If f(x) = 2x + 6 and g(x) = -4x - 8 find f(g(x)) = ?x+?

HELPPPP 100 points if you help!!!!

nignag [31]

Answer:

Part A)

Chorus:

$c(t)=15(1.12)^t$

Band:

$b(t)=2t+30$

Part B)

After 9 years:

The chorus will have about 41 people.

And the band will have 48 people.

Part C)

About approximately 11 years.

Step-by-step explanation:

We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.

There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.

Part A)

Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.

So, using the standard form for exponential growth:

$c(t)=a(r)^t$

Where a is the initial population and r is the rate of change.

We will substitute 15 for a and 1.12 for r. Hence:

$c(t)=15(1.12)^t$

This represents the number of people in the chorus after t years.

We are given that 2 new people join the band each year. So, it increases linearly.

Since there are already 30 people in the band, our initial point or y-intercept is 30.

And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:

$b(t)=mt+b$

And by substitution:

$b(t)=2t+30$

This represents the number of people in the band after t years.

Part B)

We want to find the number of people in the chorus and the band after 9 years.

Using the chorus function, we see that:

$c(9)=15(1.12)^9\approx41.59\approx41$

There will be approximately 41 people in the chorus after 9 years.

And using the band function, we see that:

$b(9)=2(9)+30=48$

There will be 48 people in the band after 9 years.

Part C)

We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for t. So:

$15(1.12)^t=2t+30$

Unfortunately, it is impossible to solve for t using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.

Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).

Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.

5 0

3 years ago

What is the value of x ??

ruslelena [56]

Answer:

A

Step-by-step explanation:

The Tangent-Secant Exterior Angle Measure Theorem states that if a tangent and a secant or two tangents/secants intersect outside of a circle, then the measure of the angle formed by them is half of the difference of the measures of its intercepted arcs. Basically, what that means here is that $x$ equals half of the difference of $30\textdegree$ and the measure of the unlabeled arc.

First, we need to find the measure of the unlabeled arc, since we can't find $x$ without it. We know that the measure of the full arc formed by the circle is $360\textdegree$ , so the measure of the unlabeled arc must be $360-30-100-100=130\textdegree$ by the Arc Addition Postulate.

Now, we can find $x$ . Using all of the information known, we can solve for $x$ like this:

$\\x=\frac{1}{2} (130\textdegree-30\textdegree)\\=\frac{1}{2} (100\textdegree)\\=50\textdegree$

Hope this helps!

5 0

2 years ago

in a company 95% of the workers are women if 220 people work for the company who aren't women how many workers are there in all?

dybincka [34]

So 5% of workers are not women, and 220 workers are not women, so 220 is 5% of the total workers. 220 is 5% of 4400, so there are 4400 workers in all.

7 0

3 years ago

Please helpppp. It's due in an hour

TEA [102]

Answer:

sowwy

Step-by-step explanation:

i can't help WITH MY SMALL BRAIN

4 0

3 years ago

lynn takes her puppy, olive, to a doggie daycare. The price for the daycare is 21 per day along with a monthly admission fee of

sashaice [31]

D=426-48(21)
I got 18 days.
So, D=18
Hope this helps! :)

3 0

3 years ago

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