Math Midterm

Name the constant of variation for the equation. Then find the slope of the line that passes through each of the point: y = -5x

Constant of Variation: -5 Slope: -5

Classify the function f (x) = x(x + 1) (x + 2)

Cubic

Chose the best method to solve the following system of equations: 4x + 2y = 12 -4x + 5y = -5

Elimination

What would be the best method to solving the following system of equations: 3x + 2y = 8 -3x + 6y = 12

Elimination

Which functions have asymptotes

Exponential & Rational

Which function will have a MAXIMUM value?

F (x) = -x^2 + 3

What is the inverse of f (x) = √x-4

F -1 (x) = x^2 + 4

What is the inverse of f (x) 3√x

F -1 (x) = x^3

What is the shape of the graph f (x) = 1/x

Hyperbola

Paul is in the landscaping business. He charges $25 per job for lawn mowing. Write an equation to model Paul's income from lawn mowing. Let I = income and x = lawn mowing job.

I = 25x

Solve the following systems of equations using ANY method: X - y = 3 4x - 4y = 12

Infinitely Many Solutions

What is the slope of a line parallel to the line y = 1/2x + 2

M = 1/2

What is the slope of a line perpendicular to the line y = -3/4x + 4

M = 4/3

27(1)=27

Multiplicative Identity

7(0)=0

Multiplicative Property of Zero

What is the 1st step in solving the equation 6-10x/3=5?

Multiply by 3

Determine whether or not the following is a linear equation. If it is write it in standard form: x^2 - y = 13

NO; Exponent

Substitution should be used to solve which of the following systems?

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

Write the equation for the following problem in point slope form: A line passing through the point (10,-20) with a slope of 13

Y + 20 = 13(x -10)

Which function will have a line of symmetry at x = 4

Y = (x - 4) ^ 2

Write the slope intercept equation of a line PERPENDICULAR to y = 3x -8 and passes through the point (6,1)

Y = -1/3x + 1

Write the equation for the following problems in SLOPE INTERCEPT form: A line passing through the points (2,1) and (-3,9)

Y = -2x + 3

Write the equation of the asymptote for the equation y = 2^x - 3

Y = -3

Use the points (2,330) and (5,165) to write an equation for the line of best fit. Let x = # of hours Sarah has traveled let y = # of miles Sarah is away from home

Y = -55x + 440

A tax charges a $3.50 flat fee Ann $0.55 per mile. Write an equation to model this scenario when x represents the number of miles and y represents the total cost

Y = 0.55x + 3.50

Find the equation of a line through (4,12) that is PERPENDICULAR to y = -2x

Y = 1/2x + 10

Let x = a number. Let y = a different number. The following two equations describe their relationship . x + y = 28 2y + x = 30

Y = 24

Which equation is PARALLEL to the line 2y = 10x + 8 is directly proportional?

Y =5x

Write the slope intercept equation of a line PARALLEL to y = -4x + 5 and through the point (-2,3)

Y= -4x -5

The x- coordinate of the y- intercept is always...

Zero

Solve the following proportion: 7 a ---- = ----- 12 a + 5

a = -7

Solve: -3(2a- 6) = 4(a + 7)

a = 1

Solve for the specific variable: 6a + b = c, for a

a = c-b ------ 6

What is the slope of the line x = 6

m = undefined

Solve the following systems of equations using ANY method: X = 5 - 3y 8y + 2x = 14

(-1,2)

Solve the following systems of equations using ELIMINATION: X - 5y = -5 -X - 2y = 12

(-10,-1)

Which if the following points would NOT be on the line for y + 12 = -4(x -2)

(-2,12)

Solve the following systems of equations using ANY method: 7x + 4y = 6 5x + 6y = 20

(-2,5)

What is the vertex of (x) = (x + 6) ^ 2

(-6,0)

Solve the following systems of equations using SUBSTITUTION: -5x + 2y = 12 y = x - 6

(-8,-14)

What is the y intercept of f (x) = (x + 6) ^ 2

(0,36)

Solve the following systems of equations using ANY method: 9x - 2y = -8 -7x + 3y = 12

(0,4)

Solve the following systems of equations using ELIMINATION: X + y = 9 3x + 8y = 2

(14,-5)

The sum of two numbers is 34. The difference of these two numbers is 6. Find the two numbers.

(20,14)

Solve the following systems of equations using SUBSTITUTION: X = 4y + 5 X = 5y - 2

(33,7)

Find the x- intercept of 3x + 4y = 12.

(4,0)

Solve the following proportion: 6 3 ---- = ---- n 12

n = 24

The sum of three consecutive integers is 153. What equation models this?

(x) + (x+1) + (x+2) = 153

If x = 5y - 1 and 2x + 5y = -32 what is the value of x that makes both equations true?

-11

Simplify: 9(4 - w) - 5(10w- 4)

-59w+ 56

If f (x) = 4x + and g (x) = x^2 - 4x + 10 find the following: f (-3)

0

Your mom put $50 on your ID card at the beginning of the semester for lunch. Every day you purchase lunch for $4.75. Let x = # of lunches purchased. Let y = $ left on the card. What is the domain of this scenario?

0 to 10 lunches

Sarah buys 10 dresses and 2 jeans for $300. Tiffany buys 3 dresses and 6 jeans for $200. Write a system where d represents the number of dresses and j represents the number of jeans

10d + 2j = 300 3d + 6j = 200

Determine whether or not the following is a linear equation. If it is write it in standard form: -30y = 20 + 10x

10x + 30y = -20

Solve: 17+1*4-9/3

18

Solve: 108/[3(9+^2]

2

Find the slope of the line that passes through each pair of points: (-3,14) and (2,16)

2 ---- 5

If f (x) = 4x + and g (x) = x^2 - 4x + 10 find the following: g (4) + 11

21

If f (x) = 4x + and g (x) = x^2 - 4x + 10 find the following: g (-2)

22

Simplify: 3(y^2 -3y +12) -y^2 +5y

2y^2 -4y +36

Solve: 5 + 2(n - 1) = 2n

3 doesn't = 0; False

The scale on a blueprint says 4 inches is 9 feet. The house Sally is building will have a bathroom that is 16 feet wide. Write a proportion to find the width of the bathroom in inches on the blueprint.

4 in = x in ------ ------ 9 ft = 16 ft

If f (x) = 4x + and g (x) = x^2 - 4x + 10 find the following: f (k - 5)

4k - 8

If you rent 25 movies from Netflix it costs about $100. How many MORE movies could you rent at Family Video for $100

5

Using the taxi scenario from above how many miles could you ride in the taxi for $50. Your answer should be rounded to the nearest whole mile

85 miles

Solve the following equation for c = 5/9 (f-32)

9/5c + 32= f

2/3*3/2=1

Additive Identity

The following is using which property (-28) + 5x +28= -12+ (-28)?

Additive Inverse

x + (-x) = 0

Additive Inverse

Todd is comparing on-line video rental memberships. Netflix has a $12 membership fee and rents one movie at a time for $3.50. Family Video has a $40 membership fee, but rents one movie at a time for $2.00. Write a system of equations to model this scenario. Let C = total cost of membership and rentals let v = number of videos.

C = 3.50v + 12 C = 2v + 40

Christy's cell phone costs her $3 per minute plus $50 a month. Write an equation to represent the cost of Christy's cell phone for one month. Use the variable C for the cost for one month and m for number of minutes.

C = 3m + 50

The equation c (h) = -7h + 35 models a student passing out cards on Valentine's day at the beginning of each class hour. Let h = class hour and C = # of cards left. You passed out your first set of cards at the beginning of first hour. When will you have 14 cards left at the end of the hour?

end of 3rd hour

Solve for the specific variable: 5g + h = g, for g

g = h ---- - 4

Jane is offered a job with two pay options. Option A pays $30 a week plus a one time signing bonus of $500. Option B pays $400 per week. The following equations represent Jane's two pay options. C = amount of Jane's paycheck, w = number of weeks. Option a: C = 300w + 500 Option b: C = 400w

Choose option A if planning at the job for less than 5 weeks. Choose option b if planning on working at the job for more than 5 weeks. If plan on working for just 5 weeks then it doesn't matter what plan you pick because you'll make the same amount with either or

Identify the name of each form of a linear equation: y - y1 = m(x - x1)

Point Slope

Write the equation for the following problems in STANDARD and SLOPE INTERCEPT form: y - 5 = 6(x + 7)

Slope Intercept form: y = 6x + 47 Standard form: 6x - y = -47

Write the equation for the following problems in STANDARD and SLOPE INTERCEPT form: y + 8 = -3(x - 6)

Slope Intercept: y = -3x + 10 Standard: 3x + y = 10

Identify the name of each form of a linear equation: y = mx + b

Slope- Intercept form

Identify the name of each form of a linear equation: Ax + By = C

Standard Form

How would you find the y intercept of a function y = |x + 2| - 1

Substitute 0 in for x

Choose the best method to solve the following system of equations: X = 2y + 1 3x + y = 17

Substitution

The equation 5x = 10y = 60 represents the number of children and adults who can attend the rodeo for $60. Tickets for a rodeo cost $5 for children and $10 for adults. Let x = # of children and ley y = # of adults. If this scenario were graphed what would the y- intercept model?

The most number of adults that could attend would be 6

Using the Valentine's day card scenario from above, what does C (2) represent?

The number of cards left 2 hours after you started

Consider the system y = 6x - 3 and y = 3x - 7

The solution is the point where the lines intersect

The domain represents what in a relation?

The x values

What is the shape of the graph f (x) = x^2

U shaped Parabola

What is the shape of the graph f (x) = |x|

V shaped

Find the slope of the line that passes through each pair of points: (-4,10) and (-4,5)

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Romeo Plank Road is modeled by the equation x = 5. What would be the equation for Garfield Road?

x = -5

Which equation has a slope of zero?

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

Graph the following and determine the x- intercept and y- intercept: 9x - 6y = 18

x- intercept: (2,0) y- intercept: (0,-3)

Write the equation of a horizontal line with a y- intercept of (0,5)

y = 5

What is the range of the following relation?: {(-4,3) , (0,3) , (2,1) , (-3,5) , (-3,1)}

{1,3,5}