3 1/2 is to 5 as X is to 15

Continue the given solution and solve for B and C :

[tex](s+1)\dfrac{s^2+1}{(s-1)(s+1)(s-2)} = (s+1)\left(-\dfrac1{s-1} + \dfrac B{s+1} + \dfrac C{s-2}\right)[/tex]

[tex]\dfrac{s^2+1}{(s-1)(s-2)} = -\dfrac{s+1}{s-1} + B + \dfrac{C(s+1)}{s-2}[/tex]

[tex]s=-1 \implies B = \dfrac13[/tex]

Similar steps lead to C = 5/3, and so

[tex]\dfrac{s^2+1}{(s-1)(s+1)(s-2)} = -\dfrac1{s-1} + \dfrac13\times\dfrac1{s+1} + \dfrac53\times\dfrac1{s-2}[/tex]

Now take the inverse transform of each term.

[tex]Y(s) = -\dfrac1{s-1} \implies y(t) = -e^t L^{-1}\left\{\dfrac1s\right\} = -e^t[/tex]

[tex]Y(s) = \dfrac13\times\dfrac1{s+1} \implies y(t) = \dfrac{e^{-t}}3 L^{-1}\left\{\dfrac1s\right\} = \dfrac{e^{-t}}3[/tex]

[tex]Y(s) = \dfrac53\times\dfrac1{s-2} \implies y(t) = \dfrac53e^{2t} L^{-1}\left\{\dfrac1s\right\} = \dfrac{5e^{2t}}3[/tex]

Then the inverse transform of F(s) is

[tex]F(s) = \dfrac{s^2+1}{(s-1)(s+1)(s-2)} \implies f(t) = -e^t + \dfrac{e^{-t}+5e^{2t}}3[/tex]

[tex]\implies f(t) = \boxed{\dfrac{5e^{3t} - 3e^{2t} + 1}{3e^t}}[/tex]

Answer:

The Answer is B! 3√5 I hope this helped u

Answer:

The answer is x=15/2

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

Mr. Ford selects 5 people who tried out.

He then chooses 5 more people to assist with the show.

Together he has 5 + 5 = 10 people altogether.

We're given:

Let x equal the calorie count per serving of the original popcorn.

The light popcorn has a calorie count of 120, which is 25% fewer calories than regular popcorn. This means that 75% of the calorie count of regular popcorn is equal to that of the light popcorn:

[tex]x*0.75=120[/tex]

[tex]x*0.75=120[/tex]

⇒ Divide both sides by 0.75:

[tex]\dfrac{x*0.75}{0.75}=\dfrac{120}{0.75}\\\\x=160[/tex]

Therefore, each serving of regular popcorn has 160 calories.

Answer: L= 90-3 i hope this helps u :)

Answer:

[tex]\sf length = 8b+2[/tex]

Explanation:

Given:

using the formula:

[tex]\hookrightarrow \sf 64b^2 - 4 = length * (8b - 2)[/tex]

[tex]\hookrightarrow \sf \dfrac{64b^2 - 4 }{(8b - 2)} = length[/tex]

[tex]\hookrightarrow \sf length = 8b+2[/tex]

Answer:

Diameter

Step-by-step explanation:

If it was from the middle to the edge it would be a radius,

but since it goes all the way across its a diameter.

Answer:

Step-by-step explanation:

3.Diameter.

To find the equation of line take any two points on graph,

Point A = (0,3) = (X1,Y1)

Point B = (3,0) = (X2,Y2)

Y intercept is = 3,

Now find the slope of line using two point formula,

[tex]Slope = \frac{Y2-Y1}{X2-X1} \\ \

Slope = \frac{3-0}{0-3} = -1[/tex]

Equation of the line in standard form is,

[tex]Y - Y1 = m(X - X1)[/tex]

where m is the slope of line!

Now substituting Y1, m, X in above equation!

[tex]Y - Y1 = m(X - X1) \\ Y - 3 \: = - 1(X - \: 0) \\ Y - 3 = - X \\

X + Y = 3 \\

Y = 3 - X[/tex]

The equation of line in Slope intercept form,

[tex]\fbox{Y = - X + 3}[/tex]

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1. {1, 2, 3, 4, 5, 6}
2. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

3. {B1, B2, B3, R1, R2, R3, R4, R5, R6, R7, R8, G1, G2, G3, G4, Y1, Y2, Y3, Y4, Y5, Y6, Y7}
B for blue, R for red, G for green, Y for yellow.
4. {TT, TH, HT, HH}
T for tails and H for heads

Explanation:
sample space is all possible outcomes

1. ((--1, 2, 3, 4, 5, 6--))

2. ((--1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15--))

3. ((--B1, B2, B3, R1, R2, R3, R4, R5, R6, R7, R8, G1, G2, G3, G4, Y1, Y2, Y3, Y4, Y5, Y6, Y7--))

B for blue, R for red, G for green, Y for yellow.

4. ((--Tail tail, Tail Heads, heads tails, heads heads--))

Answer:

42

Step-by-step explanation:

Let's say the number=X

x/7=6

7*6=42

and 42/7=6

Answer:

c

Step-by-step explanation:

it just is

Answer:

I would do it at your own pace. Find yourself a habit that helps you focus.

Step-by-step explanation:

For some people, like me, music helps me focus. For others, utter silence is best. I would suggest that if you finding a focal point does not help that you get a tutor. You can also come up with multiple ways to study like Quizlets, videos, flashcards, podcasts, depending on what type of learner you are!

Answer:

120.75 ounces

Step-by-step explanation:

It's just a multiplication you will multiply 23 ×5.25 will get you your answer

Answer:

-24/5

Step-by-step explanation:

I did the math...your welcome:)

Answer: There are 16 houses

Step-by-step explanation: Why? Because of the fact that every house is 1/4 house and you can multiply that by every time 1/4x4 then 1/4x4 1/4x4 and 1/4x4 and you have 16 houses.

Answer:

There are (14 - 8) daisies = 6 daisies

roses / daises = 8 / 6 = 4 / 3

flowers / daises = 14 / 6 = 7 / 3

Answer:

70

Step-by-step explanation:

angles in a triangle add up to 180 so both of the other angles added equal to 110. 180-110=70

Answer:

347

Step-by-step explanation:

This is Arithmetic Sequence where its common difference= 11-4 = 18-11 = 7

The Geometric Sequence General Formula = [tex]a_{n} =a_{1}+ d(n-1)[/tex]

where a1 is the 1st Term and d is the common difference

[tex]a_{50} =4+7*(50-1)=347[/tex]

Answer:

y=2x-5

y=-x+7

answer is (4,3)

Step-by-step explanation:

brainliest pls

Answer:

y=(-3/5)x + 5

Step-by-step explanation:

Looking at the graph, we can see two clear points; (0,5) and (5, 2). We know that the y-intercept is (0,5) so the b value of the standard form of a line, y=mx+b, is 5. Since we know two points, we can figure out the slope. So, the slope is (5-2)/(0-5) = 3/-5. Therefore the equation of this line is y=(-3/5)x+5. We can check this answer by plugging in points.

volume: 113.1 and SA:138.23

Answer:

45

Step-by-step explanation

Its actually quite simple all you have to do is multiply 15 by 3 and then you will get 45.

Answer: A: √x+5

Step-by-step explanation:

The parent square root function is √x

Transformations to this graph come in the form y =√(x-h) +k, where h is responsible for left-right movements, and k is responsible for up down movements.

For the image, we can see that f(x) is simply the parent square root function, √x. To get h(x) from f(x), there is a translation of 5 units to the left, which can be algebraically represented by a value of h = -5. Putting this into our form, we get h(x) = √x+5, which is your answer :)

The function h(x) is after transformation is √(x + 5).

Option A is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The square root parent function is f(x) = √x, which starts from the point (0, 0) and increases as x increases.

To transform the parent function to h(x) starting from the point (-5, 0), we need to perform a horizontal translation of 5 units to the right.

This is because if we plug in x = -5 into the parent function,

We get f(-5) = √(-5), which is not a real number.

Therefore, we need to shift the function horizontally so that it starts from

x = -5.

The transformation of the square root parent function with a horizontal translation of 5 units to the right is given by the equation:

h(x) = √(x + 5)

This function starts from the point (-5, 0) and increases as x increases.

We can verify this by plugging in x = -5 to get h(-5) = √(0) = 0, which is the starting point of the function, and by observing that h(x) increases as x increases.

Thus,

The function h(x) is √(x + 5).

Learn more about functions here:

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Answer:

0.50 cent per ounces

Step-by-step explanation:

0.50 cent per ounces

Answer:

3rd option is correct

.........................................

Answer:

option c

Step-by-step explanation:

Linear equation in slope intercept form: y = mx +b

m is slope and b is y-intercept.

m = 5/6

[tex]y=\dfrac{5}{6}x+b\\[/tex]

The point P(-6 ,-2) passes through the line. So, plugin s and y values in the above equation.

[tex]-2=\dfrac{5}{6}*(-6)+b\\\\\\-2= -5 + b\\\\-2 + 5 = b\\[/tex]

b = 3

Equation of the line:

[tex]y=\dfrac{5}{6}x+3[/tex]

Answer:

13.333333...

Step-by-step explanation:

divide 20 by 3/2