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2 years ago

Select the best description for the sum of the expression below.

Mathematics

1 answer:

Aliun [14]2 years ago

6 0

Answer:

D. Irrational

Step-by-step explanation:

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Match the following rational expressions to their rewritten forms.

Nookie1986 [14]

Answer:

Answer image is attached.

Step-by-step explanation:

Given rational expressions:

$1.\ \dfrac{x^2+x+4}{x-2}\\2.\ \dfrac{x^2-x+4}{x-2}\\3.\ \dfrac{x^2-4x+10}{x-2}\\4.\ \dfrac{x^2-5x+16}{x-2}$

And the rewritten forms:

$(x-2)+\dfrac{6}{x-2}\\(x+3)+\dfrac{10}{x-2}\\(x+1)+\dfrac{6}{x-2}\\(x-3)+\dfrac{10}{x-2}$

We have to match the rewritten terms with the given expressions.

Let us consider the rewritten terms and let us solve them one by one by taking LCM.

$(x-2)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x-2)^{2}+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+4+6 }{x-2}\\\Rightarrow \dfrac{x^2-4x+10}{x-2}$

So, correct option is 3.

$(x+3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x+3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{(x^2+3x-2x-6)+10}{x-2}\\\Rightarrow \dfrac{x^2+x+4}{x-2}$

So, correct option is 1.

$(x+1)+\dfrac{6}{x-2}\\\Rightarrow \dfrac{(x+1)(x-2)+6}{x-2}\\\Rightarrow \dfrac{x^{2} +x-2x-2+6}{x-2}\\\Rightarrow \dfrac{x^{2} -x+4}{x-2}$

So, correct option is 2.

$(x-3)+\dfrac{10}{x-2}\\\Rightarrow \dfrac{(x-3)(x-2)+10}{x-2}\\\Rightarrow \dfrac{x^2-3x-2x+6+10}{x-2}\\\Rightarrow \dfrac{x^2-5x+16}{x-2}$

So, correct option is 4.

The answer is also attached in the answer area.

7 0

3 years ago

Find the first three terms of the sequence below.<br> T, = n2 + 2n +9

NikAS [45]

Answer:

12, 17, 24

Step-by-step explanation:

To find the first 3 terms, substitute n = 1, 2, 3 into the rule, that is

T₁ = 1² + 2(1) + 9 = 1 + 2 + 9 = 12

T₂ = 2² + 2(2) + 9 = 4 + 4 + 9 = 17

T₃ = 3² + 2(3) + 9 = 9 + 6 + 9 = 24

7 0

3 years ago

Read 2 more answers

Steve cycled 35 miles in 2 1/2 hours. What is the average speed that Steve traveled? miles per hour

Evgesh-ka [11]

Answer:

14 miles per hour

Step-by-step explanation:

The average speed would be the total distance divided by the total time = 35 miles divided by 2.5 hours is 14 miles per hour

5 0

3 years ago

Jessica has 300 cm³ of material. She uses 12.6 cm³ to make a right triangular prism. She wants to make a second prism that is a

Rzqust [24]

Answer:52.8

Step-by-step explanation:

5 0

2 years ago

F f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f circle g) (x)?

seraphim [82]

f°g mean apply g(x) and then use result of g(x) as "x" in f(x)

so as g(x) = x² +1 and f(x) = 3x+2

so if we call g(x) X we have

f( X) = 3 X +2

now we replace " X" for it's value

f(X) = 3 ( x² +1) +2

f(X) = 3x² +3 +2

f(X) = 3x² +5

so f°g = 3x² +5

8 0

1 year ago