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3 years ago

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Write an equation of a line that has the same slope as 2x – 5y = 12 and the same y-intercept as 4y + 24 = 5x.

1 answer:

Alekssandra [29.7K]3 years ago

4 0

In ax+by=c form
slope=-a/b

y intercept is when x=0

sloope of 2x-5y=12 is -2/-5=2/5

y intercept of 4y+24=5x
4y+24=5(0)
4y+24=0
4y=-24
y=-6
y int=-6

y=mx+b
m=slope
b=y intercept
y=2/5x-6

answer is 2nd optoin

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or in decimal form

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Step-by-step explanation:

The midpoint of the line with endpoints $(x_1,y_1)$ and $(x_2,y_2)$ is $\bigl(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\bigr)$ . just take the average between the points

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Which of the following have the property that a(x)=a−1(x)? I. y=x II. y=1/x III.y=x^2 IV. y=x^3 A. I and II, only B. IV, only C.

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Answer:

<em>Correct answer:</em>

<em>A. I and II</em>

<em></em>

Step-by-step explanation:

First of all, let us have a look at the steps of finding inverse of a function.

1. Replace y with x and x with y.

2. Solve for y.

3. Replace y with $f^{-1}(x)$

Given that:

$I.\ y=x \\II.\ y=\dfrac{1}x \\III.\ y=x^2 \\IV.\ y=x^3$

Now, let us find inverse of each option one by one.

I. y = x, a(x) = x

Replacing y with and x with y:

x = y

x = $a^{-1}(x)$ = $a(x)$ Hence, I is true.

II. $y =\dfrac{1}{x}$

Replacing y with and x with y:

$x =\dfrac{1}{y}$

$x=\dfrac{1}{a^{-1}(x)}$

$\Rightarrow a^{-1}(x) = \dfrac{1}{x}$

$a^{-1}(x)$ = $a(x)$ Hence, II is true.

III. $y =x^{2}$

Replacing y with and x with y:

$x =y^{2}\\\Rightarrow y = \sqrt x\\\Rightarrow a^{-1}(x) = \sqrt{x} \ne a(x)$

Hence, III is not true.

IV. $y =x^{3}$

Replacing y with and x with y:

$x =y^{3}\\\Rightarrow y = \sqrt[3] x\\\Rightarrow a^{-1}(x) = \sqrt[3]{x} \ne a(x)$

Hence, IV is not true.

<em>Correct answer:</em>

<em>A. I and II</em>

<em></em>

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