Compared to last year, the population has increased 25%. The population is now 6,600. What was the population last year?

What number of population do I put for each for percentage?

The pool dimensions that will minimize the cost of construction are length of square bottom = 20 ft and height of pool = 5 ft

Let l be the length of side of the square bottom of the pool and h be the height of the pool.

Its volume V = l²h

Now, the total surface area of the pool equal the area of its sides plus the area of its base.

The area of its 4 sides is 4lh.

Since the cost of the side of the pool is $80 per square foot, the total cost for the sides of the pool is C = $80 × 4lh = $ 320lh

Also, The area of its square bottom is l².

Since the cost of the side of the pool is $40 per square foot, the total cost for the square bottom of the pool is C' = $40 × l² = $ 40l²

So, the total cost of the pool is C" = C + C' = 320lh + 40l²

C" = 320lh + 40l²

Since the volume equals 2000 ft³, V = l²h

2000 = l²h

h = 2000/l²

Substituting h into C", we have

C" = 320lh + 40l²

C" = 320l × 2000/l² + 40l²

C" = 640000/l + 40l²

To find the value of l which makes C" minimum, we differentiate C" with respect to l and equate it to zero.

So, dC"/dl = d(640000/l + 40l²)/dl

dC"/dl = d(640000/l)/dl + d(40l²)/dl

dC"/dl = -640000/l² + 80l

Equating dC"/dl to zero, we have

-640000/l² + 80l = 0

-640000/l² = -80l

Cross-multiplying, we have

640000 = 80l³

Dividing through by 80, we have

l³ = 640000/80

l³ = 8000

Taking cube root of both sides, we have

l = ∛8000

l = 20 ft

We differentiate C" twice to determine if this value of l gives a minimum for C".

So, d²C"/dl² = d(-640000/l² + 80l)/dl

d²C"/dl² = d(-640000/l²)/dl + d(80l)/dl

d²C"/dl² = 640000/l³ + 80

Substituting l = 20, we have

d²C"/dl² = 640000/l³ + 80

d²C"/dl² = 640000/20³ + 80

d²C"/dl² = 640000/8000 + 80

d²C"/dl² = 80 + 80

d²C"/dl² = 160 > 0

Since d²C"/dl² = 160 > 0. So, l = 20 ft gives a minimum for C".

Since h = 2000/l²

Substituting l = 20 into the equation, we have

h = 2000/l²

h = 2000/20²

h = 2000/400

h = 5 ft

So, the pool dimensions that will minimize the cost of construction are length of square bottom = 20 ft and height of pool = 5 ft

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Answer:

3. x = 96

4. x = 6

Step-by-step explanation:

[tex] \frac{2}{5} + \frac{3}{10} - \frac{7}{9} \\ = \frac{2 \times 18 + 3 \times 9 - 7 \times 10}{90} \\ = \frac{36 + 27 - 70}{90} \\ = \frac{ - 7}{90} [/tex]

[tex] \frac{ - 7}{90} [/tex]

Answer:

5

52

52

52 +

52 + 10

52 + 103

52 + 103

52 + 103 −

52 + 103 − 9

52 + 103 − 97

52 + 103 − 97

52 + 103 − 97

52 + 103 − 97 =

52 + 103 − 97 = 90

52 + 103 − 97 = 902×18+3×9−7×10

52 + 103 − 97 = 902×18+3×9−7×10

52 + 103 − 97 = 902×18+3×9−7×10

52 + 103 − 97 = 902×18+3×9−7×10 =

52 + 103 − 97 = 902×18+3×9−7×10 = 90

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 =

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90}

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90} 90

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90} 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90} 90−7

Answer:

9

Hope this helps, have a nice day/night! :D

Answer:

3/7*2 5/6= 17/14 = 1 3/14 ≅ 1.2142857

Step-by-step explanation:

Conversion a mixed number 2 5/6 to a improper fraction: 2 5/6 = 2 5/6 = 2 ·6+ 5/6 = 12 + 5/6 = 17/6 1) Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/6 = 12/6

2) Add the answer from previous step 12 to the numerator 5. New numerator is 12 + 5 = 17

3) Write a previous answer (new numerator 17) over the denominator 6.

Two and five-sixths is seventeen sixths Multiple: 3/7 * 17/6 = 3 · 17/7 · 6 = 51/42

= 17 · 3/14 · 3 = 17/14. then you simplify.

I hope this helps

Answer:

y=-4x+25

Step-by-step explanation:

If this is Point-Slope then:

y-y1=m(x-x1)                         m=slope

m= -4  Coordinates=(6,1)

y-1=-4(x-6)

y-1= -4x +24

y=-4x+25

Hi there!

5=5+r-2r

Combine like terms:

5=5-r

Move all the variables to the left, using the opposite operation:

r+5=5

r=5-5

r=0

r=0 is the answer

Hope it helps

~Just a gloomy gal

#CarryOnLearning

[tex]SilentNature :)[/tex]

Answer:

r = 0

Step-by-step explanation:

5 = 5 +r - 2r

5 = 5 -r

c.l.t   r = 5 - 5

r = 0

Answer:

5 units

Step-by-step explanation:

Distance between two points can be found by using the pythagorean theorem

The distance in y = 4

The distance in x = 3

3² + 4² = c²

9 + 16 = c²

25 = c³

c = √25

c = 5

-Chetan K

Answer:

5

Step-by-step explanation:

[tex]\mathrm{Distance \:\:Formula:}\\\\\mathrm{d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}}[/tex]

[tex]\underline{\mathrm{Plug \:the\: points:}}[/tex]

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]

[tex]d = \sqrt{(5 - 2)^2 + (2-6)^2}[/tex]

[tex]\underline{\mathrm{Solve:}}[/tex]

[tex]d = \sqrt{(5 - 2)^2 + (2-6)^2}[/tex]

[tex]\sqrt{(5 - 2)^2 + (2-6)^2}[/tex]

[tex]\sqrt{3^2 + 4^2}[/tex]

[tex]3^2 = \sqrt{9+4^2} =\boxed{9}\\\\4^2=\sqrt{9+16} = \boxed{16}[/tex]

[tex]\sqrt{25}[/tex]

[tex]\sqrt{5^2}=5[/tex]

Answer:

0

Step-by-step explanation:

Slope = Change in Y/Change in X

Slope = -6 - (-6)/3 - (-7)

Slope = 0/10

Slope = 0

This is a horizontal line

-Chetan K

Answer:

Let (-7, -6) be (x1, y1)

and (3, -6) be (x2, y2)

The slope can be found with [tex]\frac{y2-y1}{x2-x1}[/tex]

Substitute in values:

[tex]\frac{-6-(-6)}{3-(-7)} =0[/tex]

The slope is 0. (It is a horizontal line.)

Answer:

1.-profit

2.-$300

3.-25%

Step-by-step explanation:

1.- 1500-1200=300+

2.-(1)

3.-1200/100= 12

300/12= 25

Answer:

21 she has 21 nickels

Step-by-step explanation:

Googel

The number of nickels LeAnne has 20 and the number of dimes LeAnne has 30.

Given that, LeAnnne has $4 in dimes and nickels.

Let the number of dimes be d and the number of nickels be n.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

She has 10 more dimes than nickels.

That is, d=n+10

So, 0.05n+0.10d=4

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

5n+10(n+10)=400

5n+10n+100=400

15n=300

n=20

d=n+10

d=30

Therefore, the number of nickels LeAnne has 20.

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Answer:

1.8

Step-by-step explanation:

-2 1/4 x -4/5 = 9/5

= 1 4/5

= 1.8

Answer:

$40,516.86

Step-by-step explanation:

start by taking 35,000 and multiplying it by 0.05 to get 5% of the number. then add that number (1,750) to the original 35,000 and you should get 36,750. this would be the first year. Then multiply 36,750 by 0.05 again and add that number (1837.5) to the original 36,750 and you should get 38,587.5. Finally multiply that by 0.05 and add that number (1,929.375) to the original 38,587.5 and you should get 40516.875. Round to the hundredths since it is money.

Answer:

A = $40,516.88

Step-by-step explanation:

Assuming that interest is compounded annually:

The AMOUNT will be A = P(1 + r)^2, which here is

                                    A = $35,000(1 + 0.05)^3, or

                                     A = $40,516.88

Answer:

8

Step-by-step explanation:

2(-2)^2 =10 +-2 =8

10 nickels = $0.50

10 dimes = $1.00

So- 10 nickels + 10 dimes = $1.50

Answer:

The answer is C

Step-by-step explanation:

An arithmetic sequence with common difference 6

(-3)-(-9) = 6

3 - (-3) = 6

9 - 3 = 6

15 - 9 = 6

Answer:

B

Step-by-step explanation:

Answer:

b)

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

got it right

Answer:

8:1

Step-by-step explanation:

Answer:

y = ac / (a - b - c)

Step-by-step explanation:

y(a - b) = c(y + a)

Distribute

ay - by = cy + ac

Subtract cy from both sides

ay - by - cy = ac

Factor out y

y(a - b - c) = ac

Divide both sides by (a - b - c)

y = ac / (a - b - c)

Answer:

15 very simple

Step-by-step explanation:

im always right

Step-by-step explanation:

I don't see the equations.

but I can build some myself :

x = number of hamburger packages

y = number of hotdogs packages

x + y = 9

9x + 2y = 25

the first equation tells us after moving y to the right side

x = -y + 9

and that we are using now in the second equation :

9(-y + 9) + 2y = 25

-9y + 81 + 2y = 25

-7y = -56

y = 8

x = -y + 9 = -8 + 9 = 1

Answer:

y ≥ 2

Step-by-step explanation:

Domain is x  > 1 . So, range will be greater than or equal to 2

The zeros of the function g(x) = (x² - 36)(x + 7) are x = 6 and x = -6.

To find the zeros of the function g(x) = (x² - 36)(x + 7), we need to identify the values of x that make the entire function equal to zero.

For a function to be equal to zero, at least one of its factors must be zero. Therefore, we set each factor to zero and solve for x:

Setting the first factor, x² - 36, to zero:

x² - 36 = 0

Now, add 36 to both sides of the equation:

x² = 36

Next, take the square root of both sides:

x = ±√36

x = ±6

Setting the second factor, x + 7, to zero:

x + 7 = 0

Now, subtract 7 from both sides of the equation:

x = -7

The zeros of the function g(x) = (x² - 36)(x + 7) are x = 6 and x = -6.

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