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
4 months ago
4 months ago
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
4 months ago
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.
4 months ago
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 β€ 160; s β€ 20100 - 3s β€ 160; s β€ 20 B 100 + 3s β₯ 160; s β₯ 18100 + 3s β₯ 160; s β₯ 18 C 100 - 3s β€ 160; s β€ 18100 - 3s β€ 160; s β€ 18 D 100 + 3s β₯ 160; s β₯ 20
4 months ago
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 β₯ $160
$3s β₯ $60
s β₯ 20
So, the correct inequality should be 100 + 3s β₯ 160, s β₯ 20, which corresponds to option D.
4 months ago
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 β€ 35,000; 11 plowing disks2,500x + 6,250 β€ 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 β€ 35,000; 12 plowing disks
4 months ago
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.
4 months ago
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 β₯ 60s β₯ 60 B s β₯ 30s β₯ 30 C s β€ 30s β€ 30 D s β€ 60
4 months ago
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 β€ 60, which corresponds to option D.
4 months ago
Mark and Anson each have a video game collection. β’ The number of video games in Mark collection can be represented by x. β’ The number of video games in Anson collection is 5 times the number in Mark collection. β’ The total number of video games is no more than 72. What is the solution set for x, the number of video games in Markβs collection? Responses A x β€ -12x β€ -12 B x β€ 12x β€ 12 C x β₯ -1x β₯ -1 D x β₯ 15
4 months ago
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 β€ 72.
This simplifies to 6x β€ 72. Divide both sides by 6 to solve for x:
x β€ 12
Therefore, the solution set for x, the number of video games in Mark's collection, is x β€ 12, which corresponds to option B.