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Algebra 2B
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Terms in this set (291)
Which statement best describes how to determine whether f(x) = x^4 - x^3 is an even function?
A. Determine whether (-x)^4 - (-x)^3 is equivalent to x^4 - x^3.
Which graph represents an even function?
C (shape of n)
Which graph shows rotational symmetry?
A (shape of squiggle line)
Which of the following is an even function?
b. g(x) = 2x^2 + 1
Which graph represents an odd function?
B. (squiggle line)
Which of the following is an odd function?
f(x) = 6x^3 + 2x
The graph of f(x) consists of 14 points. Six of the points lie in Quadrant I of the coordinate plane. If f(x) is an odd function, what is the greatest number of points that can lie in Quadrant II?
a. one
Which of the following is an even function?
a. f(x) = |x|
If f(x) is an even function, which statement about the graph of f(x) must be true?
c. It has line symmetry about the y-axis.
Which statement best describes how to determine whether f(x) = 9 - 4x^2 is an odd function?
c. Determine whether 9 - 4(-x)^2 is equivalent to -(9 - 4x^2).
If f(x) is an odd function, which statement about the graph of f(x) must be true?
a. It has rotational symmetry about the origin.
If f(x) is an even function and (6, 8) is one the points on the graph of f(x), which reason explains why (-6, 8) must also be a point on the graph?
a. Since the function is even, the output of a negative x-value and its opposite is the same.
Which graph represents an odd function?
c
Suppose f(x) is a function such that if p < q, f(p) < f(q). Which statement best describes f(x)?
b. f(x) can be odd but cannot be even.
Which of the following is an odd function?
d. g(x) = 4x
Which graph shows line symmetry about the y-axis?
b
If g(x) is an odd function, which function must be an even function?
c.f(x) = g(x)^2
What is the solution to the following system?
{4x+3y-z=-6
{6x-y+3z=12
{8x+2y+4z=6
B. x = 1, y = -3, z = 1
A system of three linear equations in three variables is inconsistent. How many solutions to the system exist?
A. none
What is the solution to the following system?
{x+2y+z=9
{x-y+3z=13
{ 2z=10
C. x = 0, y = 2, z = 5
Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?
B. The system can be either independent or dependent.
What is the solution to the following system?
{3x+3y+6z=9
{x+3y+2z=5
{3x+12y+12z=18
C. (2, 1, 0)
What is the solution to the following system?
{ -4y=8
{x+3y-3z=-26
{2x-5y+5=19
D. x = 1, y = -2, z = 7
The cost for three packages of moving boxes is modeled by the system of equations below. Let s represent small boxes, m represent medium boxes, and l represent large boxes. Which ordered pair (s, m, l) represents the costs of the three boxes?
{7s+4m+2/=24
{5s+3m+6/=30
{3s+7m+10/=46
C. (1.50, 2.00, 2.75)
Which classification best describes the following system of equations?
{ 5x+y+2z=13
{4x+3y+6z=17
{ x+2y=4
C. consistent and independent
A system of three linear equations in three variables is consistent and independent. How many solutions to the system exist?
B. one
Which classification best describes the following system of equations?
{12x+5y-3z=36
{ x-2y+4z=3
{9x-10y+5z=27
C. consistent and independent
Solve 2x^2 - 5x + 1 = 3 for x.
D.
Solve x^2 + 20x + 100 = 36 for x.
A. x = -16 or x = -4
Solve x^2 - 10x + 25 = 35 for x.
B.
Which value must be added to the expression x^2 + 12x to make it a perfect-square trinomial?
B. 36
What are the solutions of the equation x^2+4x+4=25
A. x=3 or x= -7
Solve x^2 - 14x + 31 = 63 for x.
C. x = -2 or x = 16
If x^2 + mx + m is a perfect-square trinomial, which equation must be true?
C. x2 + mx + m = (x + 2)^2
Solve x^2 - 8x + 41 = 0 for x.
D. x = 4 Â± 5i
Which value must be added to the expression x^2 - 3x to make it a perfect-square trinomial?
B. 9/4
Solve X^2+11x+121/4=125/4 for x
D
Which equation has the solutions x= 5+2squareroot7/3
D. 3x^2 - 10x - 1 = 0
For which value of m does the graph of y = 18x^2 + mx + 2 have exactly one x-intercept?
12
The graph of an equation with a negative discriminant always has which characteristic?
A. no x-intercept
Using the quadratic formula to solve 4x^2 - 3x + 9 = 2x + 1, what are the values of x?
C
If the discriminant of a quadratic equation is 4, which statement describes the roots?
B. There are two real roots.
What is the discriminant of 3x^2-10x=-2
76
If x = -3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?
C. The discriminant is 0.
Which statement about the following equation is true?
3x^2 - 8x + 5 = 5x^2
B. The discriminant is greater than 0, so there are two real roots.
Which equation could generate the curve in the graph below?
A. y = 3x^2 - 2x + 1
What is the discriminant of 3x^2 + 6x = 2?
60
If X=6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?
A. The discriminant is 0.
Using the quadratic formula to solve 5x = 6x^2 - 3, what are the values of x?
B.
If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?
A. There are two complex roots.
Using the quadratic formula to solve x^2 + 20 = 2x, what are the values of x?
D.
Which equation shows the quadratic formula used correctly to solve 7x^2 = 9 + x for x?
D
A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box?
C. y = 5(14 - x)(x)
A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = -16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are -0.2 s and 2.7 s. Which solution can be eliminated and why?
A. The solution -0.2 s can be eliminated because time cannot be a negative value.
A skydiver jumps from an airplane at an altitude of 2,500 ft. He falls under the force of gravity until he opens his parachute at an altitude of 1,000 ft. Approximately how long does the jumper fall before he opens his chute?
B. 9.7 s
Carmen is using the quadratic equation (x + 15)(x) = 100 where x represents the width of a picture frame. Which statement about the solutions x = 5 and x = -20 is true?
B. The solution x = 5 should be kept, but x = -20 is unreasonable.
A car's stopping distance in feet is modeled by the equation d(v)= 2.15v^2/58.4f where v is the initial velocity of the car in miles per hour and f is a constant related to friction. If the initial velocity of the car is 47 mph and f = 0.34, what is the approximate stopping distance of the car?
C. 239 feet
Alice's backyard is a rectangular piece of property that is twice as long as it is wide. The total area of her yard is 1,000 m2. What is the approximate width of her backyard?
C. 22.4 m
The owner of an office building is expanding the length and width of a parking lot by the same amount. The lot currently measures 120 ft by 80 ft, and the expansion will increase its area by 4,400 ft^2. By how many feet should the length of the parking lot be increased?
B. 20 ft
A projectile is launched straight up with an initial velocity of 120 ft/s. If acceleration due to gravity is -16 ft/s^2, after about how many seconds will the object reach a height of 200 ft?
C. 2.5 s
The total area of two square windows is 1,025 in.^2. Each side of the larger window is 5 in. longer than the sides of the smaller window. How long are the sides of the smaller window?
B. 20 in.
A rectangular pan has a length that is 4/3 the width. The total area of the pan is 432 in.^2. What is the width of the cake pan?
18
Which equation is the inverse of y = x^2 - 36?
B
Which equation is the inverse of (x-4)^2-2/3=6y-12?
B
If f(x)= square root/4x+9+2, which inequality can be used to find the domain of f(x)?
B. 4x+9+2
If f(x) squareroot/ 1/2x-10+3, which inequality can be used to find the domain of f(x)?
C.
What is the domain of the function y=2squareroot/x-5
C. x>5
Which equation is the inverse of y = x^2 + 16?
C
What is the domain of the square root function graphed below?
D. X>3
What is the domain of the function Y=squareroot/x+4
C
If f(x)=squareroot/x-3, which inequality can be used to find the domain of f(x)?
B. x-3>0
Which function has the domain x>-11
A.
Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. Which ordered pair generated by this model should be discarded because the values are unreasonable?
A. (-4, 1)
Dimitri is solving the equation x^2 - 10x = 21. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?
C. 25
A soccer ball is kicked into the air from the ground. If the ball reaches a maximum height of 25 ft and spends a total of 2.5 s in the air, which equation models the height of the ball correctly? Assume that acceleration due to gravity is -16 ft/s^2.
A. h = -16(t - 1.25)^2 + 25
Which equation can be simplified to find the inverse of y = x^2 - 7?
C. x = y^2 - 7
Which could be the function graphed below?
A. f(x)= sqaureroot/x-2
Which equation can be solved using the expression ^ -3+-squareroot/(3)^2+4(10)(2)/ 2(10) for x
B. 2 = 3x + 10x2
What is the domain of the square root function graphed below?
A. X>-4
A firework is launched into the air from ground level with an initial velocity of 128 ft/s. If acceleration due to gravity is -16 ft/s^2, what is the maximum height reached by the firework?
A. 256 ft
Solve x^2 - 12x + 36 = 90 for x.
A.
Use completing the square to solve (x - 12)(x + 4) = 9 for x.
D.
For what values of m does the graph of y = 3x^2 + 7x + m have two x-intercepts?
C
Which equation could generate the curve in the graph below?
D. y = 2x^2 + 8x + 8
The financial planner for a beauty products manufacturer develops the system of equations below to determine how many combs must be sold to generate a profit. The linear equation models the income, in dollars, from selling x plastic combs; the quadratic equation models the cost, in dollars, to produce x plastic combs. According to the model, for what price must the combs be sold?
{y=x/2
{y=-0.03(x-95)^2+550
B. $0.50 each
The first equation in the system models the heights in feet, h, of a falling baseball as a function of time, t. The second equation models the heights in feet, h, of the glove of a player leaping up to catch the ball as a function of time, t. Which statement describes the situation modeled by this system?
{h=35-16t
{h=6+18t-16t^2
C. The height of the baseball is 35 feet at the moment the player begins to leap.
A coordinate grid is mapped on a video game screen, with the origin in the lower-left corner. A game designer programs a helicopter to follow a path that can be modeled by a quadratic function with a vertex at (16, 20) and passing through the point (4, 25). She also programs an airplane to move along a linear path that passes through the points (0, 18) and (30, 20). Which system of equations can be used to determine whether the paths of the helicopter and airplane cross?
A
Graham and Hunter are circus performers. A cable lifts Graham into the air at a constant speed of 1.5 ft/s. When Graham's arms are 18 ft above the ground, Hunter, who is standing directly underneath Graham, throws Graham a ball as the cable continues to lift him higher. Hunter throws the ball from a position 5 ft above the ground with an initial velocity of 24 ft/s. Which system of equations can be used to model this situation?
A
The center of an ice rink is located at (0, 0) on a coordinate system measured in meters. Susan is skating along a path that can be modeled by the equation y = 6x - x^2 - 5. Luke starts at (10, -21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, -9). If the rink is a circle with a radius of 35 meters, which statement best interprets the solution(s) of a system of equations modeling the paths of the skaters?
C. The skaters path intersect twice, but only one of those points is inside the rink.
Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. When Susan jumps, Megan throws a beach ball up to Susan with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. To the nearest hundredth of a second, how long after she jumps does the ball reach Sharon?
C. 1.08 seconds
A basketball player is shooting a basketball toward the net. The height, in feet, of the ball t seconds after the shot is modeled by the equation h = 6 + 30t - 16t^2. Two-tenths of a second after the shot is launched, an opposing player leaps up to block the shot. The height of the shot blocker's outstretched hands t seconds after he leaps is modeled by the equation h = 9 + 25t - 16t^2. If the ball reaches the net 1.7 seconds after the shooter launches it, does the leaping player block the shot?
D. No, the shot is not blocked.
A company plans to sell a new type of vacuum cleaner for $280 each. The company's financial planner estimates that the cost, y, of manufacturing the vacuum cleaners is a quadratic function with a y-intercept of 11,000 and a vertex of (500, 24,000). Which system of equations can be used to determine how many vacuums must be sold for the company to make a profit?
A
Two boats depart from a port located at (-8, 1) in a coordinate system measured in kilometers and travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (1, 10), whereas the second boat follows a path that can be modeled by a quadratic function with a vertex at (0, -7). Which system of equations can be used to determine whether the paths of the boats cross?
A
The length of a rectangular field is 20 less than its width. The area of the field is 12,000 ft^2. What is the width of the field?
C. 120 ft
A store owner buys $4,000 worth of products. For shipping costs, it is 10% of the amount of product A and 4% of the amount of product B. If the total shipping cost is $352, which system of equations can be used to determine how much of product A and product B the store owner bought?
C
An air show is scheduled for an airport located on a coordinate system measured in miles. The air traffic controllers have closed the airspace, modeled by a quadratic equation, to non-air show traffic. The boundary of the closed airspace starts at the vertex at (10, 6) and passes through the point (12, 7). A commuter jet has filed a flight plan that takes it along a linear path from (-18, 14) to (16, -13). Which system of equations can be used to determine whether the commuter jet's flight path intersects the closed airspace?
A
A company plans to sell pens for $2 each. The company's financial planner estimates that the cost, y, of manufacturing the pens is a quadratic function with a y-intercept of 120 and a vertex of (250, 370). What is the minimum number of pens the company must sell to make a profit?
B. 174
What is the degree of 4a^5b^2+2ab^3
7
Which statement is true?
A. All constants are of degree 0.
Which polynomial is in standard form?
D. 23x^9-12x^4+19
Which expression is a polynomial?
-13
Which expression is a trinomial?
A. x + y - 13
What term describes the monomial 14xyz?
D. cubic
Which polynomial is in standard form?
C. 11x^3-6x^2+5x
Which expression is a trinomial of degree 1?
C. 6 + x - y
Which polynomial is in standard form?
B. 12x^5-6x^2-9x+12
Which polynomial is in standard form?
B. 18x^5-7x^2y-2xy^2+17y^4
What is the difference of the polynomials?
(x^4+x^3+x^2+x)-(x^4-x^3+x^2-x)
B.
What is the additive inverse of the polynomial?
-7y^2+x^2y-3xy-7x^2
A
Samuel found the difference of the polynomials.
(15x^2+11y^2+8x)-(7x^2+5y^2+2x)=___x^2+6y^2+6x
What value is missing from his solution
8
Lucia finds that (3x^2+3x+5)+(7x^2-9x+8)=10x^2-12x+13.
What error did Lucia make
c. She combined the terms 3x and -9x incorrectly.
What is the sum of the polynomials?
(9x^2-12y^2-11x)+(x^2-3y^2-7x)
D. 9x^2-12y^2-11x
What is the sum of the polynomials?
(6x+7+x^2)+(2x^2-3)
B
Which expression can be used to find the sum of the polynomials?
(9-3x^2)+(-8x^2+4x+5)
D
Marcus finds that (3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y^2-2X What error did Marcus make?
C. He combined the terms -2y^2 and 12y^2 incorrectly.
What is the sum of the polynomials?
(m + n + 3) + (m + n + 4)
C. 2m + 2n + 7
What is the sum of the polynomials?
B. 4m - 24n + 3
Which expression is equivalent to 60^20y^24/30x^10y^12
B. 2x^10y^12
Which values of a and b make the equation true?
B. a = 3, b = 3
Which expression is equivalent to (2x^4y)^3
D. 8x^12y^3
Which law would you use to simplify the expression 3^10/3^4
A. quotient of powers
Which values of a and b make the following equation true?
(5x^7 y^2)(-4x^4 y^5)=-20x^a y^b
A. a = 11, b = 7
Which expression is equivalent to 5^10 * 5^5
C. 5^5
Which expression is equivalent to (2g^5)^3/(4h^2)^3
A
Which expression is equivalent to (m^5 n/pq^2)^4
C
Which expression is equivalent to 9x^5 y^16/ 45x^5 y^4
A
Which expression is equivalent to r^9/r^3
B. r^6
What is the product?
(7x^2)(2x^3+5)(x^2-4x-9)
C.
What is the product?
(Y^2+3y+7)(8y^2+y+1)
D
What value of g makes the equation true?
(x-3)(x+5)=x^2+gx-15
2
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a - 12), and height (a + 6). Which expression represents the volume of the box?
D
What is the product?
(7x^2 y^3)(3x^5 y^8)
C
What is the product?
(x^4)(3x^3-2)(4x^2+5x)
A
What is the product?
(3a^2 b^4)(-8ab^3)
D
What is the product?
(3x-6)(2x^2-7x+1)
C
What is the product?
(4s+2)(5s^2+10s+3)
D
What is the product?
(3a^2 b^7)(5a^3 b^8)
C
Which expression is a perfect cube?
B. y^24
Which expression is a sum of cubes?
A. -27a^3 b^6+8a^9 b^12
Which expression is a sum of cubes?
C. 27x^9+y^6
Which expression is a difference of cubes?
D. 64c^15-d^27
A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored form?
C
What is the cube root of b^27
B. b^9
What is the factored form of x^3-1
C
Which number is a perfect cube?
D. 343
What is the factored form of x^12 y^18+1
B
What is the cube root of 27a^12
D. 3a^4
What is the factored form of a^2 - 121?
B. (a - 11)(a + 11)
Which polynomial is factored completely?
C. 3x(9x^2+1)
Which statement about 6x^2 + 7x - 10 is true?
A. One of the factors is (x + 2).
What is the factored form of 2x3^ + 4x^2 - x?
D. x(2x^2+4x-1)
What is the completely factored form of x^3 - 64x?
C. x(x - 8)(x + 8)
Which value of a would make the following expression completely factored?
12
A student factors 3x^2 - 12 to the following.
3(x^2-4)
Which statement about 3(x^2 - 4) is true
B. The expression is equivalent, but it is not completely factored.
What is the completely factored form of 3x^5 - 7x^4 + 6x^2 - 14x?
C
What is the completely factored form of x^4 + 8x^2 - 9?
B
If a polynomial has four terms, 3x^3 + 5x + 6x^2 + 10, which factoring method can be considered?
C. factor by grouping
What is the quotient of (x^3+3x^2-4x-12)divided(x^2+5x+6)
x-2
The quotient of (x^4 + 5x^3 - 3x - 15) and a polynomial is (x^3 - 3). What is the polynomial?
C. x + 5
What is the quotient of the following division problem?
A. x + 2
What is the remainder of the following division problem?
B. 1
What is the quotient (x^3 - 3x^2 + 5x - 3) Ã· (x - 1)
D. x^2 - 2x + 3
What is the quotient (3x^4 - 4x^2 + 8x - 1) Ã· (x - 2)?
C. 3x3 + 6x2 + 8x + 24 + 47/x-2
The volume of a rectangular prism is (x^3 - 3x^2 + 5x - 3), and the area of its base is (x^2 - 2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
A
The long division below shows the first term of the quotient. Which polynomial should be subtracted from the dividend first?
C. x^3 + 2x^2
What is the quotient (x^3 + 8) Ã· (x + 2)?
B. x2 - 2x + 4
What is the quotient (125 - 8x^3) Ã· (25 + 10x + 4x^2)?
A. -2x + 5
Which expression is equivalent to (2x^2)(3x^3)(4x)^2?
C. 96^7
Which expression is equivalent to (-7m^4+15m^3-12m^2)+3m^5-12m^4-7m^3)/m-6
C. 3m^4-m^3-2m^2
Which expression is equivalent to (x+1)^2-9/x+4
A. x-2
Which expression is equivalent to (5x^3)(2x)^3
C. 40x^6
Which expression is equivalent to (3m)(4m)^2?
C. 48m^3
Which expression is equivalent to x+2+[4x- x^2+6x+8/x+4
A. 4x
Which expression is equivalent to 9x^5+3x(4x^4-3x^2)^2
D. 48^9-72x^7+36x^5
What is the correct order of operations for simplifying the expression 2 - 3x + 5 + 7(y - 5x)2 + x?
D. square the binomial, distribute 7 inside the parentheses, and then combine like terms
What is the first step in simplifying the expression 11x-2-3(1-7x)^2 divided (x-1)
A. square the binomial
Which expression is equivalent to 7a^3(6a^2+a)^2 -4a^6
A. 252a^7+80a^6+7a^5
Anja divides (8x^3 - 36x^2 + 54x - 27) by (2x - 3) as shown below. What error does Anja make?
C. She makes a multiplication error.
Subtract 15mn - 22m +2n from 14mn - 12m +7n.
A. -mn + 10m + 5n
The area of a rectangle is (x^3 - 5x^2 + 3x - 15), and the width of the rectangle is (x^2 + 3). If area = length Ã— width, what is the length of the rectangle?
D. x - 5
Which expression shows the sum of the polynomials with like terms grouped together?
(8x+3z-8z^2)+(4y-5z)
D.
The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Which expression represents the volume of the following rectangular prism?
C
Which statement about 4x^2 + 19x - 5 is true?
D. One of the factors is (x + 5).
Which expression is equivalent to 9x - (x - 8)(x + 1) + 10x?
B.
Which polynomial is in standard form?
B. -16x^2-9x+12
Which expression is equivalent to 4 - (2m - 3)?
B. 4 - 2m + 3
What is the quotient (2x^4 - 3x^3 - 3x^2 + 7x - 3) Ã· (x2 - 2x + 1)?
D. 2x^2 + x - 3
Which statement best describes the polynomial?
6-8y+14y^7+16y^8
C. It is not in standard form because the exponents are not in order from highest to lowest.
Which expression is equivalent to (4x^3 y^5)(3x^5 y)^2
B
Which expression is equivalent to 16^3?
C. 2^12
Which expression is equivalent to 5r^6 t^4 (4r^3 s^2 t^4/ 2r^4 st^6)
B
The length of a rectangular field is represented by the expression 14x-3x^2 The width of the field is represented by the expression 5x-7x^2+7y. How much greater is the length of the field than the width?
A
Which monomial function, y = ax^n, is described by the following statements?
As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.
D. even monomial function with negative a
Which of the following could be the graph of y = x^n where n is even?
C
Which function is symmetric with respect to the y axis?
B. y=3x^6
Which function is symmetric with respect to the origin?
B. y=x^9
What function is graphed below?
C. y=-6x^5
Which monomial function is described by the following statements?
As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.
B. odd monomial function with positive a
Which is the graph of an even monomial function?
A
Which is an even monomial function?
D. y=-x^10
The formula for the volume of a cube is V(s) = s^3 where s is the side length of the cube. In which quadrant(s) is the graph of the function V(s)?
A. quadrant I
Which monomial function has a minimum value?
A. y=5x^10
Which is an odd monomial function?
A. y=2x^3
Which monomial function has a maximum value?
B. y=-5x^4
What function is graphed below?
A. -x^2
What function is graphed below?
y=5x^5
How many turning points are in the graph of the polynomial function?
B. 5 turning points
Which of the following describes the polynomial function?
B. The function has an odd degree.
What are the possible degrees for the polynomial function?
D. odd degrees of 5 or greater
Which graph shows a polynomial function of an even degree?
A.
Given that the values in the table represent the graph of a continuous function, y has at least how many zeros?
5
How many turning points are in the graph of the polynomial function?
C. 4 turning points
What is the end behavior of the polynomial function?
C.
Which graph shows a polynomial function of an odd degree?
C.
Which graph shows a polynomial function with a positive leading coefficient?
B.
Which statement describes how the graph of the given polynomial would change if the term 2x5 is added?
y = 8x4 - 2x3 + 5
B. The ends of the graph will extend in opposite directions.
What is the end behavior of the graph of the polynomial function y = 7x^12 - 3x^8 - 9x^4?
D.
How many turning points can a polynomial with a degree of 7 have?
A. 6 turning points
What is the end behavior of the graph of the polynomial function y = 10x^9 - 4x?
C.
Which graph shows a polynomial function with a negative leading coefficient?
A.
What is the end behavior of the polynomial function?
D.
What are the solutions of the quadratic equation (x - 8)^2 - 13(x - 8) + 30 = 0? Use u substitution to solve.
D. x = 11 and x = 18
What is the solution of the equation (x - 5)^2 + 3(x - 5) + 9 = 0? Use u substitution and the quadratic formula to solve.
B.
Which quadratic equation is equivalent to (x - 4)^2 - (x - 4) - 6 = 0?
D. u^2 - u - 6 = 0 where u = (x - 4)
What are the solutions of the equation x^4 - 5x^2 - 14 = 0? Use factoring to solve.
D
What substitution should be used to rewrite 4x^12 - 5x^6 - 14 = 0 as a quadratic equation?
C. u = x^6
Which quadratic equation is equivalent to (x2 - 1)^2 - 11(x^2 - 1) + 24 = 0?
A. u^2 - 11u + 24 = 0 where u = (x^2 - 1)
What are the solutions of the equation x^6 - 9x^3 + 8 = 0? Use u substitution to solve.
B. x = 1 and x = 2
Which equation is quadratic in form?
C. 7x^6 + 36x^3 + 5 = 0
What are the solutions of the equation x^6 + 6x^3 + 5 = 0? Use factoring to solve.
B.
Which quadratic equation is equivalent to (x + 2)^2 + 5(x + 2) - 6 = 0?
C. u^2 + 5u - 6 = 0 where u = (x + 2)
What substitution should be used to rewrite 16(x^3 + 1)^2 - 22(x^3 + 1) - 3 = 0 as a quadratic equation?
B. u = (x^3 + 1)
What are the solutions of the quadratic equation (x - 8)^2 - 13(x - 8) + 30 = 0? Use u substitution to solve.
D. x = 11 and x = 18
What are the solutions of the equation x^4 + 95x^2 - 500 = 0? Use factoring to solve.
C.
What are the solutions of the equation x^4 + 3x^2 + 2 = 0? Use u substitution to solve.
B
Which system of equations can be used to find the roots of the equation 4x^2=x^3+2x
D.
Let a and b be real numbers where a mc021-1.jpg b mc021-2.jpg 0. Which of the following functions could represent the graph below?
B. f(x) = (x - a)^2(x - b)^4
Which statement describes the graph of f(x) = -4x^3 - 28x^2 - 32x + 64?
D. The graph touches the x axis at x = -4 and crosses the x axis at x = 1.
What are the roots of the polynomial equation x^4+x^2=4x^3-12x+12? Use a graphing calculator and a system of equations. Round noninteger roots to the nearest hundredth.
C. -1.73, 1.73
Which equation can be solved by using this system of equations?
{y=3x^3-7x^2+5
{y=7x^4+2x
B. 3x^3-7x^2+5=7x^4+2x
Which equation can be solved by using this system of equations?
{y=3x^5-5x^3+2x^2-10x+4
{y=4x^4+6x^3-11
B.
At which root does the graph of f(x) = (x - 5)^3(x + 2)^2 touch the x axis?
B. -2
What are the roots of the polynomial equation x^3-6x=3x^2-8? Use a graphing calculator and a system of equations.
D. -2, 1, 4
Arlana graphed the system of equations that can be used to solve x^3-5x^2+2=-x^3+17x
What are the roots of the polynomial equation? Round noninteger roots to the nearest hundredth.
D. -2, 0.11, 4.39
Which statement describes the graph of f(x) = 4x^7 + 40x^6 + 100x^5?
C. The graph crosses the x axis at x = 0 and touches the x axis at x = -5.
What are the roots of the polynomial equation x^3-7x=6x-12? Use a graphing calculator and a system of equations.
B. -4, 1, 3
Arlana graphed the system of equations that can be used to solve x^3-5x^2+2=-x^3+17x
What are the roots of the polynomial equation? Round noninteger roots to the nearest hundredth.
D. -2, 0.11, 4.39
Which system of equations can be used to find the roots of the equation 4x^2=x^3+2x
D.
Sandra graphed the system of equations that can be used to solve x^3-2x^2-11x+12=x^3-13x-12
C. -3, 4
A rectangular prism with a volume of 400 cubic centimeters has the dimensions x + 1 centimeters, 2x centimeters, and x + 6 centimeters. The equation 2x^3+14x^2+12x=400 can be used to find x. What is the length of the longest side? Use a graphing calculator and a system of equations to find the answer.
D. 10 centimeters
The polynomial equation x^6-16x^2=4x^4-64 has complex roots Â±2i. What are the other roots? Use a graphing calculator and a system of equations.
B.-2, 2
A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation x^3+6x^2-27x=140 can be used to find x
What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer.
B. The length is 5 inches, the width is 2 inches, and the height is 14 inches.
A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation 2x^3+8x^2=450 can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.
B. 5 inches
What are the roots of the polynomial equation x^4+x^2=4x^3-12x+12? Use a graphing calculator and a system of equations. Round noninteger roots to the nearest hundredth.
C. -1.73, 1.73
Which equation can be solved by using this system of equations?
{y=3x^5-5x^3+2x^2-10x+4
{y=4x^4+6x^3-11
B
The graph of this system of equations is used to solve 4x^2-3x+6=2x^4-9x^3+2x
What represents the solution set?
D. x coordinates of the intersection points
A function is a sixth-degree polynomial function. How many turning points can the graph of the function have?
B. 5 or less
What are the solutions of the equation (x + 2)^2 - 2(x + 2) - 15 = 0? Use u substitution to solve.
B. x = -5 and x = 3
What are the solutions of the equation x^4 - 5x^2 - 36 = 0? Use factoring to solve.
B. x = Â±2i and x = Â±3
Which expression is a possible leading term for the polynomial function graphed below?
D. 22x^9
Which statement best describes the equation x^5 + x^3 - 14 = 0?
C. The equation is not quadratic in form because it cannot be rewritten as a second-degree polynomial.
What are the roots of the polynomial equation x^3-5x+5=2x^2-5? Use a graphing calculator and a system of equations. Round noninteger roots to the nearest hundredth.
C. -2.24, 2, 2.24
What are the solutions of the equation (x + 2)^2 + 12(x + 2) - 14 = 0? Use u substitution and the quadratic formula to solve.
A.
What are the roots of the polynomial equation x^4+x^3=4x^2+4x? Use a graphing calculator and a system of equations.
A. -2, -1, 0, 2
The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly's reasoning is correct or incorrect?
A. She is incorrect because systems may have only complex solutions which are not visible on a graph.
Which statement best compares the graphs of y = -3x^n and y = 3x^n?
B. The graph of y=-3x^n is the reflection of the graph of y=3x^n about the x axis.
The president of a company creates a graph of the price of the company's stock over one year. He describes the graph as follows:
â€¢ The price of the stock rose to about $17 before falling to about $4.
â€¢ There have only been two periods during which the price of the stock decreased.
â€¢ The price of the stock is expected to increase in the long run.
Which graph correctly shows the price of the stock?
D
A polynomial function has a root of -7 with multiplicity 2, a root of -1 with multiplicity 1, a root of 2 with multiplicity 4, and a root of 4 with multiplicity 1. If the function has a positive leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (-oo, -7).
Which best describes the end behavior of y=7x^2?
C. As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
A rectangular prism with a volume of 400 cubic centimeters has the dimensions x + 1 centimeters, 2x centimeters, and x + 6 centimeters. The equation 2x^3+14x^2+12x=400 can be used to find x. What is the length of the longest side? Use a graphing calculator and a system of equations to find the answer.
D. 10 centimeters
Dylan uses the expressions (x^2 - 2x + 8) and (2x^2 + 5x - 7) to represent the length and width of his bedroom. Which expression represents the area (lw) of Dylan's room?
C.
Which expression is a possible leading term for the polynomial function graphed below?
D. 22x^9
Which of the following could be the graph of y = -x^n where n is odd?
A.
The graph of this system of equations is used to solve 4x^2-3x+6=2x^4-9x^3+2x
{y=4x^2-3x+6
{y=2x^4-9x^3+2x
D. x coordinates of the intersection points
Which expression is equivalent to (2g^3+4)^2
B.
Subtract 15mn - 22m +2n from 14mn - 12m +7n.
A. -mn + 10m + 5n
Which statement best compares the graphs of y = -3x^n and y = 3x^n?
b. The graph of y=-3x^n is the reflection of the graph of y=3x^n about the x axis.
The president of a company creates a graph of the price of the company's stock over one year. He describes the graph as follows:
â€¢ The price of the stock rose to about $17 before falling to about $4.
â€¢ There have only been two periods during which the price of the stock decreased.
â€¢ The price of the stock is expected to increase in the long run.
Which graph correctly shows the price of the stock?
D.
What are the solutions of the equation (x + 2)^2 - 2(x + 2) - 15 = 0? Use u substitution to solve.
b. x = -5 and x = 3
A function is a sixth-degree polynomial function. How many turning points can the graph of the function have?
B. 5 or less
Which statement best describes how to determine whether f(x) = x^2 - x + 8 is an even function
b. Determine whether (-x)^2 - (-x) + 8 is equivalent to x^2 - x + 8.
Which expression is equivalent to 9x - (x - 8)(x + 1) + 10x?
b.
What is the remainder when (3x^3 - 2x^2 + 4x - 3) is divided by (x^2 + 3x + 3)?
D. 28x + 30
Which expression is equivalent to 15a^8 b^4/5a^4 b?
B. 3a^4 b^3
If the discriminant of a quadratic equation is 4, which statement describes the roots?
B. There are two real roots.
Which polynomial is in standard form?
B. -16x^2-9x+12
Sharon is jumping from an 18-foot diving board with an initial upward velocity of 4 ft/s. When Susan jumps, Megan throws a beach ball up to Susan with an initial upward velocity of 16 ft/s from a height 5 feet off the ground. To the nearest hundredth of a second, how long after she jumps does the ball reach Sharon?
C. 1.08 seconds
The area of a rectangle is (x^3 - 5x^2 + 3x - 15), and the width of the rectangle is (x^2 + 3). If area = length Ã— width, what is the length of the rectangle?
D. x-15
Which term, when added to the given polynomial, will change the end behavior of the graph?
y = 14x^8 - 6x^5 - 2x^4 - 10
A. -6x^9
Which graph represents an even function?
D.
Which expression is equivalent to (4x^3 y^5)(3x^5 y)^2?
B.
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ALGEBRA
the terminal side of Î¸ lies on the given line in the specified quadrant. Find the values of the six trigonometric functions of Î¸ by finding a point on the line. Line 4x + 3y = 0 Quadrant IV
ALGEBRA
In slow-pitch softball, the ball is pitched in an underhand motion. A batter in a softball game is pitched a ball that has an initial height of 2 feet above the ground and an initial vertical velocity of 35 feet per second. a. Write an equation for the height h (in feet) of the ball as a function of the time t (in seconds) after it is pitched. b. The batter hits the ball when it is 2.5 feet above the ground. How long after the ball is pitched is the ball hit? Round your answer to the nearest tenth of a second.
PRECALCULUS
Rudy leaves home and walks to school at a steady pace of 2 ft/s. His sister Rosa leaves at the same time but rides a bike at a speed of 8 ft/s. On a number line, let x = 0 represent their home and t = 0 the time since they left the house. Suppose the school is 5000 feet to the east of Rudy and Rosa's home. On the way home, Rudy rides the bike at 8 ft/s and Rosa walks at 2 ft/s. Let $x_{A}$ represent Rudy's position and $x_{B}$ represent Rosa's position compared to their home at time t in seconds. Write expressions for $x_{A}$ and $x_{B}.$
COLLEGE ALGEBRA
For a certain bowling league, a beginning bowler computes her handicap by taking 90% of the difference between 220 and her average score in league play. Determine the average scores that would produce a handicap of 72 or less. Also assume that a negative handicap is not possible in this league.
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