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3 years ago

Complete solutions to 2-variable ec

Mathematics

1 answer:

Igoryamba3 years ago

4 0

Answer:

x=-1/3=10/3 y=-3x+10

Step-by-step explanation:

1. distribute

y+2=-3x+12

2. subtract 2

y=-3x+10

1.subtract 12

y-10=-3x

2. divide by -3

-1/3y+10/3=x

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Fofino [41]

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3 years ago

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Gala2k [10]

Answer:

(- 2, 4 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) , then the midpoint is

( $\frac{x_{1}+x_{2} }{2}$ , $\frac{y_{1}+y_{2} }{2}$ )

Here (x₁, y₁ ) = A (4, 6 ) and (x₂, y₂ ) = B (- 8, 2 )

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3 years ago

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Rooter Plus charges a $25 service fee plus $40 per hour of work done. Is this a proportional or non-proportional relationship?

Dominik [7]

Answer:

Non-proportional; the rate of change is $40/hour

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

x -----> the number of hours

y ----> The total charge in dollars

The equation of the line in slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

we have

$m=40\ \$/h\\b=\$25$

substitute

$y=40x+25$

This relationship is not proportional, because the line not passes through the origin

therefore

Non-proportional; the rate of change is $40/hour

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3 years ago

In a video game, the chance of rain each day is always 30%. At the beginning of each day in the video game, the computer generat

Scorpion4ik [409]

Answer:

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2 years ago

Could someplease explain the whole problem? For the first part my the answer I got was x= .618, -.618, and <img src="https://tex

algol13

9514 1404 393

Answer:

a) x = (√5 -1)/2 ≈ 0.618034

b) 1/x = (√5 +1)/2 ≈ 1.618034

Step-by-step explanation:

Given:

x/(1 -x) = 1/x

Find:

Exactly, and as a decimal approximation, ...

a) x, using the quadratic formula

b) 1/x

Solution:

a) We can multiply the given equation by x(1 -x) to obtain ...

x² = 1 -x

x² +x -1 = 0 . . . . . . add x-1

The coefficients for use in the quadratic formula are a=1, b=1, c=-1. The solution using the quadratic formula is ...

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-1\pm\sqrt{1^2-4\cdot1\cdot(-1)}}{2\cdot1}=\dfrac{-1\pm\sqrt{5}}{2}$

We are only interested in the positive solution, which is ...

$\boxed{x=\dfrac{\sqrt{5}-1}{2}\approx0.618034}$

b) The quadratic we developed in the first part can be rearranged like this:

x² +x = 1 . . . . . . add 1 to both sides

x(x +1) = 1 . . . . . factor out x

x +1 = 1/x . . . . . .divide by x

Then to find the value of 1/x, we simply need to add 1 to the value of x we have:

$\dfrac{1}{x}=\dfrac{\sqrt{5}-1}{2}+1=\dfrac{\sqrt{5}-1}{2}+\dfrac{2}{2}=\dfrac{\sqrt{5}-1+2}{2}\\\\\boxed{\dfrac{1}{x}=\dfrac{\sqrt{5}+1}{2}\approx1.618034}$

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2 years ago