Alg 1 2nd semester test review

Use substitution to solve the system x+2y=1 and 2x+5y=3

(-1,1)

Where on the graph of 2x-6y=7 is the x-coordinate twice the y-coordinate?

(-7,-3½)

Use graph D on the board to find a solution of the system of inequalities.

(1,1)

Use substiution to solve the system of equations. n=3m-11 2m+3n=0

(3,-2)

Use elimination to solve the system of equations. x-y=5 x+y=3

(4,-1)

Use elinination to solve the system of equations. x+6y=10 x+5y=9

(4,1)

Use substiution to solve the system x-2y=1 and 6x-5y=20.

(5,2)

Simplify (m⁶n³)/(m²n⁶)

(m⁴)/(n³)

216^(x+1) = 6

-(2/3)

If x=2 and 3x+y=5, what is the value of y?

-1

If x=2y+3 and 4x-5y=9, what is the value of y?

-1

Solve (2^(3x+10))=128

-1

Solve the system and find the value of y 3x+4y=-30 2x-5y=72

-12

If x=5y-1 and 2x+5y=-32, what is the value of y?

-2

Solve the system and find the value of y. 6x+3y=12 5x+3y=0

-20

(3x + x² - x³) - (x³ +2x² + 5x)

-2x³ - x² - 2x

(3y³-11y+3) - (5y³+y²+2)

-2y³-y²-11y+1

Use elimination to solve the system 8x-7y=5 and 3x-5y=9 for y.

-3

(10x⁸y⁵)/(-2xy²)

-5x⁷y³

Simplify (3w²r²)²(-2w⁵r²)³

-72w¹⁹r⁸

(-2x²y⁻⁵)³

-8x⁶y⁻¹⁵

Use elimination to solve the system 5x+4y=-10 and 3x+6y=-6 for y.

0

10⁰

1

4⁰

1

a⁷/a⁷

1

Evaluate (6.08x10⁷)/(3.8x10^-2)

1.6x10⁹

10⁻²

1/100

5⁻³

1/125

15⁻²

1/225

5⁻¹

1/5

2⁻³

1/8

Simplify (z²w^-1)³/(z³w²)²

1/w⁷

(3y+7)(4y+5)

12y² + 43y + 35

Use elimination to solve the system x-4y=1 and x+2y=19 for x.

13

When solving the system of equaitons, which expression could be substituted for y in the second equation? 3x+y=14 x+4y=3

14-3x

When solving the system of equations, which expression could be substituted for x in the second equation? x+2y=15 5x+y=21

15-2y

The length of a rectangle is three times the width. The sum of the length and the width is 24 inches. What is the length of the rectangle?

18 inches

Simplify (2x³y⁵)/5(x⁴y²)³

2/5x⁹y

Colortime Bakers wants to make 30 pounds of a berry mix that costs $3 per pound to use in their pancake mix. They are using buleberries that cost $2 per pound and blackberries that cost $3.50 per pound. How many pounds of blackberries should be used in this mixture?

20lb

(-5x⁴yz⁸)²

25x⁸y²z¹⁶

The solution to which system of equations has an x-value of 3?

2x+3y=0 x+2y=-1

Solve the system and find the value of y. 2x+3y=1 5x-4y=-32

3

(7.8x10^-3)(4x10^-4)

3.12x10^-6

(2xy)⁵

32x⁵y⁵

(5x+7)(7x+3)

35x² + 64x + 21

(2a³ + 3a² + 7a) + (a³ + a² - 2a)

3a³ + 4a² + 5a

(k+4)(3k-4)

3k² + 8k - 16

The solution to which system of equations has a y-value of -2?

3x-y=2 y=-x-2

(2x²+9x-17) + (x²-6x-3)

3x² +3x - 20

Use elimination to solve the system 4x+7y=-14 and 8x+5y=8 for x.

3½

Solve the system and find the value of y 3x-5y=-35 2x-5y=72

4

To eliminate the variable y in the system of equations, multiply the second equation by which number? 6x+4y=22 2x-y=1

4

Use elimination to solve for x in the system of equations. 2x+2y=10 2x-3y=5

4

Use elimination to solve the system 3x+5y=16 and 8x-5y=28 for x.

4

When solving the system of equatoins, which expression could be substituted for r in the second equation? r=4-t 3r+2t=15

4-t

8^x = 16

4/3

(24a²b) / (6ab)

4a

(5n³ - 2n² + 2) - (n³ + 3n² - 2)

4n³ - 5n² + 4

(4x+3)(x-7)

4x² - 25x - 21

An airport shuttle company owns sedans that have a maximum capacity of 3 passengers and vans that have a maximum capacity of 8 passengers. Their 12 vehicles have a combined mazimum caplacity of 61 passengers. How many vans does the company own?

5

Use elimination to solve the system x+7y=14 and 3x-7y=4 for x.

5

Use elimination to solve the system x-5y=20 and x+3y=-4 for x.

5

Simplify (-10m^-1y⁰r)/(-14m^-7y^-3r^-4)

5m⁶y³r⁵/7

5x⁴/x²

5x²

Use eliminaiton to solve the system 4x+6y=10 and 2x+5y=1 for x.

5½

(4.2x10⁹)(1.6x10^-5)

6.72x10⁴

Coffee Cafe makes 90 pounds of coffee that costs $6 per pound. The types of coffe used to make this mixture cost $7 per pound and $4 per pound. How many pounds of the $7 per pound coffee should be used in this mixture?

60lb

(4x⁵y)³

64x¹⁵y³

(3w+4)(2w-1)

6w² - 5w - 4

(x² - 6) + (5x² + x - 3)

6x² + x - 9

(3x+4)(2x-1)

6x²+5x-4

Express 0.000702 in scientific notation

7.02x10^-4

(3x)⁴

81x⁴

exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself.

zero power property

Any nonzero number raised to the power of zero equals 1.

(2a - 5)(2a + 5)

Factor Completely

(3a + 7)(2a + 3)

Factor Completely

(3v + 2)(v - 1)

Factor Completely

(3x - 1)(x + 3)

Factor Completely

(4k + 1)(4k - 1)

Factor Completely

(4m + 1)²

Factor Completely

(4n - 1)²

Factor Completely

(n - 7)(10n + 1)

Factor Completely

(r + 6)(r - 9)

Factor Completely

(x - 9)(x - 4)

Factor Completely

2n(n-8)

Factor Completely

3b(b+10)

Factor Completely

r(r+1)

Factor Completely

3n(n-1)

Factor completely

Manuel is 8 years older than his sister. Three years ago he was 3 times older than his sister. How old is each now?

Manuel is 15 years old; his sister is 7 years old.

base

The number that is multiplied by itself

Negative Exponents

To make a negative exponent positive do one of the following: If the negative exponent is in the numerator position, shift the power to the denominator position. OR If the negative exponent is in the denominator position, shift the power to the numerator position.

quotient rule

When dividing two powers that have the same base, you can subtract the exponents.

product rule

When multiplying two powers that have the same base, you can add the exponents.

power to a power rule

When you have an exponent raised to another exponent you keep the base and multiply the exponents.

(a-11)(a+5)

a² - 6a -55

(d+9)(d-11)

d² + 2d - 99

Determine the best method to solve the system of equations 5x-2y=4 2x+2y=8

elimination using addition

Use graph C on the board to determine the number of solutions for the system 3x-3y=-6 and y=x+2

infinitely many solution

Use graph A on the board to determine the number of solutions for the system y=2x and y-2x=0

infinitely many solutions

Use graph A on the board to determine the number of solutions for the system y=2x and y=2x-4

no solution

Use graph B on the board to determine the number of solutions for the system y=3x+3 and 3x-y=2

no solution

Simplify (n⁵)(n²)(r³)(r⁴)

n⁷r⁷

Use graph A on the board to determine the number of solutions for the system y=-3x+2 and y=2x

one solution

Use graph B on the board to determine the number of solutions for the system x+2y=-1 and 2x+3y=0

one solution

Use graph C on the board to determine the number of solutions for the system x+y=0 and 3x-y=2

one solution

Determine the best method to solve the system of equation y=3x+12 2x+y=16

substituion

Determine the best method to solve the system of equations. Then solve the system. x-3y=0 2x-7y=0

substitution; (0,0)

The solution to which sytem of equaitons has a y-value of 0?

x+2y=-1 y=3x+3

The solution to which system of equations has an x-value of -1?

x+y=0 3x-3y=-6

Your teacher is giving a test that has 12 more three point questions than five point questions. The test is worth 100 points. Which system represents this information?

x-y=12 3x+5y=100

Your teacher is giving a test that has 5 more four point questions than six point questions. The test is worth 120 points. Which system represents this information?

x-y=5 4x+6y=120

The substitution method should be used to solve which system of equations?

x=3y+1 2x+y=7

(x+7)(x+5)

x² + 12x + 35

(3x³+7x²) + (x² - 2x³)

x³ + 8x²

(x⁴)³

x¹²

(x²)⁵

x¹⁰

x² ⋅ x³

x⁵

x⁵⋅x

x⁶

x² ⋅ x⁵

x⁷

x² ⋅ x⁶

x⁸

What system of inequalities is represented by graph D?

y<x+2 y≥-x+1

Use the graph A on the board to determine to which system of equations the ordered pair (3,2) is the solution.

y=(-1/3)x+3

The substitution mehtod should be used to solve which system of equations?

y=3x+1 2x+4y=5

What system of inequalities is represented by graph E on the board?

y>-2x+1 y≥(1/5)x-1

Which system of inequalites is represented by graph F on the board?

y≥-3x y<(1/4)x-(2/3)

2⁻²

¼