Use the graph to answer the question.
Graph of polygon ABCD with vertices at negative 6 comma negative 2, negative 4 comma 5, 1 comma 5, negative 1 comma negative 2. A second polygon A prime B prime C prime D prime with vertices at negative 6 comma 2, negative 4 comma negative 5, 1 comma negative 5, negative 1 comma 2.
Determine the line of reflection used to create the image.
x = 2
y = 2
y-axis
x-axis
11 answers
The line of reflection used to create the image is the x-axis. This is because the points of the second polygon A' B' C' D' are the mirror image of the points of the first polygon A B C D when reflected across the x-axis.
What is the solution set for 2x + 5 > 7? Responses A x > -1x > -1 B x < 3x < 3 C x < -2x < -2 D x > 1
To solve the inequality 2x + 5 > 7, we first subtract 5 from both sides:
2x + 5 - 5 > 7 - 5
2x > 2
Next, we divide by 2 to solve for x:
2x/2 > 2/2
x > 1
Therefore, the solution set is x > 1, which corresponds to option D.
2x + 5 - 5 > 7 - 5
2x > 2
Next, we divide by 2 to solve for x:
2x/2 > 2/2
x > 1
Therefore, the solution set is x > 1, which corresponds to option D.
As a salesperson, you are paid $100 per week plus $3 per sale. This week you want your pay to be at least $160. Write and solve an inequality for the number of sales you need to make. Responses A 100 - 3s ≤ 160; s ≤ 20100 - 3s ≤ 160; s ≤ 20 B 100 + 3s ≥ 160; s ≥ 18100 + 3s ≥ 160; s ≥ 18 C 100 - 3s ≤ 160; s ≤ 18100 - 3s ≤ 160; s ≤ 18 D 100 + 3s ≥ 160; s ≥ 20
Let s be the number of sales. The total pay is given by $100 (base pay) + $3 \times \text{number of sales}.
We are looking for the number of sales needed to make a total pay of at least $160. This can be represented by the inequality:
$100 + $3s ≥ $160
$3s ≥ $60
s ≥ 20
So, the correct inequality should be 100 + 3s ≥ 160, s ≥ 20, which corresponds to option D.
We are looking for the number of sales needed to make a total pay of at least $160. This can be represented by the inequality:
$100 + $3s ≥ $160
$3s ≥ $60
s ≥ 20
So, the correct inequality should be 100 + 3s ≥ 160, s ≥ 20, which corresponds to option D.
You are a farmer and want to spend under $35,000 on farm equipment. You need a hay baler that costs $6,250 and several plowing disks cost $2,500 each. Write an inequality that models how many plowing disks could be purchased within your budget. What is the maximum number of plowing disks you can buy? Responses A 2,500x + 6,250 < 35,000; 11 plowing disks2,500x + 6,250 < 35,000; 11 plowing disks B 2,500x + 6,250 ≤ 35,000; 11 plowing disks2,500x + 6,250 ≤ 35,000; 11 plowing disks C 2,500x + 6,250 < 35,000; 12 plowing disks2,500x + 6,250 < 35,000; 12 plowing disks D 2,500x + 6,250 ≤ 35,000; 12 plowing disks
Let x be the number of plowing disks purchased. The total cost C is given by:
Total Cost = $6,250 (cost of hay baler) + $2,500 (cost of each plowing disk) * x (number of plowing disks)
We want the total cost to be less than $35,000, so the inequality is:
$6,250 + $2,500x < $35,000
Solving this inequality gives:
$2,500x < $28,750
x < 11.5
Since you cannot purchase a fraction of a plowing disk, the maximum number of plowing disks you can buy is 11. This means the correct choice should be 2,500x + 6,250 < 35,000; 11 plowing disks which corresponds to option A.
Total Cost = $6,250 (cost of hay baler) + $2,500 (cost of each plowing disk) * x (number of plowing disks)
We want the total cost to be less than $35,000, so the inequality is:
$6,250 + $2,500x < $35,000
Solving this inequality gives:
$2,500x < $28,750
x < 11.5
Since you cannot purchase a fraction of a plowing disk, the maximum number of plowing disks you can buy is 11. This means the correct choice should be 2,500x + 6,250 < 35,000; 11 plowing disks which corresponds to option A.
An online music club has a one-time registration fee of $20 and charges $0.50 for each song download. If Ella has $50.00 to join the club and buy songs, which inequality gives the maximum number of songs, s, she can buy? Responses A s ≥ 60s ≥ 60 B s ≥ 30s ≥ 30 C s ≤ 30s ≤ 30 D s ≤ 60
Let s be the number of song downloads. Ella has $50 to spend, so the total cost C is given by:
Total Cost = $20 (registration fee) + $0.50 (cost per song download) * s = $50
This gives the inequality:
$20 + $0.50s = $50
Solving for s gives:
$0.50s = $30
s = 60
So Ella can buy a maximum of 60 songs. The correct inequality should be s ≤ 60, which corresponds to option D.
Total Cost = $20 (registration fee) + $0.50 (cost per song download) * s = $50
This gives the inequality:
$20 + $0.50s = $50
Solving for s gives:
$0.50s = $30
s = 60
So Ella can buy a maximum of 60 songs. The correct inequality should be s ≤ 60, which corresponds to option D.
Mark and Anson each have a video game collection. • The number of video games in Mark collection can be represented by x. • The number of video games in Anson collection is 5 times the number in Mark collection. • The total number of video games is no more than 72. What is the solution set for x, the number of video games in Mark’s collection? Responses A x ≤ -12x ≤ -12 B x ≤ 12x ≤ 12 C x ≥ -1x ≥ -1 D x ≥ 15
Let's set up the relationships given:
- The number of video games in Mark's collection is x.
- The number of video games in Anson's collection is 5 times the number in Mark's collection, so Anson has 5x games.
- The total number of video games is no more than 72, so x + 5x ≤ 72.
This simplifies to 6x ≤ 72. Divide both sides by 6 to solve for x:
x ≤ 12
Therefore, the solution set for x, the number of video games in Mark's collection, is x ≤ 12, which corresponds to option B.
- The number of video games in Mark's collection is x.
- The number of video games in Anson's collection is 5 times the number in Mark's collection, so Anson has 5x games.
- The total number of video games is no more than 72, so x + 5x ≤ 72.
This simplifies to 6x ≤ 72. Divide both sides by 6 to solve for x:
x ≤ 12
Therefore, the solution set for x, the number of video games in Mark's collection, is x ≤ 12, which corresponds to option B.
1 answer