At the end of the summer, I decide to drain the swimming pool
(which has 1500 gallons of water in it). I noticed that it drains
faster when there is more water in the pool. That was interesting
to me, so I decided to measure the rate at which it drains. I found
that it was draining at a rate of 1% every minute.
How long will it take to empty the pool?

Answer:

n = 4

Step-by-step explanation:

3 = 2 + n/4

1 = n/4

4 = n

Answer:

n = 4

Step-by-step explanation:

take the 2 and subtract it from itself then you gotta do it to the other side so it be 3 -2 and you get 1 then you multiply 4 to n/4 and it crosses it out and what you do to one side you do to the other so you multiply 4 by 1 & get 4

Answer:

3/5

Step-by-step explanation:

[tex]10x-25+8[/tex]

Simplify:

[tex]10x+-25+8[/tex]

Combine Like Terms:

[tex](10x)+(-25+8)\\10x+-17(ANSWER)[/tex]

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Answer:

[tex]y = 4(0.5) {}^{x} [/tex]

Step-by-step explanation:

By looking at your graph, The y intercept is (0,4).

This is an exponential function so it is represented by

[tex]y = ab {}^{x} [/tex]

where a is the vertical stretched and b is the constant rate and x is the nth power.

let plug in 0,4

[tex]4 = ab {}^{0} [/tex]

[tex]b {}^{0} = 1[/tex]

since anything to the 0 power is 1.

[tex]4 = a \times 1[/tex]

[tex]4 = a[/tex]

Know let plug it in to this equation.

[tex]y = 4b {}^{x} [/tex]

Let use 2,1 another point on the graph

[tex]1 = 4b {}^{2} [/tex]

Divide 4 by both sides

[tex]0.25 = {b}^{2} [/tex]

take sqr root of 0.25

[tex]0.5 = b[/tex]

So

the answer is

[tex]y = 4(0.5) {}^{x} [/tex]

Answer:

-4√6-6√5

Step-by-step explanation:

-3√6-3√20-√6 = (-3√6-√6)-3√20 = -4√6-3√20

√20 = √4*√5 or 2√5

substitute that in and you get -4√6-3(2√5) which then becomes

-4√6-6√5

Answer:

60

Step-by-step explanation:

75,000/1,250= 60 mins or an hour

Answer:

Visit geogebra.com

Step-by-step explanation:

none needed <3

Answer:

answer is

Step-by-step explanation:

2+4=6

and 6-32=26 answer

Answer:

Solve the linear equation [tex]2.25 - 11 - 7.75 + 1.5j= 0.5j - 1[/tex]

✔ [tex]j[/tex] = –0.45

[tex]j[/tex]  = –0.25

[tex]j[/tex] = 0.25

[tex]j[/tex] = 0.45

Simplify [tex]2.25 - 11j - 7.75 + 1.5j[/tex] .

Subtract [tex]7.75[/tex] from [tex]2.25[/tex] .

[tex]- 11j - 5.5 + 1.5j = 0.5j -1[/tex]

Add [tex]-11j[/tex] and [tex]1.5j[/tex] .

[tex]- 9.5j - 5.5 = 0.5j - 1[/tex]

Move all terms containing [tex]j[/tex] to the left side of the equation.

Subtract [tex]0.5j[/tex] from both sides of the equation.

[tex]- 9.5j - 5.5 = 0.5j - 1[/tex]

Subtract [tex]0.5j[/tex] from [tex]- 9.5j[/tex].

[tex]- 10j - 5.5 = - 1[/tex]

Move all terms not containing [tex]j[/tex] to the right side of the equation.

Add [tex]5.5[/tex] to both sides of the equation.

[tex]-10j = -1 +5.5[/tex]

Add [tex]-1[/tex] and [tex]5.5[/tex] .

[tex]10j=4.5[/tex]

Divide each term in [tex]-10[/tex][tex]j[/tex] [tex]=4.5[/tex] by [tex]-10[/tex] and simplify.

Divide each term in [tex]-10j = 4.5[/tex] by [tex]-10[/tex].

[tex]\frac{-10j}{-10} = \frac{4.5}{-10}[/tex]

Simplify the left side.

Cancel the common factor of [tex]-10[/tex].

[tex]j= \frac{4.5}{-10}[/tex]

Cancel the common factor.

[tex]\frac{-10j }{-10} = \frac{4.5}{-10}[/tex]

Divide [tex]j[/tex] by [tex]1[/tex]

[tex]j=\frac{4.5}{-10}[/tex]

Simplify the right side.

Divide [tex]4.5[/tex] by [tex]-10[/tex].

[tex]j=-4.5[/tex]

The Final Answer is

[tex]j=-4.5[/tex]

Answer:

50°

Step-by-step explanation:

The sum of angles in a triangle is 180 degrees

Hence given that in a triangle ACB with angles 90°, 4x°, 7x - 20

As such

90 + 4x + 7x -20 = 180

simplify

11x + 70 = 180

11x = 180 - 70

11x = 110

Divide both sides by 11

x = 110/11

x = 10

m∠ACB is 7x - 20

Substitute the value of x into the expression

= 7(10) - 20

= 70 - 20

= 50

Answer:

The answer is 50 degrees

Step-by-step explanation:

Answer:

Let w be the width of the rectangle. The length would be 2w+3. The area of the rectangle would be w(2w+3)=189.

So 2w2+3w-189=0 Solving for w you get w=9 or -10.5. Ignoring negative value Width of the rectangle would be 9mm and length of the rectangle would be 21mm giving you the area 189 square mm.

Hope this helps:)

Answer:

a leveled line or a straight line

Answer:

10.04 × 8.8 =?, ? = 88.352 :)

Answer:

88.352

Step-by-step explanation:

10.04

x. 8.8

=88.352

Answer:

(A): As year increases the number of pikas reduces.

(B): As year increases the number of pikas increases as opposed to when the rate reduces.

Step-by-step explanation:

See comment for complete question

Given

[tex]a = 144[/tex] --- Initial Population

[tex]r = 8\%[/tex] --- rate

(A) WHEN THE RATE DECREASES

First, we need to write out the function when the population decreases.

This is given as:

[tex]f(x) = a(1-r)^x[/tex]

Substitute values for a and r

[tex]f(x) = 144(1-8\%)^x[/tex]

Convert % to decimal

[tex]f(x) = 144(1-0.08)^x[/tex]

[tex]f(x) = 144(0.92)^x[/tex]

Next, we calculate the average rate of change for both intervals using:

[tex]Rate = \frac{f(b) - f(a)}{b-a}[/tex]

For 1 to 5:

[tex]Rate = \frac{f(5) - f(1)}{5-1}[/tex]

[tex]Rate = \frac{f(5) - f(1)}{4}[/tex]

Calculate f(5) and f(1)

[tex]f(x) = 144(0.92)^x[/tex]

[tex]f(1) = 144*0.92^1 =144*0.92=132.48[/tex]

[tex]f(5) = 144*0.92^5 =144*0.66=95.04[/tex]

[tex]Rate = \frac{95.04 - 132.48 }{4}[/tex]

[tex]Rate = \frac{-37.44}{4}[/tex]

[tex]Rate = -9.36[/tex]

For 6 to 10:

[tex]Rate = \frac{f(10) - f(6)}{10-6}[/tex]

[tex]Rate = \frac{f(10) - f(6)}{4}[/tex]

Calculate f(6) and f(10)

[tex]f(x) = 144(0.92)^x[/tex]

[tex]f(6) = 144*0.92^6 =144*0.61=87.84[/tex]

[tex]f(10) = 144*0.92^{10} =144*0.43=61.92[/tex]

[tex]Rate = \frac{61.92-87.84}{4}[/tex]

[tex]Rate = \frac{-25.92}{4}[/tex]

[tex]Rate = -6.48[/tex]

So, we have:

[tex]Rate = -9.36[/tex] for year 1 to 5

This means that the number of pikas reduces by 9.36 yearly

[tex]Rate = -6.48[/tex] for year 6 to 10

This means that the number of pikas reduces by 6.48 yearly

So, we can say that, as year increases the number of pikas reduces.

(B) WHEN THE RATE INCREASES

First, we need to write out the function when the population decreases.

This is given as:

[tex]f(x) = a(1-r)^x[/tex]

Substitute values for a and r

[tex]f(x) = 144(1+8\%)^x[/tex]

Convert % to decimal

[tex]f(x) = 144(1+0.08)^x[/tex]

[tex]f(x) = 144(1.08)^x[/tex]

Next, we calculate the average rate of change for both intervals using:

[tex]Rate = \frac{f(b) - f(a)}{b-a}[/tex]

For 1 to 5:

[tex]Rate = \frac{f(5) - f(1)}{5-1}[/tex]

[tex]Rate = \frac{f(5) - f(1)}{4}[/tex]

Calculate f(5) and f(1)

[tex]f(x) = 144(1.08)^x[/tex]

[tex]f(1) = 144(1.08)^1 = 144*1.08= 155.52[/tex]

[tex]f(5) = 144(1.08)^5 = 144*1.47= 211.68[/tex]

[tex]Rate = \frac{211.68 - 155.52}{4}[/tex]

[tex]Rate = \frac{56.16}{4}[/tex]

[tex]Rate = 14.04[/tex]

For 6 to 10:

[tex]Rate = \frac{f(10) - f(6)}{10-6}[/tex]

[tex]Rate = \frac{f(10) - f(6)}{4}[/tex]

Calculate f(6) and f(10)

[tex]f(x) = 144(1.08)^x[/tex]

[tex]f(6) = 144(1.08)^6 = 228.52[/tex]

[tex]f(10) = 144(1.08)^{10} = 310.89[/tex]

[tex]Rate = \frac{310.89-228.52}{4}[/tex]

[tex]Rate = \frac{82.37}{4}[/tex]

[tex]Rate = 20.59[/tex]

So, we have:

[tex]Rate = 14.04[/tex] for year 1 to 5

This means that the number of pikas increases by 14.04 yearly

[tex]Rate = 20.59[/tex] for year 6 to 10

This means that the number of pikas increases by 20.59 yearly

So, we can say that, as year increases the number of pikas increases as opposed to when the rate reduces.

Answer:

A x=1/4

Step-by-step explanation:

2/3x = 1/6

Divide by 2/3

so 1/6 ÷ 2/3

= 1/6 • 3/2

= 3/12

= 1/4

Answer:

10 and 11

Step-by-step explanation:

The square root of 104 is 10.1980390272. This falls between the whole numbers 10 and 11.

Answer:

3

Step-by-step explanation:

I'm going to assume you meant "How many 2/9 cup serving are in 7/9 cup of juice" (since there are no 7/9 cups of serving in 2/9 cups of juice, since 7/9>2/9, and you can't have a serving of something greater than the amount you have).

In this case:

7/9 divided by 2/9=3

Since 7/9 and 2/9 have the same denominater, you can cross them off, since when you divide them, 9 divided by 9=1. 7 divided by 2=3.5, but I'll assume you want full cups.

Answer:

The exterior angle of triangle XYZ is;

∠JXM

Step-by-step explanation:

The question is a word problem with the given parameters;

The points on line 'a' = L and M

The points on line 'b' = O and N

The point line 'c' intersect line 'a' = X

The point line 'c' intersect line 'b' = Z

The points on line 'c' = H and G

The point line 'd' intersect line 'a' = X

The point line 'd' intersect line 'b' = Y

The points on line 'd' = J and K

From the drawing of triangle XYZ created with Microsoft Visio, the exterior angle is ∠JXM

Answer:

Step-by-step explanation:

the answer is JXZ

Answer:

Let the angle be x it's supplement = (180-x)

x = 3 (180-x)

⇒x=540−3x

⇒4x=540⇒x=135°

Step-by-step explanation:

Hope it is helpful....

Answer:

Thanks for the point!

Step-by-step explanation:

Have a great day

[tex] - 2 \frac{1}{2} - ( - 1 \frac{3}{4} )[/tex]

[tex] - \frac{5}{2} - ( - \frac{7}{4} )[/tex]

[tex] - \frac{10}{4} - ( - \frac{7}{4} )[/tex]

[tex] - \frac{3}{4} [/tex]

Answer:

-2, -1, 0, 1, 2.

Solution

Let x be the middle term of this sequence of 5 terms.

Then the sequence is x-2, x-1, x, x+1, x+2.

The sum of the terms is (x-2) + (x-1) + x + (x+1) + (x+2) = 5x.

Thus 5x = 0.

It gives x = 0.

So the sequence is -2, -1, 0, 1, 2.

Answer:

-2

Step-by-step explanation:

-9=4n-1

4n=-9+1

4n=-8

n=-8/4

n=-2

Answer:

x= -2

Step-by-step explanation:

you add 1 to both sides

-9+1=4n-1+1

which gives you

-8=4n

and then divide both sides by 4

-2=n

Answer:

2.5

Step-by-step explanation:

it's the midpoint of XZ

Answer:

I would say the answer is D because the figure is rotated 180 degrees. Letters C and D are pretty much the same just with some differences, but I would say D. Let me know if it's wrong :)

Step-by-step explanation:

Answer:

im going to say c

Step-by-step explanation:

if its has 160 units and goes to half-life after 2 months im assuming it loses 1/2 of the units so in order for it to lose that many it will have to lose 40 units a month so i say its c after 10 months there will be less than 1 unit in the potion

hope this helps im sorry if im wrong have a blessed day :)

Answer: 5,15,20,25,45

Step-by-step explanation:

1st is 20, 2nd is 25, 3rd is 15, 4th is 45, 5th is 5