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Bezzdna [24]
3 years ago
10

Solve the following equation for x.

Mathematics
1 answer:
Vaselesa [24]3 years ago
7 0

Solve for x (isolate/get x by itself)

\frac{1}{4}x-7=\frac{3}{8}x-5    Add 5 on both sides

\frac{1}{4}x-7+5=\frac{3}{8}x-5+5

\frac{1}{4}x-2=\frac{3}{8}x   Subtract 1/4x on both sides

\frac{1}{4}x-\frac{1}{4}x-2=\frac{3}{8}x-\frac{1}{4}x

-2=\frac{3}{8}x-\frac{1}{4}x   Make the denominators the same of the fractions in order to combine them. Multiply 2 to the top and bottom of 1/4x

-2=\frac{3}{8}x-\frac{2}{8}x

-2=\frac{1}{8}x    Multiply 8 on both sides

-2(8)=(8)\frac{1}{8}x

-16 = x

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A scuba diving company currently charges $100per dive. On average, there are 30 customers per day. The company performed a study
Semenov [28]

A. Total Revenue (R) is equal to price per dive (P) multiplied by number of customers (C). We can write R=PC.

Per price increase is $20. So four price increase is $20*4=$80. Hence, price per dive is 100+80=$180.

Also per price increase, 2 customers are reduced from 30. For 4 price increases, 4*2=8 customers are reduced. Hence, total customers is 30-8=22.

So Total Revenue is:

R=180*22=3960


B. Each price increase is 20. So x price increase is 20x. Hence, new price per dive would be equal to the sum of 100 and 20x.

Also per price increase, customers decrease by 2. So per x price increases, the customer decrease is 2x. Hence, new number of customers is the difference of 30 and 2x.

Therefor we can write the quadratic equation for total revenue as the new price times the new number of customers.

R=(100+2x)(30-2x)=-40x^{2}+400x+3000


C. We are looking for the point (x) at which the equation modeled in part (B) gives a maximum value of revenue (y). That x value is given as x=-\frac{b}{2a}, where a is the coefficient of x^{2} and b is the coefficient of x. So we have,

x=-\frac{b}{2a}=- \frac{400}{(2)(-40)}=5

That means, the greatest revenue is achieved after 5 price increases. Each price increase was 20, so 5 price increase would be 5*20=100. So the price that gives the greatest revenue is 100+100=200.

ANSWERS:

A. $3960

B. R=-40x^{2}+400x+3000

C. $200

4 0
3 years ago
Sam’s basketball team won 70% of the games they played. How many games did they win?
maw [93]
Assuming it’s out of 100 it would 70 games they have won, but if it provides a number you will need to provide that for the correct answer.
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A.Sum of integer and its additive inverse is ___________.B.Sum of -22 and -44 is ______________.C.-36 ÷ ( ___)=-9d._________ is
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Answer:

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  D. 998

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Step-by-step explanation:

A. By definition, the sum of anything and its additive inverse is zero.

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B. If you have trouble with sums, your calculator can help.

  -22 + (-44) = -22 -44 = -66

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C. -36/x = -9 can be solved by multiplying by x and dividing by -9:

  -36 = -9x

  -36/-9 = x = 4

Since the product of the divisor and quotient is the dividend, dividing the dividend by either gives the other. Here, your dividend is -36 and your quotient is -9. To find the divisor, you can divide -36 by -9, as we did.

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D. The absolute value function changes the sign of negative numbers to positive:

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E. If you have trouble with sums, your calculator can help.

  (−2)−[(−3)−(−7)−(−6)]

  = -2 -(-3 +7 +6) = -2 -10 = -12

4 0
2 years ago
Given f(x)=4x+6 and g(x)=9x+9<br> then what is f(g(−6))?
irakobra [83]
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galben [10]
I THINK ITS C I HOPE I HELPED!  :D
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