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3 years ago

I was wondering if how you would plot a point using this information, also how you would answer this question. Thanks!

Mathematics

1 answer:

lukranit [14]3 years ago

4 0

for the y value you would go up the top line by 2 in problem 3 for the x value you would go to the left by 4 and follow the same steps but with different numbers for problem 4

Have a great day

Hope that helps :)

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Let f be the function defined by f(x)=cx−5x^2/2x^2+ax+b, where a, b, and c are constants. The graph of f has a vertical asymptot

Musya8 [376]

Answer:

a) $a = 2$ and $b = -4$ , b) $c = -10$ , c) $f(-2) = -\frac{5}{3}$ , d) $y = -\frac{5}{2}$ .

Step-by-step explanation:

a) After we read the statement carefully, we find that rational-polyomic function has the following characteristics:

1) A root of the polynomial at numerator is -2. (Removable discontinuity)

2) Roots of the polynomial at denominator are 1 and -2, respectively. (Vertical asymptote and removable discontinuity.

We analyze each polynomial by factorization and direct comparison to determine the values of $a$ , $b$ and $c$ .

Denominator

i) $(x+2)\cdot (x-1) = 0$ Given

ii) $x^{2} + x-2 = 0$ Factorization

iii) $2\cdot x^{2}+2\cdot x -4 = 0$ Compatibility with multiplication/Cancellative Property/Result

After a quick comparison, we conclude that $a = 2$ and $b = -4$

b) The numerator is analyzed by applying the same approached of the previous item:

Numerator

i) $c\cdot x - 5\cdot x^{2} = 0$ Given

ii) $x \cdot (c-5\cdot x) = 0$ Distributive Property

iii) $(-5\cdot x)\cdot \left(x-\frac{c}{5}\right)=0$ Distributive and Associative Properties/ $(-a)\cdot b = -a\cdot b$ /Result

As we know, this polynomial has $x = -2$ as one of its roots and therefore, the following identity must be met:

i) $\left(x -\frac{c}{5}\right) = (x+2)$ Given

ii) $\frac{c}{5} = -2$ Compatibility with addition/Modulative property/Existence of additive inverse.

iii) $c = -10$ Definition of division/Existence of multiplicative inverse/Compatibility with multiplication/Modulative property/Result

The value of $c$ is -10.

c) We can rewrite the rational function as:

$f(x) = \frac{(-5\cdot x)\cdot \left(x+2 \right)}{2\cdot (x+2)\cdot (x-1)}$

After eliminating the removable discontinuity, the function becomes:

$f(x) = -\frac{5}{2}\cdot \left(\frac{x}{x-1}\right)$

At $x = -2$ , we find that $f(-2)$ is:

$f(-2) = -\frac{5}{2}\cdot \left[\frac{(-2)}{(-2)-1} \right]$

$f(-2) = -\frac{5}{3}$

d) The value of the horizontal asympote is equal to the limit of the rational function tending toward $\pm \infty$ . That is:

$y = \lim_{x \to \pm\infty} \frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x -4}$ Given

$y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot 1\right]$ Modulative Property

$y = \lim_{x \to \infty} \left[\left(\frac{-10\cdot x-5\cdot x^{2}}{2\cdot x^{2}+2\cdot x-4}\right)\cdot \left(\frac{x^{2}}{x^{2}} \right)\right]$ Existence of Multiplicative Inverse/Definition of Division

$y = \lim_{x \to \pm \infty} \left(\frac{\frac{-10\cdot x-5\cdot x^{2}}{x^{2}} }{\frac{2\cdot x^{2}+2\cdot x -4}{x^{2}} } \right)$ $\frac{\frac{x}{y} }{\frac{w}{z} } = \frac{x\cdot z}{y\cdot w}$

$y = \lim_{x \to \pm \infty} \left(\frac{-\frac{10}{x}-5 }{2+\frac{2}{x}-\frac{4}{x^{2}} } \right)$ $\frac{x}{y} + \frac{z}{y} = \frac{x+z}{y}$ / $x^{m}\cdot x^{n} = x^{m+n}$

$y = -\frac{5}{2}$ Limit properties/ $\lim_{x \to \pm \infty} \frac{1}{x^{n}} = 0$ , for $n \geq 1$

The horizontal asymptote to the graph of f is $y = -\frac{5}{2}$ .

4 0

4 years ago

Some government leaders propose allowing oil companies to drill in currently protected lands that may be rich in oil reserves. E

TEA [102]

The type of bias in this survey is question-wording bias because the question is influencing the response (option D).

Question-wording bias occurs when the words selected in the question influence a specific response. Here is one example:

Do you believe a cruel practice such as bullfighting should be forbidden?

In this question, the use of the word cruel qualifies bullfighting as negative, and therefore in most cases, people will answer that bullfighting should be forbidden.

This effect occurs in the question for this survey because the section given that an increase in drilling could result in increased tax revenue and additional jobs to the region indirectly states drilling is positive and therefore influences the response of those surveyed.

Note: This question is incomplete because some of the options are missing; here are the complete options:

What type of bias could be most likely affecting the survey results?

A. This is undercoverage bias because some segments of the population will be excluded from the sample.

B. This is response bias because those selected for the survey may not provide truthful opinions about oil drilling.

C. This is voluntary response bias because those most passionate about drilling will be more likely to register an opinion.

D. This is question-wording bias because the information given at the start of the question may lead those surveyed towards a desired response.

Learn more about bias in: brainly.com/question/6078134

3 0

2 years ago

What are all the shapes my quadrilateral Must be and could be if it has a pair of equal sides and a pair of parallel sides

masha68 [24]

If the parallel sides are the same length, then the figure must be a parallelogram. You can prove this by dividing the parallelogram into two triangles, and then using SAS (side angle side) to prove the triangles congruent, which leads to you showing the corresponding angles are the same measure, therefore the other set of sides must be parallel as well.

If the non parallel sides are the same length, then you have an isosceles trapezoid. A trapezoid is any figure with exactly one pair of parallel sides. An isosceles trapezoid is one where the non-parallel sides are the same length. The non-parallel sides are sometimes considered the legs of the trapezoid (and the parallel sides are the bases).

If you have two adjacent sides that are same length, and you have one set of parallel sides, then you could have a trapezoid (not isosceles but just a more generalized trapezoid)

7 0

3 years ago

Okay google how many pennies are in $25,000

GalinKa [24]

There are 2,500,000 pennies in $25,000

4 0

3 years ago

The equation tan(x- pi/3) is equal to _____.

kherson [118]

Answer:

Step-by-step explanation:

Using the expansion