Which angles are linear pairs ?

1. Find two functions f(x) and g(x) such that f[g(x)] = x but g[f(x)] does not equal x.2. State the vertical, horizontal asympto

Harman [31]

Answer:

1. $f(x)=x^{2}$ and $g(x)=-\sqrt{x}$

2. Vertical Asymptote: x=-4

Horizontal Asymptote: y=1

Zeros: (-2,0)

Because the graph will have a hole at x=-1. This is, the graph is not defined for that particular x-value.

3. $f(x)=x^{2}+4$

It has two complex roots, so there is no place in the graph where it crosses the x-axis.

Step-by-step explanation:

1. If we find the composite function f[g(x)] with the functions:

$f(x)=x^{2}$ and g(x)=-x, we will get the following:

$f[g(x)]=(-\sqrt{x})^{2}$

which simplifies to

f[g(x)]=x

on the other hand, if we find g[f(x)] we will get the following:

$g[f(x)]=-\sqrt{x^2}$

which simplifies to:

g[f(x)]=-x

2.

Before finding the asymptotes, it's a good idea to factor both the numerator and denominator of the function, so we get:

$f(x)=\frac{x^{2}+3x+2}{x^{2}+5x+4}$

$f(x)=\frac{(x+2)(x+1)}{(x+4)(x+1)}$

we can now see that this function can be simplified. It is important to simplify this function so we don't confuse vertical asymptotes with holes in the graph, so when simplifying we get the following:

$f(x)=\frac{x+2}{x+4}$

now we can set the denominator equal to zero.

x+4=0

and solve for x:

x=-4 this is our vertical asymptote.

For the horizontal asymptote, there is a rule that tells us that if the polynomials on the numerator and denominator have the same degree (the same greatest power), then the horizontal asymptote is found by dividing the lead coefficient of the polynomial on the numerator by the lead coefficient on the denominator. In this case the lead coefficients are 1 and 1 so the horizontal asymptote is:

$y=\frac{1}{1}$

so the horizontal asymptote is at:

y=1.

The zeros of the function are located at the x-values that will turn the numerator of the simplified fraction equal to zero, so we get:

x+2=0

x=-2

so the only zero will be located at (-2,0)

x=-1 is not a zero because the original function is not defined for x=-1, there is a hole in the graph at this x-value.

Take a look at the graph of the function (See attached picture)

3.

This will happen when there are no real zeros. Take for example the function:

$f(x)=x^{2}+4$

In this case this problem has 2 non-real zeros:

$x^{2}+4=0$

$x^{2}=-4$

$x=\sqrt{-4}$

so:

x=2i or x=-2i

since they are complex numbers they cannot be graphed on a coordinate axis, so the graph will not cross the x-axis. See attached picture.

6 0

3 years ago

To measure the distance across a pond, Sandy and Garrett mark a spot at on

DerKrebs [107]

Answer:

distance across the pond: 13 yd

distance walked by Garret: 12 yd

Step-by-step explanation:

Data:

distance across the pond: x yd

distance walked by Sandy: 5 yd

distance walked by Garret: x-1 yd

A right triangle is formed where the distance across the pond is the hypotenuse. From Pythagorean theorem:

x² = 5² + (x-1)²

x² = 25 + x² - 2x + 1

0 = 26 - 2x

x = 13

4 0

3 years ago

Battery packs in electric go-carts need to last a fairly long time. The run-times (time until it needs to be recharged) of the b

pav-90 [236]

Answer:

The minimum level for which the battery pack will be classified as highly sought-after class is 2.42 hours

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 2, \sigma = 0.33$

What is the minimum level for which the battery pack will be classified as highly sought-after class

At least the 100-10 = 90th percentile, which is the value of X when Z has a pvalue of 0.9. So it is X when Z = 1.28.

$Z = \frac{X - \mu}{\sigma}$

$1.28 = \frac{X - 2}{0.33}$

$X - 2 = 0.33*1.28$

$X = 2.42$

The minimum level for which the battery pack will be classified as highly sought-after class is 2.42 hours

4 0

3 years ago

The question is below, plz answer, will give brainliest

Elina [12.6K]

By comparing the right triangle ABC with the triangle XYZ, we will see that:

AC = 5
BC = 10.

<h3>How to find the given segments?</h3>

So we know that the largest triangle is a dilation of scale factor 2 of the smaller one.

Also, remember that for right triangle we have the relation:

Tan(θ) = (opposite cathetus)/(adjacent cathetus).

Now, the problem tells us that:

tan(x) = 5/2.5

For the angle x, the adjacent cathetus is XY, and the opposite cathetus is YZ.

Then we have:

YZ = 5

XY = 2.5

Knowing that the correspondent sides in the larger triangle will be 2 times the above ones, we can see that:

AC = 2*XY = 2*2.5 = 5

CB = 2*YZ = 2*5 = 10

If you want to learn more about right triangles, you can read:

brainly.com/question/2217700

5 0

2 years ago

Pls help me with the solution I need help.

Rashid [163]

Answer:

Y=180

X=90

Step-by-step explanation:

5 0

3 years ago