Alg

Which is the graph of the function f(x) = x2 + 2x + 3?

a

Dependent events can best be described as

a group of events whose later outcomes are affected by previous outcomes.

The table shows the shoe sizes of women of different ages.Which best describes the strength of the model

a weak positive correlation

Compute the missing data in the table for the following exponential function 4072-06-01-03-00_files/i0050000.jpg. Round your answer to the nearest tenths place.x0123456f(x)?1.011.021.031.041.051.06a.0c.1.001b.1.01d.1

d

Leona has a bag containing lettered tiles. Which describes dependent events?

removing a vowel, not replacing it, and then removing another vowel

What are the zeros of the quadratic function f(x) = 2x2 + 8x - 3?

x = -2 - and x = -2 + (A)

The function g(x) is defined as g(x) = 6x^2 + 23x - 4. When does g(x) = 0?

x = -4 or x = 1/6

Solve x2 - 8x = 20 by completing the square. Which is the solution set of the equation?

{-2, 10}

Solve x2 + 6x = 7 by completing the square. Which is the solution set of the equation?

{-7, 1}

Solve x^2 − 24x = −80 by completing the square.What is the solution set of the equation?

{4, 20}

What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)?The y-value of the vertex is

121

what is the multiplicative rate of change of the function shown on the graph? express your answer in decimal form. round to the nearest tenth.(-1,0.8)(0,2)(1,5)(2,12.5)

2.5

Mariya is solving the quadratic equation by completing the square.4x2 - 20x + 3 = 04x2 - 20x = -3A(x2 - 5x) = -3What is the value of A?

4

The first few steps in solving the quadratic equation 5x2 + 27x = 14 − 13x by completing the square are shown.5x2 + 27x = 14 − 13x5x2 + 40x = 145(x2 + 8x) = 14Which is the best step to do next to solve the equation by completing the square?

5(x^2 + 8x + 16) = 94

The first step in solving the quadratic equation -5x2 + 8 = 133 is to subtract from each side.

8

what are the domain and range of the function on the graph?

D. the domain includes all real numbers, and the range is y > 0

What is the growth factor of the following example? Assume time is measured in the units given.Water usage is increasing by 3% per year.a.3 per yearc.1.03 per yearb.0.03 per yeard.103 per year

c

Which equation represents an exponential function that passes through the point (2,80)?

f (x) = 5 (4)^x

Marco has a bag of red, blue, and green tiles. Which set of events would be considered independent?

x.Two tiles are drawn at the same time.

The product of two consecutive integers is 272. Which quadratic equation can be used to find x, the smaller number?

x2 + x − 272 = 0

Geraldine is asked to explain the limits on the range of an exponential equation using the function f (x)=2^x. She makes these two statements:1. As x increases infinitely, the y-values are continually doubled for each single increase in x.2. As x decreases infinitely, the y-values are continually halved for each single decrease in x.

D. the conclusion is incorrect because the range is limited to the set of positive real numbers.

Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiahs account, y, after x years?

D. y = 360 (1.03)^x

Heather has a bag containing 4 marbles: 1 red, 1 blue, and 2 green. She draws 1 marble out of the bag, replaces it, and then draws another marble. What is the denominator of the simplified fraction that represents P(red then blue then green)?

P(red then blue then green) = x.3

A box contains different-colored marbles. If P(blue) = , P(green) = , and P(blue and green) = , which statement is true?

The events are independent because P(blue) P(green) P(blue and green).D

The function f(x) = -x2 - 4x + 5 is shown on the graph.Which statement about the function is true?

The range of the function is all real numbers less than or equal to 9.

Which is the graph of f (x)= 5 (2)^x?

a

the value of a collector's item is expected to increase exponentially each year. the item is purchased for $500. After 2 years, the item is worth $551.25. Which equation represents y, the value of the item after x years?

b: y= 500 (1.05)^x

What is the domain and range of the function f(x)=a^xa.domain = negative real numbers, range = negative real numbersc.domain = positive real numbers, range = positive real numbersb.domain = all real numbers, range = all real numbersd.domain = real numbers, range = positive real numbers

d

Which is the graph of f (x)= 1/4 (4)^x?

d

an object is dropped from a building and allowed to freefall to the ground. the height of the object over time is shown in the table. ( for reference h(t)= 144-16^2 )

d: the rate of change increases over time. the object drops 16 feet in the first second, but 80 feet in the last second.

Aaron, Bob, and Charlotte are running a race. Which event would be considered dependent

determining first, second, and third place runners

All-Star Trinkets estimates its monthly profits using a quadratic function. The table shows the total profit as a function of the number of trinkets produced.Which function can be used to model the monthly profit for x trinkets produced?

f(x) =1/4 (x - 50)(x - 250)

Fiona is completing the square to solve the polynomial equation.x2 - 4x + 1 = 0What should be her first step?

isolating the constant 1

What are the solutions to m2 - 9 = 0?

m = -3 and m = 3

Which is a pair of dependent events?

removing a marble from a bag, not putting it back, and then removing a second marble

Luka has a bag containing 5 socks: 3 red, 1 white, and 1 black. He draws 1 sock out of the bag, replaces it, and then draws another sock.What is the probability that he will draw a black sock and then a red sock, P(black, then red)?

x. 1/15 x.3/15

The theoretical probability of a couple having a baby girl is . What is P(girl, girl, girl)?

x.1/3x.1/6x.3/8

Keshawn is asked to compare and contrast the domain and range for the two functions.f (x)=5xg (x)=5^x

A. the domain of both functions is all real numbers.F. the range of g (x) is y > 0

A function of the form f (x) = ab^x is modified so that the b value remains the same but the a value is increased by 2. how do the domain and range of the new function compare to the domain and range of the original function? Check all that apply.

A. the range stays the same.C. the domain stays the same.

A limited-edition poster increases in value each year. After 1 year, the poster is worth $20.70. After 2 years, it is worth $23.81. Which equation can be used to find the value, y, after x years? ( round money values to the nearest penny. )

A. y=18 (1.15)^x

The graph shows the relationship between the price of frozen yogurt and the number of ounces of frozen yogurt sold at different stores and restaurants.

According to the line of best fit, about how many ounces of frozen yogurt can someone purchase for $5? 13

The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground.A line of best fit for the data is represented by h = -21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table?

According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.

what is the rate of change of the function described in the table?x= -1,0,1,2,3y= 1/10, 1/2, 5/2, 25/2, 125/2

B. 5

Sergey is solving 5x2 + 20x - 7 = 0. Which steps could he use to solve the quadratic equation? Check all that apply.

BCD

Which equation represents an exponential function with an initial value of 500?

C. f (x)= 500 (2)^x

Spinning a 4-section spinner twice can be described as which type of event?

It is an independent event. The outcome of the second spin is unaffected by the outcome of the first spin

Below is a graph of exponential functions label I though VI.4072-06-01-03-00_files/i0300000.jpgDetermine which of the following exponential formula(s) represents II and IV in the graph above.

a

Below is a graph of exponential functions labelled I through VI.Determine which of the following exponential formula(s) represents exponential function II in the graph above.

a

On the graph of an exponential function representing growth, what happens to the slope of the graph? The slope:a.increasesc.stays the sameb.decreasesd.there is no slope

a

Which is the graph of f(x)= 0.5 (4)^x ?

a

Which equation represents an exponential function that passes through the point (2,36)?

a: f (x)= 4 (3)^x

The graph of the function f(x) = (x + 2)(x − 4) is shown.Which describes all of the values for which the graph is negative and increasing?

all real values of x where 1 < x < 4

Below is a graph of exponential functions label I though VI.4072-06-01-03-00_files/i0290000.jpgDetermine which of the following exponential formula(s) represents I, V, VI in the graph above.

c

Events A and B are independent. The probability of A occurring is 2/5 . The probability of B occurring is1/4 . What is P(A and B)?

x.13/201/10

a box contains different-colored marbles. If P(blue) =1/4 , P(green) = 1/4, and P(blue and green) =1/12 , which statement is true?

x.Ax.Bx.C

Juan rolls a 6-sided number cube 4 times. Each time, the result is 2. Which best describes the events?

x.Dependent: Each outcome was the same.Simple: One single number cube was rolled.

Consider a situation in which P(X) =4/5 and P(Y) = 1/4. If P(X and Y) is = , which best describes the events?

x.They are dependent because P(X) · P(Y) = P(X and Y).

A line of best fit is drawn for the set of points shown on the graph.Which point is an approximate extrapolation for x = 30 from the line of best fit?

(30, 38)

Jace gathered the data in the table. He found the approximate line of best fit to be y = -0.7x + 2.36.What is the residual value when x = 5?

-0.86

A quadratic equation has zero real number solutions. Which could be the discriminant value associated with this equation?

-5

A quadratic equation of the form 0 = ax2 + bx + c has one real number solution. Which could be the equation?

0 = -2x^2 - 4x - 2

A coin is flipped, then a number cube is rolled. The tree diagram shows the possible outcomes.What is P(heads, then 2)?

1/12

Which best describes the graph of the function f (x)= 4 (1.5)^x ?

B. the graph passes through the point (0,4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5.

Which table represents exponential growth?

B. x= 1,2,3,4y= 2,4,8,16