Algebra 2 Final

Solve the system of equations by substitution. 2x+y=2 -3x-8y=-42

(-2,6)

Use elimination to solve the system of equations 2x-5y=1 5x-2y=-4

(-22/21, -13/21)

Use a graph to solve the system of equations x+y=-1 y=3x+19

(-5,4)

Use elimination to solve the system of equations 7x-3y=-43 5x+6y=-47

(-7,-2)

Determine which ordered pair (x, y) is a solution of 3x-y is less than or equal to 15

(3,-6)

Solve the system of equations by substitution. 3x+4y=32 3x+y=17

(4,5)

Solve the system of equations by substitution 4y=4 x+2y+z=10 y-2z=-5

(5,1,3)

For the pair of functions, f and g, find (g*f)(x) and (f*g)(x). f(x)=6-x g(x)=x^2-2

(g*f)(x)=x^2-12x+34 (f*g)(x)=-x^2+8

Which inequality has (1, 7) as a solution?

-5x-2y is greater than or equal to -24

Evaluate the expression 3-14*6/7+3

-6

If f(x)=3x+4 and g(x)=2+x, which is the rule of function 3g(x) - 3f(x)

-6x-6

Simplify the expression (-2a^3b^2c^0)/7a^4b^3c^4)^-5

-7^5a^5b^5c^20/2^5

Find the determinant, and tell whether the matrix has an inverse. det[10 -7 -5 -6]

-95, yes

Find the determinant, and tell whether the matrix has an inverse. det[-2 2 -5 -10]

30, yes

Abbiville is a small town that has been steadily growing since 1960. Use the table below to create a linear equation that estimates Abbiville's population over time. What will the population be in 2014 if the growth remains constant?

364 people

Which is the equation of the line with slope -4 and y-intercept 5?

4x+y-5=0

Solve the proportion x-8/8=4/5

72/5

Given the graph of y=3(x+1),what function would be obtained by moving the graph up 4 and moving it 6 to the right?

f(x)=3(x-5)+4

Find the inverse of the function f(x)= (-6,-4) (-4,-6) (6, -7)

f^-1 (x)=(-4,-6) (-6,-4) (-7,6)

The graph of f(x)=x^2 is stretched vertically by a factor of 3, translated 4 units to the right, and translated 8 units downward. Determine the equation of the transformed function, g(x).

g(x)=3(x-4)^2-8

Find the slope and the y-intercept of the line 2x-8y=7

m=1/4, b=-7/8

Find the inverse of the following matrix (if it exists): [-1 -3 0 4]

[-1 -3/4 0 1/4]

Let A= [1 -3 B= [5 2 C=[1 1 -3 2], 0 -5], 3 -5] Find AC-CB

[-13 19 -12 -44]

Write the augmented matrix for the system of equations. x-y=-9 5x=0

[1 -1| -9 5 0| 0]

The band and the cheerleading squad at a local school are ordering supplies. The supplies they need are listed in the table. If a bottle of paint costs $5, a roll of paper costs $12, and a roll of tape costs $2, which of the following shows the use of matrices to find the total cost of supplies for each group?

[10 13 5 [5 [216 10 16 8] 12 = 258] 2]

Write the system of equations as a matrix equation. Then solve the system, if possible, by using a matrix equation. If not possible, classify the system. 4x+y=7 4x+y=8

[4 1 [x [7 4 1] y] = 8] inconsistent, no solution

Find [1 17 14] [11 3 19 7 9 5]

[460 192]

Write the augmented matrix for the system of equations. 8x+2y+6z=-3 3x-y+10z=3 -9x-2y-4z=-7

[8 2 6| -3 3 -1 10| 3 -9 -2 -4| -7]

The Student Government secretary, and two teacher's aides are ordering supplies. The supplies they need are listed in the table. If a spiral notebook costs $2.25, a box of pens costs $4.50, and a box of paperclips costs $1.50, which of the following shows the use of matrices to find the total cost of supplies for each person?

[9 8 7 [$2.25 [$66.75 7 11 5 $4.50 = $72.75 8 1 2] $1.50] $25.50]

A T-shirt company estimates that the average cost per shirt can be approximated by the function A(x)=3.75x+200/x,where x is the number of T-shirts made. Find the average cost per T-shirt when the company makes 10 shirts.

$23.75

Write a proportion that models the statement 10 is to 5 as 16 is to 8.

10/5=16/8

If x = 78 when y = 130 and x varies directly as y, then find x when y = 190.

114

Kozinski played in 16 basketball games this season, Hussein played in 32 games, and Johnson played in 55 games. Kozinski averaged 6 points and 2 rebounds per game, Hussein averaged 8 points and 11 rebounds, and Johnson averaged 18 points and 16 rebounds. Multiply the following matrices to get the total number of points scored and the total number of rebounds made, by all three players combined.

1342 points, 1264 rebounds

Since 1993, Daphne Hamilton has owned a franchise of take-out restaurants called The Burger Barn. The number of customers, C, in thousands, that The Burger Barn has served each year can be modeled by the function C(t)=t^2+38t+600 where t is the number of years from 1993. Using this model, estimate the number of customers served in 1999.

864,000

Evaluate the expression 27^2/8

9

Evaluate the expression (-3/8)^2

9/64

Evaluate the expression (3/8)^-2

9/64

Solve the equation or formula for the variable specified. B=7/8(A-11) for A.

A= 8B+77/7

Which property is shown by the following statement? (13 + 3)+ 8 = 13 + (3 + 8)

Associative Property of Addition

Graph and classify the system of equations as independent, inconsistent, or dependent. If the system is independent, find the solution from the graph. 3x+2y=2 3x-y=8

Independent (2,-2)

In May, Victor bought 24 styrofoam balls and decorated them as toy figurines. In June, he sold 17 figurines. In May, Wanda bought 28 styrofoam balls to decorate and in June, she sold 12 figurines. Which matrix represents all of their May purchases and their June sales?

May June Victor [24 -17 Wanda 28 -12]

Ms. Kim, an analyst at Multi-Fastener Corp, has developed a model to forecast the company's total production of metal fasteners. Under this model, production, P, is equal to 4500 times the man-hours spent producing machine screws (S) plus 2900 times the man-hours spent producing nuts and bolts (P). Manpower constraints mean that total number of man-hours per year cannot exceed 44,000; logically, the number of man-hours assigned to either task cannot be negative. Express the model in mathematical form.

P=4500S+2900B S+B is less than or equal to 44,000 S is greater than 0 B is greater than 0

Hans pays $205 in advance on his account at the athletic club. Each time he uses the club, $10 is deducted from the account. Write an equation that represents the value remaining in his account after x visits to the club. Find the value remaining in the account after 11 visits.

Response: V = 205 - 10x; $95

A server at a restaurant kept track of the number of requests for the daily special, and the time of day the request was made. The data is displayed below. If the data were displayed on a scatter plot, could the correlation of the data be represented by a linear model? If there is a linear correlation, is there a positive or negative correlation?

The data have no reliable correlation.

Ivan Bogdanovich plans to decorate stuffed animals to sell at a crafts fair. The decorations cost $44.00 and the stuffed animals cost $5.25 each. a. Write a function expressing the cost, C(x), of the project in terms of the number of stuffed animals decorated, x. b. Determine the cost of decorating 25 stuffed animals. c. How many stuffed animals can be decorated with a budget of $227.75?

a. C(x) = 5.25x + 44.00 b. $175.25 c. 35

Describe how the graph of the function y=15(x+2)+4 can be obtained from y=3(x+2)

shift up 4 units, and vertically stretch by a factor of 5

Write the system of equations as a matrix equation. Then solve the system, if possible, by using a matrix equation. If not possible, classify the system. x+2y+z=-17 3x+7y+2z=-56 x-y+2z=0

x=-4, y=-6, z=-1

Write the pair of parametric equations as a single equation in x and y. x=8t^2 -3 y=6t-7

x=8(y+7/6)^2 -3

If f(x)=49-x^2 and g(x)=7-x, which is the rule of function (f*g)(x)

x^3-7x^2-49x+343

If f(x)=1-x^2 and g(x)=1-x, which is the rule of function (f times g) (x)

x^3-x^2-x+1

Write the slope-intercept form of an equation of the line that passes through the point (3, - 6) and has the slope .

y=-4x+6

Write an equation in slope-intercept form of the line that passes through (- 5, 4) and is parallel to the graph of .

y=-4x-16

Write the pair of parametric equations as a single equation in x and y. x=t+6 y=-t-4

y=-x+2

Write the equation of the line, in slope-intercept form, that contains the point (-1, - 5) and is perpendicular to the line -8x-4y=3.

y=1/2x-9/2

Write the pair of parametric equations as a single equation in x and y. x= 8t-4 y=6t^2-2

y=6(x+4/8)^2 -2

Write the pair of parametric equations as a single equation in x and y. x=9t y=7t-4

y=7/9x-4