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amm1812
2 years ago
8

Last year a banquet hall charged $65 per person to attend a function. The function C(p) = 65p represents the total cost, C, to r

ent the hall based on the number of people, p, that would attend the event. If the hall can hold a total of 50 people, what is the domain and range for this function?
Mathematics
1 answer:
zlopas [31]2 years ago
8 0

Answer:

Domain = [0, 50]

Range   = [0, 3250]

Step-by-step explanation:

A function shows the relationship between two variables (independent variable and dependent variable). The independent variable is a variable not dependent on any variable, it is the input of the function while the dependent variable is a variable dependent on other variable, it is the output of the function.

The domain of a function is the set of all input variables (independent variable) and the range of a function is the set of all output variables (dependent variables).

In the function C(p) = 65p, p is the independent variable and C(p) is the dependent variable.

Since the hall can hold a total of 50 people, the domain of the function = [0, 50]

C(0) = 65(0) = 0, C(50) = 65(50) = 3250

Hence, the range of the function = [0, 3250]

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The area of a trapezoid is 144 square inches. if the height is 12 inches, find the length of the median.
deff fn [24]

Answer: 12 inches

Step-by-step explanation: In this problem, since we're asked to find the length of the median, let's use our formula for the area of a trapezoid that involves the median which is shown below.

Area = median · height

We know that the area is 144 and the height is 9 so we can set up the equation 144 = M · 12. Now to solve for <em>m</em>, we divide both sides of the equation by 12 and we find that 12 = M.

So the length of the median of the trapezoid is 12 inches.

6 0
2 years ago
Jake made a total of 7 copies at a copy shop, with some being black-and-white copies and some being color copies. Black-and-whit
Arada [10]
Jake spent a total of 70 cents.
b = black-and-white = 8 cents
c = color = 15 cents

70 = 8b + 15c

he made a total of 7 copies
b + c = 7

system of equation:
70 = 8b + 15c
b + c = 7

--------------------------

b + c = 7
b + c (-c) = 7 (-c)
b = 7 - c

plug in 7 - c for b

70 = 8(7 - c) + 15c
Distribute the 8 to both 7 and - c (distributive property)

70 = 56 - 8c + 15c
Simplify like terms

70 = 56 - 8c + 15c
70 = 56 + 7c

Isolate the c, do the opposite of PEMDAS: Subtract 56 from both sides

70 (-56) = 56 (-56) + 7c
14 = 7c

divide 7 from both sides to isolate the c

14 = 7c
14/7 = 7c/7
 c = 14/7
 c = 2

c = 2
---------------

Now that you know what c equals (c = 2), plug in 2 for c in one of the equations.
b + c = 7
c = 2
<em>b + (2) = 7
</em><em />Find b by isolating it. subtract 2 from both sides
b + 2 = 7
b + 2 (-2) = 7 (-2)
b = 7 - 2
b = 5

Jake made 5 black-and-white copies, and 2 color copies

hope this helps
8 0
2 years ago
Read 2 more answers
A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than t
belka [17]

system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y is  x+8y=68 and 3x+4y=64   .

<u>Step-by-step explanation:</u>

Here we have , A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. We need to find Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y . Let's find out:

Let the price in dollars of each large candle, x, and each small candle, y .So

A customer at a store paid $64 for 3 large candles and 4 small candles

Equation is  :

⇒ 3x+4y=64  .....(1)

At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles.

Equation is  :

⇒ x+8y=68  .......(2)

3(2)-(1) i.e.

⇒ 3(x+8y)-(3x+4y)=68(3)-64

⇒ 20y=140

⇒ y=7

So , x+8y=68  

⇒  x+8(7)=68

⇒  x=12

Therefore , system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y is  x+8y=68 and 3x+4y=64   .

7 0
2 years ago
The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 128 feet, what is the length of the
Serga [27]

Answer: B

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
The equation of a circle is (x + 12)2 + (y + 16)2 = (r1)2, and the circle passes through the origin. The equation of the circle
Furkat [3]
For an equation to pass through the origin, (0,0) must be a solution of the equation. So, for the first one, 

(x + 12)^{2} + (y + 16)^{2} = r_{1}^{2}

(0, 0) must satisfy the equation and we can solve for the value of r₁ as shown below.

(0 + 12)^{2} + (0 + 16)^{2} = r_{1}^{2}
12^{2} + 16^{2} = r_{1}^{2}
r_{1} = \sqrt{12^{2} + 16^{2}}
r_{1} = 20

Since the second equation of the circle also passes through the origin, we use the same steps from the first one.

(0 - 30)^{2} + (0 - 16)^{2} = r_{2}^{2}
r_{2} = \sqrt{30^{2} + 16^{2}}
r_{2} = 34

Thus, we have the values for r₁ and r₂ as 20 and 34, respectively.

Answer: r₁ = 20 and r₂ = 34
7 0
2 years ago
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