7 of 147 of 14 Items

Question

Question
Determine the rise, run, and slope of the given graph.

(1 point)
Rise from (-5,0) to (0,4) =

Run from (-5,0) to (0,4) =

Slope is equal to the rise/run
=
(Enter your response as a fraction in simplest form.)

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Answer 1

To determine the rise, run, and slope from the points \((-5, 0)\) to \((0, 4)\), follow these steps:

1. Calculate the rise: The rise is the difference in the y-coordinates of the two points: \[ \text{Rise} = y_2 - y_1 = 4 - 0 = 4 \]

2. Calculate the run: The run is the difference in the x-coordinates of the two points: \[ \text{Run} = x_2 - x_1 = 0 - (-5) = 0 + 5 = 5 \]

3. Calculate the slope: The slope (m) is calculated as the rise over the run: \[ \text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{4}{5} \]

Now, summarize the results:

• Rise from (-5, 0) to (0, 4) = 4
• Run from (-5, 0) to (0, 4) = 5
• Slope = \(\frac{4}{5}\)

So, the answers are:

• Rise: 4
• Run: 5
• Slope: \(\frac{4}{5}\)

Answer 2

8 of 148 of 14 Items

Question
Consider the table.

















The weight of the pet ferret varies directly with its length.

(1 point)
The constant of proportionality is
.

The following equation may be used to determine the weight of ferret given its length:

y =
x

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Answer 3

To help you with this question, I'll guide you on how to determine the constant of proportionality and formulate the equation based on the information provided.

1. Understanding Variation: Since the weight of the pet ferret varies directly with its length, this means that if you know the length (let's call it \( x \)), you can find the weight (let's call it \( y \)) using the form of a direct variation equation: \[ y = kx \] where \( k \) is the constant of proportionality.

2. Finding the Constant of Proportionality: To find \( k \), you need pairs of values from your table that relate the weight and length of the ferret. The constant \( k \) can be calculated by rearranging the equation: \[ k = \frac{y}{x} \] Take one of the pairs \((length, weight)\) from the table and plug them into this equation to find \( k \).

3. Formulating the Equation: Once you have determined \( k \), you can substitute it back into the equation \( y = kx \) to represent the relationship between the weight and the length of the ferret.

Since the table and specific values are not provided here, if you have a pair (e.g., a length of 10 inches and a weight of 2 pounds), you would find \( k \) as follows: \[ k = \frac{2}{10} = \frac{1}{5} \] Then, your equation would be: \[ y = \frac{1}{5}x \]

Please replace the example values above with those from your actual table to find the specific value of \( k \) and write the accurate equation.

Answer 4

12 of 1412 of 14 Items

Question 1
Consider this graph.

(1 point)
Determine the speed (unit rate) for each student participating in the walk. Round the value to the hundredths place. Remember to include the zero on the left side of the decimal.

Millie walks at a speed of
miles per minute.

Sam walks at a speed of
miles per minute.

Zola walks at a speed of
miles per minute.

Question 2
(1 point)

walks the fastest and
walks the slowest.
will arrive at the finished line first.
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Answer 5

To determine the speeds of Millie, Sam, and Zola based on their walking distances over time as illustrated in the graph (which I cannot see), you would generally follow these steps:

1. Identify the Values from the Graph: Look at the graph and determine the distances each student walked (in miles) and the time it took (in minutes).

2. Calculate the Speed: The speed (unit rate) can be calculated using the formula: \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] For each student, apply the formula to get their speed in miles per minute. Be sure to round to the hundredths place.

   For example, if Millie walked 3 miles in 12 minutes: \[ \text{Millie's Speed} = \frac{3 \text{ miles}}{12 \text{ minutes}} = 0.25 \text{ miles per minute} \] Similarly calculate the speeds for Sam and Zola.

3. Comparison of Speeds:

   • Fastest and Slowest: After calculating speeds for all three students, compare their speeds to determine who walked the fastest and who walked the slowest.
   • Who Arrives First: The student with the highest speed will reach the finish line first.

Example:

Assuming the calculated speeds based on the graph:

• Millie walks at a speed of 0.25 miles per minute.
• Sam walks at a speed of 0.30 miles per minute.
• Zola walks at a speed of 0.20 miles per minute.

Then you would conclude:

• Sam walks the fastest, Zola walks the slowest, and Sam will arrive at the finish line first.

Please replace the example values with the actual values from your graph to complete the solution.

Answer 6

13 of 1413 of 14 Items

Question
Select all of the expressions that are equivalent to this algebraic expression.

(3x−8)+(2x+5)−(4x−8)


(1 point)
Responses

3x−8+2x+5−4x−8
3 x minus 8 plus 2 x plus 5 minus 4 x minus 8

3x−8+2x+5−4x+8
3 x minus 8 plus 2 x plus 5 minus 4 x plus 8

3x+2x−4x−8+5+8
3 x plus 2 x minus 4 x minus 8 plus 5 plus 8

5x−4x−8+5+8
5 x minus 4 x minus 8 plus 5 plus 8

x−8+5+8
x minus 8 plus 5 plus 8

x−13+8
x minus 13 plus 8

x−3+8
x minus 3 plus 8

x−21
x minus 21

x+5
x plus 5
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Answer 7

To determine which of the given expressions are equivalent to the original expression \((3x - 8) + (2x + 5) - (4x - 8)\), we will first simplify the original expression step by step.

Step 1: Expand and Group the Original Expression

Start with the original expression: \[ (3x - 8) + (2x + 5) - (4x - 8) \] Distribute the negative sign and rewrite it: \[ 3x - 8 + 2x + 5 - 4x + 8 \]

Step 2: Combine Like Terms

Now combine the \(x\) terms and the constant terms:

• Combine \(3x + 2x - 4x\): \[ 3x + 2x - 4x = (3 + 2 - 4)x = 1x = x \]
• Combine the constant terms: \[ -8 + 5 + 8 = (-8 + 8) + 5 = 0 + 5 = 5 \] Thus, the simplified expression is: \[ x + 5 \]

Step 3: Evaluate the Given Responses

Now, we will check each of the provided responses against the simplified expression \(x + 5\):

1. \(3x - 8 + 2x + 5 - 4x - 8\):

   • Simplifying gives \(x + 5\). Equivalent.

2. \(3x - 8 + 2x + 5 - 4x + 8\):

   • Simplifying gives \(x + 5\). Equivalent.

3. \(3x + 2x - 4x - 8 + 5 + 8\):

   • Simplifying gives \(x + 5\). Equivalent.

4. \(5x - 4x - 8 + 5 + 8\):

   • Simplifying gives \(x + 5\). Equivalent.

5. \(x - 8 + 5 + 8\):

   • Simplifying gives \(x + 5\). Equivalent.

6. \(x - 13 + 8\):

   • Simplifying gives \(x - 5\). Not equivalent.

7. \(x - 3 + 8\):

   • Simplifying gives \(x + 5\). Equivalent.

8. \(x - 21\):

   • This does not simplify to \(x + 5\). Not equivalent.

9. \(x + 5\):

   • This is identical to our simplified expression. Equivalent.

Conclusion

The equivalent expressions are:

• \(3x - 8 + 2x + 5 - 4x - 8\)
• \(3x - 8 + 2x + 5 - 4x + 8\)
• \(3x + 2x - 4x - 8 + 5 + 8\)
• \(5x - 4x - 8 + 5 + 8\)
• \(x - 8 + 5 + 8\)
• \(x - 3 + 8\)
• \(x + 5\)

The responses that are equivalent to the expression \((3x - 8) + (2x + 5) - (4x - 8)\) are:

• \(3x - 8 + 2x + 5 - 4x - 8\)
• \(3x - 8 + 2x + 5 - 4x + 8\)
• \(3x + 2x - 4x - 8 + 5 + 8\)
• \(5x - 4x - 8 + 5 + 8\)
• \(x - 8 + 5 + 8\)
• \(x - 3 + 8\)
• \(x + 5\)