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4 years ago

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A watering can dispenses water at the rate of 0.20 gallon per minute. The original volume of water in the can was 8 gallons. Whi

ch set of ordered pairs shows the volume of water in the can in gallons (y), as a function of time in minutes (x), from the first minute after can starts dispensing water? {(7.8, 1), (7.6, 2), (7.4, 3)} {(1, 7.8), (2, 7.6), (3, 7.4)} {(8.0, 1), (7.8, 2), (7.6, 3)} {(1, 8.0), (2, 7.8), (3, 7.6)}

2 answers:

Juliette [100K]4 years ago

8 0

<span> {(1, 7.8), (2, 7.6), (3, 7.4)}</span>

Evgen [1.6K]4 years ago

7 0

{(1, 7.8), (2, 7.6), (3, 7.4)}<span>
</span>

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1. A line passes through the ordered pairs (7,2) and (5,4). What is the slope? please show work

Minchanka [31]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 7 &,& 2~) 
% (c,d)
&&(~ 5 &,& 4~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{4-2}{5-7}\implies \cfrac{2}{-2}\implies -1$

since the sphere has a diameter of 20, its radius is half that, or 10.

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}~~
\begin{cases}
r=radius\\
-----\\
r=10
\end{cases}\implies V=\cfrac{4\pi (10)^3}{3}$

3 0

3 years ago

Find the dimensions of the rectangular box of maximum volume if the sum of the length, width, and height equals 180. (Give exact

Cloud [144]

Step-by-step explanation:

Let the dimension of the box be x, y and z.

Volume of the box V = xyz

Since the box is a rectangular box, the base will be a square of equal length.

V = x²h where h is the height of the box

If the sum of the length, width, and height equals 180, then x+x+h = 180

2x+h = 180

h = 180-2x

Substitute h = 180-2x into the volume of the box

V = x²(180-2x)

V = 180x²-2x³

The box has its maximum volume when $\frac{dV}{dx} = 0$

$\frac{dV}{dx} = 360x-6x^{2}$

$360x-6x^{2} = 0\\360x = 6x^2\\360 = 6x\\6x = 360\\x = \frac{360}{6}\\ x = 60$

Since 2x+h = 180

Substitute x = 60 into the equation ang get the height h

2(60)+h = 180

120+h = 180

h = 180-120

h = 60

Hence the dimension of the rectangular box is 60 by 60 by 60

6 0

4 years ago

koban [17]

Answer: It would be 4b+44

Step-by-step explanation:

This is the distributive property! so a(b+c)=ab+ac

In this case–4b+44!

6 0

2 years ago

Read 2 more answers

Change each standard form equation to slope-intercept form!

goldenfox [79]

Hello!

Slope-intercept form is this one: $y=a*x+b$ where a is the slope and b the intercept.

So, for transforming these equations to Slope-Intercept you'll need to rearrange the equations by adding or subtracting the same amounts on both sides of the equation (as a rule of thumb, sums are transformed into subtractions and multiplications into divisions).

<span>1) 3x + y = 12

You should notice that Y and X are on the same side of the equation, so by subtracting 3x on both sides of the equation you'll cancel X on the left side:

</span> $3x+y-3x=12-3x \\ y=12-3x$
<span>
To finish, we rearrange this equation to the form y=a*x+b

</span> $y=-3x+12$
<span>
So, the slope is -3 and the intercept is 12

2) 8=y+5x

</span>You should notice that Y and X are on the same side of the equation, so by subtracting 5x on both sides of the equation you'll cancel X on the right side:

$8-5x=y+5x-5x \\ 8-5x=y$

To finish, we rearrange this equation to the form y=a*x+b

$y=-5x+8$

So, the slope is -5 and the intercept is 8

3) 6x + 3y = -9

You should notice that Y and X are on the same side of the equation, so by subtracting 6x on both sides of the equation you'll cancel X on the left side:

$6x+3y-6x=-9-6x \\ 3y=-9-6x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 3 to cancel this number on the left side.

$\frac{3}{3}y= \frac{9}{3}- \frac{6}{3}x \\ y=3-2x$

To finish, we rearrange this equation to the form y=a*x+b

$y=-2x+3$

So, the slope is -2 and the intercept is 3

4) x - 5y = 55

You should notice that Y and X are on the same side of the equation, so by subtracting x on both sides of the equation you'll cancel X on the left side:

$x-5y-x=-55-x \\ -5y=-55-x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -5 to cancel this number on the left side.

$\frac{-5}{-5}y= \frac{55}{-5}- \frac{1}{-5}x \\ y=-11+ \frac{1}{5}x$

To finish, we rearrange this equation to the form y=a*x+b

$y=\frac{1}{5}x-11$

So, the slope is 1/5 and the intercept is -11

5) -4x-y=-2
You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the left side:

$-4x-y+4x=-2+4x \\ -y=2+4x$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by -1 to cancel this number on the left side.

$\frac{-1}{-1} y= \frac{-2}{-1}+ \frac{4}{-1}x \\ y=2-4x$

To finish, we rearrange this equation to the form y=a*x+b

$y=-4x+2$

So, the slope is -4 and the intercept is 2

6) -16 = -4x + 2y

You should notice that Y and X are on the same side of the equation, so by adding 4x on both sides of the equation you'll cancel X on the right side:

$-16+4x=-4x+2y+4x \\ -16+4x=2y$

Now, you should notice that y has a number that is multiplying it, so you'll need to divide the entire equation by 2 to cancel this number on the right side.

$\frac{-16}{2}+ \frac{4}{2} x= \frac{2}{2}y \\ -8+2x=y$

To finish, we rearrange this equation to the form y=a*x+b

$y=2x-8$

So, the slope is 2 and the intercept is -8

I hope that this helps. Have a nice day!

8 0

4 years ago

X²= 4y<br> Focus and directrix

Inessa05 [86]

The focus is (0,1) and the directix is y=-1

8 0

3 years ago