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1 year ago

The university theatre department is selling tickets to their

Mathematics

1 answer:

olya-2409 [2.1K]1 year ago

3 0

Answer:

(8,14)

Step-by-step explanation:

3x+2y=52

3x+1y=38 Subtract these equations using elimination method to get y=14

Then substitute y=14 to either equation

the bottom one is easier so

3x+1(14)=38 distribute 1 to 14 and any number times one is 1

3x+14=38 Subtract 14 from both sides

3x=24 Divide by 3

x=8 so check now

3(8)+1(14)=38

24+14=38?

38=38? yes

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Joe's annual income has been increasing each year by the same dollar amount. The first year his income was $17 comma 90017,900

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Answer:

In 17th year, his income was $30,700.

Step-by-step explanation:

It is given that the income has been increasing each year by the same dollar amount. It means it is linear function.

Income in first year = $17,900

Income in 4th year = $20,300

Let y be the income at x year.

It means the line passes through the point (1,17900) and (4,20300).

If a line passes through two points $(x_1,y_1)$ and $(x_2,y_2)$ , then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The equation of line is

$y-17900=\frac{20300-17900}{4-1}(x-1)$

$y-17900=\frac{2400}{3}(x-1)$

$y-17900=800(x-1)$

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Add 17900 on both sides.

$y=800x-800+17900$

$y=800x+17100$

The income equation is y=800x+17100.

Substitute y=30,700 in the above equation.

$30700=800x+17100$

Subtract 17100 from both sides.

$30700-17100=800x$

$13600=800x$

Divide both sides by 800.

$\frac{13600}{800}=x$

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Therefore, in 17th year his income was $30,700.

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