A hose fills a hot tub at a rate of 3.45 gallons per minute. How many hours will it take to fill a 280 ​-gallon hot​ tub?

ANSWER

[tex]\frac{5( \sqrt{11} + \sqrt{3} )} {8} [/tex]

EXPLANATION

The given rational function is

[tex] \frac{5}{ \sqrt{11} - \sqrt{3}} [/tex]

We need to rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of

[tex] \sqrt{11} - \sqrt{3} [/tex]

which is

[tex]\sqrt{11} + \sqrt{3} [/tex]

When we rationalize we obtain:

[tex] \frac{5( \sqrt{11} + \sqrt{3} )}{(\sqrt{11} - \sqrt{3} )( \sqrt{11} + \sqrt{3} )} [/tex]

The denominator is now a difference of two squares:

[tex](a - b)(a + b) = {a}^{2} - {b}^{2} [/tex]

We apply this property to get

[tex]\frac{5( \sqrt{11} + \sqrt{3} )}{( \sqrt{11}) ^{2} - ( \sqrt{3}) ^{2} )} [/tex]

[tex]\frac{5( \sqrt{11} + \sqrt{3} )}{11 - 3} [/tex]

This simplifies to

[tex]\frac{5( \sqrt{11} + \sqrt{3} )} {8} [/tex]

Or

[tex]\frac{5 } {8}\sqrt{11} + \frac{5 } {8}\sqrt{3} [/tex]

Answer:

B

Step-by-step explanation:

Answer: The corresponding segments in the in the figure and the image are :

AB and EF,  

AD and EH,

CD and HG,

BC and FG,

Step-by-step explanation:

Given: Polygon ABCD is the result of a translation of polygon EFGH .

AB is parallel to DC in the pre-image.

We know that a translation is a rigid transformation which produces congruent images such that the corresponding segments have equal lengths.

So from the given statements the corresponding segments in the figure and the image are :

AB and EF,  

AD and EH,

CD and HG,

BC and FG,

the two consecutive odd integers that have a product of fifteen are 3 and 5.

The question asks for the two consecutive odd integers whose product is fifteen. To solve this, we can use algebraic methods or observe that the square root of 15 is less than 4, and since 15 is an odd number, we look for odd numbers around 4 that multiply to 15.

Let's define the smaller integer as n. Since the integers are consecutive and odd, the next odd integer after n is n+2. The equation to represent their product is n*(n+2) = 15. Solving for n gives us the integers 3 and 5, since 3*5 = 15.

Therefore, the two consecutive odd integers that have a product of fifteen are 3 and 5.

Answer:

[tex]m = \frac{9}{12} = \frac{3}{4} [/tex]

The correct answer is C.

60 miles per hour
Or
60/1

Answer: c

Step-by-step explanation: hope this helps

Answer is Exponential Decay.

Exponential Growth and Decay:

Exponential decay is a process that decreases quantity over time.

Exponential growth is a process that increases quantity over time.

(Given),

[tex]A = 21000(1-0.12)^{t}[/tex]

Let's take,

[tex]B = (1 - 0.12)^{t}[/tex]

As the t increases the B value decreases exponentially. So, the  A = 21000*B also decreases exponentially as t increases.

And the rate of change per time period is (0.12 x 100)% = 12%.

So, It is exponential decay.

Learn more about Exponential Growth and Delay here: https://brainly.com/question/13674608?referrer=searchResults

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The friend lives in a town that is 10° farther north than 40° N. The latitude of that town is 40° +10° = 50° N. When that latitude is reflected across the equator, N changes to S. The new latitude would be c. 50° S.

The smaller triangular prism's surface area is calculated by squaring the scale factor of 1/5 (which is 1/25) and then multiplying it by the surface area of the larger prism. The result is 2.4 square centimeters.

The question asks about the surface area of a similar but smaller triangular prism given that the larger prism has a surface area of 60 square centimeters and the scale factor of the smaller prism is 1/5. When the size of an object changes by a scale factor, the surface area changes by the square of that scale factor. For the smaller triangular prism, the surface area will be the square of 1/5, which is 1/25, times the surface area of the larger prism.

To calculate it:

Therefore, the surface area of the similar smaller triangular prism by the given scale factor is 2.4 square centimeters.

The third fraction [tex]\frac{10}{80}[/tex] is not equivalent to the other options. The other options,  0.8, 80% and [tex]\frac{24}{30}[/tex] are all equivalent.

In mathematics, a fraction is a composition that represents a part of a whole. Fractions can be written in a few different ways, but the most frequent way is to utilize a numerator and a denominator. The numerator is the number of parts we have, and the denominator is the total number of parts. For illustration, the fraction 1/2 represents one part out of two.

Option 1 is 0.8.

Option 2 is 80% which is in fact equal to [tex]\frac{80}{100}[/tex] .

[tex]\frac{80}{100}[/tex] = [tex]\frac{8}{10}[/tex] = 0.8.

Option 3 is [tex]\frac{24}{30}[/tex] .

[tex]\frac{24}{30}[/tex] = [tex]\frac{8}{10}[/tex] = 0.8.

So, only the third option is not equivalent to the others.

Learn more about fractions here:

https://brainly.com/question/10354322

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