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ehidna [41]
3 years ago
7

Henry's height is 3 inches more than one-half of Charlie's height. If Henry is 24 inches tall, how tall is Charlie?

Mathematics
2 answers:
postnew [5]3 years ago
8 0

Answer:

9 inches

Step-by-step explanation:

henry = 3 inches more than 1/2 of charlie

24=henry

24/2= 12-3=9 inches hope this helps

True [87]3 years ago
6 0

Answer:

Charlie is 20.5 inches tall

Step-by-step explanation:

Henry: 24 inches

            3 and 1/2 inches taller than Charlie

Charlie: 24 - 3.5 inches

            20.5 inches

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Answer:x=29

Step-by-step explanation:

You want to add all the like terms together so in this case 2x and x

29,30,20,8

3x=87

Divide 3 by both sides

X=29

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A figure maps to another figure using one or more translations, reflections, or rotations. What must be true about the two figur
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<span>Any point in figure A can be mapped to a point in figure B.</span>
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the volume of hemisphere is 1527.4cm^3.find the radius of the hemisphere to the nearest whole whole number.(take π to be 22/7)​
skelet666 [1.2K]

Answer:

radius of the hemisphere = 9 cm approx

Step-by-step explanation:

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3 years ago
A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in t
Zinaida [17]

Answer:

a) p(x) = 300 - 3

b) P(x) = -3 x² + 285 x

c) Price of per room per day  = $ 157.5

when Number of rooms occupied , x = 47.5

Step-by-step explanation:

Given - A motel owner observes that when a room is priced at $60 per day, all 80 rooms of the motel are occupied. For every $3 rise in the charge per room per day, one more room is vacant. Each occupied room costs an additional $15 per day to maintain.

To find - a) Find the demand function, expressing p, the price charged for each room per day, as a function of x, the number of rooms occupied.

             b) Find the profit function P(x).

             c) Find the price of per room per day the motel should charge in order to maximize its profit.

Proof -

a)

Let

(x, y) be the point

where x represents number of rooms occupied

and y represents price of room per day.

Now,

Given that,

a room is priced at $60 per day, all 80 rooms of the motel are occupied.

So, point becomes (80, 60)

And  given that For every $3 rise in the charge per room per day, one more room is vacant.

So, point becomes (79, 63)

Now, we have two points (80, 60), (79, 63)

Let us assume that,

p(x) be the price charged for each room per day

Now,

By using point - slope formula , we get

p -60 = \frac{(63 - 60}{(79 - 80)} (x - 80)

⇒p -60 = (-3)(x-80)

⇒p-60 = 240 -3 x

⇒p(x) = 240 + 60 -3 x

⇒p(x) = 300 - 3 x

b)

Given that,

Each occupied room costs an additional $15 per day to maintain.

Let C(x) be the cost function,

Then C(x) =15 x

now,

Revenue function,

R(x) =x*p

      = x*(300 -3 x )

      = 300 x - 3 x²

⇒R(x) = 300 x - 3 x²

Now,

We know

Profit function = Revenue function - Cost function

⇒P(x) = R(x)-C(x)

⇒P(x) = (300 x -3 x²) -15 x

⇒P(x) = -3 x² + 285 x

c)

P'(x) = -6 x +285

For Maximize profit , Put P'(x) = 0

⇒-6 x+ 285 =0

⇒6 x= 285

⇒x = \frac{285}{6}

⇒x= 47.5

∴ we get

Maximize profit is when price, p = 300 - 3x

                                                      = 300 -3(47.5)

                                                      = $157.5

⇒Price of per room per day  = $ 157.5

when Number of rooms occupied , x = 47.5

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