Ask question

Ask question

All categories

VladimirAG [237]

3 years ago

6

When ordering tickets online, a collage theater charges a $5 handling fee no matter how large the order. Tickets to a comedy con

cert cost $58 each. If you had the line showing the total cost, y, of buying tickets, x, what would the slope of your line be? Explain your thinking.

1 answer:

aivan3 [116]3 years ago

7 0

Answer:

58

Step-by-step explanation:

Given that :

Handling fee = $5

Cost of ticket to comedy concert = $58 each

The total cost y of buying ticket x ;

Using the slope - Intercept relation

y = mx + c

m = slope ; c = intercept

The constant handling fee = $5 = c = intercept

Cost of x tickets = (cost per ticket * number of tickets) = 58 * x = 58x

Hence,

y = 58x + 5

Comparing with the intercept slope equation :

Slope (m) =58

You might be interested in

A farmer has 300 ft of fence to enclose 2 adjacent rectangular pens bordering his barn. Find the maximum area he can close.

Margarita [4]

Answer:

Width of 37.5 feet and length of 50 feet will maximize the area.

Step-by-step explanation:

Let w represent width and l represent length of the pen.

We have been given that a farmer has 300 ft of fence to enclose 2 adjacent rectangular pens bordering his barn. We are asked to find the dimensions that will maximize the area.

We can see from the attachment that the perimeter of the pens would be $4w+3l$ .

We can set our given information in an equation $4w+3l=300$ .

The area of the two pens would be $A=2l\cdot w$ .

From perimeter equation, we will get:

$w=\frac{300-3l}{4}$

Substituting this value in area equation, we will get:

$A=2l\cdot (\frac{300-3l}{4})$

Since we need to maximize area, so we need to find derivative of area function as:

$A=\frac{600l-6l^2}{4}$

Bring out the constant:

$A=\frac{1}{4}*\frac{d}{dl}(600l-6l^2)$

$A=\frac{1}{4}*(600-12l)$

$A=150-3l$

Now, we will set our derivative equal to 0 as:

$150-3l=0$

$150=3l$

$\frac{150}{3}=\frac{3l}{3}$

$50=l$

Now, we will substitute $l=50$ in equation $w=\frac{300-3l}{4}$ to solve for width as:

$w=\frac{300-3(50)}{4}$

$w=\frac{300-150}{4}$

$w=\frac{150}{4}$

$w=37.5$

Therefore, width of 37.5 feet and length of 50 feet will maximize the area.

8 0

3 years ago

A cone has a height of 8.4 centimeters and a base with a radius of 5.2 centimeters. what is the volume of the cone??

wlad13 [49]

<span>Cone Volume = (<span>π<span> • r² •<span> h) ÷ 3

</span></span></span></span>
<span>Cone Volume = (<span>π<span> • (5.2)² •<span> 8.4) ÷ 3

</span></span></span></span><span><span><span><span>Cone Volume = (3.14159 * </span>27.04 * 8.4) / 3</span> </span> </span>

<span><span><span><span>Cone Volume = </span>237.85606208 </span> </span> </span>

3 0

3 years ago

The diameter of a quarter is 2.5 cm. What is it’s circumference?

anastassius [24]

Answer:

7.85 cm

Step-by-step explanation:

The circumference of a circle can be found using the following formula.

$c=\pi d$

The diameter is 2.5 centimeters. Therefore, we can substitute 2.5 cm in for d.

$c=\pi *2.5 cm$

Now, find the circumference.

- In terms of pi:

$c=\pi *2.5 cm$

$c= (2.5)\pi cm$

$c= 2.5\pi cm$

-Using 3.14 as pi

$c=\pi *2.5 cm$

$c=3.14 *2.5 cm$

$c=7.85 cm$

-Using 3.14159... as pi

$c=\pi *2.5 cm$

$c=7.85398163 cm$

7 0

3 years ago

A car travels 270 miles in 4.5 hours. What is the rate in miles per hour?

jok3333 [9.3K]

270 divided by 4.5 = 60

6 0

3 years ago

Read 2 more answers

Clara has 8 coins worth 17¢. if the coins are all dimes and pennies, how many dimes and pennies does she have?

Sliva [168]

Let x = the number of dimes
Let y = the number of pennies.

There are 8 coins, therefore
x + y = 8 (1)

The coins are worth 17 cents, therefore
10x + y = 17 (2)

Subtract equation (1) from equation (2).
10x + y - (x + y) = 17 - 8
9x = 9
x = 1

From (1), obtain
y = 8 -x = 8 - 1 = 7

Answer: 1 dime, 7 pennies.

4 0

4 years ago

Read 2 more answers