algebra 2 LUOA

The equation of a line of best fit relating the money earned e at a bake sale to the number of customers c is e = 1.1c + 19. Use the equation to predict the earnings from a bake sale with 80 customers.

$107

Identify the coordinates that result when the point (−4, 5), is translated 8 units right and 3 units down.

(4, 2)

Identify the coordinates of the point (3, −2), translated 5 units left and 6 units up.

(−2, 4)

Evaluate the expression 6^−3.

1/216

Evaluate the expression 2−5.

1/32

Simplify √16/25

4/5

Evaluate the expression (4/9)−2.

81/16

Identify the domain and range for the relation.{(4, 3), (7, 6), (10, 9), (13, 6), (16, 9)}

D = {4, 7, 10, 13, 16}R = {3, 6, 9}

Find the value of k in the data set such that the data set represents a linear function.

k = 3

Evaluate the expression uv2 + 5uv + u2 for u = 3 and v = 4.

117

add 6√2 + √50

11√2

identify an algebraic expression that represents Jo's age y years after her 20th birthday.

20 + y

Simplify. Write the answer in scientific notation. 3.3 x 10^-8/1.1x10^2

3.0 × 10^ −10

Evaluate the expression (3/7)−3.

343/27

For the function f(x) = x2 + 4, identify the values of f(0), f(1/2), and f(−1).

4; 17/4; 5

Simplify by rationalizing the denominator 4√15/√5

4√3

Which of the following correctly represents the set of numbers using interval notation?−3 ≤ x < 7

[−3, 7)

Which of the following correctly represents the set of numbers using interval notation?

[−4, −1] or (2, ∞)

Identify the relation that is a function.

age of a plant to its height

Which of the following represents the set in words?{x | x < 0}

all negative real numbers

Classify the system and identify the number of solutions.3x + 5y + 4z = −112x − 4y − z = −114x + 3y − 2z = 11

consistent, independent; one

Classify the system and identify the number of solutions.3x − y + z = 4x + y − 2z = 02x − y + 2z = 3

consistent, independent; one

Classify the system and identify the number of solutions.2x + y + 5z = 43x − 2y + 2z = 25x − 8y − 4z = 1

inconsistent; none

Classify the system and identify the number of solutions.x − 2y − 2z = 82x + 6y − 2z = 98x − 6y − 14z = 11

inconsistent; none

Solve the proportion.2.8/k=5.6/84

k = 42

Marie requires 2 gallons of paint to cover an area of 400 square feet. Identify the graph that shows the relationship between the quantity of paint and the area covered and the parent function that best describes it. Then use the graph to estimate how many gallons of paint Marie requires to paint an area of 2,400 square feet.

linear; 12 gallons

Complete the statement.The line x = −2 is _______.

vertical

Solve the proportion.36/1.6 =13.5/w

w = 0.6

10% of the fruits in a basket are apples. If there are 15 apples, how many fruits are in the basket?

150

Identify the additive and multiplicative inverse of −17.

17; −1/17

Harry is organizing a picnic. He can spend at most $24.00 on beverages. Iced tea costs $2.00 per gallon and lemonade costs $2.50 per gallon. If x represents the number of gallons of iced tea and y represents the number of gallons of lemonade, which inequality shows the number of gallons of each drink that he can buy? Identify the number of gallons of iced tea that Harry can buy if he buys 5 gallons of lemonade.

2x + 2.5y ≤ 24; no more than 5 gallons

Susan needs to buy apples and oranges to make fruit salad. She needs 15 fruits in all. Apples cost $3 per piece, and oranges cost $2 per piece. Let m represent the number of apples. Identify an expression that represents the amount Susan spent on the fruits. Then identify the amount she spent if she bought 6 apples.

30 + m; $36

A cell phone service provider offers a plan that charges $30.35 per month and $0.05 per minute for phone calls. If a person received a bill of $45.35 last month, how many minutes of phone calls were they charged for?

300 min

The equation of a line of best fit relating the number of cats c at an animal shelter to the number of dogs d is c = 2.1d − 26. Predict the number of cats at a shelter where there are 30 dogs.

37

A blueprint of a shopping complex shows the bottom edge of the roof to be 93 feet above the ground. If the roof rises to a point 171 feet above the ground over a horizontal distance of 6.5 yards, what is the slope of the roof? 1.2

4

A 27-foot pole casts a 25-foot shadow. At the same time, a nearby tower casts a 45-foot shadow. How tall is the tower?

48.6 ft

Simplify.7a2 + 3b + 6a − 2a2

5a2 + 3b + 6a

Give the domain and range of the relation. Indicate whether the relation is a function.

D: {0, 1, 2, 3}R: {−5, −2, 3, 4}The relation is a function.

Classify the system and identify the number of solutions.x − 3y − 8z = −102x + 5y + 6z = 133x + 2y − 2z = 3

consistent; dependent; infinite

Identify the parent function for the function g(x) = (x + 1)3 based on its function rule. Then graph g and identify the transformation of the parent function that it represents.

cubic; translation left 1 unit

A truck rental company charges $65 plus $32 per hour to rent a truck. Identify the function that represents the total charge for renting a truck for a certain number of hours. What is the value of the function for an input of 6, and what does it represent?

f(h) = 32h + 65$257, which is the total charge in dollars for renting a truck for 6 hours

An interior designer charges $100 to visit a site, plus $55 to design each room. Identify a function that represents the total amount he charges for designing a certain number of rooms. What is the value of the function for an input of 6, and what does it represent?

f(x) = 100 + 55x$430, which is the total charge in dollars for designing 6 rooms

Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through.

function

Lucy takes 20 minutes to cover a mile on foot. Identify the graph that shows the relationship between time taken and distance covered and the parent function that best describes it. Then use the graph to estimate the time it would take Lucy to cover 3.5 miles.

linear; 70 minutes

Identify the parent function for the function g(x) = x + 4 based on its function rule. Then graph g and identify the transformation of the parent function that it represents.

linear; translation up 4 units

Identify the parent function for the function g(x) = x + 9 from its function rule. Then graph g and identify what transformation of the parent function it represents.

linear; translation up 9 units

Solve the equation |2m − 6 | = 10.

m = −2 or m = 8

Simplify. Assume all variables are non-zero. (mn^8/n^9)^3

m^3/n^9

Solve the equation. -2(3z+8)=1/3(9-18z)

no solution

Use the vertical-line test to determine whether the relation is a function. If not, identify two points a vertical line would pass through.

not a function; (2, −2) and (2, 2)

Identify the relation that is a function.

number of apples purchased to the cost of the apples

Solve the equation |p + 5| = 3.

p = −8 or p = −2

Solve the equation |7q| + 3 = 24.

q = 3 or q = −3

Simplify. Assume all variables are non-zero. (p^4q/p8)

q^2/p^8

Identify the parent function for the function g(x) = x2 − 4 based on its function rule. Then graph g and identify the transformation of the parent function that it represents.

quadratic; translation down 4 units

The data in the table show how long (in minutes, t) it takes several commuters to drive to work. Find the correlation coefficient and the equation of the line of best fit for the data. Treat the commute distance d as the independent variable.

r ≈ 0.75t ≈ 0.8d + 11.5

The data in the table show the number of boys b and girls g in several different classes. Find the correlation coefficient and the equation of the line of best fit for the data. Treat the number of girls in the class as the independent variable.

r ≈ −0.18b ≈ −0.13g + 17.9

Identify the relation that is not a function.

weight of a person to a person's height

Solve the equation.(5x + 19) − 10 = 6x + 27 + 8x

x = −2

Identify the solution of the compound inequality x + 4 > 9 or 2x ≥ 14 and the graph that represents it.

x > 5

Find the intercepts.4x − 6y = 12

x-intercept 3y-intercept −2

Find the intercepts.3x − 2y = −6

x-intercept −2y-intercept 3

Write the equation in in slope-intercept form.18x − 6y = 12

y = 3x − 2

Identify the slope-intercept form and the graph of the line described by the equation 3x − 3y = 15.

y = x − 5

Identify the slope-intercept form and the graph of the line described by the equation 8x + 2y = −6.

y = −4x − 3

Which of the following represents the set "all values of x greater than 1 and less than 15" in set builder notation? {x | x < 15}

{x | 1 < x < 15}

Which of the following represents the set "all values of x greater than or equal to −1 and less than 2" in set builder notation?

{x | −1 ≤ x < 2}

Identify the solution of the compound inequality−6m −4 < 2m and m − 3 ≤ −4m + 12.

−1/2 < m ≤ 3

Simplify 3m2 (−6m3 ). Assume all variables are non-zero

−18m5

For the function in the graph, identify the values of f(1), f(3), and f(−1).

−1; 1; −3

For the function f(x) = 6x − 8, identify the values of f(0), f(1/2), and f(−2).

−8; −5; −20