Ask a New Question
Menu

14 of 1814 of 18 Items

Question 1
Jenny wants to buy soda at the grocery store. The store offers three different packages.

Determine the unit price for each soda in the packs. Round your answer to the hundredths place.

(1 point)
6-pack for $2.99 has a unit price of $
per soda.

12-pack for $3.99 has a unit price of $
per soda.

24-pack for $5.99 has a unit price of $
per soda.

Question 2
Which package has the best unit price?(1 point)
Responses

6-pack
6-pack

12-pack
12-pack

24-pack
24-pack

They have the same unit price.
They have the same unit price.
Skip to navigation

page 1 of 1
Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

11 answers

To determine the unit price for each soda pack, you simply divide the total price by the number of sodas in the pack.

Here's the calculation for each pack:

1. For the 6-pack for $2.99: \[ \text{Unit price} = \frac{2.99}{6} \approx 0.4983 \text{ (rounding to hundredths place gives)} \approx 0.50 \]

2. For the 12-pack for $3.99: \[ \text{Unit price} = \frac{3.99}{12} \approx 0.3325 \text{ (rounding to hundredths place gives)} \approx 0.33 \]

3. For the 24-pack for $5.99: \[ \text{Unit price} = \frac{5.99}{24} \approx 0.2496 \text{ (rounding to hundredths place gives)} \approx 0.25 \]

Now, let's summarize the unit prices for each soda pack:

  • 6-pack: $0.50 per soda
  • 12-pack: $0.33 per soda
  • 24-pack: $0.25 per soda

Question 2: Which package has the best unit price?

The 24-pack has the best unit price at $0.25 per soda.

15 of 1815 of 18 Items

Question 1
Consider the graph.

(1 point)
The rise from (0, 0) to (6, -1) =
.

The run from (0, 0) to (6, -1) =
.

Question 2
What is the slope of this line?(1 point)
Responses

6
6

-6
-6

16
1 sixth

−16
negative 1 sixth
Skip to navigation

page 1 of 1
Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

To find the rise and run from the point (0, 0) to (6, -1), we use the definitions of rise and run in the context of a graph of a linear equation.

Question 1:

  1. The rise: This is the change in the y-coordinates.

    • From (0, 0) to (6, -1), the initial y-coordinate is 0 and the final y-coordinate is -1.
    • The rise = final y - initial y = -1 - 0 = -1.

  2. The run: This is the change in the x-coordinates.

    • From (0, 0) to (6, -1), the initial x-coordinate is 0 and the final x-coordinate is 6.
    • The run = final x - initial x = 6 - 0 = 6.

In summary:

  • The rise from (0, 0) to (6, -1) = -1.
  • The run from (0, 0) to (6, -1) = 6.

Question 2: What is the slope of this line?

The slope (m) of a line can be calculated using the formula: \[ m = \frac{\text{rise}}{\text{run}} = \frac{-1}{6} \]

So the slope of the line is:

  • \(-\frac{1}{6}\)

Thus, for the responses, the correct one would be:

  • negative 1 sixth.
16 of 1816 of 18 Items

Question 1
The distance John ran is directly proportional to his time in minutes. Consider the table of this relationship.

(1 point)
Determine the constant of proportionality.

miles per minute.

Question 2
Using the variables for distance (d) and time (t), select the equation to model this situation.(1 point)
Responses

d=12.5t
d is equal to 12 point 5 t

d=0.08t
d is equal to 0 point 0 8 t

t=12.5d
t is equal to 12 point 5 d

t=d+57.5
t is equal to d plus 57 point 5
Skip to navigation

page 1 of 1
Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

To determine the constant of proportionality and the model equation, we first need to understand the relationship described—distance is directly proportional to time.

Since the specific table data is not provided, I'll outline the general method for finding the constant of proportionality and the equation.

Question 1:

To find the constant of proportionality (k), you typically use the formula: \[ d = kt \] where \(d\) is the distance and \(t\) is the time. The constant of proportionality \(k\) can be calculated using the formula: \[ k = \frac{d}{t} \]

For example, if the table showed the following data:

| Time (minutes) | Distance (miles) | |----------------|-------------------| | 1 | 0.08 | | 2 | 0.16 | | 3 | 0.24 | | ... | ... |

You would compute \(k\) using one of the entries in the table. Let's say with the entry \(t = 1\) minute and \(d = 0.08\) miles: \[ k = \frac{0.08}{1} = 0.08 \text{ miles per minute} \]

Question 2:

With the relationship defined as \(d = kt\), and assuming we found \(k = 0.08\), the equation to model this situation would be: \[ d = 0.08t \]

Given the answer options:

  • \(d = 12.5t\)
  • \(d = 0.08t\) (This is the correct answer)
  • \(t = 12.5d\)
  • \(t = d + 57.5\)

Based on this analysis, the constant of proportionality is 0.08 miles per minute, and the correct equation that models the situation is \(d = 0.08t\).

Simplify the following expression:

(x+1)−(−2x−5)

To simplify the expression \((x + 1) - (-2x - 5)\), we first distribute the negative sign across the second expression:

  1. Rewrite the expression: \[ (x + 1) - (-2x - 5) = (x + 1) + (2x + 5) \]

  2. Now, combine the like terms:

    • Combine the \(x\) terms: \(x + 2x = 3x\)
    • Combine the constant terms: \(1 + 5 = 6\)

So, the simplified expression is: \[ 3x + 6 \]

Thus, the final answer is: \[ \boxed{3x + 6} \]

Determine the value of x in this equation. You can choose the method you use to solve, but you must list ALL steps and the solution.

25(x+15)=26

To solve the equation \( 25(x + 15) = 26 \), we will follow these steps systematically.

Step 1: Distribute the 25

First, we distribute \( 25 \) across the terms inside the parentheses:

\[ 25(x) + 25(15) = 26 \]

This simplifies to:

\[ 25x + 375 = 26 \]

Step 2: Isolate the \( 25x \) term

Next, we need to isolate the term \( 25x \) on one side of the equation by subtracting \( 375 \) from both sides:

\[ 25x + 375 - 375 = 26 - 375 \]

This simplifies to:

\[ 25x = 26 - 375 \]

Calculating the right side gives:

\[ 25x = -349 \]

Step 3: Solve for \( x \)

Now, we solve for \( x \) by dividing both sides by \( 25 \):

\[ x = \frac{-349}{25} \]

Step 4: Simplify the result (if necessary)

Now to simplify \( \frac{-349}{25} \):

Since \( -349 \) cannot be simplified further with \( 25 \) (as there are no common factors), we leave it as is.

Final Solution

Thus, the value of \( x \) is:

\[ \boxed{\frac{-349}{25}} \]

summarize it

To solve the equation \( 25(x + 15) = 26 \):

  1. Distribute the 25: \[ 25x + 375 = 26 \]

  2. Isolate \( 25x \) by subtracting \( 375 \) from both sides: \[ 25x = 26 - 375 \implies 25x = -349 \]

  3. Solve for \( x \) by dividing both sides by \( 25 \): \[ x = \frac{-349}{25} \]

Final Answer:

\[ \boxed{\frac{-349}{25}} \]