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zubka84 [21]
3 years ago
11

What is the quotient of the rational expression below?

Mathematics
1 answer:
ss7ja [257]3 years ago
6 0

Answer:

first answer

Step-by-step explanation:

Hello, you know that

\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\cdot \dfrac{d}{c}

So, the quotient we need to estimate is

\begin{aligned}\dfrac{x^2-36}{x+8}\cdot\dfrac{4x+32}{x^2+12x+36}&=\dfrac{x^2-6^2}{x+8}\cdot \dfrac{4(x+8)}{(x+6)^2}\\\\&=\dfrac{4(x-6)(x+6)}{(x+6)^2}\\\\&=\dfrac{4(x-6)}{x+6}\end{aligned}

Thank you

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1. Explain the similarities and differences between the graphs of y = 5x and y = 3x. Include domain, range, intervals of increas
Dmitry_Shevchenko [17]

Answer:

1. Equal domain, range, interval of increase and lack of asymptotes

The difference is the difference in slope

2. Equal domain, range, no increase or decrease (constant value) and lack of asymptotes

The difference is the difference in the y-intercept

Step-by-step explanation:

1. The similarities between the functions, y = 5·x and y = 3·x are;

a. The domain of y = 5·x is the set of all real numbers and the range is (-∞; ∞)

b.There are no critical point and the interval of increase is (-∞; ∞)

There are no asymptotes the line crosses the origin

The x and y intercept are both zero

Similarly, The domain of y = 3·x is the set of all real numbers and the range is (-∞; ∞)

There are no critical point and the interval of increase is (-∞; ∞)

There are no asymptotes the line crosses the origin

The x and y intercept are both zero

The difference between the functions, y = 5·x and y = 3·x is that the slope of y = 5·x is 5 and the slope of y = 3·x is 3

2.

The similarities between the functions, y = 4 and y = (2)  are;

a. The domain of y = 4 is the set of all real numbers (-∞; ∞), \left \{ x\mid x\in R \right \} and the range is {4}

b.There are no critical point and no interval of increase or decrease

There are no asymptotes the line does not cross the origin

There are no x-intercept and y intercept is (0, 4)

Similarly, the domain of y = (2) is the set of all real numbers (-∞; ∞), \left \{ x\mid x\in R \right \} and the range is {2}

There are no critical point and no interval of increase or decrease

There are no asymptotes the line does not cross the origin

There are no x-intercept and y intercept is (0, 2)

The difference between the functions, y = 4 and y = (2) is that the y-intercept of y = 4 is 4 and  the y-intercept of y = (2) is 2

4 0
3 years ago
6,000 people voted in a town election. Of the two candidates, the winning candidate received 4,000 more votes than the losing ca
AVprozaik [17]

Answer:

Step-by-step explanation:

let x = the number of votes of the first person

winner  = x + 4000

x+ x+4000 = 6000

2x=2000

x=1000

first person = x = 1000

winner  = x+4000 = 5000

The winner got 5000 votes

8 0
2 years ago
Can anyone help me with these two problems? I found the distance to one. Please, assignment is due tonight. Thank you.
klasskru [66]

Answer:

  32 mi @ N77°E

Step-by-step explanation:

The route of travel forms legs of a right triangle, so the final distance (d) from harbor can be found using the Pythagorean theorem:

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___

The angle (α) added to the original N47°E bearing can be found using the fact that opposite and adjacent sides are given. So, they can tell you the tangent of the angle:

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Then the bearing to the final position is ...

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Rounded to whole numbers, the final position from harbor is ...

  32 miles @ N 77° E

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3 years ago
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Answer:

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Step-by-step explanation:

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