Algebra II Midterm Exam Study Guide

Which is the other point of intersection?

( 1 1 /2 , 4 1/ 2 )

Find the exact solution for the following system of equations: 2x + 3y = 4 8x + 6y = 11

( 3/4, 5/6)

Identify the roots of the function pictured below. (0, 0) (-2, 0) (-1, -1) (2, 0)

(0, 0) (-2, 0)

Select the solution(s) to the system of equations.

(0,-1)

Graph to estimate the solution(s) of this system. (1, 0) (0.65, -1.19) (-2, 0) (3.73, 0) (0.74, -1.42)

(0.65, -1.19)

Use the given information on the graph to determine the coordinates of Point Q. Point Q: (____,___)

(2,6)

Solve the system of linear equations: (___,___)

(3,-4)

Choose the two equations that describe the ticket prices and revenue for the two shows. Let c equal the number of children tickets and a equal the number of adult tickets. * 2c + 5a = 200 * 5c + 15a = 550 * 5c + 15a = 200 * 2c + 15a = 550

* 2c + 5a = 200 * 5c + 15a = 550

Choose the two equations that represent the quantity of nuts, quantity of raisins, and total cost. Let n represent the price of nuts per pound, and r represent the price of raisins per pound. * 5n + 2.5r = 12 * 2n + 1r = 30 * 5n + 2.5r = 30 * 2n + 1r = 12

* 5n + 2.5r = 30 * 2n + 1r = 12

Which of these inequalities can be represented by the graph? * Y > -x -4 * Y ≤ 4 - x * Y > x - 4 * Y > 4 - x * Y < -x + 4 * Y ≥ -x - 4

* Y > -x -4

Which of the following are endpoints of the feasible region? Select all that apply. - (8, 6) - (9, 1) - (1, 5) - (6, 8) - (1, 9) - (9, 5) - (-3, 2.5)

- (9, 1) - (1, 5) - (6, 8)

Choose the statements that describe this system of equations. Select all that apply. - Exactly one solution to the system of equations. - No solution to the system of equations. - This system represents parallel lines. - There are infinitely many solutions to the system. - Both equations represent the same line.

- No solution to the system of equations. - This system represents parallel lines.

Choose the statements that describe this system of equations. Select all that apply. - No solution to the system of equations. - There is exactly one solution to the system. - The system of equations is parallel. - All real number ordered pairs are solutions to the system. - The system of equations can be represented by one linear equation. - There are infinitely many solutions to the system.

- The system of equations can be represented by one linear equation. - There are infinitely many solutions to the system.

Malcolm and Trish

11

When x = 10 meters, the anchor will be placed on the tower at ____ meters. Round your answer to the nearest tenth if necessary.

14.5

What is the height, in meters, where the pumpkin lands on the hill?

8

Emily wants to purchase a mix of used paperback and hardcover books. She would like to maximize the total number of books,p + h, where p is the number of paperbacks and h is the number of hardcovers. She does have constraints, however. She only has $75 to spend, only has 86 centimeters of self-space available, and would like to make sure the mix of books she buys includes at most twice as many paperbacks as hardcovers. Paperbacks are $2.00 each and 3 centimeters wide, and hardcovers are $8.50 each and 6 centimeters wide. Enter values in the spaces provided to complete mathematical statements of the three constraints on cost, space, and mix. Cost: (___)p + (___)h ≤ ____ Space: (___)p + (___)h ≤ ___ Mix: ___p ≤ ___h

Blank 1: 2 Blank 2: 8.5 Blank 3: 75 Blank 4: 3 Blank 5: 6 Blank 6: 86 Blank 7: 1 Blank 8: 2

Describe the relationship between Suzie's pay function and Brenan's pay function using the appropriate vocabulary. The system has ________. The graph of the functions are _______. Blank 1: - No solutions - One solution - Infinitely many solutions Blank 2: - Parallel lines - Colinear - Intersecting lines

Blank 1: no solutions Blank 2: parallel lines

Plot the functions on the same axes. The system has _______. The graph of the functions are _______. Blank 1: - No solution - One solution - Infinitely many solutions Blank 2: - Intersecting lines - Parallel lines - Collinear

Blank 1: one solution Blank 2: intersecting lines

Complete the profit function P. P(b,p) = 3___ ___ ___ ____ Blank 1: - P - b Blank 2: + - Blank 3: 2 13 11 Blank 4: b P

Blank 1: p Blank 2: + Blank 3: 2 Blank 4: b

A group of friends wants to spend no more than $50 on pizza and soda. Soda costs $2 per bottle, and pizza costs $8 per pizza. They want to make sure they have at least two pizzas for each bottle of soda. Let s be the number of sodas, P be the number of pizzas, and C be the total cost of their order. Identify the linear equations or inequalities in the system that allows the friends to determine possible orders that meet their requirements. Select all that apply.

C ≤ 50 C = 2s + 8p p ≥ 2s

Match each graph with the number of solutions: one real solution, two real solutions, infinitley many real solutions, or no real soluions

Graph 1: no real solutions Graph 2: one real solution Graph 3: two real solutions Graph 4: infinitely many real solutions

The lines correspond to these inequalities are shown in the graph to the right, along with the lettered regions they define. In the space provided, enter the letter of the region that defines the solution to the system of inequalities. J E B I C A G H K D F

H

Determine the coordinates of point P algebraically. P =( ___,___)

P = (0, -6)

Ali has been helping out a family by taking their kids to various activities, and then waiting for thme and taking them home after the activities. Normally, Ali is paid a fixed amount of $6 per week for gas money, as well as $4 per hour to wait for any time spent transporting or waiting for the kids. During the holiday weeks, however, both Ali's hourly rate and gas money are doubled due to the inconvenience. Choose the function(S) that represent Ali's holiday pay, P, in terms of the number of hours, h, that she works.

P(h) = 8h + 12 P(h) = 2(4h + 6)

Write a separate linear equation for both Suzie and Brenan that relate their babysitting hours (h) to their weekly pay.

Suzie: P(h)=8h+10 total weekly pay,P,=$8h + $10 Brenan: P(h) =8h+12 total weekly pay,P,=$8h+ $12

Classify each systems of equations and inequalities by how many solutions it has. No real solutions, infinitely many solutions, exactly 2 solutions, exactly one solution

System 1: Exactly one solution System 2: Exactly two solutions System 3: No real solutions System 4: Infinitely many solutions System 5: No real solutions

Which systems of equations and systems of inequalities have "no solution," "one solution," or "infinite solutions"?

System 1: no solution System 2: infinite solutions System 3: one solution System 4: infinite solutions System 5: one solution System 6: no solution

Solve the system algebraically, and compare it with the graph you created. Explain the intersection point of the two equations in terms of the context.

The intersection point of the two equations tells us that there is only one solution to these equations, meaning that there has to be a specific number of both children and adults that would work with both of the equations.

Solve this system of lines algebraically, uploading your justification. Explain what the solution means in terms of the context.

When you solve this system of equations algebraically, the equations end up equal to each other. When you substitute to solve one of the equations, you just end up with an infinite number of solutions.

Describe the difference between this infinite solution set and a solution of all real numbers.

With this infinite solution set, the solutions could be all natural numbers, or natural numbers between two boundaries. But with a solution set of all real numbers, the solution could contain natural numbers, whole numbers, integers, fractions, or irrational numbers.

graph the constraints on the same coordinate plane to find the feasible region. Find all vertex points. Test various points from the feasible region to determine values for c and k that will maximize the profit. How many of each type of lanyard should the lanyard maker make each week to maximize profit? a.) 15 keychain lanyards and 30 neck lanyards b.) 0 keychain lanyards and 36 neck lanyards c.) 0 keychain lanyards and 35 neck lanyards d.) 30 keychain lanyards and 20 neck lanyards e.) 30 keychain lanyards and 15 neck lanyards f.) 60 keychain lanyards and 0 neck lanyards

a.) 15 keychain lanyards and 30 neck lanyards

Between which two integer x-values is there certainly a point of intersection? a.) 3 and 4 b.) 2 and 3 c.) -1 and 0 d.) 1 and 2 e.) It cannot be determined from the information given.

a.) 3 and 4

How many quarters did Marco have? a.) 31 b.) 27 c.) 25 d.) 10

a.) 31

What can you conclude about the roots of the function and the solutions of the related system of equations? a.) The roots of the function are the solutions or the x-coordinates for the x-intercepts of the function. b.) The roots of the function are the solutions or the y-coordinates for the y-intercepts of the function.

a.) The roots of the function are the solutions or the x-coordinates for the x-intercepts of the function.

Rewrite the following system as one equation in standard form:

a.) h ( x ) = x^ 2 + x + 3

For what values is... a.) x = -2 and x = 14 b.) x = 4 c.) x = 2 and x = 14 d.) x = -14 c.) x = 2 and x = -14

c.) x = 2 and x = 14

Solve: no real solutions (0, 3) infinitely many real solutions (1, 2) (0, 0) (2, 0) (1, 1)

no real solutions

What is the solution for t?

no solutions

What does the discriminant tell you about the relationship between f(x) and g(x)? Since ________________________________they will never intersect.

the discriminant is less than 0

How does the cost per pound for the nuts at the online store compare to the cost at the brick-and-mortar store? The cost per pound for nuts at the online store is _________the cost at the brick-and-mortor store.

the same as

for which value of x...

x < 2 or x > 7

For what value(s) does... x = - 0.8 x = 4 x = 0.8 x = - 1.8 x = 1.8 x = 3 x = - 4 x = - 3

x = - 0.8 x = 4

Solve the system algebraically to find all real solutions. X = ___ y = ___

x = -1 + _/11i y = -1 - _/11i -------- --------- 2 2

Enter the values of x and y in the spaces below. x= ____ y=____

x = -11 y = 17

Solve: (1.637,2.406) (0, 4) (1, -1) infinitely many real solutions (1, 0) (-2.137, 11.844) no solution (0.167,-4.083)

(1.637,2.406) (-2.137, 11.844)

Find the sum and the difference of the linear functions f(x) + g(x) = ___ + ___ f(x) - g(x) = ___ + ___ Blank 1: 13x 2x -8x -2x Blank 2: -13 13 1 -1 Blank 3: 2x -8x -2x 13x Blank 4: -13 -1 1 13

Blank 1: 2x Blank 2: 1 Blank 3: -8x Blank 4: 13

Choose the statements that describe this system of equations. Select all that apply. No solution to the system. Exactly one solution Infinite solutions to the system.

exactly one solution

Solve: infinitely many real solutions no real solutions (-2, 0) (1, -1) (0, 4)

infinitely many real solutions

What are the possible solutions of a system composed of two quadratic equations? Select all that apply. infinitely many real solutions no real solution two real solutions one real solution

infinitely many real solutions no real solution two real solutions one real solution

Kiley earns $8 an hour as a cashier and $11 an hour babysitting. Last week she worked x hours as a cashier and y hours as a babysitter, for a total of 25 hours. She earned $227 . Select two equations that represent this situation.

x + y =25 8x + 11y = 227

Find the solution to the following system of linear equations. X = ___ Y = ___

x = -11 y = 17

For which of the following values of x is

x = 1 and x = 0.14

If the end-cable is to run from the shoreline bridge anchor, 3 meters below the deck, up to Tower 1 at the same height as the suspension cable, what is the equation of the line that models this end-cable? Y = ____ x = ____

x = 1.72 y = 3

If the system of inequalities includes the points (1, 1) and (0.2, 0), but does not include the points (2, 2), (4, 2), or (0, 4), what is the system of inequalities? Select the two inequalities that represent this system.

y > 2x - 2 y ≤ log2 (5x)

(___,___) and (___,___)

(3,4) and (4,1)

What is the solution to this system of equations?

(4,-3)

What is the solution to the following equation?

6

Which value of x is a solution to the system of equations? a.) -1 b.) 1 c.) 2 d.) -4 e.) 4

b.) 1

Choose all the inequalities that are constraints in this scenario. Consider time and materials. Let k equal the number of keychain lanyards and n equal the number of neck lanyards.

8k + 21n ≤ 750 k ≥ 0 1/3k + 1/2n ≤ 20 n ≥ 0

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graph is on study guide document

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Use the discriminant of h(x) to predict the number of solutions. a.) one real solution b.) no real solutions c.) two real solutions d.) three real solutions

b.) no real solutions

The discriminant of a function is: b² + 4ac ax² + bx + c b² - 4ac b - 4ac

b² - 4ac

The brown family has a cell phone plan with a flat rate for their family. The flat rate of $175 per month includes unlimited calls and texts with 15GB (gigabytes) of shared data. They are considering a similar plan whose flat rate is $150 per month but only includes 6GB of shared data. After 6GB, data charges are $5 per GB. What is the point where the cost for both plans is the same?

(12, 175)

Choose a single equation that can be used to solve the system of equations: f(x) = 2x + 5 g(x) = 3x -2

(2x + 5) - (3x - 2) = 0 2x + 5 = 3x -2

Some order combinations of fruit expressed as (# of oranges, # of apples) are shown below. Determine if the order combination meets the constraints or not. (7, 21): (8, 17): (8, 21): (8, 23): (9, 17): (9, 21): (10, 20): (10, 21):

(7, 21): does not meet the constraints (8, 17): meets the constraints (8, 21): meets the constraints (8, 23): does not meet the constraints (9, 17): does not meet the constraints (9, 21): meets the constraints (10, 20): does not meet the constraints (10, 21): does not meet the constraints

graph the constraints on the same coordinate plane to find the feasible region. Find all vertex points. Test various points from the feasible region in the profit function to find the maximum profit. Determine values for b and c that maximize the profit. How many bowls and cups should the potter make each week to maximize profit? - 72 bowls and 72 cups - 160 bowls and 0 cups - 147 bowls and 22 cups - 146.7 bowls and 22.2 cups - 146 bowls and 22 cups - 0 bowls and 120 cups

- 72 bowls and 72 cups - 147 bowls and 22 cups - 0 bowls and 120 cups

The city board limits the size of flyers that can be posted in public places. The graph below represents the constraints where x represents length, in inches, and y represents width, in inches. Which of the following statements are true? Select all that apply. - A flyer that is 4 inches long and 6 inches wide is acceptable. - The sum of the lengths and width must be greater than 20 inches. - The sum of the length and width must be no greater than 20 inches. - A flyer that is 10 inches long and 8 inches wide is acceptable. - The width of a flyer must be at least 2 inches greater than its length. - The width of a flyer must be at least 2 inches less than its length.

- A flyer that is 4 inches long and 6 inches wide is acceptable. - The sum of the length and width must be no greater than 20 inches. - The width of a flyer must be at least 2 inches greater than its length.

Which of the following statements are true about the graph of this system? Select all that apply. - Because the graph of the equations will be parallel lines, the system has infinitely many solutions. - Because the graph of the equations will be parallel lines, the system has no solution. - Because the equations are both linear, the graph will show that they intersect in one point. - Because the graph of each equation will have the same slope but different y-intercepts, the system has no solution. - Because the graph of the equations will be the same line, the system has infinitely many solutions.

- Because the graph of the equations will be parallel lines, the system has no solution. - Because the graph of each equation will have the same slope but different y-intercepts, the system has no solution.

Putting all this information together, explain what you notice about the following lines: - For equations that result in a system with no solution, what do you notice about the equations? - For equations that result in infinitely many solutions, what do you notice about the equations? - For equations that result in one solution, what do you notice about the equations?

- For equations that result in a system with no solution, I notice that the slopes are the same and the y-intercepts are different. - For equations that result in infinitely many solutions, I notice that the slopes and the y-intercepts are the same - For equations that result in one solution, I notice that the slopes are different.

Choose the statements that describe this system of equations. Select all that apply. - The system of equations is parallel. - The system of equations is inconsistent. - The system of equations can be represented by one linear equation. - There are infinitely many solutions to the system. - There is exactly one solution to the system. - The system of equations is dependent. - All real number ordered pairs are solutions to the system. - No solution to the system of equations.

- The system of equations can be represented by one linear equation. - There are infinitely many solutions to the system. - The system of equations is dependent.

If your task is to find intersections of f(x) and g(x), why would you need to find the complex roots? Select all that apply. - When we can't determine the roots based on the graphs. - When the number of real roots does not match the degree of the polynomial - Once there are no real roots, we need to find the rest

- When we can't determine the roots based on the graphs. - When the number of real roots does not match the degree of the polynomial - Once there are no real roots, we need to find the rest

rite your own equations: One equation of a system is 2y - 3x = 5. Write a second equation for each scenario: - the lines are parallel - the lines are coinciding (the same line) - intersecting at (1, 4)

- the lines are parallel: y = 3/2x + 5 - the lines are coinciding: y = 3/2x + 5/2 - intersecting at (1, 4): y= -2/3x + 14/3

Cheyenne correctly graphed the system of linear inequalities shown below. What was the system of linear inequalities that Cheyenne graphed?

2x - y < 3 x + 2y ≤ 2

A group of families is going on a camping trip to the mountains. They need to rent vehicles to transport every person and their camping equipment. They are renting both a number of vans (v), which hold 8 passengers in each vehicle, and a number of sedans (s), which hold 5 passengers in each vehicle. Between the two types of vehicles, they need to have room for 42 passengers. The vans cost (c) is based on $68 the first day and $50 for each additional day. The sedans cost $55 per day. They plan to rent 6 vehicles in total.

42 = 8v + 5s v + s =6

Identify the inequalities that represent constraints on the number of cans of dog food this company can produce each hour

4b + 7g ≤ 330 b ≥ 0 g ≥ 0 8b + 5g ≤ 340

Choose all the inequalities that are constraints in this scenario. Consider time and materials. let b equal the number of bowls and c equal the number of cups she makes during the week.

5/4b + 3/4c ≤ 200 1/6b + 1/4c ≤ 30 b ≥ 0 and c ≥ 0

Which system of equations could be used to determine the price per pound of almonds, a, and for peanuts, p, at the Nutty Factory?

6a + 10p = 84.84 3a + 7p = 50.40

Angela is purchasing supplies for a company picnic and has a maximum of $100 to spend. A package of hot dogs contains 10 hot dogs and costs $6. A package of hot dog buns contains 8 buns and costs $3.50. Angela wants the total number of buns to be within 10% of the total number of hot dogs. Which of the following inequalities represent constraints on the number of hot dogs (h) and the number of packages of buns (b)?

8b - 11h ≤ 0 9h -8b ≤ 0 6h + 3.5 ≤ 100

Complete the profit function: P(k,n) = ___ ___ ___ ___ ___ Blank 1: 3 20 30 Blank 2: n k Blank 3: + - Blank 4: 24 4 34 Blank 5: n k

Blank 1: 3 Blank 2: k Blank 3: + Blank 4: 4 Blank 5: n

The next tower location would be _____meters from the foundation, and _____ meters to the right of the first tower, anchoring at the same height of _____ meters. The representing linear equation is _____.

Blank 1: 30 Blank 2: 20 Blank 3: 14.5 Blank 4: x = 30

Complete the table by matching the nonlinear and linear parts that make up the original function.

Blank 1: 4x³ Blank 2: 2x - 2 Blank 3: -2ˣ Blank 4: -3x + 4 Blank 5: log₂ (2x) Blank 6: 2x - 1 Blank 7: |3x + 2| Blank 8: x - 2 Blank 9: x - 2 Blank 10: 3x

Which system of inequalities does this describe? >, <, ≥, ≤

Blank 1: > Blank 2: ≤

Compare Ali's holiday pay to Brenan's pay. Solve the system algebraically to determine under what conditions Ali and Brenan are paid equally for the same number of hours they work during the holidays. Describe the relationship between Ali's holiday pay function and Brenan's pay function using appropriate vocabulary. The system has _____. The graph of the two functions are _______. Blank 1: - One solution - Infinitely many solutions - No solution Blank 2: - Intersecting lines - Parallel lines - Collinear

Blank 1: infinitely many solutions Blank 2: collinear

Explain how you can use the structure of a complicated function to help you find its roots.

By graphing a complex function, you can determine if the function has any roots or not, if it touches the x-axis.

What characteristics of the graphs support for your previous answer?

By plotting the equations on the graph, the lines end up to be the same line, and in that case, if the solutions lie on the same line, then that would mean that the cost per pound for nuts at the online store is the same as the cost at the brick-and-mortor store.

Under what real-world conditions would the solutions for Ali and Brenan not be exactly the same?

Real-world situations such as Ali, not being able to help out the family due to getting too sick to go out, and in that case, that would affect the amount of money she's paid if she requests days off. That case, her weekly pay would decrease and Brennan's would stay the same.

he parabola y = f(x) and the line y = g(x) are shown in the graph below. Which region satisfies the following system? Select all that apply. Y > f(x) Y < g(x)

Region 5 Region 3

Identify each of the following systems of linear equations as having no solution, one solution, or infinite solutions.

System 1: no solution System 2: one solution System 3: infinite solutions System 4: infinite solutions System 5: one solution

How can you check your solution? What does this solution mean in context of the ticket-selling situation?

You can check your solution by solving the system of equations algebraically and if the solution works for both equations, then that is the right answer. The solution, (50, 20), tells us that there were 50 children at both of the shows along with 20 adults.

A party decorator uses a mix of green and red balloons. The difference in the number of green and red balloons should be less than 2, and the total number of balloons should be at least 25 and no more than 30. graph the related inequalities to analyze the feasible region of balloon display options. How many possible display options of green and red balloons can you determine from the feasible region you graphed? a.) 9 b.) 14 c.) 8 d.) 15 e.) 12 d.) 6 f.) 10

a.) 9

After college, Maria has to decide between two jobs. Job A would have a starting salary of $25,000 with a raise of8% of her starting salary per year. Job B would have a starting salary of $30,000 with a raise of 5% per year of her starting salary. Which job would pay more after 5 years? a.) Job B b.) They are the same. c.) Job A d.) It cannot be determined.

a.) Job B

What does it mean if the discriminant is a perfect square? a.) The quadratic is factorable. b. ) The solution for the quadratic are two complex imaginary solutions. c.) There are no solutions for the quadratic. d.) The quadratic is not factorable so you have to use the quadratic formula to find the solutions.

a.) The quadratic is factorable.

A scout troop with 12 third graders is planning a cookie sale. The troop has 300 boxes of cookies to sell. Some of the scouts will sell at a booth the troop sets up and some will sell individually by asking their friends and families. Each scout will choose to sell either individually or at the booth, but not both. At least 5 scouts are needed to run the booth. If they sell at the booth, they can sell at least 20 boxes each, but individually they can sell at least 24 boxes. all 12 scouts will sell cookies. Let x represent the number of scouts at the booth and y represent the number of scouts selling individually. Which system of inequalities best represents this situation?

b.

Select the scenario that best represents the constraints shown by the shaded region of the graph. a.) You are buying no more than 4 milks, at least 4 loaves, and limiting the cost to $40. b.) You are buying at least 4 milks, no more than 4 loaves, and limiting the cost to $40. c.) You are buying at least 4 milks, no more than 4 loaves, and limiting the cost to $20. d.) You are buying no more than 4 milks, no more than 4 loaves, and limiting the cost to $20. e.) You are buying no more than 4 milks, no more than 4 loaves, and limiting the cost of $40. f.) You are buying no more than 4 milks, at least 4 loaves, and limiting the cost to $20. g.) You are buying at least 4 milks, at least 4 loaves, and limiting the cost to $40. e.) You are buying at least 4 milks, at least 4 loaves, and limiting the cost to $20.

b.) You are buying at least 4 milks, no more than 4 loaves, and limiting the cost to $40.

What is the solution to this system of equations? (____, ____) 4x - 6y = -14 x + 3y = 19

blank 1 = 2 blank 2 = -14 blank 3 = 38 blank 4 = 6 blank 5 = 24 blank 6 = 4 blank 7 = 5

Plot both functions on the same axes The system has ________. The graph of the functions are ______. Blank 1: - No solution - One solution - Infinitely many solutions Blank 2: - Intersecting lines - Parallel lines - Collinear

blank 1: infinitely many solutions blank 2: collinear

Eli said that he found the combination of 40 children and 24 adults worked for Saturday night. Complete the sentences to explain whether this is a solution to the system or not. This ______ a solution since the point ____ _____ on both graphs and ______ make both equations true when substituting the values. Blank 1: - Is - Is not Blank 2: - (40,24) - (24,40) Blank 3: - Is - Is not Blank 4: - Does - Does not

blank 1: is not blank 2: (40,24) blank 3: is not blank 4: does not

Solve this system of equations. a. (5, -1) b. (-1, 2) c. (2, 1) d. (-4, 3)

c. (2, 1)

However, the students cannot agree on the solution set. Which student is correct? a.) Charles says the solutions are (-1, 6) and (-1, -2). b.) Dawn says the solutions are (-3, 2) and (1, 2). c.) Dionne says the solutions are -3 and 1. d.) Kesha says the solutions are -3.5, -2.5, 0.5, and 1.5.

c.) Dionne says the solutions are -3 and 1.

Choose the statements that describe this system of equations. a.) Infinite solutions to the system. b.) No solution to the system. c.) Exactly one point.

c.) Exactly one point.

What solution strategy can empower us to realize the nature of roots with minimal effort? a.) Dividing the functions b.) Multiplying the functions c.) Using the discriminant

c.) Using the discriminant

Can Vidya do this and get the correct answer? a.) No; she will get different values. b.) Yes; but she should use the points of intersection between the quadratic and the line and the original curve. c.) Yes; the x-values of the points of intersection will be the same as the solutions to the original equation. d.) Yes; but she needs to take the opposite of each x-value to get the solutions to the original equation. e.) No; but the line intersects the original curve in a point that is a solution.

c.) Yes; the x-values of the points of intersection will be the same as the solutions to the original equation.

Which of the following is parallel to the line y = -3 and passes through the point (-1,4)? a.) x = 4 b.) x = -1 c.) y = 4 d.) y = -1

c.) y = 4

An ice skating rink charges an admission fee of $5 for members and $10 for nonmembers. Last Saturday, the number of members was at least twice the number of nonmembers. The rink had collected at most $300 in admissions. If m is the number of members and n is the number of nonmembers, which graph represents the possible solutions for the number of each kind of skater?

d.

In art class, you made a self-portrait. You want to frame it and give it to your mother for Mother's Day. The portrait is a non-standard size, a square measuring 7 inches by 7 inches. The local craft store sells wooden frames by the foot and the store sells only by the foot and 1/2 foot. One foot costs $4, and 1/2 foot sells for $2.50. How much it cost to buy the wooden frame for this self-portrait? a.) $18.50 b.) $4.00 c.) $2.50 d.) $10.50

d.) $10.50

How many solutions and what type of solutions would there be if the discriminate is negative. a.) 2 irrational solutions b.) 2 rational solutions c.) 1 real solution d.) 2 complex solutions

d.) 2 complex solutions

In the graph, assume that the bus starts at its first stop. Which of the following is a true statement? a.) This school bus never went faster than 25 mph. b.) This school bus made 13 stops. c.) The bus stops about once every 2 minutes. d.) This school bus made only 5 stops.

d.) This school bus made only 5 stops.