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4 years ago

I WILL GIVE YOU 40 POINTS PLEASE HELP (2)/(x^2-9) - (3x)/( x^2-5x+6) please show work

Mathematics

1 answer:

mars1129 [50]4 years ago

4 0

Answer:

$\frac{-3x^2-7x-4}{x^3-2x^2-9x+18}$

Step-by-step explanation:

$\frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}$

Factor x²-9 and x²-5x+6.

$\frac{2}{\left(x+3\right)\left(x-3\right)}-\frac{3x}{\left(x-2\right)\left(x-3\right)}$

Least common multiple of (x+3), (x-3), (x-2), and (x-3) is (x+3), (x-3), and (x-2).

Adjust the fractions based on LCM.

$\frac{2\left(x-2\right)}{\left(x+3\right)\left(x-3\right)\left(x-2\right)}-\frac{3x\left(x+3\right)}{\left(x-2\right)\left(x-3\right)\left(x+3\right)}$

Subtract the fractions since denominators are equal.

$\frac{2\left(x-2\right)-3x\left(x+3\right)}{\left(x+3\right)\left(x-3\right)\left(x-2\right)}$

Expand.

$\frac{-3x^2-7x-4}{x^3-2x^2-9x+18}$

The fraction can be in factored form.

$\frac{-\left(x+1\right)\left(3x+4\right)}{\left(x-2\right)\left(x+3\right)\left(x-3\right)}$

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catering service offers 8 appetizers, 11 main courses, and 7 desserts. A banquet committee is to select 7 appetizers, 8 main

guapka [62]

Answer: The required number of ways is 46200.

Step-by-step explanation: Given that a catering service offers 8 appetizers, 11 main courses, and 7 desserts.

A banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts.

We are to find the number of ways in which this can be done.

We know that

From n different things, we can choose r things at a time in $^nC_r$ ways.

So,

the number of ways in which 7 appetizers can be chosen from 8 appetizers is

$n_1=^8C_7=\dfrac{8!}{7!(8-7)!}=\dfrac{8\times7!}{7!\times1}=8,$

the number of ways in which 8 main courses can be chosen from 11 main courses is

$n_2=^{11}C_8=\dfrac{11!}{8!(11-8)!}=\dfrac{11\times10\times9\times8!}{8!\times3\times2\times1}=165$

and the number of ways in which 4 desserts can be chosen from 7 desserts is

$n_3=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.$

Therefore, the number of ways in which the banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts is given by

$n=n_1\times n_2\times n_3=8\times165\times35=46200.$

Thus, the required number of ways is 46200.

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4 years ago

Tamara bought a sweater for $24 before tax.She had a coupon for 1/2 off. The Sales tax rate was 6%.How much did Tamara pay for t

Sliva [168]

Answer:

Tamara paid $22.64 before tax

Step-by-step explanation:

In marketing, a coupon is a ticket or document that can be redeemedfor a financial discount or rebate when purchasing a product.

Let the discounted price = P

The Sales tax rate was 6%

The money Tamara pay for the sweater before including tax will be P which is:

(100 + 6)/100 × P = 24

1.06P = 24

P = 24/1.06

P = 22.64 dollars

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3 years ago

What is the total cost of a sweatshirt if the regular price is $55 and the salses tax is 5.5% round to the nearest cent

garik1379 [7]

Answer:

I believe it is $65

Step-by-step explanation:

$55/5.5

Divide the $55 by 5.5 and you get $10, then add it to your original $55, that makes $65, right?

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3 years ago

g The term pure rolling refers to a special case, a combination of rotation and translation. Which of these conditions is requir

natka813 [3]

Answer:

When the object is rolling without sliding is referred to as pure rolling.

Step-by-step explanation:

If we talk about rolling, we have to use as a definition a combination of rotation and translation of object with respect to a surface. Now, when the object is rolling without sliding is referred to as pure rolling.

I hope it helps you!

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3 years ago

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weeeeeb [17]

Answer:

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