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3 years ago

I need help with this you are helping me graduate! I would appreciate help

Mathematics

1 answer:

d1i1m1o1n [39]3 years ago

4 0

Answer:

y=250x

Step-by-step explanation:

every 2 minutes 500 gallons of water flow from a fountain,

x represents how much gallons of water flow from the fountain each minute:

500/2=250

thus, the equation is y=250x

You might be interested in

find the centre and radius of the following Cycles 9 x square + 9 y square +27 x + 12 y + 19 equals 0

Citrus2011 [14]

Answer:

Radius: $r =\frac{\sqrt {21}}{6}$

$Center = (-\frac{3}{2}, -\frac{2}{3})$

Step-by-step explanation:

Given

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Solving (a): The radius of the circle

First, we express the equation as:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

So, we have:

$9x^2 + 9y^2 + 27x + 12y + 19 = 0$

Divide through by 9

$x^2 + y^2 + 3x + \frac{12}{9}y + \frac{19}{9} = 0$

Rewrite as:

$x^2 + 3x + y^2+ \frac{12}{9}y =- \frac{19}{9}$

Group the expression into 2

$[x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}$

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

Next, we complete the square on each group.

For $[x^2 + 3x]$

1: Divide the $coefficient\ of\ x\ by\ 2$

2: Take the $square\ of\ the\ division$

3: Add this $square\ to\ both\ sides\ of\ the\ equation.$

So, we have:

$[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}$

$[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Factorize

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2$

Apply the same to y

$[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}$

Add the fractions

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}$

$[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}$

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

By comparison:

$r^2 =\frac{7}{12}$

Take square roots of both sides

$r =\sqrt{\frac{7}{12}}$

Split

$r =\frac{\sqrt 7}{\sqrt 12}$

Rationalize

$r =\frac{\sqrt 7*\sqrt 12}{\sqrt 12*\sqrt 12}$

$r =\frac{\sqrt {84}}{12}$

$r =\frac{\sqrt {4*21}}{12}$

$r =\frac{2\sqrt {21}}{12}$

$r =\frac{\sqrt {21}}{6}$

Solving (b): The center

Recall that:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$r = radius$

$(h,k) =center$

From:

$[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}$

$-h = \frac{3}{2}$ and $-k = \frac{2}{3}$

Solve for h and k

$h = -\frac{3}{2}$ and $k = -\frac{2}{3}$

Hence, the center is:

$Center = (-\frac{3}{2}, -\frac{2}{3})$

6 0

2 years ago

Name:<br> 11. Find the measure of each acute angle.<br> (2x + 6°<br> (5x + 14°

Westkost [7]

Answer:

Step-by-step explanation:

Dc is a little bit more than a few other things but I think it’s Going and the kids have to be in a different room yet I think it’s going on for me and my kids are in my car so I’m going to go get my car off at my moms and I can go pick it out I have a lot to go

4 0

2 years ago

Read 2 more answers

Which expression is equivalent to ^

mash [69]

Answer:

Step-by-step explanation:

lets break down 120 to see what it is divisible by and see if any of those numbers are perfect squares.

120/2=60

120/3=40

120/4=30

we can stop there because 4 is a perfect square and 30 can not be reduced any further to produce a perfect square.

do not forget there is only one x so it must stay in side the radical.

your answer is 2sqrt(30x)

5 0

3 years ago

A delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lbs and each b

german

Answer:

16 boxes

Step-by-step explanation:

160+50x=1000

Solve for the x and you'll get 16.8. Now, because you can't have a fraction of a box, and you can't go over the limit, the answer is 16 boxes.

(How to solve for x:

Get x by itself by subtracting 160 to both sides.

50x=1000-160

50x=840

Divide both sides by 50.

x=16.8)

8 0

3 years ago

A property map is drawn at a scale of 1:1000. Calculate the corresponding actual distance if the distance between two points on

zvonat [6]

Answer:10 m

Step-by-step explanation:

Given

Scaling ratio 1:1000

i.e. one unit in map is equal to 1000 unit in actual distance

therefore if the distance between two points is 1 cm in map then

it is 1000 cm in reality

8 0

3 years ago