You fill a large water tank with 3400 gallons of water. About 10% of the water is not fresh water. How many gallons of fresh water are in the tank?

We can actually see that the statements that are true are:

A. x = 1 is a solution.

C. x = –1 is a solution.

Rational equation is actually known as an equation that contains at least one fraction. The denominator and numerator are known to be polynomials.

We can see then that:

[tex] \frac{4}{x + 6} + \frac{1}{ {x}^{2} } = \frac{x + 10}{ {x}^{3} + 6 {x}^{2} } [/tex]

It's clear that: x ≠ 0 and x ≠ -6.

Looking for the LCM of the left hand side, we will have:

[tex] \frac{4}{x + 6} + \frac{1}{ {x}^{2} } = \frac{4 {x}^{2 } + (x + 6)}{(x + 6) {x}^{2} } [/tex]

So, we will see that left hand side and right hand side are equal.

[tex]4 {x}^{2} + x + 6 = x + 10[/tex]

[tex]4 {x}^{2} = 10 - 6[/tex]

[tex]4 {x}^{2} = 4[/tex]

[tex] {x}^{2} = 1[/tex]

[tex] x = 1[/tex]

or

[tex]x = - 1[/tex]

So, we can see that options A and C are correct.

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Answer:

-1 and 1  or A and C

Step-by-step explanation:

46204 ft³

Volume of cube: length³ ⇒ 36³ ⇒ 46656 ft³

Volume of cylinder: πr²h ⇒ π(2)²(36) ⇒ 144π ⇒ 452.39 ft³

Volume of the figure: 46656 - 452.15 = 46203.61 ft³ ≈ 46204 ft³

For cube

For cylinder

Area of base:-

Volume:-

Volume of figure:-

Answer:

-3

Step-by-step explanation:

The equation for slope is y2-y1/x2-x1 so put you numbers in and you get

-6-6/-9+5

-12/4

and then -3

Answer:

-3

Step-by-step explanation:

[tex]y=mx+b[/tex] is equation of a straight line.

Here, the slope is m.

[tex]m=\frac{y_{2}-y_{1} }{{x_{2}-x_{1}}} =\frac{-6-6}{-9-(-5)} =\frac{-12}{-4}=-3[/tex]

1 mile = 1.6 kilometers so 24*1.6 = 38.4
24 miles = 38.4 kilometers

1 kilometer = 1000 meters so 38.4*1000 = 38,400 meters
38.4 kilometers = 38,400 meters

1 hour = 60 minutes so 2*60 = 120
2 hours = 120 minutes

To calculate meters per minute, divide.
38,400 / 120 = 320

So that means that Calvin's approximate speed is 320 meters per minute.

Answer:

1,200

Step-by-step explanation:

Divide 800 by 40

Then take that answer which is 20 and multiply it by 60

Then you get 1,200

Answer:

8a³b²c(9a²b - 4c)

Step-by-step explanation:

The GCF of 72 and 32 is 8.

72a^5b^3c - 32a^3b^2c^2 = 8a³b²c(9a²b - 4c)

5 is the awsterstdysytghujfhds

Answer:

2) -1, 0, 1, 2, 3, 4

3) 78, -2 , 1

Step-by-step explanation:

2) Substitute the x into the equation.

3) Substitute the 9 as the x value into the function so ([tex]9^2[/tex]) -3 = 78 etc.

Answer:

c = -13.78.

Step-by-step explanation:

21.2x + c  ≡ 5.3(4x - 2.6)

21.2x + c  ≡ 21.2x - 13.78

Equating constant terms:

c = -13.78.

Answer:

13.78

Step-by-step explanation:

21.2x + c = 5.3(4x - 2.6)

open the bracket

21.2x + c = 21.2x - 13.78

collect like terms

c + 13.78 = 21.2x - 21.2x

c + 13.78 = 0

c = -13.78

The value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.

In mathematics, the summation is the addition of a sequence of any kind of numbers, called addends or summands.

Now we have a given term

[tex]\sum_{n=1}^{4} 3(4)^{n-1}[/tex]

By solving the above term;

[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^{1-1}+3(4)^{2-1}+3(4)^{3-1}+3(4)^{4-1}[/tex]

[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3(4)^0+3(4)^1+3(4)^2+3(4)^3[/tex]

[tex]\sum_{n=1}^{4} 3(4)^{n-1}=3 + 12 +48 + 192[/tex]

Hence the value of the term in the series will be equal to 3 + 12 +48 + 192 after calculation.

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Answer:

1. 3 + 12 +48 + 192

2. 255 edge

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The radius is 4.5cm.

Step-by-step explanation:

Circumference is the distance around the outside of a circle, the perimeter of the circle. Circumference formula is:

C = pi•d OR

C = 2•pi•r

Since we are looking for radius, use the second formula.

C = 2•pi•r

28.26 = 2pi•r

Divide by 2pi.

28.26/2pi = r

r = 4.5

The radius is 4.5 cm.

Answer:

See below

Step-by-step explanation:

This will create a cylinder    volume = 1/2 pi  r^2 h = 1/2  pi  4  *  12

                                                            = 24 pi = 75.398 in^3

Answer:

Step-by-step explanation:

Answer:

Area of shaded region=41 square feet

Area of non shaded region= 87 square feet

Step-by-step explanation:

As, Shaded area is made of different shapes including two rectangles and one triangle

So,

Area of shaded region,

[tex]=(8\times2)+(10\times 1)+(\frac{1}{2}\times 3\times10)\\\\ =16+10+15=41 \quad \text{square feet}[/tex]

Area of non shaded region=total area of rectangular region-Shaded region

[tex]=(16\times 8)-(41)\\=128-41\\=87 \quad \text{square feet}[/tex]

Answer:

( 16 × 8 )-40

128 -40

=87 square feet

Answer:

The surface area of cone = 54π cm²

Step-by-step explanation:

Given ;

Radius = 3 cm

slant height = 15cm

The surface area of cone = πr ( r + l )

=> π × 3 ( 3 + 15)

=> π × 3 ( 18)

=> 54 π cm²

Answer:

Option a

Explanation :

check out my attached work

Hope it helps, let me know if you have any questions !

Have a nice rest of your day :)

Answer:

The vertex of the function is (1.333, 4.667)

Step-by-step explanation:

1. Calculate -b / 2a. This is the x-coordinate of the vertex.

2. simply plug -b / 2a into the equation for x and solve for y.

[tex]Y = 3x^{2} - 8x + 10\\Compare with the form of y = ax^{2} + bx + c\\So that means a = 3, b = -8, and c = 10.[/tex]

Calculate -b/2a:

[tex]X = -(-8)/2(3)[/tex]

[tex]X = 8/6[/tex]

This is equal to 1.33 recurring

Plug 8/6 for x and solve for y:

[tex]Y = 3x^{2} - 8x + 10[/tex]

[tex]Y = 3(\frac{8}{6})^{2} - 8(\frac{8}{6}) + 10[/tex]

[tex]Y = \frac{48}{9} - \frac{64}{6} + 10\\[/tex]

This is equal to 4.66 reccuring.

The inequalities that Heather could have written to compare the temperatures will be:

B. 2 < -10

C. 4 >-20

E. -8 < -15

It should be noted that inequality us the relation between two expressions that aren't equal.

Therefore, the inequalities that Heather could have written to compare the temperatures will be: 2 < -10, 4 >-20,and -8 < -15.

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Answer:

x = 18

Step-by-step explanation:

given y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition y = 15 when x = 9 , then

15 = 9x ( divide both sides by 9 )

[tex]\frac{15}{9}[/tex] = x , that is

x = [tex]\frac{5}{3}[/tex]

y = [tex]\frac{5}{3}[/tex] x ← equation of variation

when y = 30 , then

30 = [tex]\frac{5}{3}[/tex] x ( multiply both sides by 3 to clear the fraction )

90 = 5x ( divide both sides by 5 )

18 = x

Answer:

Step-by-step explanation:

22000-18700=3300

3300/22000x100=15%

Answer:

It is a 15 percent decrease

Step-by-step explanation:

Divide 18700 by 22000, and your answer will be 0.85 but its asking for the decrease, 100-85=15, so 15% is the decrease.

Answer:

12 1/6

It wants me to add more but there's nothing to add

Answer:

y-intercept = (-2,0)

Step-by-step explanation:

the "C" is the answer

Answer:

It is attached

Step-by-step explanation:

Answer:

A=34 B=20

Step-by-step explanation:

A: y=6(5)+4 (34)

B: y=45-(9(2)+7)

y= 45-(18+7)

y=45-25 (20)

Answer:

27/2 in^3 or 13.5 in^3 as a mixed fraction

Step-by-step explanation:

V=whl

Simplify the following:

(1 + 1/2) (2 + 1/4)×4

Put 1 + 1/2 over the common denominator 2. 1 + 1/2 = 2/2 + 1/2:

(2/2 + 1/2) (2 + 1/4)×4

2/2 + 1/2 = (2 + 1)/2:

((2 + 1)/2) (2 + 1/4)×4

2 + 1 = 3:

3/2 (2 + 1/4)×4

Put 2 + 1/4 over the common denominator 4. 2 + 1/4 = (4×2)/4 + 1/4:

(3×4)/2 ((4×2)/4 + 1/4)

4×2 = 8:

(3 (8/4 + 1/4)×4)/2

8/4 + 1/4 = (8 + 1)/4:

(3×4)/2 ((8 + 1)/4)

8 + 1 = 9:

3/2×9/4×4

3/2×9/4×4 = (3×9×4)/(2×4):

(3×9×4)/(2×4)

(3×9×4)/(2×4) = 4/4×(3×9)/2 = (3×9)/2:

(3×9)/2

3×9 = 27:

Answer: 27/2 or 13.5 as a mixed fraction

Step-by-step explanation:

Answer:

Step-by-step explanation:

the 2nd and 4th answers look good.  the 1st answer is correct as well.

To solve this look at the x axis and y axis,  the x axis is in inches, the y axis is in pounds.  So you know that as the distance increase per inch,  the force in pounds is increasing too.  

so the force applied is going up,   0.73 pounds , for each inch of travel ( or stretch) of the spring.  

Answer:

[tex]0 = log_{10} 1[/tex]

Step-by-step explanation:

Base for the exponent and for the logarithm are the same!

10^0 is the exponential form where 10 is the base and 0 the exponent

[tex]log_{10} 1[/tex] is the logarithm form where 10 is the base

To solve [tex]log_{10} 1 =[/tex]   ask the question :

To what power should I raise the base 10 to obtain the number 1 ?

The answer to the power 0 therefore

[tex]log_{10} 1 = 0[/tex]

[tex]1 = 10^{0} -is-the- exponential -form\\0 = log_{10} 1 - is -the -logarithmic -form[/tex]