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Given the table for x, tickets sold and y, money earned:

x - tickets 4 9 8 5 7
y - $ earned 48 108 96 60 84


(4 points)
a. Every ticket sold is [Response area] dollars earned.

b. Dollars/1 ticket is called a [Response area] .

c. This relationship is [Response area], because 0 tickets sold is [Response area] dollars earned.
response area
variable
constant
unit rate
proportional
non proportional
0
1
5
12
60

7 answers

Based on the provided data and the responses you need to fill, the answers are as follows:

a. Every ticket sold is 12 dollars earned. (Since $48 for 4 tickets, $108 for 9 tickets, etc., you can calculate the unit rate.)

b. Dollars/1 ticket is called a unit rate.

c. This relationship is non-proportional, because 0 tickets sold is 0 dollars earned. (If there were no tickets sold, there would be no money earned, but the relationship does not maintain a constant ratio throughout.)

So, the filled-out responses would be:

a. 12
b. unit rate
c. non proportional, 0

Given the table for x, time in minutes and y, distance traveled:

x - time 4 3 10 7 9
y - distance 76 57 190 133 171


(4 points)
a. Every minute [Response area] meters are traveled.

b. Write an equation to show the relationship between x and y. [Response area]

c. This relationship is [Response area[ because the y-intercept is [Response area] .
responses
y = 133x
[0,19]
-19
19y = x
y = x - 19
[0, 57]
57
[4, 76]
y = 19x
y = x/19
non proportional
133
[0, 0]
proportional

Based on the data provided for time (x) in minutes and distance (y), let's analyze the information for the required responses:

  1. First, we can calculate the rate of distance per minute:

    To find the unit rate (distance per minute), we can calculate the slope using points from the table. Let's take one point, for example, (4, 76):

    • Each minute corresponds to a certain distance. For example, if we calculate distances based on the 4 minutes: \[ \text{Rate} = \frac{76 \text{ meters}}{4 \text{ minutes}} = 19 \text{ meters/minute}. \]

    Since this consistency seems to hold for other distances too, we can generalize that: \[ y = 19x. \]

Now we can fill in the blanks:

a.

Every minute 19 meters are traveled.

b.

Write an equation to show the relationship between x and y: y = 19x.

c.

This relationship is proportional because the y-intercept is [0, 0]. (The relationship passes through the origin, indicating that for 0 minutes, the distance traveled is also 0 meters.)

So the filled-out responses would be:

a. 19
b. y = 19x
c. proportional, [0, 0]

Use the graph to answer the questions.

(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
a. The constant of proportionality is Response area

b. Write an equation that represents the linear graph. Response area

c. This is a proportional relationship because the graph shows Response area .

To provide accurate responses, I would need to see the graph you are referencing. However, I can help guide you on how to determine the answers based on what is usually expected while interpreting such graphs.

  1. Constant of Proportionality (k): This value can be determined by finding the slope of the line on the graph. Choose two points from the line, (x₁, y₁) and (x₂, y₂), then use the formula: \[ k = \frac{y₂ - y₁}{x₂ - x₁} \]

  2. Equation of the Line: You can use the slope (constant of proportionality) and one point to write the equation in the form: \[ y = kx \] or if the graph is in slope-intercept form: \[ y = mx + b \] however, if it's proportional, b will be 0.

  3. Proportional Relationship: To identify if the relationship is proportional, look at the graph. It should pass through the origin (0,0). So you would say, "the graph shows that it passes through the origin."

If you have specific values or points from the graph, I can help you fill those in directly! If you provide me with the numerical values or any specific data points, I can give you a more tailored answer.

Solve this equation for y: y3=2x
(1 point)
Responses

y=23x
y is equal to 2 thirds x

y=6x
y is equal to 6 x

y=2x−3
y is equal to 2 x minus 3

y=2x+3

To solve the equation \(y3 = 2x\) for \(y\), we need to isolate \(y\). The given equation seems to have a formatting issue; if we interpret it correctly, it might mean \(y \cdot 3 = 2x\). Let's proceed with this assumption:

  1. Start with the equation: \[ y \cdot 3 = 2x \]

  2. Divide both sides by 3 to solve for \(y\): \[ y = \frac{2x}{3} \]

Now we can interpret this as:

  • \(y = \frac{2}{3} x\)
  • or in terms of the provided response: y is equal to 2 thirds x.

Thus, the correct answer is:

  • y is equal to 2 thirds x.