A cab company charges $12 per mile for a lift to the airport. What change would the company make to their charges to make this a non proportional situation?
• Charge $15 per mile instead of $12
• Charge a flat rate of $20 and then $12 per mile
• Charge $4 per mile instead of $12
• No changes are needed.
The correct answer is: Charge a flat rate of $20 and then $12 per mile.
Currently, the cab company charges a flat rate of $12 per mile for a lift to the airport, which means the cost increases in direct proportion to the number of miles traveled. However, to make the situation non-proportional, the company would introduce a fixed fee regardless of the distance traveled.
By charging a flat rate of $20 and then an additional $12 per mile, the total cost would no longer be solely dependent on the number of miles, but also include a fixed fee component. Therefore, this change would make the situation non-proportional.
6. One business charges $22 per t-shirt that is custom made.
Another business charges $16 per t-shirt plus a $15 set up fee for custom made t-shirts.
How would you transform the first graph to make it become a non proportional graph with the same y-intercept as the second graph?
(1 point)
Responses
Down 4
Down 4
Left 15
Left 15
Up 4
Up 4
Down 15
Down 15
Up 15
Up 15
Right 4
To transform the first graph to make it become a non-proportional graph with the same y-intercept as the second graph, you would move the graph "left 15".
The second graph includes a $15 set up fee in addition to the $16 per t-shirt charge. By moving the first graph "left 15", you are essentially introducing a fixed fee of $15 to the cost of each t-shirt, making the situation non-proportional. This aligns with the pricing structure of the second business.
7. Solve this equation for y: 7y=12x
(1 point)
Responses
y=712x
y is equal to 7 over 12 x
y=12x+7
y is equal to 12 x plus 7
y=127x
y is equal to 12 sevenths x
y=12x−7
The correct answer is: y = 12x/7
To solve the equation 7y = 12x for y, divide both sides of the equation by 7. This gives us:
(7y)/7 = (12x)/7
Simplifying, we get:
y = 12x/7
7. Solve this equation for y: 7y=12x
(1 point)
Responses
y=7/12x
y is equal to 7 over 12 x
y=12x+7
y is equal to 12 x plus 7
y=12/7x
y is equal to 12 sevenths x
y=12x−7
Apologies for the confusion in my previous response. The correct answer is:
y = 12x/7
To solve the equation 7y = 12x for y, you divide both sides of the equation by 7.
(7y)/7 = (12x)/7
This simplifies to:
y = 12x/7
7. Solve this equation for y: 7y=12x
(1 point)
a. y=7/12x
b. y=12x+7
c. y=12/7x
d. y=12x−7
The correct answer is:
c. y = 12/7x
To solve the equation 7y = 12x for y, divide both sides of the equation by 7:
(7y)/7 = (12x)/7
Simplifying, we get:
y = 12/7x
Change the equation from standard form to slope-intercept form by solving for y.
8x−4y=24
Determine who changed the equation correctly:
Bob:
Subtract 8x from both sides: −4y=−8x+24
Divide by -4 on both sides: y=2x−6
Bill:
Subtract 8x from both sides: −4y=16x
Divide by -4 on both sides: y=−4x
Bud:
Subtract 8x from both sides: −4y=−8x+24
Divide by -4 on both sides: y=2x+24
(1 point)
Responses
Bill
Bill
Bob
Bob
Bud
Bud
None of them are correct
The correct answer is:
Bob.
Bob changed the equation correctly by subtracting 8x from both sides, resulting in -4y = -8x + 24. Then, dividing by -4 on both sides gives the equation y = 2x - 6, which is in slope-intercept form (y = mx + b).
9. Solve 3x+2b=6c
for x.
Step 1: 3x+2b−2b=6c−2b
subtract 2b from both sides
Step 2: 3x=6c−2b
combine like terms/simplify
Step 3: 3x3=6c3−2b
divide by 3 on both sides to get x isolated
Step 4: x=2c−2b
simplify/final answer
Which statement is TRUE?
(1 point)
Responses
The process has an error. The correct answer is x=4bc3
The process has an error. The correct answer is x is equal to the fraction with numerator 4 b c and denominator 3
The process has an error. The correct answer is x=−4b−c
The process has an error. The correct answer is x is equal to negative 4 b minus c
The process is correct.
The process is correct.
The process has an error. The correct answer is x=2c−23b
The correct answer is:
The process is correct.
The steps taken to solve the equation are accurate and lead to the correct solution. The final answer, x = 2c - 2b, is correct.
9. Solve 3x+2b=6c
for x.
Step 1: 3x+2b−2b=6c−2b
subtract 2b from both sides
Step 2: 3x=6c−2b
combine like terms/simplify
Step 3: 3x/3=6c/3−2b
divide by 3 on both sides to get x isolated
Step 4: x=2c−2b
simplify/final answer
Which statement is TRUE?
(1 point)
Responses
a. The process has an error. The correct answer is x=4bc/3
The process has an error. The correct answer is x is equal to the fraction with numerator 4 b c and denominator 3
b. The process has an error. The correct answer is x=−4b−c
The process has an error. The correct answer is x is equal to negative 4 b minus c
c. The process is correct.
The process is correct.
d. The process has an error. The correct answer is x=2c−2/3b
The correct answer is:
c. The process is correct.
The steps taken to solve the equation are accurate and lead to the correct solution. The final answer, x = 2c - 2b, is correct.
10. Looking at the graph:
(3 points)
a. Triangles ABC and CDE are called
triangles.
b. The slope of the line AE can be written as
.
c. This is a
relationship.
Unfortunately, without a visual representation of the graph, I am unable to accurately answer the questions regarding triangles, the slope of a line, and the relationship. If you can provide more specific information or share the graph, I would be happy to assist you further.
Katrina:
Time (seconds) Jumping Jacks
2 10
5 25
12 60
20 100(3 points)
a. Which person is doing more jumping jacks per second?
b. Which person had done more jumping jacks initially before the timer started?
c. Which person shows a proportional relationship?
To answer the questions, let's analyze the information provided:
Person: Katrina
Time (seconds) Jumping Jacks
2 10
5 25
12 60
20 100
a. To determine who is doing more jumping jacks per second, we can calculate the rate by dividing the number of jumping jacks by the time in seconds.
For Katrina:
Jumping jacks per second at 2 seconds = 10/2 = 5
Jumping jacks per second at 5 seconds = 25/5 = 5
Jumping jacks per second at 12 seconds = 60/12 = 5
Jumping jacks per second at 20 seconds = 100/20 = 5
Since the rate for Katrina is constant at 5 jumping jacks per second, no other person is doing more jumping jacks per second.
b. To determine who had done more jumping jacks initially before the timer started, we need to look at the data provided. It seems that the table does not have any information about the number of jumping jacks performed before the timer started. Therefore, it is impossible to determine which person did more jumping jacks initially.
c. To identify a proportional relationship, we need to examine whether there is a constant ratio between the number of jumping jacks and the time in seconds for each person. Since the rate for Katrina is constant at 5 jumping jacks per second, we can determine that the relationship between the number of jumping jacks and time is proportional for Katrina.
Therefore, the correct answers are:
a. No one is doing more jumping jacks per second than Katrina.
b. It is impossible to determine who did more jumping jacks initially.
c. The relationship between the number of jumping jacks and time is proportional for Katrina.
14. Suppose that the water level of a river is 45 feet after 3 days of no rain and 10 feet after 10 days of no rain. Given the two points we know: (3, 45) and (10, 10), what would the point slope equation look like?(1 point)
Responses
(y−3)=−5(x−45)
open paren y minus 3 close paren is equal to negative 5 times open paren x minus 45 close paren
(y+10)=−5(x−10)
open paren y plus 10 close paren is equal to negative 5 times open paren x minus 10 close paren
(y−45)=−5(x−3)
open paren y minus 45 close paren is equal to negative 5 times open paren x minus 3 close paren
(y−10)=−5(x+10)
The correct answer is:
(y - 45) = -5(x - 3)
The point slope equation form is represented by (y - y₁) = m(x - x₁), where (x₁, y₁) are the coordinates of one point, and 'm' is the slope of the line. In this case, the points given are (3, 45) and (10, 10). Using the formula, the equation becomes:
(y - 45) = -5(x - 3)