Algebra 2
Solve
-1/16
Find AB,
-22 74
Find 49° in radians.
0.86 radians
Write A. 1 - 4i B. 1 + 4i C. 3i D. -3i
1 - 4i
Multiply
180 sqr 10
Which sample size will produce a margin of error of ±6.3%?
252
Evalute 9!
362,880
Find the missing term of the arithmetic sequence 25, ___, 49, ....
37
Write
3^13^ sqr x^7
Use summation notation to write the arithmetic series -3.9 + (-1.9) + 0.1 + ... for six terms.
6 x=1 -5.9 +2n
Which line, having the given slope and passing through the given point, represents a direct variation?
C.
Which system of equations is graphed below?
C.
Describe the pattern 16, -8, 4, -2, 1, ....
Divide the previous number by -2.
The capacity of the gas tank in a car is 16.5 gallons. The car uses 10.5 gallons to travel 178.5 miles. After driving 85 more miles, only 1 gallon of gasoline remains in the tank. Which linear equation and graph model the amount of gas g left in the tank after driving m miles?
Graph A
Solve and graph 5x - 2 ≤ 8.
Graph B
Which is the graph of 0.4x + 0.1y ≥ 1?
Graph B
Factor 18ab + 9ax -4b - 2x.
(9a - 2)(2b + x)
Identify the vertex and y-intercept of the graph of f(x) = -4(x + 3)2 + 7.
(-3, 7), y-intercept -29
Solve the system of equations. x = 3y + 2z 2x + 3y + 2z = 3 -x + y - z = 6
(1, 3, -4)
Factor 4x2 + 5x - 21.
(4x - 7)(x + 3)
Determine the coordinates of the x-intercept of 3x - 4y = 24.
(8, 0)
Find the annual percent increase or decrease that y = 0.35(2.3)x models.
+130%
Find
-3 5 9 0
Ten candidates are running for three seats in the student government. You may vote for as many as three candidates. In how many ways can you vote for three or fewer candidates?
176 ways
The diagram shows one solution to the equation 3 - sin θ = 5 sin θ. Find the complete solution of the equation.
30° + n • 360°, 150° + n • 360°
The table gives data about municipal waste collected and recycled by type. Find P(paper | not recycled).
31.7%
Find f(-5) if f(x) = -8x - 1.
39
Graph the figure and its image after the given rotation.
4
Use the properties of logarithms to evaluate log4 256.
4
A summer reading list has 20 books on it. In how many ways can you choose four books to read?
4,845 ways
After taking 7 quizzes, your average is 75 out of 100. What must your average score be on the next five quizzes to increase your average to 80?
87
Complete the square: x2 + 6x + ____ .
9
Evaluate the series 3 - 12 + 48 - 192 + ... to the seventh term. Round your answer to the nearest hundredth, if necessary.
9831
Evaluate the area under g(x) = -x2 - 3x + 7 for -4 ≤ x ≤ 1.
C. 35.83
A rubber ball dropped on a hard surface takes a sequence of bounces,
C. 54 24/125
Graph
D. vertex (-3,-1) x= -3
Name the property of real numbers illustrated by the equation 3(2x - 14) = 6x - 42.
Distributive Property
The vertex of f(x) = 2(x-2)2 +10 is (-2, 10).
False
Find the inverse of f(x) = 3x2. Is the inverse a function?
x/3 no
Solve w + 12 = -6 - 2w.
w = -6
Match the given graph with its corresponding equation.
x + 4y = -4
Which polynomial is NOT a factor of 3x4 - 16x3 - 3x2 + 36x + 20?
x - 1
Which polynomial is NOT a factor of 3x4 - 10x3 - 29x2 + 16x + 20?
x - 2
Simplify
x -1/2 y 3/4
Write (x - 2)(x + 9) as a polynomial in standard form.
x2 + 7x - 18
Divide (5x3 - 6 - 5x) ÷ (10 + 5x) using synthetic division.
x2 - 2x + 3, R -36
Let f(x) = 4 - x2 and g(x) = 2 - x. Find f(x) • g(x).
x3 - 2x2 - 4x + 8
What are the dimensions of the matrix?
5 × 4
Graph
C.
Multiply
xy/2 0 0
Rationalize the denominator of
-5 -2 sqr 6
Simplify C. -500i
B.
Solve x2 - 10x + 29 = 0.
No Solution
Log4 64 = 3
True
Solve
no solution
Graph y = -x2 - 1.
A.
What is the domain and range of this function? Domain: all real numbers; Range: y ≥ -4 Domain: -2 ≤ x ≤ 2; Range: y ≥ -4 Domain: x ≥ -4; Range: all real numbers Domain: x ≥ 0; Range y ≥ 0
Domain: all real numbers; Range: y ≥ -4
An annual rate of change is -10%. The corresponding growth or decay factor is 0.10.
False
Reciprocal functions cannot be evaluated in radians.
False
The expression 2y - 5x + 3y + 2x evaluated for x = 3 and y = 2 is -11.
False
The expression | 2 + 4n | - 4 = 14 produces the answers n = 4 and n = 5.
False
The fifth root of 12 is equal to the fifth root of 7 times the fifth root of 5.
False
Two matrices can be subtracted if they have an equal number of rows, regardless of how many columns they have.
False
Two matrices with dimensions 3x1 and 2x4 will produce a product matrix with dimensions 3x4 when multiplied.
False
What is the graph of
Graph D
What point has coordinates of (-5, 4)?
Point N
The table shows the number of hybrid cottonwood trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of cottonwoods planted in 1998.
T(x) = 0.1x3 + 0.3x2 + 0.3x + 0.1; 172.8 thousand trees
A car salesman receives $50 for each car sale plus 2% of the purchase price. How much must a car sell for in order for the salesperson to earn at least $500?
The car must sell for at least $22,500.
If f(x) = 3x + 7 and g(x) = 5x - 2 then (f+g)(x) = 8x + 5.
True
Probability over a continuous range of events is cumulative probability.
True
The amplitude of y = 3 sin(2x) is 3.
True
This is the graph of y < |x - 3|.
True
When finding the maximum value for an objective function, it is necessary to check the vertices of the graph.
True
Find
[6 -34]
Write and evaluate a sum to approximate the area under y = (x - 4)2 - 1 for the domain 0 ≤ x ≤ 2. a. Use inscribed rectangles 0.5 units wide. b. Use circumscribed rectangles 0.5 units wide.
a. 13.75 units2; b. 19.75 units2
Graph Y=-pi/4 cot ( x-pi/4)
about 112 women
Find the amplitude and period of y = -5 sin (5x).
amplitude=5,period=2/5
Use substitution to solve the system of equations given below.
(-10, -12)
Evaluate the series
-5.81
Find all the real square roots of 0.0036.
0.06 and -0.06
Determine whether
1/10 -3/10 -1/5 -2/5
Use inscribed rectangles to approximate the area under g(x) = -0.5x2 + 7 for -3 ≤ x ≤ 0 and rectangle width 0.5.
15.3 units2
The sequence -14, -9, -4, 1, ... , 41 has 12 terms. Evaluate the related series.
162
Find
2
Simplify 2i(5 - i).
2 + 10i
How many combinations of four can you make from the set? {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
210 combinations
Multiply
22 + 8 sqr 6
Factor 3q3 - 81.
3(q - 3)(q2 + 3q + 9)
In ΔABC, b = 1, c = 3 ma= 138
3.8
Find 8P3.
336
Solve the question below.
4
In ΔABC, b = 4, c = 1, and ma =118
4.56
Use the frequency table to find P(2 or 3 children).
42%
The value of y varies directly with x. If y is 24 when x is 72, what is the value of y when x is 144?
48
Find
4ax^2 /3by
Multiply
5
Ms. Chin collected data about how long students in two of her classes spent doing homework. This table shows the result. Suppose a student from her third or fourth period class is selected at random.
5/23
Find the real-number root of
5/7
A linear model for the situation below passes through the origin. A manufacturer can produce 4,200 gears in 8 hours. How many gears can be made in 1 hour?
525
What is the maximum for the objective function for this graph?
560
pi/3 radians in degrees
60°
A fifth-degree polynomial equation with rational coefficients has the roots 2, -7i, and -7 + i. Find the remaining roots.
7i, -7 - i
Solve |5x - 3| ≤ 3.
b
Graph f ( x ) = 2 x + 1 + 3 as a translation of its parent function.
backwards L high
Solve
x = 3
The points in the table have been graphed in the scatter plot below. What is the best equation for the trend line, and the value of y when x is 16?
y = 1.25x + 1; y = 21
Identify a31 in the matrix.
10
Solve the question below.
29/4
Evaluate the infinite series
It does not have a sum.
The point-slope formula of a line that passes through the point (8,5) and has a slope of ¼ is y = 1/4x + 3.
false
Evaluate the series 3 + 9 + 15 + 21 + 27 + ... to the 16th term.
128
Simplify
81
If a group of dogs has an average weight of 40 pounds and a standard deviation of 15.2 pounds, 16% of the dogs will weigh more than 55.2 pounds.
True
3x2 -5x - 2 factors to (3x+1)(x-2).
True
4x2 - 36 = 0 has a solution of x = +/- 3.
True
Which of the following describes the system of equations 2x - y + 4 = 0 and 4x - 2y + 7 = 0?
inconsistent
Is the sequence -9.9, -13, -16, -19.2, ... arithmetic? If so, identify the common difference.
no
Solve the system of equations by using substitution. -2x + 3y = 7 4x - 6y = 8
no solution
Simplify
1/ 4 sqr x^7
Which statement about 5y = 2x is true?
A.
Which system of inequalities has this graph?
A.
For 3x9 -7x6 + 4x3 + 15 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.
D.
Simplify the expression |-3| - |-5|.
-2
Use matrices A, B, and C. Find B-C if possible.
-2 -7 14 -4 7 0
Graph y= 2.5 tan 4x/5
/ closer together
Use synthetic division and the Remainder Theorem to find P(-3) if P(x) = x4 + 19x3 + 108x2 + 236x + 176.
8
-25 has no real 4th root.
True
15x3 - 10x2 + 3x -2 factors to (5x2 + 1) (3x - 2).
True
The expression | -2 | - |-7 | simplifies to 5.
false
If m varies directly as the square root of y, inversely as p2, and directly as n, what happens to m when y is quadrupled, p is tripled, and n is multiplied by 5?
multiply 10/9
What is the GCF of 3n3 + 5np2 + n2p2?
n
Write an explicit formula for the sequence
n+1/n^2+3
Use substitution to solve the system of equations given below.
no solution
Find
-70 44 70 -24 71 -73 -71 -71 -35
Solve
3/2
Solve 6x2 = 48. If necessary, round your answer to the nearest hundredth.
A.
Use elimination to solve the system given below. 5x - 2y = 25 5x + 3y = 5
A.
Use elimination to solve the system of equations given by -7x + 3y = 14 and 7x - 2y = -11.
A.
Is the sequence
A. yes .5
Describe the pattern
Add 1 to the numerator and 2 to the denominator of the previous number.
Make a box-and-whisker plot for the set of values. 5.2, 9.2, 5.2, 3.2, 3.2, 7.2, 6.2, 8.2, 5.2, 4.2, 5.2, 6.2, 9.2, 9.2, 8.2
B.
The sum of a geometric series containing five terms, a common ratio of 3, and a first term of 1/2 is 62.5.
False
A dependent system of equations will have infinitely many answers.
True
Find the zeros of the function. State the multiplicity of multiple zeros. y = (x - 4)2
x = 4 multiplicity 2
Use the Law of Sines to solve for a to the nearest tenth.
38.1
Determine the coordinates of the y-intercept of 2x + 4y = 8.
(0, 2)
Find the next three terms in the sequence 1, 2, 4, 8, ....
16, 32, 64
Find the arithmetic mean an of the terms
19/40
Evaluate the infinite geometric series 1.9 + 0.19 + 0.019 + ....
19/9
The expression 200 - 16t2 models the height in feet of an object that falls from an initial height of 200 feet t seconds after being dropped. Find the height of the object after 0.75 seconds.
191 feet
Find the missing terms of the geometric sequence 480, ___, ___, ___, 12.288, .... (Hint: The geometric mean of the first and fifth terms is the third term.)
192, 76.8, 30.72
Write an equation of the cosine function with amplitude 2 and period 8π.
2 cos 1/4 x
A class of 30 students has 11 honor students and 13 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is known that the student is not an honor student.
C. 10/19
Evaluate the series
C. 5461/ 16,384
Graph y = (x - 3)2 + 1.
D.
Solve 9x2 + 6x + 1 = 64.
D.
Which expression completes the equation to make it an identity? cos+ sin + cos / 1+ sin
cos θ
Simplify cot/cos
csc θ
Solve
f = 0, g = -4, h = 9 or -9
Solve x2 - 4x - 5 = 0 by factoring.
x = -1, x = 5
Solve x3 + 4x2 - x - 4 = 0.
x = -4, x = -1, x = 1
Solve |x + 8| ≤ 5.
-13 ≤ x ≤ -3
Find
-14 -1 3 7
Evaluate. 9!/6!
504
Solve the question below.
505
Evaluate e4.
54.5982
y = -4* 2x is a reflection of y = -1/4* 2x.
False
Which is the graph of
Graph C
Find the equation of the line that passes through the point (-7, 2) and has a slope m = -5 in point-slope form.
y - 2 = -5(x + 7)
Find the exact coordinates of the point at which the terminal side of -135° intersects the unit circle.
- sqr 2 / 2
Find the radian measures of the angles whose sine is -0.8. Round to the nearest hundredth.
-0.93 + 2πn and 4.07 + 2πn
Use the graph to find the value of y = sin θ for θ = 270°.
-1
Evaluate sec 3.
-1.0101
Find the perimeter of the figure shown below. Simplify the answer. 8a + 2b 10a + 4b 10a + 2b 10a - 2b
10a + 2b
Write 11pi/18 radians in degrees
110°
The selling price of x number of a certain stereo can be modeled by the function R ( x ) = 160 x . The total cost of making x stereos is C ( x ) = 71 x - 0.02 x 2. What is the percent markup for 31 stereos?
127%
Find
13 -9 -12 -1 -6 18 1 -1 2
Solve |5x - 7| = 3.
2, 4/5
Determine the number of standard deviations which include all data values listed for the situation.The mean time employees take of a company to commute to work is 40.75 minutes; the standard deviation is 12.9 minutes.42 min, 45 min, 53 min, 34 min, 12 min, 48 min, 52 min, 24 min, 56 min, 47 min, 28 min, 48 min
3 standard deviations
What are the dimensions of the matrix?
3 × 2
Simplify
3|x5|y4
A quadratic equation factored to 0 = (x-4)(x+3) would have solutions of x = -4 and x = 3.
False
A situation may not be described by more than one sample space.
False
If x is at the 63rd percentile, then 37% of the data are less than or equal to x.
False
If y varies inversely with x and y = 6 when x = 9, then y = 96/x.
False
17 1/3 is the same as the cube root of 17.
True
A box-and-whisker plot is a method of displaying data that uses quartiles to form the center box and the minimum and maximum values to form the whiskers.
True
A complex fraction is a fraction that has a fraction in either its numerator or denominator, or in both its numerator and denominator.
True
Factor 8a4b - 3ab2c.
ab(8a3 - 3bc)
There are 135 girls in the junior class at West High School. Of these 135 girls, 16 are on the volleyball team (V), 22 are on the softball team (S), and 8 are on both the volleyball and softball team. One student is selected at random. Find the probability that the student plays on the softball team but not the volleyball team.
about 10%
The table gives data about municipal waste collected and recycled by type. Find P(recycled | glass).
about 6.7%
Graph y = 3 x + 1 as a translation of its parent function.
backwards L high
Graph y = 4x - 3 as a translation of its parent function.
backwards L low
A certain box of cereal should have a net weight that is within 1.5 grams of 510. After the first phase of production, the weight of the cereal is 308 grams. By how much should the weight of the cereal increase to remain within the specified weight?
between 200.5 and 203.5 grams
Use Pascal's Triangle to expand (s - v)5.
s5 - 5s4v + 10s3v2 - 10s2v3 + 5sv4 - v5
In which quadrant does the terminal side of a 117° angle lie?
second quadrant
Simplify sin2 θ(1 - csc2 θ).
sin2 θ - 1
Solve x2 - 6x = 0 by graphing or by factoring.
x = 0, x = 6
Find the roots of x3 - x2 + 2 = 0.
x = 1 + i, x = 1 - i, x = -1
Find the zeros of y = (x - 1)(x + 2).
x = 1, x = -2
Solve
x = 6
Assume red and green are equally likely occurrences. What is the probability that you will get zero green lights in a row of five lights?
1/32
The lengths of a certain species of fish were found to be normally distributed. The mean length is 79 cm with a standard deviation of 10 cm. In a school of 310 of these fish, about how many would be longer than 69 cm?
260 fish
Suppose that x and y vary inversely. Write a function rule for the function that x = 4 when y = 7.
28/x
4n3 + 5n2 + 6n + 15 factors to (3n2 + 2) (3n + 5).
False
4x3y4 is a 4th degree monomial.
False
Given log 5 = P and log 2 = Q , find log 10.
P + Q
The table shows the number of oak trees planted in tree farms in Oregon since 1987. Find a cubic function to model the data and use it to estimate the number of oaks planted in 1998.
T(x) = 0.2x3 + 0.7x2 + 0.2x + 0.1; 353.2 thousand trees
Which property was used to rewrite log
power property
Solve x3 + 5x2 - 9x - 45 = 0.
x = -5, x = -3, x = 3
A continuously compounded account starts with $2500 in principal. The annual interest rate is 11.3%. What is the balance after 15 years?
$13,616.61
Find 311° in radians.
5.43 radians
This statement simplifies to 16a2.
True
How much money invested at 5% compounded continuously for 2 years will yield $1150?
$1040.56
Use elimination to solve the system of equations given by 3x - 2y = 10 and 5x + 2y = 6.
(2, -2)
Factor 5r2 + 13r - 6.
(5r - 2)(r + 3)
The roots of a certain polynomial are -2/5, -6 and 4/3. What might the linear factors of the polynomial be?
(5x + 2)(x + 6)(3x - 4)
Evaluate sec 131°.
-1.52
Solve
13/3 2/3
On a baseball field, the pitcher's mound is 60.5 feet from home plate. During practice, a batter hits a ball 265 feet at an angle of 35° to the right of the pitcher's mound. An outfielder catches the ball and throws it to the pitcher. How far does the outfielder throw the ball?
218.2 ft
Simplify
2a3/3b
For the sum
6 terms, 25, 0; 75
Find the degree measures of the angles whose tangent is sqr 3
60° + n • 180°
Find the area of the triangle. Round your answer to the nearest tenth, if necessary.
67.3 in.2
Find the angles in the triangle when a = 13, b = 12, and c = 11. Round your answers to the nearest tenth.
68 59 52
Solve -9x + 6 + 5x2 = 0 using the Quadratic Formula.
B.
If you use the elimination method to solve the system of equations 3x - 4y = 9 and 2x + 3y = 7, which of the following would be the best method? Method I: Multiply both sides of the first equation by 2, and multiply both sides of the second equation by 3. Then add the two equations. Method II: Multiply both sides of the first equation by 3, and multiply both sides of the second equation by 4. Then add the two equations.
Method II
A biologist took a count of the number of migrating waterfowl at a particular lake and recounted the lake's population of waterfowl for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of waterfowl at the lake on week 8.
P(x)= 41x2 - 162x + 433; 1761 waterfowl
A biologist took a count of the number of migrating geese in a state park and recounted the park's population of geese for each of the next six weeks. a. Find a quadratic function that models the data shown as a function of x, the number of weeks. b. Use the model to estimate the number of geese at the lake on week 8.
P(x)= 42x2 - 186x + 762; 1962 geese
A frequency table is a list of the outcomes in a sample space and the number of times each outcome occurs.
True
A multiple zero has a multiplicity equal to the number of times the zero occurs.
True
Find the mean and standard deviation for the set of values. 25, 19, 5, 21, 18, 22, 17, 10, 7
mean: 16, standard deviation: 6.62
Graph the system of equations to determine whether it has no solution, infinitely many solutions, or one solution. If the system has one solution, name it.
no solution
Is y = (2x)2 + 5x - 7 + 1 linear or quadratic? Identify the quadratic, linear, and constant terms.
quadratic function quadratic term: 4x2 linear term: 5x constant term: -6
Identify the graph of y = 2x2 - 5 and its inverse.
up right
Find the zeros of y = x(x + 5)(x - 8).
x = 0, x = -5, x = 8
Find the zeros of y = (x - 2)(x + 1)(x + 3).
x = 2, x = -1, x = -3
Write the equation of the parabola in vertex form.
y = (x + 1)2 - 3
Write the equation of the parabola in vertex form.T
y = (x - 1)2 - 3
Rewrite y = x2 - 10x + 3 in vertex form. Then find the vertex.
y = (x - 5)2 - 22; (5, -22)
Write y = -3x2 + 12x - 21 in vertex form.
y = -3(x - 2)2 - 9
Write y = -4x2 - 64x - 265 in vertex form.
y = -4(x + 8)2 - 9
Find the equation of the graph.
y = 1.5x
You can use a linear model to represent the relationship between the hours worked h and the money earned m. When h = 0, then m = 0. If a person earned $39 after working 6 hours, how much will the person earn after working 25 hours?
$162.50
Jim's wages vary directly with the numbers of hours he works. For 7 hours, he makes $38.85. How much will he make in 37 hours?
$205.35
The cost of ten different portable MP3 players is shown in the table. What is the mean cost?
$90
Use elimination to solve the system of equations. -x + 2y = 18 x + 8y = -38
(-22, -2)
Which ordered pair is the solution to the given system of equations?
(-3, -4)
What is the vertex of the graph of y = |x| - 6?
(0, -6)
A small fish market sells only tuna and salmon. A tuna costs the fish market $0.75 per pound to buy and $2.53 per pound to clean and package. A salmon costs the fish market $3.00 per pound to buy and $2.75 per pound to clean and package. The fish market makes $2.50 per pound profit for each tuna it sells and $2.80 per pound profit for each salmon it sells. The fish market owner can spend only $159.00 per day to buy fish and $197.34 per day to clean and package the fish. The graph below represents the feasible region for this linear programming model. What are the coordinates of the vertices of the feasible region, and what are the vales of t and s that maximize the objective function?
(0, 0), (0, 53), (71.76, 0), (28, 46); t = 28 and s = 46.
Which point is in the solution set of this system of inequalities?
(0, 4)
Find the values of x and y that maximize the objective function for this graph.
(1, 8)
The objective function for this graph is P = 5x + y. What values of x and y maximize this function?
(1000, 0): The maximum is 5000.
Use elimination to solve the system of equations given by 10x - 40y = 60 and 15x + 40y = -10.
(2, -1)
Solve the system of equations. 2x + y - z = 3 x + y + z = 5 x - 2y + z = 2
(2, 1, 2)
Factor 8ac + 12ad + 10bc + 15bd.
(2c + 3d)(4a + 5b)
Factor 4x2 - 49.
(2x + 7)(2x - 7)
A point (x, y, z) can be used to represent the location of a geographical point in space, where x represents the latitude in degrees, y represents the longitude in degrees, and z represents the elevation in feet above or below sea level. Jerimoth Hill is the highest point of elevation in Rhode Island. It is 812 feet above sea level and lies at about 42° north latitude and 72° west longitude. What ordered triple represents the location of Jerimoth Hill?
(42°, -72°, 812)
Factor 4y2 - 3y - 1.
(4y + 1)(y - 1)
Solve the system of equations by using substitution. y = 2x + 1 3x - y = 4
(5, 11)
Which point lies in the plane represented by the equation 2x + 7y + 3z = 25?
(6, 4, -5)
Factor m3 - 4m2 + 6m - 24.
(m - 4)(m2 + 6)
Factor t2 - 10t + 25.
(t - 5)2
Factor xy - 6 + 2y - 3x.
(x + 2)(y - 3)
An expression for the area of a rectangle is xy - 2x + 3y - 6. Express this area in factored form.
(x + 3)(y - 2)
Factor x2 - 16.
(x + 4)(x - 4)
Factor x2 - 81.
(x + 9)(x - 9)
Factor x2 - 6x + 8.
(x - 4)(x - 2)
Factor 3xy - 2by + 3ax - 2ab.
(y + a)(3x - 2b)
Write the coordinates of the image after a translation 3 units right and 2 units down.
-1 3 -1 -6 -6 -3
Find the inverse of -2 2 -1
-1/2 1 -1/10
Solve
-1/3
What is the slope of the line through the points P(-5, -6) and Q(-12, 5)?
-11/7
Evaluate the infinite geometric series
-12
Which matrix has determinant -7?
-14 -1 7 1
Find the coordinates of the image of
-14 -3 10 14
Find the inverse of the relation. Graph the given relation and its inverse.
-2 1 5 10
Write the coordinates of the image after a dilation three times the original size.
-21 -12
Evaluate 2a - 5b - 3a for a = -2 and b = 5.
-23
Find
-3 9 1 -3 -6 9 -14 0 6
Two matrices with dimensions 2x2 and 2x2 will result in a product matrix with dimensions 2x2 when multiplied.
-32 28
Evaluate -1x + 7y + 4x + 1y for x = 4 and y = -2.
-4
Solve 11c - 2(2c + 1) = 3(c - 6).
-4
Simplify (3 + 3i) - (7 + 6i).
-4 - 3i
Find g(-2) if g(x) = 4x + 3.
-5
Find the coordinates of the image after the reflection in the given line.
-5 6 -1 -3 -9
Solve the question below.
-6
Find the additive inverse of 6 - 3i.
-6 + 3i
Solve for each variable
-6 -1/4
Let f(x) = 3x + 7 and g(x) = 4x - 2. Find (f composited with g) (-6).
-71
Find all the real cube roots of
-8/9
Let f(x) = 3x2 + 10x- 8 and g(x) = x + 4.
-9x + 6, all real numbers x ≠ -4
Solve 5x - 4 = |2x + 1|. Check for extraneous solutions.
...
A graph of a system of three linear equations in three variables is shown below. How many solutions does the system have?
0
Find the slope of the line that passes through (5, -5) and (9, -5).
0
Determine whether
0 -1/3 -1/2 1/6
State the excluded values of a and b in the expression
0 0
Which matrix is the multiplicative inverse of
0 1 -1 -5 5 -4 1 -1 1
What are the coordinates of the image after a rotation of 90°?
0 1 -4 0 -3 1
Find a third-degree polynomial equation with rational coefficients that has the roots 2 and -3 + i.
0 = x3 + 4x2 - 2x - 20
Use the graph to find the value of y = sin θ for θ = 150°.
0.5
For an annual rate of change of -31%, find the corresponding growth or decay factor.
0.69
Find the values of cos θ and sin θ for -25°. Round your answers to the nearest hundredth.
0.91, -0.42
Complete the square: x2 + 2x + ____ .
1
Simplify cos θ sec θ.
1
Simplify cot θ tanθ.
1
Simplify csc θ sin θ.
1
Solve
1
Without graphing, tell how many x-intercepts y= 2x2 + 4x + 2 has.
1 intercept
Which expression completes the equation to make it an identity?
1+csc2 0 / 1-sin 0
The formula for the volume of a sphere is
1.63 in.
Find the opposite and reciprocal of -1.8.
1.8, -5/9
You roll a twelve-sided die with the numbers 1 through 12 on the faces of the die. You roll the die once. Find the theoretical probability P(factor of 12).
1/2
Each person in a group of students was identified by hair color and then asked whether he or she preferred taking classes in the morning, afternoon, or evening. The results are in the table. Find the probability that a student preferred morning classes given that he or she has blonde hair.
1/3 .33333333
The expression 200 - 16t2 models the height in feet of an object that falls from an initial height of 200 feet t seconds after being dropped. Find the height of the object after 2.5 seconds.
100 feet
The table lists the results of a survey of the students at a community college. Suppose a student is selected at random. Find P(male | student takes physiology).
13/22
Solve the question below.
13x-30/x^2-36
A group of students rolled two number cubes 100 times and recorded a sum of six 14 times. Find the experimental probability of rolling a sum of six.
14%
A farmer wished to construct a rectangular fence with one side along a barn. The farmer has 240 feet of fence and wishes to have the length be three times the width. If the side of the barn accounts for the length of the fence, find the dimensions of the fence.
144 feet by 48 feet
Find the GCF of 14a2b4c and 56ab2c2.
14ab2c
Which number is an outlier in the data shown in the table?
19
The sequence -12, -6, 0, 6, ... , 48 has 11 terms. Evaluate the related series.
198
A spinner is divided into eight equally-sized areas. The central angle for pink is 90°, for teal is 225°, and for blue is 45°. Which is the correct frequency table for this spinner?
2 5 1
State the excluded values of x in the expression
2 or 3
Divide and simplify sqr 24/ sqr 2
2 sqr 3
Let f ( x ) = x 2 + 2 x - 1 and g ( x ) = 2 x - 4. Find 2 f ( x ) - 3 g ( x ).
2 x 2 - 2 x + 10
For the function f ( x ) = (4 - 2 x )2, find f -1 and the domain and range of f and f -1. Determine whether f -1 is a function.
2 x/2 0
What are the dimensions of the matrix?
2 × 1
A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Katalin can paint a certain room in 3 hours. Lena can paint the same room in 8 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room?
2.18
Make a box-and-whisker plot for the set of values. 7.2, 3.2, 5.2, 3.2, 4.2, 7.2, 5.2, 3.2, 6.2, 4.2, 6.2, 3.2, 6.2, 2.2, 4.2
2.2 7.2
The heights of all the 12-year-old boys in the United States are normally distributed with a mean of 59 inches and a standard deviation of 3 inches. What is the probability that a boy chosen randomly from that age group will have a height greater than 65 inches?
2.5%
Use the properties of logarithms to evaluate
2/3
Use the frequency table to find P(more than 3 children).
20%
Simplify
21 16 50 54 / 72
Use the Law of Sines to solve for a to the nearest tenth.
21.2
Seven skiers enter a downhill race. First, second, and third places will be given to the three fastest skiers. How many arrangements of first, second, and third places are possible with seven skiers?
210
The Bangor Coat Factory found that the number of coats sold N varies directly as their advertising budget A and inversely as the price of each coat P . The Bangor Coat Factory sold 10,800 coats when $30,000 was spent on advertising and the price of a coat was set at $50. Determine the number of coats sold when the amount spent on advertising is increased to $70,000.
25,200 coats
Four cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of four cards are possible?
270,725
There are 17 students participating in a spelling bee. How many ways can the students who go first and second be chosen?
272 ways
Solve 2 cos θ + 4 = 3 for 0 ≤ θ < 2π.
2pi/3 4pi/3
Write 2r3 + 8r2 - 10r in factored form.
2r(r - 1)(r + 5)
Divide (2x3 + 4x2 + 3x + 4) ÷ (x + 1) using long division.
2x2 + 2x + 1, R 3
Simplify
2y +1 / y+1
Suppose you take a true/false quiz that contains five true/false questions. Let an even digit represent a correct answer and an odd digit represent an incorrect answer. In the five trials shown, how often did you get at least 3 questions correct? (Note: Assume there is a 0 before the number 4908 in the first trial.)
3
Use the properties of logarithms to evaluate log7343.
3
Rationalize the denominator of
3 sqr t
What are the dimensions of the matrix? Identify a12.
3 × 2, -4
Solve the problem below.
3.1 m2
Find the value of csc 165°. Round your answer to the nearest hundredth.
3.86
For a circle of radius 9 feet, find the arc length s cut off by a central angle of 6°.
3/10
What is the probability of getting two heads when tossing a coin four times?
3/8
For the geometric sequence 2, -10, 50, -250, ..., find the seventh term.
31, 250
In May, Suzanne bought 32 styrofoam balls and decorated them as toy figurines. In June, she sold 12 figurines. In May, Carrie bought 36 styrofoam balls to decorate and in June, she sold 22 figurines. Which matrix represents all of their May purchases and their June sales?
32 -12 36 -22
A large asteroid crashed into a moon of another planet, causing several boulders from the moon to be propelled into space toward the planet. Astronomers were able to measure the speed of one of the projectiles. The distance (in feet) that the projectile traveled each second, starting with the first second, was given by the arithmetic progression 20, 60, 100, 140, .... Find the distance that the projectile traveled in the 9th second.
340 ft
A set of data that is normally distributed has a mean of 35.6 and standard deviation of 2.5. Which number is between 1 and 2 standard deviations of the mean?
38.3
Solve 3 cos 0 = cos 0 - sqr2 for 0 < 0 < 2pi
3pi/4 5pi/4
Use the GCF to factor 15x2 + 6x.
3x(5x + 2)
Divide (3x3 + 4x2 - 5x - 2) ÷ (x + 2) using long division.
3x2 - 2x - 1
Simplify
4/3
Solve
4/3
A jar contains 12 blue marbles, 8 red marbles, and 20 green marbles. You pick one marble from the jar. Find the theoretical probability, P(blue or green).
4/5
How many different ways can a chairperson and an assistant chairperson be selected for a research project if there are seven scientists available?
42 ways
The scores of 36 students on a recent geography test are in the table. If Lupe got a 69 on the test, what percentile would that score represent?
44%
In May, Marcus bought 48 styrofoam balls and decorated them as toy figurines. In June, he sold 19 figurines. In May, Lin bought 44 styrofoam balls to decorate and in June, she sold 21 figurines. Which matrix represents all of their May purchases and their June sales?
48 -19 44 -21
Simplify
4a^2b sqr 3a
Suppose that 80% of people surveyed answered 'Yes' to a certain question. Let the digits 0-7 to represent 'Yes' and let 8 and 9 represent 'No.' Use the random numbers shown below to determine how many people out of 20 answered 'No.'
5
A school bought a special type of lock for all student lockers. Every student had to create his or her own pass code made up of 4 different numbers from 0-9. How many different pass codes are possible?
5,040
Assume red and green are equally likely occurrences. What is probability that you will get one green light in a row of five lights?
5/32
The box-and-whisker plot represents the test scores of 25 students. What percent of the scores were between 88.5 and 65?
50%
Use the Law of Sines to solve for c to the nearest tenth.
51.4
Evaluate 3(2m - 3n) - 2(m + 2n) for m = -9 and n = -7.
55
Evaluate 8C3.
56
Which sample size will produce a margin of error of ±4.1%?
595
Simplify
5x
In how many ways can the three letters A, B, and C be arranged?
6
Use the frequency table to find P(0 - 2 children).
68%
Find the angles in the triangle when a = 19, b = 20, and c = 10. Round your answers to the nearest tenth.
69 80 29
Multiply and simplify
6x^2 sqr3^ x
Solve the question below.
7
For x7 - 2x6 + 3x2 - 2x + 5 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.
7 complex roots; 1, 3, 5, or 7 real roots possible rational roots: ±1, ±5
Use inscribed rectangles to approximate the area under f(x) = -x2 + 6 for -1.5 ≤ x ≤ 0 and rectangle width 0.5.
7.25 units2
Write the related series for the finite sequence 7.6, 6.3, 5, ... , -1.5. Then evaluate the series.
7.6 + 6.3 + 5 + ... + (-1.5) = 24.4
Evaluate the infinite geometric series 2.1 + 0.21 + 0.021 + ... .
7/3
Identify the outlier in the temperature data shown.
71°
The value of y varies directly with x. If y = 64 when x is 16, what is x when y is 288?
72
The probability that a city bus is ready for service when needed is 85%. The probability that a city bus is ready for service and has a working radio is 64%. Find the probability that a bus chosen at random has a working radio given that it is ready for service.
75.3%
Solve the problem below.
80.3°
Which sample size will produce a margin of error of ±3.5%?
816
Use Pascal's Triangle to expand (3a - b)4.
81a4 - 108a3b + 54a2b2 - 12ab3 + b4
A grocery clerk sets up a display of 12-pack cartons of cola. There are 40 cartons at the base of the triangle and one at the top. How many cartons of cola are needed for the complete display?
820 cartons
After taking 3 quizzes, your average is 79 out of 100. What must your average score be on the next five quizzes to increase your average to 84?
87
Write
8x -15/7
One side of a triangle is 4 cm longer than the shortest side and 2 cm shorter than the longest side. The perimeter is 38 cm. Find the dimensions of the triangle.
9 1/3, 13 1/3, 15 1/3
Find the 11th term of the sequence 11, 19, 27, 35, ....
91
Find the arithmetic mean an of the terms
91/60
In one survey, the shoe sizes of women are distributed normally about the mean. The mean of the data is 7.17, and the standard deviation is 1.44. About what percent of the women are within two standard deviations of the mean in shoe size?
96%
A computer supply store sells two types of printers. Type A, costs $135, and the store makes a $40 profit on each sale. Type B, costs $120, and the store makes a $35 profit on each sale. The store manager expects to sell at least 100 printers this month and to make at least $4,400 profit on them. If x represents the number of type A printers sold, and y represents the number of type B printers sold, what are the constraints for a linear program that models this problem?
A.
Find the quadratic function
A.
Graph the system of inequalities.
A.
Identify the graph that shows the solution to the system of inequalities.
A.
Identify the vertex and the axis of symmetry of the parabola.
A.
Which series will converge?
A.
Given log 15 = B and log 3 = C , find log 5.
B - C
An ice cream shop makes $1.25 on each small cone and $2.25 on each large cone. On a typical Saturday, it sells between 60 and 80 small cones and 120 and 150 large cones. The total sales have never exceeded 200 cones. If x represents the number of small cones sold, and y represents the number of large cones sold, what inequalities represent the constraints and what is the objective function in this linear programming problem?
B.
Solve 8x3 + 27 = 0.
B.
Solve the system of equations. 2x - 4y = 3 -3x + 5y = 1
B.
Use the Rational Root Theorem to determine all possible rational roots of 5x3 + 4x2 + 4x + 10 = 0. Do NOT find the actual roots.
B.
Brenda and Anne left their homes for their morning runs at the same time. Brenda can run a 10-minute mile and Anne can run a 12-minute mile. Combined, they ran 15 miles in a total of 2 hours and 42 minutes (162 minutes). How many miles did each woman run?
Brenda ran 9 miles; Anne ran 6 miles
A bus leaves a terminal traveling at a rate of 45 miles per hour. When the bus has traveled 90 miles, a car leaves the same terminal, traveling at a rate of 60 miles per hour. Which pair of equations model the distances d covered by each vehicle after t hours?
Bus: d1 = 45t + 90; Car: d2 = 60t
Factor x4 - 8x2 + 15.
C.
For 3x3 -2x + 6 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.
C.
Graph y = - (x - 1)2 + 4.
C.
Graph y = x2 - 6.
C.
In chemistry, Charles Law states that if the pressure remains constant, the volume of an ideal gas varies directly with the temperature in degrees Kelvin. Suppose a gas has a volume of 100 mL at 250°K. Which proportion could you use to find the volume v of the gas if the temperature decreases to 150°K?
C.
Solve -11x + 9 + 5x2 = 0 using the Quadratic Formula.
C.
Solve 7x2 + 28x = 49 by completing the square.
C.
Solve 8x2 - 80x = -24 by completing the square.
C.
Which statement describes the relationship between the graph of the equation
C.
A rocket is launched from atop a 54-foot cliff with an initial velocity of 119 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t2 + 119t + 54. Graph the equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the nearest hundredth of a second.
C. 7.87 sec
Solve the question below.
C. h= 3v/piR^2
For 8 - 4x3 + 4x6 = 0, state the number of complex roots, the possible number of real roots, and the possible rational roots.
D.
Solve x2 - 12x + 41 = 0
D.
Write in standard form. Then classify by degree and by number of terms.
D.
Each person in a group of students was identified by hair color and then asked whether he or she preferred taking classes in the morning, afternoon, or evening. The results are in the table. Find the probability that a student preferred morning classes given that he or she has blonde hair.
D. 1/6
Write the explicit formula for the sequence with a1 = 120 and r = 0.3. Then generate the first five terms.
D. an = 120 • 0.3n - 1; 120, 36, 10.8, 3.24, 0.972
What is the domain and range of this function? Domain: x > 0; Range: y > 0 Domain: x ≥ 0; Range: y ≥ 0 Domain: all real numbers; Range: all real numbers Domain: positive integers; Range: positive integers
Domain: x > 0; Range: y > 0
4y is the greatest common factor of 4y2 + 6y.
False
5, 7, 11, 15, 21 is an infinite series.
False
7! Is another way of writing 7 * 6 * 5.
False
A data set that appears to be a random group of dots spread throughout the graph has a negative correlation.
False
A graph showing the inequalities "greater than or equal to" or "less than or equal to" will use dotted lines.
False
A matrix with 4 columns and 3 rows is a matrix of dimensions 4x3.
False
An angle in standard position with a positive measurement will extend below the x-axis.
False
If flipping a coin is equally likely to result in heads or tails, the odds of flipping a coin six times and getting only one head are 3 out of 16.
False
It is not necessary to check all solutions of the derived equation in the original equation to find whether any of them are not solutions of the original equation.
False
Point M is at the coordinates (-5, 5).
False
The determinant of this matrix is 7.
False
The domain of a relation and its inverse are the same.
False
The graph of an absolute value function will always be an upward-pointing V shape.
False
The image shows the graph of 3x + 2 < 11 and - x + 2 < 3.
False
The length of side RP is approximately 42 cm.
False
The line y = 7x - 2 has a slope of 7 and a y-intercept of (-2 ,0).
False
The missing term of the arithmetic sequence 13, __, 27 is 21.
False
The only restriction of the variable in this equation is that x cannot equal positive or negative 5.
False
The polynomial 3x2 - 7 + 4x3 + x6 is written in standard form.
False
The polynomial x4- 2x2 + x4 - x is written in standard form.
False
The possible rational roots of x3 + 3x2 - 4x + 2 are +/- 3 and +/- 2.
False
The range of the set 12, 18, 19, 22, 25 is 19.
False
The sequence 3, 6, 9, 12 is geometric.
False
The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse.
False
The solution to this equation is x = 11.
False
The vertex of a parabola will never be on the axis of symmetry.
False
These are two like radicals.
False
Transforming a figure 3 units to the right and 2 units up can be accomplished by adding 3 to each x-coordinate of the vertices and subtracting 2 from the y-coordinates.
False
Using substitution, the equations 2x - 3y = -21 and 3x + 3y = -24 give a solution of (-9,-1).
False
When solving a quadratic equation by completing the square, the coefficient of the highest power must be any positive integer.
False
You cannot use a table or graph to show a probability distribution.
False
What steps would you use to plot (-3, -4, 0) in a three-dimensional coordinate system?
From the origin, move back 3 units and left 4 units.
Which steps would you use to plot the point (7, -6, -5) in a three-dimensional coordinate system?
From the origin, move forward 7 units, left 6 units, and down 5 units.
Graph 2x + 3y = 9.
Graph A
Solve and graph -2x + 7 ≥ 2(3 - x).
Graph A
Solve and graph 13 - 3y < -5.
Graph A
An electronics store makes a profit of $55 for every standard CD player sold and $77 for every portable CD player sold. The manager's goal is to make at least $385 a day on sales of both standard and portable CD players. If s represents the number of standard CD players sold, and p represents the number of portable CD players sold, which inequality and graph represent the manager's daily goal?
Graph C
Which is the graph of the equation y = |x - 1|?
Graph C
Graph the solution of -7x + 4 ≥ 11 and 10 - 3x > 1.
Graph D
How do the medians of the two sets of exam scores compare?
The median of Exam A is greater than the median of Exam B.
What is true about the system
The system is consistent and independent.
A jar contains 7 red marbles, 4 blue marble, and 6 green marbles. You draw one marble from the jar. The probability of drawing a blue or red marble is 11/17.
True
A percentile is a number from 0 to 100 which can be associated with x to indicate the percent of the data that are less than or equal to x.
True
An equation using three variables is graphed in coordinate space.
True
An extraneous solution is a solution of the derived equation, but not of the original equation.
True
From a group of 1,268 people, 172 prefer chocolate ice cream over vanilla. The proportion who prefer vanilla is approximately 86.4%.
True
If 10% of a group ate sandwiches two days in a row, and 40% of the group had a sandwich on the first day, this means that 25% of the group that ate a first sandwich had a second.
True
In the expression 2(x+4) - 12 = 44, x = 24.
True
In the expression 3(x - 6) - 12 = 33, x = 21.
True
Inscribed rectangles are completely under the curve.
True
The area approximated by circumscribed rectangles is greater than the area under the curve.
True
The equation f(x) = 4x4 + 4x2 + 9x - 2 can have at most four distinct real roots.
True
The expression 2y - 7x + 3y + 3x evaluated for x = 2 and y = 4 is 12.
True
The law of cosines is used to find the measures of a triangle when only the three sides are known, because the law of sines requires at least one angle measure.
True
The length of an object's shadow varies directly with its height. If a can that is 13 cm tall casts a shadow that is 7.5 cm long, a bottle that is 25 cm tall will cast a shadow that is approximately 14.42 cm long.
True
The minimum value of a parabola that opens upward will be its vertex.
True
The mode of the set 2, 3, 3, 4, 5, 8, 9, 10 is 3.
True
The next three terms of the sequence 1, 3, 5, 7, ... are 9, 11, 13.
True
The polynomial 5x3 - 2x2 + x - 13 is written in standard form.
True
The range of the set 2, 5, 8, 19, 33, 45 is 43.
True
The sequence 2, 6, 18, 54, ... is a geometric sequence.
True
The slope of the line that passes through (-2, 6) and (1, 15) is 3.
True
The square root of a negative number is an imaginary number.
True
The tangent of an angle is equal to the ratio of its sine divided by its cosine.
True
The vertex of f(x) = 3(x+2)2 - 4 is (-2,-4).
True
Two parallel lines form an inconsistent system of equations that has no solution.
True
Using elimination, the equations 3x - 4y = 12 and x + 4y = 20 can be solved to show that x = 8 and y = 3.
True
Using substitution, the equations 2x - y = 4 and 3x + 2y = 13 give a solution of (3,2).
True
Using the quadratic formula allows you to find the x-intercepts of a quadratic equation.
True
When dividing polynomials, every term of the numerator must be divided by the entire denominator.
True
Find AB,
[-25 25] TALL
Find
[21 -63]
Randex Manufacturing estimates that its weekly profit, P, in hundreds of dollars, can be approximated by the formula P = -2x2 + 4x + 2 where x is the number of units produced per week, in thousands. a. How many units should the company produce per week to earn the maximum profit? b. Find the maximum weekly profit.
a. 1000 units; b. $400
In a survey of 368 people, 81 drink milk straight from the milk carton. For the sample, find the sample proportion, the margin of error, and the interval likely to contain the true population proportion.
a. 22%; b. ±5%; c. 17% to 27%
Which formula does NOT describe the sequence 8, 6, 3, -1, -6, ... ?
an = -0.5n2 - n + 9
Write a recursive formula for the sequence 15, 26, 48, 92, 180, .... Then find the next term.
an = 2an - 1 - 4 where a1 = 15; 356
Determine whether the following situation would require calculating a permutation or a combination. Selecting four teachers to attend a math seminar.
combination
Classify 2 by degree and by number of terms.
constant monomial
Classify 2x3 - 2x by degree and by number of terms.
cubic binomial
Classify -4x3 - 2x2 - 2x by degree and by number of terms.
cubic trinomial
Write an explicit and a recursive formula for the sequence -7, -5.6, -4.2, -2.8, -1.4, ....
explicit: an = -8.4 + 1.4n; recursive: an = an - 1 + 1.4, where a1 = -7
Decide whether the formula an = -4n(n - 1) is explicit or recursive. Then find the first five terms of the sequence.
explicit; 0, -8, -24, -48, -80
For f ( x ) = 5 - 3 x and g ( x ) = x 2 - 1, find f ( g ( x )) and g ( f ( x )).
f ( g ( x )) = -3 x 3 + 8, g ( f ( x )) = 9 x 2 - 30 x + 24
Write an exponential function to model this situation: a population of 300 animals increases at an annual rate of 13%.
f ( x ) = 300(1.13) x
Write an exponential function to model this situation: a population of 260 animals increases at an annual rate of 9%.
f(x) = 260(1.09)x
Find a quadratic model for the values in the table.
f(x) = 3x2 + 7x - 9
Find a polynomial function to model the data.
f(x) = 4.68x3 + 8.87x2 + 4.25x + 6.32
Graph y = 5 cos x.
far apart 5 -5
In which quadrant does the terminal side of a 314° angle lie?
fourth quadrant
Determine whether the series -1024 + 256 -64 + 16 - ... is arithmetic or geometric. Then evaluate the series to the ninth term.
geometric; -819.203125
The graph below models the burning of a candle. At time t = 0, the candle was 8 inches tall. If the candle burns at a rate of 2 inches per hour, what equation models the height h of the candle after burning for t hours?
h = -2t + 8
Classify the system.
independent
Solve the system of three equations by elimination: 5x + 2y - 3z = 10 2x - 2y + 4z = 6 x - y + 2z = 3
infinitely many solutions
Which set of numbers best describes the number -4?
integers
Which set of numbers best describes the number π (pi)?
irrationals
Expand
log b (1/2 -
Write 5 log x - 4 log (x - 4) as a single logarithm.
log x^5/x-4^4
What does the dot at 47 represent?
lower quartile
Solve |8 - m| + 4 = 21.
m = -9, m = 25
Which line, having the given slope and passing through the given point, represents a direct variation?
m= 2/3 ; (9, 6)
Multiply and simplify
m^2 sqr 12 m^2
The number of patients treated at Dr. Holman's dentist office each day was recorded for seven days. Using the data 3, 10, 18, 9, 22, 20, and 2, find the mean, median, and mode.
mean: 12, median: 10, no mode
The number of patients treated at Dr. Oster's dentist office each day was recorded for nine days. Using the data 7, 4, 18, 14, 14, 11, 13, 21, and 6, find the mean, median, and mode.
mean: 12, median: 13, mode: 14
Find the mean, the median, and mode of the set of values. 5, 20, 6, 5, 15, 18, 12, 13, 14
mean: 12, median: 13, mode: 5
Find the mean and standard deviation for the set of values. 23, 16, 15, 18, 20, 17, 4, 7, 15
mean: 15, standard deviation: 5.66
Find the next two terms in the sequence -5, 8, -13, 20, -29, .... Write a formula for the nth term. Identify the formula as explicit or recursive.
none of these
The velocity of sound in air is given by the equation
none of these
Determine whether the following situation would require calculating a permutation or a combination. Assigning students to their seats on the first day of school.
permutation
Solve cot θ sin θ = 1/5 for 0 ≤ θ < 2π.
pi/3 5pi/3
What is the period of y = 3 tan 4x + 5?
pi/4
Find the range and the interquartile range of the set of values. 31, 16, 39, 15, 18, 41, 24, 26, 21, 33, 9, 12
range: 32, interquartile range: 16.5
Find the range and the interquartile range of the set of values.37, 21, 44, 19, 22, 47, 26, 32, 25, 43, 11, 15
range: 36, interquartile range: 20
Tell whether 3, 10, 17, 24, ... , 73 is a sequence or a series. Then tell whether it is finite or infinite.
sequence, finite
Find the slope and the y-intercept of the line. y = 5x - 7
slope: 5 y-intercept: (0, -7)
Simplify sin θ sec θ.
tan θ
Which polynomial function has the highest degree?
the quotient of f(x) and g(x), where f(x) = x9 - 3x and g(x) = 3x2 - 4
Given the set of axes y-axis: a car's velocity, x-axis: time, what does the area under the curve represent?
the total distance traveled by the car
Order does not matter when examining combinations, but order does matter in permutations.
true
Evaluate the discriminant of 25x2 + 350x + 49 = 0. Tell how many solutions the equation has and whether the solutions are real or imaginary.
two real solutions
Identify the graph of y = 2 x + 7 and its inverse.
up cross
Use Pascal's Triangle to expand (s - v)6.
v6 - 6v5s + 15v4s2 - 20v3s3 + 15v2s4 - 6vs5 + s6
Identify the vertex and the axis of symmetry of the parabola.
vertex: (1, -6); axis of symmetry: x = 1
Multiply
x ; x ≠ -7, -4, 0
Solve |x + 9| = 8.
x = -17, x = -1
A factory can produce two products, x and y, with a profit P approximated by P = 12x + 15y. The production of y can exceed x by no more than 200 units. Moreover, production levels are limited by the formula x + 2y ≤ 1000. What production levels yield maximum profit?
x = 1000; y = 0
Find the zeros of y = (x - 2)(x + 9).
x = 2, x = -9
Solve 3(x - 5) - 15 = 48.
x = 26
Solve 3x2 - 9x - 12 = 0 using the Quadratic Formula.
x = 4, x = -1
Find only the rational roots of x4 - 9x3 + 16x2 + 18x - 36 = 0.
x = 6, x = 3
Refer to the question below.
x = 60
Solve x - x3 = 2x4 + 3x2 - 5.
x = ±1
State the excluded value(s) of
x cannot equal -4
State the excluded value(s) of
x cannot equal 5, -5
Solve |x + 4| ≥ 1.
x ≤ -5 or x ≥ -3
Simplify
x+3/2
Find
x+4 / x+2
Simplify
x-1 / 5(x-3) 1 and 3
Find the inverse of y = 3x2 + 4. Is the inverse a function?
x-4 / 3 no
Divide
x-4/x-3 3 4
Divide
x-5/x-3
Divide
x-6 / x-5
Simplify
x-7 /2
A group of college students is volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Nita can paint a certain room in 3 hours. Jorge can paint the same room in 4 hours. Identify the equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room?
x/3 + x/4 =1, 1.71 h
Divide (x4 - 11x3 - 49x2 + 899x - 2506) ÷ (x - 8).
x3 - 3x2 - 73x + 315, R 14
Multiply
x; x ≠ -6, -3, 0
Write the point-slope form of an equation of the line that passes through (4, -3) and (2, 1).
y + 3 = - 2(x - 4)
A line passes through the point (-6, 1) and has slope m = -4. Find the equation in point-slope form.
y - 1 = -4(x + 6)
What is an inequality for this graph?
y - 3x ≥ -5
Rewrite y = x2 + 4x + 5 in vertex form. Then find the vertex.
y = (x + 2)2 + 1; (-2, 1)
The scatter plot below shows the weights in ounces of several kittens at various ages. What is the best equation of the trend line through these points?
y = 4x + 10
Which equation represents the line whose slope is 1 and whose y-intercept is (0, 0).
y = x
The scatter plot below contains the points (2, 7), (-2, 1), (5, 13), (-4, 5), and (0,5). What equation best represents the trend line drawn on the scatter plot?
y = x + 6
What is the equation of the graph?
y = |x + 5|
Find the equation of the line that passes through the points (-6, 3), (5, -2) in point-slope form.
y-3=-5/11(x+6)
What is an equation for a direct variation whose graph passes through the point (-5, 3)?
y=-3/5x
Is the sequence -5.4, 5.1, 15.6, 26.1, ... arithmetic? If so, identify the common difference.
yes, 10.5
Is the sequence 5.1, 10.5, 15.9, 21.3, ... arithmetic? If so, identify the common difference.
yes, 5.4
Write the specification 14.35 ≤ d ≤ 15.15 as an absolute value inequality.
|d - 14.75| ≤ 0.4
When 2251 voters were polled, 52% said they were voting yes on an initiative measure. Find the margin of error and an interval that is likely to contain the true population proportion.
±2.1%; between 49.9% and 54.1%
When 876 voters were polled, 67% said they were voting yes on an initiative measure. Find the margin of error and an interval that is likely to contain the true population proportion.
±3.4%; between 63.6% and 70.4%
The class average on a math test was 84.5 and the standard deviation was 4.4. Find the z-score for a test score of 94.
≈ 2.16
