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kari74 [83]
3 years ago
8

You and 3 friends go to the movies. Each movie ticket costs $6.25. If your mom gave you $20.00 and you bought popcorn for $3.50,

how much change are you taking home?
Mathematics
1 answer:
Sedaia [141]3 years ago
7 0

Answer:

Change = \$10.25

Step-by-step explanation:

Given

Individuals = 4 <em>(You and 3 friends)</em>

Total = \$20.00

Movie = \$6.25 per individual

Popcorn = \$3.50

Required

Determine the change

First, we need to determine the total amount spent on movie ticket.

The question does not state whether I pay for my friend's ticket.

So, we'll work on what is obvious.

i.e

Amount\ Spent\ on\ Ticket = \$6.25

Add this amount to the amount spent on popcorn

Amount\ Spent =\$6.25 + \$3.50

Amount\ Spent =\$9.75

To get the Change, we have to deduct the total amount spent from the amount given by mom

Change = \$20 - \$9.75

Change = \$10.25

Hence:

The change is $10.25

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The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

<u>Given the following data:</u>

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Translating the word problem into an algebraic expression;

W = 3 + L  ......equation 1

H = 4 + L  ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

Volume = length * width * height  .....equation 3.

Substituting the values into equation, we have;

224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}

Rearranging the polynomial, we have;

L^{3} + 7L^{2} +  12L - 224 = 0

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

(x - 3) = 0\\x = 3

P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9)  + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0

We would try with 4;

P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16)  + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224  - 224 = 0

Therefore, 4 is one of its roots.

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Find more information on polynomial here: brainly.com/question/10689855

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Answer:

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Step-by-step explanation:

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Rewriting, we have ...

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This has solution ...

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So, the complete solution is ...

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The salt in the tank increases in exponentially decaying fashion from 40 grams to 300 grams with a time constant of 50 minutes.

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