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sergiy2304 [10]
3 years ago
8

What are the coordinates of one of the vertices of a rectangle when two sides are given by the lines x - 3y = -8 and 3x + y = 6?

Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
5 0

Answer:

(1, 3)

Step-by-step explanation:

x - 3y = -8

3x + y = 6

Isolate a variable in one of the equations:

y = 6 - 3x

Substitute the value of y into the other equation:

x - 3(6 - 3x) = -8

Use distributive property:

x - 18 + 9x = -8

Combine like terms:

10x - 18 = -8

Isolate the variable:

10x = 10

x = 1

Substitute the value of x into any equation:

3(1) + y = 6

3 + y = 6

Isolate the variable:

y = 3

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Answer:

The cost of the old ball was $100.

Step-by-step explanation:

The cost of the new ball = $300

The new ball has three times the price of his old ball.

So, let the price of the old ball be = x

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3 years ago
Kelly price sells college textbooks on commission. She gets 8 % on the first $7500 of​ sales, 16% on the next $7500 of​ sales, a
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Answer:

The commission would be $ 920.

Step-by-step explanation:

Given,

Sales in 1997 ​= $ 9500,

Since, there is a commision of 8 % on the first $ 7500 of​ sales, 16% on the next $ 7500 of​ sales, and 20% on sales over $ 15,000,

If x represents the total sales,

Commission for x ≤ 7500 = 8% of x = 0.08x,

Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of (x-7500)

= 600 + 0.16(x-7500),

Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of 7500 + 20% of (x-15000)

= 600 + 1200 + 0.20(x-15000)

= 1800 + 0.20(x-15000)

Thus, the function that shows the given situation,

f(x)=\left\{\begin{matrix}0.08x & x \leq 7500\\ 600+0.16(x-7500) & 7500 < x \leq 15000\\ 1800+0.20(x-15000) & 15000 < x\end{matrix}\right.

Since, 9500 lies between 7500 and 15000,

Therefore, the commission would be,

f(9500)= 600 + 0.16(9500 - 7500) = 600 + 320 = $ 920

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3 years ago
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Step-by-step explanation:

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