The number of loaves of bread purchased and the total cost of the bread in dollars can be modeled by the equation c = 3.5b. Which table of values matches the equation and includes only viable solutions?

Question

A 2-column table with 4 rows. The first column is labeled loaves (b) with entries negative 2, 0, 2, 4. The second column is labeled cost (c) with entries negative 7, 0, 7, 14.

A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 0.5, 1, 1.5. The second column is labeled cost (c) with entries 0, 1.75, 3.5, 5.25.

A 2-column table with 4 rows. The first column is labeled loaves (b) with entries 0, 3, 6, 9. The second column is labeled cost (c) with entries 0, 10.5, 21, 31.5.

Answer 1

To determine which table of values corresponds to the equation \( c = 3.5b \), we need to calculate the cost \( c \) for each given value of loaves \( b \) in each table and check if the values match.

1. First table:

   • Loaves (\( b \)): -2, 0, 2, 4
   • Calculating cost (\( c \)):
     • \( c = 3.5(-2) = -7 \) (matches)
     • \( c = 3.5(0) = 0 \) (matches)
     • \( c = 3.5(2) = 7 \) (matches)
     • \( c = 3.5(4) = 14 \) (matches)

   All pairs in this table (including negative loaves) match the equation, but negative loaves don't make sense in this context.

2. Second table:

   • Loaves (\( b \)): 0, 0.5, 1, 1.5
   • Calculating cost (\( c \)):
     • \( c = 3.5(0) = 0 \) (matches)
     • \( c = 3.5(0.5) = 1.75 \) (matches)
     • \( c = 3.5(1) = 3.5 \) (not 3.5, value does not match)
     • \( c = 3.5(1.5) = 5.25 \) (matches)

   The second table contains invalid pairs because the cost for 1 loaf should have been 3.5 but it shows 3.5.

3. Third table:

   • Loaves (\( b \)): 0, 3, 6, 9
   • Calculating cost (\( c \)):
     • \( c = 3.5(0) = 0 \) (matches)
     • \( c = 3.5(3) = 10.5 \) (matches)
     • \( c = 3.5(6) = 21 \) (matches)
     • \( c = 3.5(9) = 31.5 \) (matches)

All pairs in the third table match the equation, and all the values for \( b \) are viable (non-negative).

Therefore, the correct table of values that matches the equation \( c = 3.5b \) and includes only viable (non-negative) solutions is the third table.

Answer 2

Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of gas, x, to the total cost of the gas, y, includes the greatest amount of gas Berto can buy?



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Answer 3

To find the ordered pair relating the number of gallons of gas \( x \) to the total cost \( y \), we can start by calculating how many gallons of gas Berto can buy with his $12.

The cost of gas is $3.75 per gallon. To determine the maximum number of gallons he can afford, use the formula:

\[ x = \frac{\text{Total Money}}{\text{Cost per Gallon}} = \frac{12}{3.75} \]

Calculating this:

\[ x = \frac{12}{3.75} = 3.2 \]

Since Berto can't purchase a fractional amount of gas at the pump and needs to round down to the nearest whole number, he can buy a maximum of 3 gallons of gas.

Now calculate the total cost \( y \) for 3 gallons:

\[ y = 3 \times 3.75 = 11.25 \]

So, the ordered pair relating the number of gallons of gas \( x \) to the total cost \( y \) is:

\[ (3, 11.25) \]

Thus, the answer is \( (3, 11.25) \).

Answer 4

it is 3.2,12

A 2-column table with 3 rows. The first column is labeled time (t) with entries negative 2, 3.5, 30. The second column is labeled Elevation(e) with entries a, b, c.
Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water’s edge. The equation of her average change in elevation over time is e = 300 – 10t, where t is the time in minutes since she left the cabin, and e is her elevation with regard to sea level. Which values are viable points, and what are their values in the table relating t and e?

a =

b =

c =

Answer 5

To find the viable points in the context of the problem, we can use the equation given for Rory's elevation:

\[ e = 300 - 10t \]

where \( e \) is the elevation in feet, and \( t \) is the time in minutes since she left the cabin.

Rory starts at an elevation of 300 feet (the elevation of the cabin) and walks down towards the water’s edge. Since we do not have a specific value for when she reaches the water's edge, we need to consider when she might still be above sea level (elevation \( e \geq 0 \)).

1. Calculate when \( e = 0 \) (this will give us the time when she reaches the water): \[ 0 = 300 - 10t \] \[ 10t = 300 \] \[ t = 30 \]

This means that Rory reaches the water's edge at \( t = 30 \) minutes. Any time \( t > 30 \) would result in a negative elevation, which is not viable in this context.

Now, we can evaluate the values of \( e \) for the provided \( t \) values:

1. For \( t = -2 \): \[ e = 300 - 10(-2) = 300 + 20 = 320 \]

2. For \( t = 3.5 \): \[ e = 300 - 10(3.5) = 300 - 35 = 265 \]

3. For \( t = 30 \): \[ e = 300 - 10(30) = 300 - 300 = 0 \]

Now let's summarize the results for \( a, b, \) and \( c \):

• For \( a \) (when \( t = -2 \)), \( e = 320 \).
• For \( b \) (when \( t = 3.5 \)), \( e = 265 \).
• For \( c \) (when \( t = 30 \)), \( e = 0 \).

So, the values are:

• \( a = 320 \)
• \( b = 265 \)
• \( c = 0 \)

Answer 6

its Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water’s edge. The equation of her average change in elevation over time is e = 300 – 10t, where t is the time in minutes since she left the cabin, and e is her elevation with regard to sea level. Which values are viable points, and what are their values in the table relating t and e?

a =
✔ not viable

b =
✔ 265

c =
✔ 0

A 28,000-gallon swimming pool is being drained using a pump that empties 700 gallons per hour. Which equation models this situation if g is the number of gallons remaining in the pool and t is the amount of time in hours the pool has been draining?

28,000 = –700t
28,000g = –700t
g = 700t – 28,000
g = 28,000 – 700t

Answer 7

To model the situation where a 28,000-gallon swimming pool is being drained at a rate of 700 gallons per hour, we need to write an equation that represents the relationship between the remaining gallons in the pool (\( g \)) and the time in hours (\( t \)) since the draining started.

Starting with the initial amount of gallons in the pool, we can express the remaining gallons after \( t \) hours as follows:

1. Initial amount of water in the pool: 28,000 gallons.
2. Rate of draining: 700 gallons per hour.

After \( t \) hours, the amount of water drained is \( 700t \) gallons. Therefore, the remaining gallons in the pool (\( g \)) can be expressed with the equation:

\[ g = \text{Initial gallons} - \text{Drained gallons} \]

So the equation becomes:

\[ g = 28,000 - 700t \]

In this equation:

• \( g \) is the number of gallons remaining in the pool.
• \( t \) is the time in hours the pool has been draining.

Thus, the correct equation that models this situation is:

\[ g = 28,000 - 700t \]

This equation reflects that as time \( t \) increases, the number of gallons \( g \) in the pool decreases.

Answer 8

Each Friday, the school prints 400 copies of the school newsletter. The equation c = 400w models the relationship between the number of weeks and the total number of copies of the newsletters printed. What is true of the graph of this scenario?



A viable point on the graph is___________

The values of w must be_____________

Answer 9

Let's analyze the scenario and the equation provided:

The equation \( c = 400w \) expresses the total number of copies of the school newsletter printed, where:

• \( c \) = total copies printed.
• \( w \) = number of weeks.

What is true of the graph of this scenario?

1. Graph Type: The equation \( c = 400w \) is a linear equation. When graphed, it will be a straight line that passes through the origin (0,0). This represents a proportionate relationship between the number of weeks and the number of copies printed.

2. Slope: The slope of the graph is 400, which indicates that for each additional week, 400 more copies of the newsletter are printed.

A viable point on the graph is ____________.

A viable point on the graph must involve non-negative values for both \( w \) and \( c \), since you can't print a negative number of newsletters or have a negative number of weeks.

For example, if \( w = 1 \) (1 week), then:

• \( c = 400(1) = 400 \).

So, a viable point on the graph could be: \[ (1, 400) \]

The values of \( w \) must be ____________.

The values of \( w \) must be non-negative integers. This means:

• \( w \) must be \( 0, 1, 2, 3, \ldots \)

In summary:

• A viable point on the graph is (1, 400).
• The values of \( w \) must be non-negative integers (i.e., \( w \geq 0 \)).

Answer 10

okay for The values of \( w \) must be the options are
Any even number
Any real number
Any real number 0 or greater
Any whole number

and A viable point on the graph is the options are

(-2, -800)
(2.5, 1,000)
(6, 1,800)
(8, 3,200)

Answer 11

Given the context of the problem, let's analyze the options again based on your additional details.

The values of \( w \) must be ____________.

Since \( w \) represents the number of weeks, it must be:

• 0 or greater (you can't have a negative number of weeks).

Thus, among the provided options:

• The values of \( w \) must be: Any real number 0 or greater. (This is the most accurate based on the context since weeks can be a decimal value, e.g., if a printed newsletter is associated with part of a week.)

A viable point on the graph is ____________.

We need to check which of the provided points is valid based on the equation \( c = 400w \).

1. For point (-2, -800): \[ c = 400(-2) = -800 \quad \text{(not viable: weeks cannot be negative)} \]

2. For point (2.5, 1,000): \[ c = 400(2.5) = 1,000 \quad \text{(this is a viable solution)} \]

3. For point (6, 1,800): \[ c = 400(6) = 2,400 \quad \text{(not viable: expected 1,800)} \]

4. For point (8, 3,200): \[ c = 400(8) = 3,200 \quad \text{(this is a viable solution)} \]

Final Answers:

• The values of \( w \) must be: Any real number 0 or greater.
• A viable point on the graph is: (2.5, 1,000) or (8, 3,200). Depending on the context, you could choose one of these points if only a single option is required.