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Valentin [98]
3 years ago
14

The quotient of x^2+x-6/x^2-6x+5*x^2+2x-3/x^2-7x+10 has ___ in the numerator and ______ in the denominator.

Mathematics
1 answer:
kari74 [83]3 years ago
7 0

Answer:

So the quotient of \frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10} has (x + 3)² in the numerator and (x + 5)² in the denominator.

Step-by-step explanation:

\frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10}

Factorizing the expressions we have

\frac{x^{2} + 3x -2x - 6}{x^{2} -x - 5x + 5} X \frac{x^{2} + 3x - x - 3}{x^{2} -2x -5x + 10}

\frac{x(x + 3)- 2(x + 3)}{x(x -1) - 5(x - 1)} X \frac{x(x + 3) - 1(x + 3)}{x(x - 2) - 5(x - 2)}

\frac{(x + 3)(x - 2)}{(x - 5)(x - 1)}X\frac{(x + 3)(x - 1)}{(x - 2)(x - 5)}

Cancelling out the like factors, (x -1) and (x - 2), we have

\frac{(x + 3)(x + 3)}{(x - 5)(x - 5)}

= \frac{(x + 3)^{2} }{(x + 5)^{2} }

So the quotient of \frac{x^{2} + x - 6}{x^{2} -6x + 5} X \frac{x^{2} + 2x - 3}{x^{2} -7x + 10} has (x + 3)² in the numerator and (x + 5)² in the denominator.

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A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. what is the approximate area
aniked [119]

The area of the regular heptagon which has a radius of approximately 27.87 cm and the length of each side is 24.18 cm is 2125 cm².

<h3>What is the area of a heptagon?</h3>

Heptagon is the closed shape polygon which has 7 sides and 7 interior angles.

The area of the regular heptagon is found out using the following formula.

A=\dfrac{7a}{4}\cot \left(\dfrac{180}{7}\right)

Here, (<em>a</em>) is the length of the heptagon.

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. Put the value of side in the above formula,

A=\dfrac{7\times24.18}{4}\cot \left(\dfrac{180}{7}\right)\\A\approx 2125\rm\; cm^2

Hence, the area of the regular heptagon which has a radius of approximately 27.87 cm and the length of each side is 24.18 cm is 2125 cm².

Learn more about the area of a heptagon here;

brainly.com/question/26271153

3 0
2 years ago
The quotient of a number and 6 is less than 20.
ozzi

Answer:

\frac{x}{6} < 20

Step-by-step explanation:

hope this help idrk how to explain this one lol

6 0
3 years ago
Given that
timofeeve [1]

Answer:

4.

Step-by-step explanation:

(sec α - tan α)(sec α + tan α) = sec^2 α - tan^2α

But sec^2  α = 1 + tan^2 α so

sec^2 α - tan^2α  = 1 + tan^2 α - tan^2α

= 1

so 1 =  (sec α - tan α)(sec α + tan α) = 1/4 * x     where x  is sec α + tan α

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Answer:

\frac{3}{11}

Step-by-step explanation:

When you have something like that, just think that the first number goes on top and the second number goes on bottom.

8 0
3 years ago
Can someone give me the answer and explanation I’ll give brainlist and points
victus00 [196]
This picture will explain the mistake. She didn’t carry down the -2/4 and add to make sure her answer was fully correct.

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3 years ago
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