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select three characteristics of proportional relationships on a graph.
a. the points will form a straight line
b. the x values are always larger than the y values
c. it passes through the origin (0,0).
d. the y values are always larger than the x values
e. the ratio of y/x is the same for all points on the line
f.
g.

Answer 1

The three characteristics of proportional relationships on a graph are:

a. the points will form a straight line
c. it passes through the origin (0,0)
e. the ratio of y/x is the same for all points on the line

Answer 2

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.
6-pack for $2.99 has a unit price of $__ per soda
12-pack for $3.99 has a unit price of $_ per soda

Answer 3

To determine the unit price for each soda in the packs, we can divide the total price by the number of sodas in each package.

1. 6-pack for $2.99: \[ \text{Unit Price} = \frac{\text{Total Price}}{\text{Number of Sodas}} = \frac{2.99}{6} \approx 0.4983 \] Rounding to the hundredths place, the unit price is $0.50 per soda.

2. 12-pack for $3.99: \[ \text{Unit Price} = \frac{3.99}{12} \approx 0.3325 \] Rounding to the hundredths place, the unit price is $0.33 per soda.

Thus, the answers are:

• 6-pack for $2.99 has a unit price of $0.50 per soda.
• 12-pack for $3.99 has a unit price of $0.33 per soda.

Answer 4

24-pack for $5.99 has a unit price of $__ per soda
which package has the best unit price?
a. 6-pack
b. 24-pack
c. 12-pack
d. they have the same unit price

Answer 5

To find the unit price for the 24-pack:

24-pack for $5.99: \[ \text{Unit Price} = \frac{\text{Total Price}}{\text{Number of Sodas}} = \frac{5.99}{24} \approx 0.2496 \] Rounding to the hundredths place, the unit price is $0.25 per soda.

Now, we can summarize the unit prices we calculated earlier:

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

Now, comparing the unit prices:

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

The package with the best unit price is b. 24-pack at $0.25 per soda.

Answer 6

the distance john ran is directly proportional to his time in minuets. consider the table of this relationship
|time(t) in minuets | distance (d) in miles|
________________________________
| 62.5 | 5 |
| 125 | 10 |
| 187.5 | 15 |
________________________________
determine the constant of proportionality
__ miles per minute
using the variables for distance (d) and time (t), select the equation to model this situation
a. t=12.5d
b. d=12.5t
c. t=d+57.5
d. d=0.08t

Answer 7

To determine the constant of proportionality between distance \( (d) \) and time \( (t) \), we can use the values from the table. The constant of proportionality (k) can be calculated as follows:

\[ k = \frac{d}{t} \]

Let's calculate \( k \) using one of the pairs from the table:

Using the first row:

• \( t = 62.5 \) minutes
• \( d = 5 \) miles

\[ k = \frac{5 \text{ miles}}{62.5 \text{ minutes}} = 0.08 \text{ miles per minute} \]

Now let's verify that this constant holds for the other pairs:

For the second row:

• \( t = 125 \) minutes
• \( d = 10 \) miles \[ k = \frac{10}{125} = 0.08 \text{ miles per minute} \]

For the third row:

• \( t = 187.5 \) minutes
• \( d = 15 \) miles \[ k = \frac{15}{187.5} = 0.08 \text{ miles per minute} \]

Thus, the constant of proportionality is: \[ \text{Constant of Proportionality} = 0.08 \text{ miles per minute} \]

Now, to select the appropriate equation to model the relationship between distance and time, we need an equation that represents this direct proportionality:

We know that: \[ d = k \cdot t \quad \text{where} , k = 0.08 \] So, we get: \[ d = 0.08t \]

Therefore, the correct equation is: d. \( d = 0.08t \).

Answer 8

simplify the following expression.
(x+1)-(-2x-5)

Answer 9

To simplify the expression \((x + 1) - (-2x - 5)\), we first distribute the negative sign in front of the parentheses:

\[ (x + 1) - (-2x - 5) = (x + 1) + (2x + 5) \]

Now, we can combine the like terms:

1. Combine the \(x\) terms: \[ x + 2x = 3x \]

2. Combine the constant terms: \[ 1 + 5 = 6 \]

Putting these together, we have:

\[ 3x + 6 \]

Thus, the simplified expression is:

\[ \boxed{3x + 6} \]

Answer 10

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.
2/5(x+15)=26

Answer 11

To solve the equation \( \frac{2}{5}(x + 15) = 26 \), we can follow these steps:

Step 1: Eliminate the Fraction

To eliminate the fraction, we can multiply both sides of the equation by \(5\):

\[ 5 \cdot \left(\frac{2}{5}(x + 15)\right) = 5 \cdot 26 \]

This simplifies to:

\[ 2(x + 15) = 130 \]

Step 2: Distribute

Now, distribute the \(2\) on the left side:

\[ 2x + 30 = 130 \]

Step 3: Isolate the Variable Term

Next, we need to isolate the term with \(x\). We can do this by subtracting \(30\) from both sides:

\[ 2x + 30 - 30 = 130 - 30 \]

This simplifies to:

\[ 2x = 100 \]

Step 4: Solve for \(x\)

Now, divide both sides by \(2\) to solve for \(x\):

\[ x = \frac{100}{2} \]

This simplifies to:

\[ x = 50 \]

Conclusion

The value of \(x\) is:

\[ \boxed{50} \]

Verification

To verify, we can substitute \(x = 50\) back into the original equation:

\[ \frac{2}{5}(50 + 15) = 26 \]

Calculating inside the parentheses:

\[ \frac{2}{5}(65) = 26 \]

Calculating the left side:

\[ \frac{130}{5} = 26 \]

Since both sides are equal, our solution \(x = 50\) is verified.