AnswersFL-1200330-Algebra 2 CRSynthetic Division and the Remainder Theorem

Exploring Systems in the Real World Answers

5 verified answers1 views
1
Free Preview

Anthony purchased 6 fruit bars and 3 chocolate-nut bars for a camping trip. He spent $4.12 on the bars. Anthony wrote the following equation: . What did he define as the variable x?

Question illustration
A
cost of a fruit bar
B
cost of a chocolate-nut bar
C
number of fruit bars purchased
D
number of chocolate-nut bars purchased
2
Free Preview

Jalynn and Emma enjoy hiking. Jalynn hikes 1 mile in 20 minutes. Emma hikes at a rate of 3 miles per hour. On Sunday at 8:00 a.m., they both left the trail head. The line representing Jaylynn’s progress is graphed. Which statements are true about the system that models this scenario?

Question illustration
A
The lines will have equal slopes so there is no solution.
B
The equations are equivalent so there are an infinite number of solutions.
C
The equations have only one solution at (0, 0) since the hikers walk at different speeds.
D
Both lines will have a y-intercept of (0, 0) since both hikers start at 8:00 a.m.
E
As shown on the graph, both lines have a slope of because one must convert to the same units of time.
Option E
3

Sudhanshu is solving a system representing a race between two remote control cars. The variable x is defined as time in seconds, and y is the distance in meters from the starting line.How many solutions should Sudhanshu find?

Question illustration
A
zero
B
one
C
two
D
infinite
4

Javier is comparing costs of two cars. Car A costs $130 per month for insurance and $0.10 per mile to run. Car B costs $108 per month for insurance and $0.15 per mile to run. He defines x as the number of miles driven each month and y as the total cost to run the car. Which set of equations can be used to find the number of miles Javier would need to drive to make the costs equal?

A
0.10 x = 130. 0.15 y = 108
Option A
B
y = 0.10 x + 130. y = 0.15 x + 108
Option B
C
0.10 x = 108. 0.15 y = 130
Option C
D
y = 0.15 x + 130. y = 0.10 x + 108
Option D
5

How many solutions does the system have?

Question illustration
A
zero
B
one
C
two
D
infinite
6

Audra counted change collected for a class fundraiser. Audra wrote the equation to represent the situation. What did she define as the variable x?

Question illustration
A
value of a dime
B
value of a quarter
C
number of dimes collected
D
number of quarters collected
7

Joe and Nate went for a walk. The system representing each boy’s progress is graphed below. Which statements about the system and scenario are true? Check all that apply.

Question illustration
A
Nate starts 5 miles away from Joe’s house and gets closer as he walks because the y-intercept is 5 and his distance is decreasing.
B
Nate walks at a negative speed because the slope of his line is negative.
C
Joe walks at 1 mile per hour because the line representing his progress rises 1 for every 1 it runs.
D
Nate walks at rate of 2 miles every 30 minutes because the difference in distance is 2 miles for every 30 minutes of time.
E
Joe is walking faster than Nate because his line is steeper, meaning the distance he travels is changing more quickly.
8

Ben and Arnoldo are sharing snacks. They have peanut treats and coconut treats. Ben ate 2 of the peanut treats and 4 of the coconut treats for a total of 160 calories. Arnoldo ate 3 of the peanut treats and 2 of the coconut treats for a total of 140 calories. They wrote the system below to represent the number of calories there are in the two types of treats.They found the solution to be (30, 25). How many calories are in each treat?

Question illustration
A
There are 25 calories in each peanut treat and 30 calories in each coconut treat.
B
There are 30 calories in each peanut treat and 25 calories in each coconut treat.
C
There are 28 calories in each peanut treat and 28 calories in each coconut treat.
D
There are 55 calories in each peanut treat and 55 calories in each coconut treat.
9

Aisha bought 15 apples and oranges for $9.00. Each orange costs $0.50, and each apple costs $0.65. Let x represent the number of oranges and y represent the number of apples. Which system can be used to find the number of apples and oranges Aisha bought?

A
x + y = 15. 0.5 x + 0.65 y = 9.00
Option A
B
x = y. 0.5 x + 0.65 y = 9.00
Option B
C
x + y = 9. 0.5 x + 0.65 y = 15.00
Option C
D
x = y. 0.5 x + 0.65 y = 15.00
Option D
10

The mechanics at Giuseppe’s Auto House specialize in changing fuel injection units and transmissions. Last week, they changed 5 fuel injection units and 10 transmissions and billed 70 hours. This week, they changed 8 fuel injection units and 8 transmissions and billed 64 hours. Let x represent the number of hours to change a fuel injection unit and y represent the number of hours to change a transmission. What is the solution to the system that represents this scenario?

Question illustration
A
(5, 8)
B
(2, 6)
C
(4, 14)
D
(7, 8)

Did you find these answers helpful?

More from this Course

Quiz
13 verified answers

Synthetic Division and the Remainder Theorem

Quiz
10 verified answers

Synthetic Division and the Remainder Theorem

Quiz
10 verified answers

Synthetic Division and the Remainder Theorem