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emmasim [6.3K]
3 years ago
7

What is the solution for this inequality? -10x < 40

Mathematics
1 answer:
alukav5142 [94]3 years ago
6 0

Answer:

Step-by-step explanation:

-10x < 40

x > -4

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Please help!
BaLLatris [955]

a) The polynomial in expanded form is f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18.

b) The slant asymptote is represented by the linear function is y = -x + 1.

c) There is a discontinuity at x = 2  with a slant asymptote.

a) In this question we are going to use the Factor Theorem, which establishes that polynomial are the result of products of binomials of the form x-r_{i}, where r_{i} is the i-th root of the polynomial and the grade is equal to the quantity of roots. Therefore, the polynomial f(x) has the following form:

f(x) = (x-6)\cdot (x+1)\cdot (x+3)

And the expanded form is obtained by some algebraic handling:

f(x) = (x-6)\cdot (x^{2}+4\cdot x +3)

f(x) = x\cdot (x^{2}+4\cdot x + 3)-6\cdot (x^{2}+4\cdot x +3)

f(x) = x^{3}+4\cdot x^{2}+3\cdot x -6\cdot x^{2}-24\cdot x -18

f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18 (1)

The polynomial in expanded form is f(x) = x^{3}-2\cdot x^{2}-21\cdot x -18.

b) In this question we divide the polynomial found in a) (in factor form) by the polynomial x^{2}-x -2 (also in factor form). That is:

g(x) = \frac{(x-6)\cdot (x+1)\cdot (x+3)}{(x-2)\cdot (x+1)}

g(x) = \frac{(x-6)\cdot (x+3)}{x-2} (2)

The slant asymptote is defined by linear function, whose slope (m) and intercept (b) are determined by the following expressions:

m =  \lim_{x \to \pm \infty} \frac{g(x)}{x} (3)

b =  \lim_{x \to \pm \infty} [g(x)-x] (4)

If g(x) = \frac{(x-6)\cdot (x+3)}{x-2}, then the equation of the slant asymptote is:

m =  \lim_{x \to 2} \frac{(x-6)\cdot (x+3)}{x\cdot (x-2)}

m =  \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x -18}{x^{2}-2\cdot x} \right)

m =  1

b =  \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x -18}{x-2}-x \right)

b =  \lim_{x \to \pm \infty} \left(\frac{x^{2}-3\cdot x - 18-x^{2}+2\cdot x}{x-2}\right)

b =  \lim_{n \to \infty} \left(\frac{-x-18}{x-2} \right)

b = -1

The slant asymptote is represented by the linear function is y = -x + 1.

c) The number of discontinuities in rational functions is equal to the number of binomials in the denominator, which was determined in b). Hence, we have a discontinuity at x = 2  with a slant asymptote.

We kindly invite to check this question on asymptotes: brainly.com/question/4084552

8 0
2 years ago
How do i solve this?
timofeeve [1]

Answer:

Measure the sides using a ruler and measure the angle using a protractor.

3 0
3 years ago
Judy is looking to buy a textbook. The book normally costs $75.82, but it is on sale for 35% below
Trava [24]

Answer:

$49.28 is the sale cost.

Step-by-step explanation:

0.35 x 75.82 = 26.537

75.82 - 26.537

= 49.283 and round

3 0
2 years ago
What is the sound level for a noise that has an intensity of 7.6 × 10-4 watts/m2?
Greeley [361]
Sound intensity: <span> 7.6 × 10-4 watts/m2?

To solve this problem you have to understand the threshold of hearing (Level) 

</span><span>Io = 10^−12 W/m²
</span>
Solve the problem: 
<span>"LI = 10×log (I / Io) dB = 10×log (7.6×10^−4 / 10^−12) dB"
</span>
and the answer is 88.81dB

Quoted answers are not mine.  All credits to their internet owners.  

Further help/Credits to: 

https://answers.yahoo.com/question/index?qid=20130217095248AALXBjj

I'm only here to help, not get into trouble.  
7 0
3 years ago
Read 2 more answers
Simplify the expression by combining like terms.
podryga [215]

Answer:

The answer: is 118

I hope this help you enjoy :D

Step-by-step explanation:

3 0
3 years ago
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