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3 years ago

7

a 18,000 - gallon pool is being filled at a rate of 20 gallons per minute. At this rate ,how many minutes will it take to fill t

his pool 2/5 full ? plssssssss help me

1 answer:

Ahat [919]3 years ago

4 0

The total capacity of the pool = 18000 gallon
The total volume of the pool when calculated to 2/5 = (2/5) * 18000
   = 35000/5 gallons
   = 7200 gallons.
Now it is given in the problem that that
Rate at which the pool is filled with water = 20 gallons per minutes
Then
20 gallons of water is filled in = 1 minute
So
7200 gallons of water will be filled in = 7200/20 minute
   = 720/2 minute
   = 360 minute
So 360 minute is required to fill the pool with 2/5 of the total volume of water.

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3 years ago

Solve the simultaneous equations<br> y = 9 - X<br> y = 2x2 + 4x + 6

kenny6666 [7]

Answer:

$\mathrm{Therefore,\:the\:final\:solutions\:for\:}y=9-x,\:y=2x^2+4x+6\mathrm{\:are\:}$

$\begin{pmatrix}x=\frac{1}{2},\:&y=\frac{17}{2}\\ x=-3,\:&y=12\end{pmatrix}$

Step-by-step explanation:

Given the simultaneous equations

$y=9-x$

$y\:=\:2x^2\:+\:4x\:+\:6$

Subtract the equations

$y=9-x$

$-$

$\underline{y=2x^2+4x+6}$

$y-y=9-x-\left(2x^2+4x+6\right)$

$\mathrm{Refine}$

$x\left(2x+5\right)=3$

$\mathrm{Solve\:}\:x\left(2x+5\right)=3$

$2x^2+5x=3$ ∵ $\mathrm{Expand\:}x\left(2x+5\right):\quad 2x^2+5x$

$\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}$

$2x^2+5x-3=3-3$

$\mathrm{Solve\:with\:the\:quadratic\:formula}$

$\mathrm{Quadratic\:Equation\:Formula:}$

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=2,\:b=5,\:c=-3:\quad x_{1,\:2}=\frac{-5\pm \sqrt{5^2-4\cdot \:2\left(-3\right)}}{2\cdot \:2}v\\$

$x=\frac{-5+\sqrt{5^2-4\cdot \:2\left(-3\right)}}{2\cdot \:2}$

$=\frac{-5+\sqrt{5^2+4\cdot \:2\cdot \:3}}{2\cdot \:2}$

$=\frac{-5+\sqrt{49}}{2\cdot \:2}$

$=\frac{-5+\sqrt{49}}{4}$

$=\frac{-5+7}{4}$

$=\frac{2}{4}$

$=\frac{1}{2}$

Similarly,

$x=\frac{-5-\sqrt{5^2-4\cdot \:2\left(-3\right)}}{2\cdot \:2}:\quad -3$

$\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}$

$x=\frac{1}{2},\:x=-3$

$\mathrm{Plug\:the\:solutions\:}x=\frac{1}{2},\:x=-3\mathrm{\:into\:}y=9-x$

$\mathrm{For\:}y=9-x\mathrm{,\:subsitute\:}x\mathrm{\:with\:}\frac{1}{2}:\quad y=\frac{17}{2}$

$\mathrm{For\:}y=9-x\mathrm{,\:subsitute\:}x\mathrm{\:with\:}-3:\quad y=12$

$\mathrm{Therefore,\:the\:final\:solutions\:for\:}y=9-x,\:y=2x^2+4x+6\mathrm{\:are\:}$

$\begin{pmatrix}x=\frac{1}{2},\:&y=\frac{17}{2}\\ x=-3,\:&y=12\end{pmatrix}$

3 0

4 years ago

Which equation is represented by the table?

MatroZZZ [7]

Answer:

$y=-|x-3|-3$

Step-by-step explanation:

The table shows values of $y$ for different values of $x$ .

Let us test each equation with the values given in the table.

Equation 1: $y=|x+3|-3$

For $x$ = 1, we get,

$y=|x+3|-3=|1+3|-3=|4|-3=4-3=1$

So, we got 1 for $y$ . But as per table, value of $y$ should be -5.

So, equation 1 is incorrect.

Equation 2: $y=-|x-3|-3$

For $x$ = 1, we get,

$y=-|x-3|-3=-|1-3|-3=-|-2|-3=-(2)-3=-5$

So, we got -5 for $y$ . It matches with the value of table.

Let us check for another value of $x$ in order to confirm.

For $x =2$ , we get,

$y=-|x-3|-3=-|2-3|-3=-|-1|-3=-(1)-3=-4$

So, we got -4 for $y$ . It matches with the value of table.

So, equation 2 is the correct answer.

We can be completely sure by checking the remaining equations too.

Equation 3: $y=|x-3|-3$

For $x$ = 1, we get,

$y=|x-3|-3=|1-3|-3=|-2|-3=2-3=-1$

So, we got -1 for $y$ . But as per table, value of $y$ should be -5.

So, equation 3 is incorrect.

Equation 4: $y=-|x+3|-3$

For $x$ = 1, we get,

$y=-|x+3|-3=-|1+3|-3=-|4|-3=-4-3=-7$

So, we got -7 for $y$ . But as per table, value of $y$ should be -5.

So, equation 4 is incorrect.

3 0

3 years ago

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Lunna [17]

Answer:

x ≤ -7

Step-by-step explanation:

7 0

3 years ago

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den301095 [7]

Answer:

a. 6

b. 4/3

c. 28

Step-by-step explanation:

For a, you multiply 9 by 2/3

For b, you would do 12 divided by 9

For c, you would do 7 divided by 1/4, or 0.25

Hope this helps.

4 0

4 years ago

Read 2 more answers