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shepuryov [24]
2 years ago
7

I need this asap: Find the Domain

Mathematics
1 answer:
rusak2 [61]2 years ago
5 0
The domain is 3 and 5
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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 <em>a</em> is the initial population and <em>r</em> is the rate of change.

We will substitute 15 for <em>a </em>and 1.12 for <em>r</em>. Hence:

c(t)=15(1.12)^t

This represents the number of people in the chorus after <em>t</em> 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 <em>t</em> 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 <em>t</em>. So:

15(1.12)^t=2t+30

Unfortunately, it is impossible to solve for <em>t</em> 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
2 years ago
What is the measure of angle C, m
Blizzard [7]
51°
Angles that are opposite to another angle are equal
7 0
2 years ago
What factors multiply to -80 and add to 6
forsale [732]

80 = -1(80), -2(40), -4(20), -5(4),

Total answers include: -81, 79, -42, 16, -9, and 1.

None of them add up to 6!

Are you doing polynomial equations?

If so, you can solve it the hard way.

x^2 + 6x -80 = 0

(x^2 + 6x + 9) - 80 = 9

(x+3)^2 = 89

(x+3) = 9.43

x = 6.43

If you're not doing those then I'm afraid your question has no answer.

Hope that helps!



7 0
3 years ago
What is the solution of the system of equations? y = –3x + 8 y = –5x – 2
jekas [21]
y=-3x+8 \\ y=-5x-2 \\  \\ -3x+8=-5x-2 \\ -3x+5x=-2-8 \\ 2x=-10 \\ x=- \frac{10}{2}  \\ x=-5 \\ y=-3(-5)+8=15+8=23  \\ \\ \boxed{-5,23}
6 0
2 years ago
Read 2 more answers
3. Which statements about the line that passes through (-2, 0) and (2, -4) are true?
diamong [38]

Answer:

B, C, and D.

Step-by-step explanation:

Let's go through each answer choice.

A: To find the slope of a line from two points, we use this formula: (y_2-y_1)/(x_2-x_1). Plugging in the values (-2,0) and (2, -4), we get:

  • (-4-0)/(2+2)
  • -4/4
  • -1

Because option A says the slope is 1, but we got -1, option A is false.

B: To find the y-intercept, we use this formula: b = y_1 - m * x_1

  • b = 0 -(-1) * (-2)
  • b = 1 * (-2)
  • b = -2  

Since we know the value of b is the y-intercept, we could write the y-intercept as (0,-2). Therefore, option B is true.

C: The equation of a line (in slope-intercept form) is y = mx + b, where y - y-coordinate, m = slope, x = x-coordinate, and b = y-intercept. Since we already solved for the y-intercept and slope, let's plug in those values:

  • y = mx +b
  • y = -x -2

As you can see, the equation we got here matches the one in option C, meaning it's true.

D: We know that a point is written like this: (x, y). If the x-coordinate is not zero but the y-coordinate is, then it's the x-intercept. Since the question says that (-2,0) is one of the points the line passes through, and option D says that the x-intercept is (-2,0), it's true.

8 0
2 years ago
Read 2 more answers
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