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wariber [46]
2 years ago
6

(100 Points) Given f of x is equal to 10 divided by the quantity x squared minus 7x minus 30, which of the following is true?

Mathematics
2 answers:
ikadub [295]2 years ago
4 0

Answer:

f(x) is positive for all x > 10

Step-by-step explanation:

Given function:

f(x)=\dfrac{10}{x^2-7x-30}

<u>Asymptote</u>

Asymptote: a line which the curve gets infinitely close to, but never touches.

Factor the denominator of the function to find the vertical asymptotes:

\implies x^2-7x-30

\implies x^2-10x+3x-30

\implies x(x-10)+3(x-10)

\implies (x+3)(x-10)

Therefore:

f(x)=\dfrac{10}{(x+3)(x-10)}

The function is undefined when the denominator is equal to zero.

Therefore, there are vertical asymptotes at x = -3  and  x = 10
and a horizontal asymptote at y = 0

f(x) is positive for (10, ∞)

f(x) is negative for (-3, 10)

f(x) is positive for (-∞, -3)

katrin2010 [14]2 years ago
3 0

\\ \rm\Rrightarrow y=\dfrac{10}{x^2-7x-10}

If we factor

\\ \rm\Rrightarrow y=\dfrac{10}{(x+3)(x-10)}

Horizontal Asymptotes

  • y=0 as there is no variable in numbers

Vertical asymptotes

solve the denominator for 0

  • x=-3
  • x=10

Henec option D is correct

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Multiply.
Crank
The main rules that we use here are :

i) \sqrt{a \cdot b}=  \sqrt{a} \cdot \sqrt{b} for nonnegative values a and b.

ii) \sqrt{a} \cdot  \sqrt{a} =a.


Thus, first 'decompose' the numbers in the radicals into prime factors:

4 \sqrt{3} \cdot 10 \cdot  \sqrt{2\cdot2\cdot3}\cdot  \sqrt{2\cdot 3}\cdot  \sqrt{2}..

By rule (i) we write:

4 \sqrt{3} \cdot 10 \cdot \sqrt{2}\cdot \sqrt{2}\cdot \sqrt{\cdot3}\cdot \sqrt{2} \cdot  \sqrt{3} \cdot \sqrt{2}.

We can collect these terms as follows:

40 \sqrt{3}\cdot (\sqrt{3}\cdot \sqrt{3}) \cdot (\sqrt{2}\cdot \sqrt{2}) \cdot( \sqrt{2} \cdot \sqrt{2}), and by rule (ii) we have:

40 \sqrt{3}\cdot 3 \cdot 2 \cdot2=40\cdot12\cdot \sqrt{3}=480 \sqrt{3}.


Answer: 480 \sqrt{3}.
8 0
3 years ago
Simplify.<br><br> –abc + 7abc – 3bc – 8abc<br><br><br> ------------- abc − ------------bc
NISA [10]
- abc + 7abc - 3bc - 8abc
= 6abc - 3bc - 8bc
= -2abs - 3bc

Therefore
- 2abc - 3bc. 

:)
7 0
3 years ago
__,__, 8.16,32,64 what is the arithmetic sequence?
seraphim [82]

Answer:

2,4,8,16,32,64

Step-by-step explanation:

There are a couple of ways one could approach this. The goal is to find out the factor by which the numbers are increasing. Looking at going from 8 -> 16, we have either added 8, or doubled 8. So the factor is either +8 or x2. Going from 16 -> 32, adding 8 no longer holds true, while multiplying by 2 (doubling 16) does. To confirm what we have found, we can further check our math by using the final two numbers, 32 -> 64, to confirm that the sequence pattern is to double the current number to achieve the next number.

Working backwards, we can half each number to find out the first two numbers in the sequence. 64/2 = 32, 32/2 = 16, 16/2 = 8, 8/2 = 4, 4/2 = 2

8 0
3 years ago
1.3 lesson help please
Airida [17]

Answer:

1. 125

2. 25

3. 40

4. 39

First question:

(15-10)^2 + (15-5)^2

parentheses first to get 5^2 + (15-5)^2

exponents next to get 25 + (15-5)^2

parentheses again 25 + 10^2

exponents again 25 + 100 = 125

Second question:

simplify the exponents (3 *3) + (4 * 4) + (2 * 2) to get 9 + 16 + 4 = 29

Third question:

simplify in the parentheses 6 1/7 - 1/7 = 6

divide 60 by 6 to get 10

multiply 10 by 4 to get 40!

Fourth question:

simplify the fractions to get 1/3 + 8/3 = 3

multiply the 3 by 13 to get 39

7 0
2 years ago
Read 2 more answers
) If the base of the panel is 31.2 inches and the height is 18 inches, what is the area of one triangular section? Show your wor
Sliva [168]
Well u do 31.2 x 18 which is 561.6 then u divide by 2 because the formula for a triangle is base x height divided by 2 so It is 280.8
8 0
3 years ago
Read 2 more answers
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