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3 years ago

Multiply or divide as indicated (3x)^12/(3x)^4

Mathematics

1 answer:

tresset_1 [31]3 years ago

5 0

Answer:

Answer will be 6561 x ∧ 8

Step-by-step explanation:

Given that:

(3x) ∧ 12 / (3x) ∧ 4

3∧(12-4) * x ∧ (12-4)

3∧8 * x ∧ 8

6561 x∧8

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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

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)

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

Write a verbal expression for 3(n + 8). (5 points) Best answer gets brainliest

Leya [2.2K]

Answer:

three times the sum of a number and eight

Step-by-step explanation:

6 0

3 years ago

Help me please numbers 3-6

NikAS [45]

A pair of supplementary angles are angles that together equal 180. A pair would be 2,3 or 9,2 etc. if m1 is 75 then 10 would be 105 because they're supplementary. Vertical angles would be 9,3 or 5,7. They're across from eachother. It would be perpendicular to line segment BA, because the angle would have to be 90 degrees to a straight line.

5 0

3 years ago

Quadrilateral EFGH is inscribed inside a circle as shown below. Write a proof showing that angles H and F are supplementary. Cir

vladimir1956 [14]

Answer:

That is called a cyclic quadrilateral. Angles E and G add up to 180 degrees and angles H and F add up to 180 degrees.

Supplementary angles are two angles whose measures add up to 180°

7 0

3 years ago

For the school play, the advance tickets cost $3, while tickets at the door cost $5. Thirty more tickets were sold at door in ad

Talja [164]

Answer:

310 tickets were sold in advance before school pay and 340 door tickets were sold in advance.

Step-by-step explanation:

Given:

Let number of tickets sold in advance be 'x'.

Cost of advance ticket = $3

Cost of door tickets = $5

Also given:

Thirty more tickets were sold at door in advance

Hence number of door tickets sold = $x+30$

Total Money Collected = $2630

Now we can say that Total Money Collected is equal to sum of number of tickets sold in advance multiplied by Cost of advance ticket and number of door tickets sold multiplied by Cost of door tickets.

Framing in equation form we get;

$3x+(x+30)5=2630$