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Olin [163]
3 years ago
13

The total number of seats in a movie theater is calculated by adding the area of the upper section given by 8x2 and the area of

the lower section given by 6x2. The theater plans to add an addition of front row seats given by 4x for a total of 138 seats. Which equation could be used to solve for the number of seats in the front row addition?
Mathematics
1 answer:
e-lub [12.9K]3 years ago
3 0
8x^2+6x^2+4x=138  combine like terms on left side

14x^2+4x=138 since the number of seats in the from row is just 4x, subtract 14x^2 from both sides

4x=138-14x^2  that would be the general solution, if you wanted the actual number you would have to solve for x and then multiply that value by 4 to know what "4x" is...

14x^2+4x-138=0

14x^2-42x+46x-138=0

14x(x-3)+46(x-3)=0

(14x+46)(x-3)=0

2(7x+23)(x-3)=0, since x>0

x=3 and thus

4x=12 seats

So there are 12 seats in the front row addition.


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3 years ago
$75 before tax. Disc: 10% Tax: 7%, Tip: 20% what’s the total?
ololo11 [35]

Answer:

$102.75

Step-by-step explanation:

Given the following question:

We are given a cost of 75 dollars and are being asked to find the total cost after adding a tip, tax, and disc to the cost. To find this answer we will use the formula to calculate percentages making sure we use 75 as our base for each addition to our total cost.

<u>Formula to calculate percentages:</u>

\frac{p\times n}{100}

<u>First the disc:</u>

\frac{10\times 75}{100}
10\times75=750
750\div100=7.5
=7.5

<u>Next the tax:</u>

\frac{7\times75}{100}
7\times75=525
525\div100=5.25
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<u>Last but not least the tip:</u>

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<u>Finally add:</u>

75+7.50+5.25+15=102.75
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The total cost after adding the disc, tax, and the tip will be "$102.75."

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