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3 years ago

What is the solution to the system of equations?

Mathematics

1 answer:

Mrac [35]3 years ago

8 0

Answer:

(4, -1)

Step-by-step explanation:

3 x minus 4 y = 16

2 x + 3 y = 5

3x - 4y = 16

2x + 3y = 5

x = 2.5 - 1.5y

3(2.5 - 1.5y) - 4y = 16

7.5 - 4.5y - 4y = 16

-8.5 = 8.5y

y = -1

x = 2.5 - 1.5(-1)

x = 2.5 + 1.5

x = 4

(4, -1)

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The number of employees working for Widget Wonders in 1997 was 17,697, with an expected decrease of 2.2% per year. At the percen

Veronika [31]

In 1997 = 17697

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3 years ago

Write the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5)

Sedbober [7]

Answer: $\bold{y=-\dfrac{1}{3}x-1}$

<u>Step-by-step explanation:</u>

(4, 1) & (2, -5)

First, find the slope (m) and then the perpendicular (opposite reciprocal) slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\\m=\dfrac{-5-1}{2-4} = \dfrac{-6}{-2}=3\quad \rightarrow \quad m_{\perp}=-\dfrac{1}{3}\\$

Next, find the midpoint of (4, 1) and (2, -5):

$Midpoint=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{4+2}{2},\dfrac{1-5}{2}\bigg)\\\\\\.\qquad \qquad=\bigg(\dfrac{6}{2},\dfrac{-4}{2}\bigg)\\\\\\.\qquad \qquad=(3, -2)$

Lastly, input the perpendicular slope and the midpoint into the Point-Slope formula to find the equation of the line:

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Artyom0805 [142]

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Hope this helps!!!

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3 years ago

sineoko [7]

Answer:

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Step-by-step explanation:

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