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3 years ago

Suppose that y varies directly with x and y=12 when x=-2. what is when x=-6?

Mathematics

2 answers:

Mnenie [13.5K]3 years ago

5 0

Answer:

Step-by-step explanation:

Y varies directly with x

First find the value of the proportionality constant K

Y=KX

Where K is d constant of proportionality

12= -2K

Divide 12 by the coefficient of K

K=12÷(-2)=-6

When X=-6, substitute the value of K

Y=KX

Y=-6×(-6)

Y=36

dlinn [17]3 years ago

4 0

Y=4

How?
When they say directly you should multiply the x and y together. You would get -24, now using that number divide -24 by the new x(-6) you would get 4.

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Barbara earns $16.50 per hour for the first 8 hours she works What

Bingel [31]

In the morning she worked 3 hours and 45 minutes. In the afternoon she worked 5 hours and 15 minutes. That is a total of 9 hours. At $16.50 per hour for 8 hours that comes to $132. Plus the 1 hour over time with breaks down to $18.50 plus $8.25 totaling $24.75. Add that to the $132 and she made a total of $156.75 for Wednesday’s work. I hope this helps with your question.

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2 years ago

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Calculate volume of hemisphere with radius 3.2 cm

Olin [163]

Answer:

V ≈ 68.63 cm³

Step-by-step explanation:

the volume (V) of a sphere is calculated as

V = $\frac{4}{3}$ πr³

the volume of a hemisphere is half the volume of a sphere, so

V = $\frac{1}{2}$ × $\frac{4}{3}$ πr³ = $\frac{2}{3}$ πr³ , then

V = $\frac{2}{3}$ π × 3.2³

= $\frac{2}{3}$ π × 32.768

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2 years ago

Please help need answer for a quiz

torisob [31]

Answer:

first one with -1...21

Step-by-step explanation:

only one that follows quadratic formula format

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2 years ago

What is the slope of this graph? −14 4 14 −4 Number graph ranging from negative 10 to 10 on both the x and y axis. A line passes

spin [16.1K]

The slope of this graph is - 4

Step-by-step explanation:

The slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ , where

$(x_{1},y_{1})$ and $(x_{2},y_{2})$ are two points on the line
The slope of a horizontal line is zero
The slope of a vertical line is undefined

∵ The graph is a line

∵ The line passes through points (1 , -2) and (0 , 2)

∴ $x_{1}$ = 1 and $x_{2}$ = 0

∴ $y_{1}$ = -2 and $y_{2}$ = 2

- Substitute these values in the rule below

∵ $m=\frac{y_{2}-y_{1}}{x_{2}-x_{2}}$

∴ $m=\frac{2--2}{0-1}=\frac{4}{-1}$

∴ m = - 4

The slope of this graph is - 4

Learn more:

You can learn more about the slope of a line in brainly.com/question/4152194

#LearnwithBrainly

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3 years ago

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4TH TIME ASKING THIS!!! Please help me! Someone pleaseeee. I need the correct answers. I don’t want to fail

Alexeev081 [22]

Answer:

The functions are inverses; f(g(x)) = x ⇒ answer D

$h^{-1}(x)=\sqrt{\frac{x+1}{3}}$ ⇒ answer D

Step-by-step explanation:

* Lets explain how to find the inverse of a function

- Let f(x) = y

- Exchange x and y

- Solve to find the new y

- The new y = $f^{-1}(x)$

* Lets use these steps to solve the problems

∵ $f(x)=\sqrt{x-3}$

∵ f(x) = y

∴ $y=\sqrt{x-3}$

- Exchange x and y

∴ $x=\sqrt{y-3}$

- Square the two sides

∴ x² = y - 3

- Add 3 to both sides

∴ x² + 3 = y

- Change y by $f^{-1}(x)$

∴ $f^{-1}(x)=x^{2}+3$

∵ g(x) = x² + 3

∴ $f^{-1}(x)=g(x)$

∴ The functions are inverses to each other

* Now lets find f(g(x))

- To find f(g(x)) substitute x in f(x) by g(x)

∵ $f(x)=\sqrt{x-3}$

∵ g(x) = x² + 3

∴ $f(g(x))=\sqrt{(x^{2}+3)-3}=\sqrt{x^{2}+3-3}=\sqrt{x^{2}}=x$

∴ f(g(x)) = x

∴ The functions are inverses; f(g(x)) = x

* Lets find the inverse of h(x)

∵ h(x) = 3x² - 1 where x ≥ 0

- Let h(x) = y

∴ y = 3x² - 1

- Exchange x and y

∴ x = 3y² - 1

- Add 1 to both sides

∴ x + 1 = 3y²

- Divide both sides by 3

∴ $\frac{x + 1}{3}=y^{2}$

- Take √ for both sides

∴ ± $\sqrt{\frac{x+1}{3}}=y$

∵ x ≥ 0

∴ We will chose the positive value of the square root

∴ $\sqrt{\frac{x+1}{3}}=y$

- replace y by $h^{-1}(x)$

∴ $h^{-1}(x)=\sqrt{\frac{x+1}{3}}$

4 0

3 years ago