The cost, C, in dollars, of playing g games at an arcade gamecenter is modeled by the linear function C = 0.5g + 2.
Determine the rate of change of the function and explain
what this value means in terms of the context.
Determine the initial value of the function and explain what
this value means in terms of the context.

Answer:5

Step-by-step explanation:there are 6 boxes between the top of the 3rd box and the bottom of the 10th box.

Since each box is 10 inches tall, the length of the 6 boxes sum up to 60 inches.

and since 12 inches =1 feet,

Then 60 inches = 5 feet

How to solve

Let "y" = the unknown number of feet's

12 inches = 1 feet

60 inches = y

Cross multiply

> 12×y =60×1

> 12y =60

Divide both sides by 12 since you want the value of "y".

> 12y÷12=60÷12

So 12 cancels out leaving the final answer to be:

> y=5

Answer:

There are 5 feet between the top of the third box and the bottom of the tenth box.

Step-by-step explanation:

We just have to count how many boxes is between the top of the third one and the bottom of the tenth box, then we transform from inches to feet.

So, the problem says "from the top of the third box" this means that the inches that matters is form the fourth box. "the bottom of the tenth box" means that it's until the ninth box. In total, there are 6 boxes. If each box is 10 inches high, the total distance would be 6(10 inches) = 60 inches.

Now we have the total distance, we transform it to feet. We know that one feet is 12 inches, using the rule of three we have:

60 inches are equivalent to 5 feet.

Therefore, there are 5 feet between the top of the third box and the bottom of the tenth box.

Answer:

80+2h=72+4h

4hours

Step-by-step explanation:

80+2h=72+4h

80-72=4h-2h

8=2h

h=8/2

h=4

Answer:

It took 4 hours for the two cities to reach the same temp.

Step-by-step explanation:

Part 1

First, you will write an expression for each city.

Austin starts at 80°F and rises 2°F per hour. 80 is our starting point. 2 is how much is added each hour. The per hour means we need a variable.

Little Rock starts at 72°F and rises 4° per hour. 72 is our starting point. 4 is how much is added per hour. The per hour means we need a variable.

Second, you want to know when the cities are equal, so you set these expressions equal to each other.

Part 2

This is an equation with variables on both sides. You will need to follow a few steps to solve these problems.

Step 1: look for grouping symbols. This problem does not have any visible or invisible grouping symbols.

Step 2: Look at the left side. Are there any like terms? This problem does not have any like terms on the left side. Look at the right side. Are there any like terms? This problem does not have any like terms on the right side.

Step 3: Are there variables on the left and right side of the equal sign? (Look to the left of the equal sign; you will see 2h. The h is a variable on the left side. Look to the right of the equal sign; you will see 4h. The h is a variable on the right side.)

• The answer is yes. You will subtract the variable with the smaller coefficient from each side of the equal sign. ()
•                

Step 4: Are there constants on the left and right sides of the equal sign?

• The answer is yes (80 is on the left, and 72 is on the right.) You will subtract the constant on the same side on the equal sign as the variable. The 72 is on the right side with the 2h. You will subtract 72 from the left and right sides of the equal sign.      
•          

Step 5: Does the variable have a coefficient other than 1? (Is there a number written with the variable? Is the variable not 1?)

• Yes, the coefficient is 2. You will divide the right and left sides by 2. (8 divided by 2 equals 2, 2h divided by 2 equals 1h)
• 

You have now solved the equation for the variable. Remember h was defined in the problem as "the number of hours it took for the cities to reach the same temperature." This means that it took 4 hours for the cities to reach the same temperature. You can check this with a simple check

You substitute the 4 in the original expressions. If you did the work correctly, you will get the same answer for both equations.

Since both expressions produced the same answer when 4 was substituted the answer is correct.