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Tju [1.3M]
3 years ago
13

The cost for a certain music plan is $9.99 per year plus $0.25 per song you download. If you paid $113.74 one year, determine th

e number of songs you downloaded
Mathematics
1 answer:
Oliga [24]3 years ago
7 0
 if you add 9.99 plus 0.25 you get 10.24     you dived 113,74 by 10.24
11.107421875 songs
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16x17=272/2=136. That is answer.
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Last HW Mr Thompson! Please Help!
TiliK225 [7]

Answer:

B, D, D, B, C

Step-by-step explanation:

1) The part of the equation that tells us the graph would open downward would be B, the negative coefficient of x^{2}.

We know this because, if we reorganize the equation into the standard form  y = mx + b, we get y = -(x²) + 1. This means that for any value we substitute for x, y will always be negative. The answer is B.

2) To find the zeroes of this function, we just have to see which answer makes the function, well, zero.

We have the equation y = (-16t - 2) (t - 1)

We set the equation equal to zero like this:

0 = (-16t - 2) (t - 1)

We also know that anything multiplied <em>by</em> zero will <em>equal</em> zero, so:

0 = (-16t - 2) and 0 = (t - 1)

Now we just solve for t in both equations:

0 = -16t - 2

-16t = 2

t = 2/-16 or -1/8

0 = t - 1

t = 1

So our answer will be D.

3) This time, we are given the same equation but the variable t represents time and y represents the height.

The zeroes are when y = 0, so the zeroes (which are 1 and -1/8 from the last problem) mean that the height is also at zero (which is the ground).

Furthermore, time cannot be negative, so the correct answer choice would be D.

4) We are given the same equation and story problem, but instead we are asked to find the height when the ball was thrown. In other words, we need to find the y-intercept.

The y-intercept is when t = 0, so:

y = (-16t - 2) (t - 1)

y = (-16(0) - 2) (0 - 1)

y = (-2) (-1)

y = 2

So, the correct answer is B, 2 feet.

5) This problem is a simple theoretical question. We know that the constant c will represent the vertical translation or y-intercept, so the correct answer is C.

8 0
3 years ago
Hunter surveyed 200 of the students in his school about their favorite color. 66 students said their favorite color was blue. Wh
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3 years ago
A triangle with a height of 5cm and a base length of 12cm what is the perimeter
Lisa [10]

Answer: 5+5+12+12

Step-by-step explanation:

7 0
3 years ago
Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 5y = sin(x)
vichka [17]

Answers:

a = -6/37

b = -1/37

============================================================

Explanation:

Let's start things off by computing the derivatives we'll need

y = a\sin(x) + b\cos(x)\\\\y' = a\cos(x) - b\sin(x)\\\\y'' = -a\sin(x) - b\cos(x)\\\\

Apply substitution to get

y'' + y' - 5y = \sin(x)\\\\\left(-a\sin(x) - b\cos(x)\right) + \left(a\cos(x) - b\sin(x)\right) - 5\left(a\sin(x) + b\cos(x)\right) = \sin(x)\\\\-a\sin(x) - b\cos(x) + a\cos(x) - b\sin(x) - 5a\sin(x) - 5b\cos(x) = \sin(x)\\\\\left(-a\sin(x) - b\sin(x) - 5a\sin(x)\right)  + \left(- b\cos(x) + a\cos(x) - 5b\cos(x)\right) = \sin(x)\\\\\left(-a - b - 5a\right)\sin(x)  + \left(- b + a - 5b\right)\cos(x) = \sin(x)\\\\\left(-6a - b\right)\sin(x)  + \left(a - 6b\right)\cos(x) = \sin(x)\\\\

I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.

The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero

a-6b = 0

a = 6b

At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)

-6a  -b = 1

-6(6b) - b = 1 .... plug in a = 6b

-36b - b = 1

-37b = 1

b = -1/37

Use this to find 'a'

a = 6b

a = 6(-1/37)

a = -6/37

8 0
2 years ago
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