the number of toys he can buy. Then identify the number of dolls Calvin can buy if he buys 10 cars.
8x + 6.50y ≤ 200; no more than 18 dolls
Identify the zeros of the function g(x) = x2 − 5x − 36.
9, −4
Add.(4b5+9b3−3)+(5b5−2b−6)
9b5+9b3−2b−9
Subtract.(10d 4 − d 3) − (d 4 + 5d 3 − 1)
9d4 − 6d3 + 1
Identify the domain and range for the relation {(4, 3), (7, 6), (10, 9), (13, 6), (16, 9)}
D = {4, 7, 10, 13, 16} R = {3, 6, 9}
Identify the domain and range of the function f(x) = −2x2 + 6x + 11
D: ℜ R: y ≤ 15.5
Identify the domain and range of the function f(x) = 2x2 − 6x − 9.
D: ℜ R: y ≥ −13.5
Identify the simplest polynomial function having integer coefficients with the given zeros. 0, 4, /3
P(x) = x4 + 4x3 − 3x2 − 12x
Wilscy owns a toy store. The number of toy trains sold (in thousands) from 2000 through 2005 can be modeled by M(x) = −0.5x3 + 2x2 − x + 9. The average cost per toy train (in dollars) can be modeled by N(x) = 0.3x + 7, where x represents the number of years since 2000. The total revenue Wilscy made by the sale of toy trains is the product of the number of toy trains sold and the average cost per toy train. Identify a polynomial P(x) that can be used to model the total revenue.
P(x) = −0.15x4 − 2.9x3 + 13.7x2 − 4.3x + 63
Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system.y > x + 5y ≥ 2x + 3
Possible solutions: (−5, 5), (−4, 2)
Identify the roots of the equation and the multiplicities of the roots.(x − 1)2(x + 5) = 0
The root 1 has a multiplicity of 2. The root −5 has a multiplicity of 1.
Identify the roots of the equation and the multiplicities of the roots.(x − 6)(x + 4)2 = 0
The root 6 has a multiplicity of 1. The root −4 has a multiplicity of 2.
Identify the roots of the equation and the multiplicities of the roots.(x − 5)2(x + 2) = 0
The root −2 has a multiplicity of 1. The root 5 has a multiplicity of 2.
Identify the roots of the equation and the multiplicities of the roots.2(x + 2)3 = 0
The root −2 has a multiplicity of 3.
Identify the roots of the equation and the multiplicities of the roots.(x + 4)3 = 0
The root −4 has a multiplicity of 3.
Identify the roots of the equation and the multiplicities of the roots.2(x − 1)2(x + 9) = 0
The root −9 has a multiplicity of 1. The root 1 has a multiplicity of 2.
Which of the following represents the set in words? {x | x < 0}
all negative real numbers
If 3 basketball game tickets and 4 football game tickets were purchased for $50.25, and if 5 basketball game tickets and 5 football game tickets were purchased for $71.25, what are the costs of basketball game tickets and football game tickets?
basketball game tickets: $6.75;football game tickets: $7.50
If 4 basketball game tickets and 5 football game tickets were purchased for $61.50, and if 5 basketball game tickets and 3 football game tickets were purchased for $55.75, what are the costs of basketball game tickets and football game tickets?
basketball game tickets: $7.25;football game tickets: $6.50
The function p(x) = −2000x2 + 18000x − 15000 models the monthly profit P of a smoothie company, where x represents the price per smoothie. Identify the price range that will generate a monthly profit of at least $25,000.
between $4 and $5; inclusive
The profit function p(x) of a tour operator is modeled by p(x) = −2x2 + 900x − 40000, where x is the average number of tours he arranges per day. What is the range of the average number of tours he must arrange per day to earn a monthly profit of at least $60,000?
between 200 and 250; inclusive
At a grocery store, Rick bought 4 bottles of water and 3 heart-healthy frozen meals for $18. Danny bought 6 bottles of water and 5 heart-health frozen meals for $29. Identify the cost of a bottle of water and the cost of a heart-healthy frozen meal.
bottle of water: $1.50; frozen meal: $4.00
At a grocery store, Rick bought 3 bottles of water and 5 heart-healthy frozen meals for $24. Danny bought 4 bottles of water and 4 heart-healthy frozen meals for $22. Identify the cost of a bottle of water and the cost of a heart-healthy frozen meal.
bottle of water: $1.75; frozen meal: $3.75
Classify the system and identify the number of solutions.4x + 3y + 6z = 25x + 5y + 7z = 132x + 9y + z = 1
consistent, independent; one
Classify the system and identify the number of solutions.x − 6y − 8z = −23x + 9y + 6z = 64x + 3y − 2z = 4
consistent; dependent; infinite
Classify the polynomial according to its degree and number of terms.7b3 + 3b2 − 7b
cubic trinomial
Solve the equation |2d − 2 | = 8.
d = 5 or d = −3
Which of the following represents the function f(x) = x2 − 14x − 1 in vertex form? Identify the vertex.
f(x) = (x − 7)2 − 50; (7, −50)
Identify a quadratic function that fits the points (−1, 9),(0, 4), and (3, 13).
f(x) = 2x2 − 3x + 4
Which of the following represents the function f(x) = 5x2 + 20x + 25 in vertex form. Identify the vertex.
f(x) = 5(x + 2)2 + 5; (−2, 5)
Identify a quadratic function that fits the points (−1, 8),(2, −1), and (0, 3).
f(x) = x2 − 4x + 3
Identify a quadratic function that fits the points (−3, −7),(0, −4), and (2, −12).
f(x) = −x2 − 2x − 4
The table shows the viscosity of an oil as a function of temperature. Identify a quadratic model for the viscosity, given the temperature. Then use the model to predict the viscosity of the oil at a temperature of 140°C.
f(x) ≈ 0.001x2 − 0.37x + 39.4The viscosity of the oil at 140°C is about 7.2 kg/ms.
Which of the following represents the function g(x) = 2x2 − 20x + 42 in vertex form? Identify the vertex.
g(x) = 2(x − 5)2 − 8; (5, −8)
Let f(x) = −2x3 + 15x2 − 9x + 21. Identify the function g that reflects f across the y-axis.
g(x) = 2x3 + 15x2 + 9x + 21
Let g(x) be the indicated transformation of f(x) = −|3x| − 4. Stretch the graph of f(x) = −|3x| − 4 vertically by a factor of 3 and reflect it across the x-axis. Identify the rule and graph of g(x).
g(x) = 3|3x| + 12
Let f(x) = −x3 − 8x2 − 9x + 11. Identify the function g that reflects f across the y-axis.
g(x) = x3 − 8x2 + 9x + 11
Let g(x) be the transformation of f(x) = |x| so that the vertex is at (−1, −3). Identify the rule for g(x) and its graph.
g(x) = |x + 1| − 3
Let g(x) be the transformation of f(x) = |x| left 2 units. Identify the rule for g(x) and its graph.
g(x) = |x + 2|
Let g(x) be the transformation of f(x) = |x| so that the vertex is at (1, −3). Identify the rule for g(x) and its graph.
g(x) = |x − 1| − 3
Let g(x) be the transformation of f(x) = |x| right 2 units. Identify the rule for g(x) and its graph.
g(x) = |x − 2|
The parent function f(x) = x2 is reflected across the x-axis, vertically stretched by a factor of 4, and translated 5 units up to create g. Identify g in vertex form.
g(x) = −4x2 + 5
Let g(x) be the reflection across the y-axis of the function f(x) = 5x + 8. Identify the rule for g(x).
g(x) = −5x + 8
Let g(x) be the indicated transformation of f(x) = |4x| − 5. Compress the graph of f(x) = |4x| − 5 horizontally by a factor of 1/2 and reflect it across the x-axis. Identify the rule and graph of g(x).
g(x) = −|8x| + 5
Identify the function that vertically stretches f(x) = −3x3 − x + 1 by a factor of 4 and shifts it 6 units right.
h(x) = −12(x − 6)3 − 4(x − 6) + 4
Identify the function that reflects f(x) = 14x3 − 7x2 + 6 across the y-axis and shifts it 6 units up.
h(x) = −14x3 − 7x2 + 12
Identify the function that reflects f(x) = 5x3 − 3 across the x-axis and shifts it 2 units up.
h(x) = −5x3 + 5
Identify the function that vertically stretches f(x) = −2x3 + 5 by a factor of 3 and shifts it 2 units left.
h(x) = −6(x + 2)3 + 15
Identify the function that reflects f(x) = 7x3 + 4x2 − 11 across the x-axis and shifts it 3 units down.
h(x) = −7x3 − 4x2 + 8
Identify the function that vertically stretches f(x) = −4x3 + 1 by a factor of 2 and shifts it 7 units left.
h(x) = −8(x + 7)3 + 2
Complete the statement.The line y = 5 is _______.
horizontal
Let f(x) = x3 − 5x2 + 2x − 7 and g(x) = f(4x). Which of the following describes g as a function of f and gives the correct rule?
horizontal compression; g(x) = 64x3 − 80x2 + 8x − 7
Classify the system and determine the number of solutions.2x + y + 5z = 44x − 3y + 2z = 28x − 6y + 4z = −1
inconsistent; none
Classify the system and identify the number of solutions.2x + y + 5z = 43x − 2y + 2z = 25x − 8y − 4z = 1
inconsistent; none
Classify the system and identify the number of solutions.x − 2y − 2z = 82x + 6y − 2z = 98x − 6y − 14z = 11
inconsistent; none
Classify the system of equations and identify the number of solutions.2x + y = 56x + 3y = 25
inconsistent; none
Classify the system of equations and identify the number of solutions.3x − y = 82y − 5 = 6x
inconsistent; none
Classify the system of equations and identify the number of solutions.7x + 3y = 103y = 9 − 7x
inconsistent; none
Classify the system of equations and identify the number of solutions.8 + y = 4x4x − y = −3
inconsistent; none
Identify the correct leading coefficient, degree, and end behaviorof P(x) = 2x5 + 4x4 + x3 − 2x2 + 5x − 3.
leading coefficient: 2 degree: 5 end behavior:as x → −∞, P(x) → −∞as x → +∞, P(x) → +∞
Identify the correct leading coefficient, degree, and end behavior of P(x) = 3x6 − 8x5 − x2 + 4x − 9.
leading coefficient: 3 degree: 6 end behavior:as x → −∞, P(x) → +∞as x → +∞, P(x) → +∞
Identify the correct leading coefficient, degree, and end behaviorof P(x) = 4x5 + 9x4 + 6x3 − x2 + 2x − 7.
leading coefficient: 4 degree: 5 end behavior:as x → −∞, P(x) → −∞as x → +∞, P(x) → +∞
Identify the correct leading coefficient, degree, and end behavior of P(x) = −2x5 + 7x4 − 5x3 − x2 + 8x − 1.
leading coefficient: −2 degree: 5 end behavior:as x → −∞, P(x) → +∞as x → +∞, P(x) → −∞
Identify the correct leading coefficient, degree, and end behavior of P(x) = −3x4 + 6x3 + x − 5.
leading coefficient: −3 degree: 4 end behavior:as x → −∞, P(x) → −∞as x → +∞, P(x) → −∞
Identify the correct leading coefficient, degree, and end behaviorof P(x) = −3x5 − 2x3 + 7x + 8.
leading coefficient: −3 degree: 5 end behavior:as x → −∞, P(x)→ +∞,as x → +∞, P(x)→ −∞
Identify the correct leading coefficient, degree, and end behavior of P(x) = −4x3 + 10x2 + 1.
leading coefficient: −4degree: 3end behavior:as x → −∞, P(x) → +∞as x → +∞, P(x) → −∞
Identify the correct leading coefficient, degree, and end behavior of P(x) = −4x6 + 2x5 − 8x − 15.
leading coefficient: −4degree: 6end behavior:as x → −∞, P(x) → −∞,as x → +∞, P(x) → −∞
At a grocery store, Rick bought 4 loaves of bread and 3 gallons of milk for $20. Danny bought 6 loaves of bread and 2 gallons of milk for $25. Identify the cost of a loaf of bread and a gallon of milk.
loaf of bread: $3.50; gallon of milk: $2.00
Add or subtract.4m2 − 10m3 − 3m2 + 20m3
m2 + 10m3
Identify the solution of the inequality −4|n + 6| ≥ 20 and the graph that represents it.
no solution
Identify the solution set of the inequality 2|f + 4| ≤ −12 and the graph that represents it. f ≥ −2
no solution
Identify the solution set of the inequality 4|f + 6| ≤ −16 and the graph that represents it.
no solution
Classify the polynomial according to its degree and number of terms.3b2 − 2
quadratic binomial
The distance traveled by a toy car can be modeled by D(t) = t3 − 3t2 + t − 3, where t > 3 represents time in seconds. If the car traveled for t − 3 seconds, identify the expression that represents the speed of the toy car.
t2 + 1
Let f(x) = 12x3 + x2 − 8x − 2 and g(x) = 0.25f(x). Which of the following describes g as a function of f and gives the correct rule?
vertical compression; g(x) = 3x3 + 0.25x2 − 2x − 0.5
Identify the binomial that is a factor of the polynomial P(x) = x3 + 5x2 − 9x − 45.
x + 3
Identify the binomial that is not a factor of the polynomial P(x) = 2x3 − 7x2 − 10x + 24.
x + 3
Identify the binomial that is a factor of the polynomial P(x) = x3 + 4x2 − 20x − 48.
x + 6
Identify the binomial that is a factor of the polynomial P(x) = 3x3 − 11x2 − 2x + 24.
x - 2
Identify the binomial that is not a factor of the polynomial P(x) = 2x3 − 5x2 − 21x + 36.
x - 3
Identify the binomial that is not a factor of the polynomial P(x) = 3x3 + 5x2 − 4x − 4.
x - 4
Solve the inequality.x2 − 9x + 4 > 14
x < −1 or x > 10
Use a table or graph to solve the inequality.x2 − 6x − 4 > 3
x < −1 or x > 7
Identify the solution of the inequality |4x − 2| > 14 and the graph that represents it. x < − 3
x < −3 or x > 4
Identify the roots of the equation x2 − 4x + 4 = 0 using factoring.
x = 2
Identify the roots of the equation x2 = 9x − 14 by factoring.
x = 2 or x = 7
Solve using Cramer's rule.4x − 5y = 233x + 4y = −6
x = 2, y = −3
Identify the roots of the equation x2 + 21 = 10x using factoring.
x = 3 or x = 7
Identify the values of x and y that make the equation 2x + 5i = 16 + (2y)i true.
x = 8, y = 5/2
Identify the axis of symmetry of the function f(x) = −x2 − x + 12.
x = −0.5
Solve using Cramer's rule.3x − 2y = 05x − 4y = 2
x = −2, y = −3
Identify the roots of the equation x2 + 8x = −15 using factoring.
x = −3 or x = −5
Identify the roots of the equation x2 + 16x + 64 = 0 by factoring.
x = −8
Identify the solution of the compound inequality x − 2 > 4 or 5x ≥ 35 and the graph that represents it.
x > 6
Identify the solution of the inequality and the graph that represents it. |4x-4| / 2 ≤ 4
x ≥ −1 and x ≤ 3
Complete the square for the expression. Also, identify the resulting expression as a binomial squared.x2 − 6x + ____
x2 − 6x + 9 = (x − 3)2
Solve the inequality.x2 + 3 ≤ 4x
1 ≤ x ≤ 3
Find |4 − 4i|.
4/2
Multiply.(m + 5)4
m4 + 20m3 + 150m2 + 500m + 625
The equation of a line of best fit relating the money earned e at a bake sale to the number of customers c is e = 0.9c + 18. Predict the earnings from a bake sale with 90 customers.
$99
Solve the equation.x2 − 6x + 10 = 12
3+- square root 11
Lee spent $29 to purchase a combination of drinks, sandwiches, and chips for himself and his friends. A drink costs $1.50, a sandwich costs $5, and chips cost $1.25. Identify the linear equation that represents this situation.
1.50x + 5y + 1.25z = 29
Jessi is making curtains for her bedroom windows. She must add the areas of two windows to determine the amount of cloth she needs. The area of the first window is modeled by 5y2 + 10y + 10, and the area of the second window is modeled by 6y2 − 10y + 2. Identify the polynomial that represents the total area of the two windows.
11y2 + 12
Find the degree of the monomial −6x7y5.
12
In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 spectators. Tickets cost $15 for students and $25 for adults. Identify the system of inequalities and the corresponding graph that determine whether the charity will reach its goal. 15x + 25y ≤ 3750x + y ≤ 180
15x + 25y ≥ 3750 x + y ≤ 180
In an auditorium, a charity show is conducted in order to raise at least $3,750. The auditorium can accommodate up to 180 spectators. Tickets cost $15 for students and $25 for adults. Identify the system of inequalities and the corresponding graph that determine whether the charity will reach its goal. 15x + 25y ≥ 3750x + y ≥ 180
15x + 25y ≥ 3750x + y ≤ 180
Multiply 3x2y(5x − 2y).
15x3y − 6x2y2
There are two identical oil tanks. The level of oil in Tank A is 12 ft and is drained at the rate of 0.5 ft/min. Tank B contains 8 ft of oil and is drained at the rate of 0.25 ft/min. After how many minutes will the level of oil in the two tanks be the same?
16 minutes
Identify the number and type of solutions for the equation 3x2 + 2x + 9 = 0.
2 nonreal complex
A nutritionist planning a diet for a runner wants him to consume 3,800 Calories and 650 grams of food daily. Calories from carbohydrates and fat will be 60% of the total Calories. There are 4, 4, and 9 Calories per gram for protein, carbohydrates, and fat, respectively. How many daily grams of fat will the diet include?
240
Identify the factors of the expression 250b6 − 16b3.
2b3 (5b − 2)(25b2 + 10b + 4)
Identify the factors of the expression 54m5 + 2m2.
2m2 (3m + 1)(9m2 − 3m + 1)
Multiply (m2 − m − 4)(2m + 6).
2m3 + 4m2 − 14m − 24
Divide.(12p3 − 24p2 + 6p) ÷ 6p
2p2 − 4p + 1
Lee spent $36 to purchase a combination of drinks, sandwiches, and chips for himself and his friends. A drink costs $2, a sandwich costs $4, and chips cost $0.50. Identify the linear equation that represents this situation.
2x + 4y + 0.5z = 36
The width of a container is 5 feet less than its height. Its length is 1 foot longer than its height. The volume of the container is 216 cubic feet. How tall is the container?
8 ft
Subtract.(9a3 + 6a2 − a) − (a3 + 6a − 3)
8a3 + 6a2 − 7a + 3
Subtract.(9c5 − c4 ) − (c5 + 3c4 − 1)
8c5 − 4c4 + 1
Identify the simplest polynomial function having integer coefficients with the given zeros.3i, 2, −4
P(x) = x4 + 2x3 + x2 + 18x − 72
Identify the simplest polynomial function having integer coefficients with the given zeros. -4, 1, /5
P(x) = x4 + 3x3 − 9x2 − 15x + 20
Identify the simplest polynomial function having integer coefficients with the given zeros.3i, −1, 2
P(x) = x4 − x3 + 7x2 − 9x − 18
Identify the solution of the inequality |7p| + 36 > 15 and the graph that represents it.
all real numbers
A golfball is hit from ground level with an initial vertical velocity of 64 ft/s. Use the function h(t) = −16t2 + v0t + h0, where h(t) is the height of a golfball hit with initial vertical velocity v0 from initial height h0 after t seconds in the air, to find the time at which the golfball will hit the ground.
after 4 s
A golfball is hit from ground level with an initial vertical velocity of 80 ft/s. Use the function h(t) = −16t2 + v0t + h0, where h(t) is the height of a golfball hit with initial vertical velocity v0 from initial height h0 after t seconds in the air, to find the time at which the golfball will hit the ground.
after 5 s
Does the function g(x) = −2x2 + 10x + 2 have a minimum or a maximum? Identify its value.
maximum; 14.5
Does the function f(x) = 2x2 − 6x + 9 have a minimum or a maximum? Identify its value.
minimum; 4.5
Does the function f(x) = 3x2 − 12x + 1 have a minimum or a maximum? Identify its value.
minimum; −11
Identify the solution of the inequality −3|n + 5| ≥ 24 and the graph that represents it.
no solution
Solve by finding all roots.x4 − 2x3 + x2 − 8x − 12 = 0
−1, 3, 2i, −2i
Identify the solution of the compound inequality−6m −4 < 2m and m − 3 ≤ −4m + 12.
−1/2 < m ≤ 3
Solve the inequality.x2 − 4x − 2 < 10
−2 < x < 6
Barbara requires 2 gallons of paint to cover an area of 800 square feet. Identify the graph for the relationship from quantity to the area covered, and the parent function that best describes it. Then use the graph to estimate how many gallons of paint Barbara requires to paint an area of 2,400 square feet.
linear; 6 gallons
Lucy takes 20 minutes to cover a mile on foot. Identify the graph that shows the relationship between time taken and distance covered and the parent function that best describes it. Then use the graph to estimate the time it would take Lucy to cover 3.5 miles.
linear; 70 minutes
Identify the parent function for the function g(x) = (x − 8)3 from its function rule. Then graph g and identify what transformation of the parent function it represents.
cubic; translation right 8 units
A truck rental company charges $65 plus $32 per hour to rent a truck. Identify the function that represents the total charge for renting a truck for a certain number of hours. What is the value of the function for an input of 6, and what does it represent?
f(h) = 32h + 65$257, which is the total charge in dollars for renting a truck for 6 hours
Write the equation in in slope-intercept form.18x − 6y = 12
y = 3x − 2
Identify the slope-intercept form and the graph of the line described by the equation 8x + 2y = −6.
y = −4x − 3
Solve the inequality for y, and identify the graph for the solution. -3y < 6x-18
y > −2x + 6
Which of the following represents the set "all values of x greater than or equal to 0 and less than or equal to 5" in set builder notation?
{x | 0 ≤ x ≤ 5}
Which of the following represents the set "all values of x greater than or equal to −1 and less than 2" in set builder notation?
{x | −1 ≤ x < 2}
For the function f(x) = x2 − 2, identify the values of f(0), f(1/2), and f(−1).
−2; −7/4; −1
Identify the additive and multiplicative inverse of 4/11.
−4/11; 11/4
Identify the coordinates of the point (3, −2), translated 5 units left and 6 units up.
(-2, 4)
Identify the coordinates that result when the point (−4, 5), is translated 8 units right and 3 units down.
(4, 2)
Identify the coordinates of the point (2, −1), translated 6 units left and 3 units up.
(−4, 2)
Simplify 3m2 (−6m3 ). Assume all variables are non-zero.
-18m5
Solve the equation.(7m + 69) − 6 = 8m + 3 − 5m
m =-15
Simplify 9m2 + 2n + 5m − 8m2
m2 + 2n + 5m
Simplify 9m2 + 2n + 5m − 8m2
m2 + 2n + 5m
Julie sells 80 packets of tea. She makes a profit of $5 on each packet of green tea, and $2 on each packet of black tea. Let g represent the the number of packets of green tea. Identify an expression that represents the profit Julie makes selling the tea packets. Then identify the profit she makes if she sells 35 packets of green tea.
160 + 3 g; $265
Identify the additive and multiplicative inverse of −17.
17; −1/17
A 34-foot pole casts a 30-foot shadow. At the same time, a nearby tree casts a 24-foot shadow. How tall is the tree?
27.2ft
Harry is organizing a picnic. He can spend at most $24.00 on beverages. Iced tea costs $2.00 per gallon and lemonade costs $2.50 per gallon. If x represents the number of gallons of iced tea and y represents the number of gallons of lemonade, which inequality shows the number of gallons of each drink that he can buy? Identify the number of gallons of iced tea that Harry can buy if he buys 5 gallons of lemonade.
2x + 2.5y ≤ 24; no more than 5 gallons
The equation of a line of best fit relating the number of cats c at an animal shelter to the number of dogs d is c = 2.1d − 26. Predict the number of cats at a shelter where there are 30 dogs.
37
Calvin owns a toy store. He can spend at most $180 on restocking cars and dolls. A doll costs $8.25, and a car costs $7.00. If x represents the number of cars, and y represents the number of dolls, identify an inequality for the number of toys he can buy. Then identify the number of dolls Calvin can buy if he buys 10 cars.
7x + 8.25y ≤ 180; no more than 13 dolls
Identify the domain and range for the relation.{(1, 3), (2, 5), (3, 7), (4, 9), (5, 9)}
D = {1, 2, 3, 4, 5}R = {3, 5, 7, 9}
Which of the following represents the set in words? {x | x ≥ 0}
None of these
The rent for an apartment is represented by R(a) = 2.00a + 50.00, where a is the area of the apartment in square feet. The rent increases by $50.00 when the apartment is furnished. Identify the new function S(a) for the rent of a furnished apartment and the transformation that has been applied.
S(a) = 2.00a + 100.00; shift 50 units up
Describe the transformation from the graph of f(x) = x + 8 to the graph of g(x) = x − 3.
The graph g(x) = x − 3 is the result of translating the graph of f(x) = x + 8 down 11 units.
Describe the transformation from the graph of f(x) = x + 3 to the graph of g(x) = x − 7.
The graph g(x) = x − 7 is the result of translating the graph of f(x) = x + 3 down 10 units.
Which of the following correctly represents the set of numbers using interval notation? −3 ≤ x < 7
[−3, 7)
Identify the relation that is a function.
age of a plant to its height
Solve the equation.2p + 15 − 11p = 3(5 − 3p)
all real numbers
A truck rental company charges $50 plus $10 per hour. Identify a function that represents the total charge for renting a truck for a certain number of hours. What is the value of the function for an input of 4, and what does it represent?
f(h) = 50 + 10h;$90, which is the total charge in dollars for renting a truck for 4 hours
An interior designer charges $100 to visit a site, plus $55 to design each room. Identify a function that represents the total amount he charges for designing a certain number of rooms. What is the value of the function for an input of 6, and what does it represent?
f(x) = 100 + 55x$430, which is the total charge in dollars for designing 6 rooms
An interior designer charges $80 to visit a site, plus $65 to design each room. Identify a function that represents the total amount he charges for designing a certain number of rooms. What is the value of the function for an input of 5, and what does it represent?
f(x) = 80 + 65x$405, which is the total charge in dollars for designing 5 rooms
Complete the statement.The line y = 2 is _______.
horizontal
Marie requires 2 gallons of paint to cover an area of 400 square feet. Identify the graph that shows the relationship between the quantity of paint and the area covered and the parent function that best describes it. Then use the graph to estimate how many gallons of paint Marie requires to paint an area of 2,400 square feet.
linear; 12 gallons
Identify the parent function for the function g(x) = x − 3 from its function rule. Then graph g and identify what transformation of the parent function it represents.
linear; translation down 3 units
Identify the parent function for the function g(x) = x + 4 based on its function rule. Then graph g and identify the transformation of the parent function that it represents.
linear; translation up 4 units
Solve the equation.5(4m − 8) = 20
m = 3
Identify the relation that is not a function.
telephone area code to city name
The cost of creating a software program is $5000. Every extra feature added to the software costs $100. The total charge of the software with x extra features is given by the function f(x) = 100x + 5000. How will the graph of this function change if the basic cost is raised to $5200 and the cost of each extra feature is increased to $120?
the graph will be translated 200 units up and rotated about (0, 5200)
Find the intercepts.4x − 6y = 12
x-intercept 3y-intercept −2
Find the intercepts and graph.4x − 3y = 12
x-intercept 3y-intercept −4
Find the intercepts.3x − 2y = −6
x-intercept −2y-intercept 3
Find the intercepts.5x − 2y = −10
x-intercept: −2y-intercept 5
Identify the equation of a line in slope-intercept form that is parallel to y = 2.5x + 5 and passes through (2, 3).
y = 2.5x − 2
Identify the slope-intercept form and the graph of the line described by the equation 12x − 3y = −9.
y = 4x + 3
Identify the slope-intercept form and the graph of the line described by the equation 3x − 3y = 15.
y = x − 5