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Pachacha [2.7K]
2 years ago
9

Please help me I am confused on how to do these.

Mathematics
1 answer:
MAXImum [283]2 years ago
5 0

1. There's so much wrong with the suggested solution that it's hard to pinpoint the exact error. The "logic" is inconsistent - why do the x and constant term stay in the denominator but the x^2 term does not?

What should be done is factorization in the numerator and denominator:

x^2 + 2x - 8 = (x + 4) (x - 2)

x^2 + 6x - 16 = (x + 8) (x - 2)

Then in the quotient, the factors of x-2 cancel so that

\dfrac{x^2+2x-8}{x^2+6x-16} = \dfrac{(x+4)(x-2)}{(x+8)(x-2)} = \boxed{\dfrac{x+4}{x+8}}

2. Use the same strategy: factorize everything everything you can, then cancel anything you can.

x^2 - 9 = (x-3) (x+3)

x^2+x-2 = (x+2)(x-1)

x^2+x-12 = (x+4)(x-3)

x^2+6x+8 = (x+4)(x+2)

Then using the algebraic properties of multiplication/division, we have

\dfrac{x^2-9}{x^2+x-2} \div \dfrac{x^2+x-12}{x^2+6x+8} = \dfrac{x^2-9}{x^2+x-2} \times \dfrac{x^2+6x+8}{x^2+x-12} \\\\ ~~~~~~~~= \dfrac{(x-3)(x+3)(x+4)(x+2)}{(x+2)(x-1)(x+4)(x-3)} \\\\ ~~~~~~~~= \boxed{\dfrac{x+3}{x-1}}

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Wewaii [24]

The answer you are looking for is no solution.

To find this, you first distribute the -5 into the parenthesis (-4r - 6). -5 x -4r = 20r and -5 x -6 = 30.Next, distribute the 5 into the parenthesis (6 - r). 5 x 6 = 30 and 5 x r = 5r.

The equation says 20r + 30 = 5r + 30. Now you solve for r.Subtract 5r from both sides. This leaves the equation to say 15r + 30 = 30. Then subtract 30 from both sides, to get 15r = 0.

At this point, since there is a zero on the opposite side of the variable, you can assume it will be no solution, since multiplying or dividing 0 by anything, is 0. However, I'll finish the problem, to show that it is no solution.

Divide 15 from both sides, leaving r = 0, which is no solution.

I hope this helps!

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4 years ago
Find the area of the circle below???
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Answer:

Area of the circle = 24.618\,feet^2

Step-by-step explanation:

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The Area of the circle is : 24.618\,feet^2

5 0
3 years ago
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nadya68 [22]

Answer:

D. negative

Step-by-step explanation:

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A line with an undefined slope is a vertical line. The x values don't change and the y values vary.

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snow_lady [41]
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~Sam
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3 years ago
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dezoksy [38]

Answer:

Step-by-step explanation:

You must state the "price before tax".  Let this be P.  Also, you must state the sales tax rate.  Let this be r, where r is a decimal fraction.  

Then the sales tax is rP, the product of the tax rate and the "price before tax."

The total cost of the item (for which it is sold) is (P + rP)($40).

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Your question would be clearer if you wrote it like this:  Given that the base price of an item is $40 and that the sales tax rate is 7%, find the total cost of the item with tax.  That would be (1 + 0.07)($40), or $42.80.

The sales tax is $42.80 - $40 = $2.80.

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