Algebra 2 Chapter 1-8

Use elimination to solve the system of equations

( - 22/21, - 13/21 )

Solve the system of equations by substitution

(-2, 6)

Which of the given ordered pairs are NOT solutions to the system of inequalities?(3, 1), (-3, -2), (5, -5), (-2, 4), (-4, 5)

(-4, 5), (3, 1), (-2, 4)

Use elimination to solve the system of equations

(-7, -2)

Use a graph to solve the system of equations

(1, -5)

Solve the system of equations by substitution

(5, 1, 3)

Factor the quadratic expression. x^2 - 11x + 30

(x - 5) (x - 6)

Solve the equation. Give exact solutions. Then approximate the solution to the nearest hundredth. 4x^2 = 8

+- squareroot 2; +-1.14

Simplify

- 1/x + 7

Solve the radical equation. If there is no real solution, write no solution

- 7/64

Find all the zeros of the polynomial function.

-3; -1 +- i squareroot 11/2

Solve the equation. Give exact solutions. Then approximate the solution to the nearest hundredth, if 2(x + 4)^2 - 48 = 0

-4 +- squareroot 6; 0.9 or - 8.9

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

-6

Find the discriminant, and determine the number of real solutions. Then solve. X^2 + 10x + 41 = 0

-64; 0; -5 +- 4i

Find the determinant, and tell whether the matrix has an inverse

-95; Yes

Simplify the expression. (- u)^3(-u^9)^8/(u^5)^3

-u^60

Use a graph, synthetic division, substitution, and factoring to solve the equation. x^3 + 8x^2 - 9x = 0

0, -9, 1

The turnstiles at the entrance to the State Fair kept track of the number of people entering the fairgrounds, for the first seven hours following the opening of the fair. Find a quadratic equation that models the data shown.

0.083x^2 - 0.197x + 7.62

Simplify. 2+5i/5+4i

30/41 + 17/41 i

Find the determinant, and tell whether the matrix has an inverse

30; Yes

Evaluate the expression. (2/5)^5

32/3125

Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary.

4, 5, +- 3.16

The function approximates the number of nematodes in a certain sample

4^9, 33,554,432

Use the quadratic formula to solve the equation. 6x^2 - 24x - 30 = 0

5, −1

Write the product as a polynomial in standard form.

5x^4 - 42x^3 + 11x^2 - 36 - 10

Use the quadratic formula to solve the equation. 2x^2 - 7x + 1 =0

7 +- squareroot 41/4

Evaluate the radical expression:

72

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

72/5

Simplify. 3x^2 - 4x - 5 + 4x^2 + 8x - 7

7x^2 +4x - 12

Simplify. 2x^2-5x+5x^2-3x-2+3

7x^2-8x+1

The magnitude of an earthquake is found by the equation , where M is the magnitude and E is the energy released. Find the magnitude of an earthquake that released ergs of energy.

8.4

Classify the polynomial by degree and number of terms. Describe the shape of its graph.

cubic monomial; 'S' shaped with 2 turns

Solve the equation for x. Write the exact solution and the approximate solution to the nearest hundredth, when appropriate. In(8x - 6) =3

e^3 + 6/8 = 3.26

Determine whether the function is a rational function. If so, find the domain and identify the horizontal and vertical asymptotes, and any holes in the graph. If the function is not rational, state why not

f(x) = (x - 1)/ (x - 7) (x + 3)

Which of the following is a quadratic function?

f(x) = -1 + 9x^2 + 7x

Write a polynomial equation in standard form by using the given information. P is of degree 3; P(0) = 24; zeros: 3, -4, 2

f(x) = x^2 - 10x + 34 5 +- 3i

The graph of 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

Classify the following system of equations as inconsistent, dependent, or independent:

independent

Write the equation in logarithmic form

log6 1/1296= -4

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

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

Write the pair of parametric equations as a single equation in x and y.

Y = -x + 2

Which inequality is best represented by the graph shown:

Y =< -x^2 + 5x

Find the real zeros of the function. Give approximate values to the nearest hundredth , if necessary.

3, -2, +- 3.16

The inflation rate of the U.S. dollar is 3.1 percent. What this means is that every year, prices increase by 3.1 percent. If a pound of meat cost $2.37 nine years ago, what does it cost now?

$3.12

If a principal of $1250 is invested at an annual interest rate of 4% compounded annually, what is the account balance at the end of 6 years?

$1582

If $1500 is invested at an interest rate of 10%, compounded continuously, determine the balance in the account after 2 years. Use the formula

$1832.10

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

$23.75

Solve the equation for x. 10^x = 18

1.26

Evaluate the expression to the nearest thousandth. If the expression is undefined, write undefined:

1.284

Use factoring and the Zero-Product Property to solve the quadratic equation. 2x^2 + 5x - 3 = 0

1/2, -3

What is the missing measure for a right triangle with lengths b: 12 inches and c: 16 inches; given that c is the length of the hypotenuse?

10.58 in

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

10/5 = 16/8

Evaluate the expression. 64 * 4^2 - 2 * 2^2

1016

Evaluate x^4 - 10x^2 + 24 when x = 3

15

Find the value of x to the nearest hundredth.

17.2

Evaluate when x=2.

18

Solve the equation. Round your answers to the nearest hundredth. 4x = 36

2.58

An airplane, flying at an altitude of 3.21 miles above the ground, has a horizontal speed of 350 miles per hour and is descending at a rate of 14 miles per hour. Use parametric equations to find the airplane's altitude above ground after it has traveled 11 miles, as measured along the ground.

2.77 mi

Simplify

21x^3 - 8x^2 + 14x - 36/36x^2

Solve the equation. Round your answers to the nearest hundredth.5^x-1 = 25

3

After taking 7 quizzes, your average is 77 out of 100. What must your average score be on the next five quizzes to increase your average to 82?

89

Evaluate 8 logs^9

9

Evaluate the expression. (27) ^2/3

9

The Associative Property of Addition (- 3/8)^2

9/64

Designer Dolls, Inc. found that the number of dolls sold, N, varies directly as their advertising budget, A, and inversely as the price of each doll, P. Designer Dolls, Inc. sold 8400 dolls when $84,000 was spent on advertising and the price of a doll was set at $70. Determine the number of dolls sold when the amount spent on advertising is increased to $98,000.

9800

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.

: (-5, -4)

Erosion gradually reduces the size of a small Pacific island that has a current area of just 460 acres. If the island's area decreases at an annual rate of 0.05%. Find the multiplier for the rate of exponential decay.

: 0.9995

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

Use a graph, synthetic division, substitution, and factoring to solve the equation. x^3-7x^2 = 14 x- 8=0

: 2, 1, 4

Use factoring and the Zero-Product Property to find the zeros of the quadratic function. f(x) = x^2 - 7 - 8

: 8, -1

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

A = 8B + 77/7

Graph and classify the system of equations as independent, inconsistent, or dependent. If the system is independent, find the solution from the graph

Independent (2, -2)

Use a graph, synthetic division, substitution, and factoring to solve the equation. x^3 - x^2 - 4x^2 + 7x -12

None of the listed answers are correct

Write a polynomial equation in standard form by using the given information. P is of degree 3; P(0) = 24; zeros: 3, -4, 2

P(x) = x^3 - x^2 - 14x + 24

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

Response: 4x +y - 5 =0

Use the graph of the feasible region for the set of constraints to find the maximum and minimum values of the objective function . Constraints:

Response: The maximum value of C is 29 at (3, 4) and the minimum value is 3 at (1, 0) .

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

The Associative Property of Addition

Solve the equation or formula for the variable specified. B = 7a^b, for b .

b = B/7a^2

Describe how the graph of the function can be obtained from the graph of .

move it 3 to the right

Which system of equations can be classified as independent?

none of these

Classify the polynomial by degree and number of terms. Describe the shape of its graph.

quadratic trinomial; parabola

Determine the end behavior of the graph of the function

rises to the left; rises to the right

Simplify the rational expression.

x + 7/2

Simplify the rational expression.

x - 5/x - 4

Solve the equation or inequality.

x = - 11

For the quadratic function, write the equation of the axis of symmetry, and find the coordinates of the vertex. y = 9x^2 - 54 + 78

x = 3; (3, -3)

Write the pair of parametric equations as a single equation in x and y.

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

Solve the equation or inequality.

x =- -4 or x > 6; undefined at -6

Solve the radical inequality

x =< 7/3

Find the domain of the radical function.

x =< 9

Solve the radical inequality.

x => 22

Solve the equation by completing the square. Give exact solutions.

x^2 - 2x - 24 = 0

If and , which is the rule of function ?

x^3 - 3x^2 - 9x + 27

If and , which is the rule of function ?

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

Write the product as a polynomial in standard form.

x^3 -5x^2 -26x + 120

Write the quadratic equation in vertex form. Give the coordinates of the vertex and the equation of the axis of symmetry. y = x^2 + 14x + 4

y = (x + 7)^2 - 45 (-7, -45); x = -7

Gupta threw a baseball off a cliff into an open field 50 feet below. The chart gives the horizontal distance, x (in feet), the baseball traveled from Gupta and the height, y (in feet), of the baseball above the field. Choose the quadratic equation that best fits the baseball's trajectory from Gupta to the open field below.

y = -0, 0383 x^2 + 2. 143x + 50

Write an equation in slope-intercept form for a line that passes through the given pair of points. (4,-7), (-2,-10)

y = 1/2 x - 9

Which equation is best represented by the following graph?

y = 5/2 x - 7

Write an equation in slope-intercept form for a line that passes through the given pair of points. (-6,5), (-9,0)

y = 5/3x + 15

Write the pair of parametric equations as a single equation in x and y.

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

Write the pair of parametric equations as a single equation in x and y.

y = 7/9 x - 4

Which function represents exponential decay?

y(x) = 5(0.44)^x

When Spheres-R-Us ships bags of golf balls, each bag must be within 5 balls of 370. Identify the inequality which results in an acceptable number of golf balls in each bag.

|370 - b| < 5 Less than equals