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3 years ago

Graph the equation y = 4/5x - 1

Mathematics

2 answers:

PSYCHO15rus [73]3 years ago

7 0

Answer:

<h2>In the attachment.</h2>

Step-by-step explanation:

$y=\dfrac{4}{5}x-1$

This is an equation for a line in the slope-intercept form.

For the straight line we only need two points on the coordinate plane.

Choose two x values. Place them in the equation and calculate the y values.

For x = 0:

$y=\dfrac{4}{5}(0)-1=0-1=-1\to(0,\ -1)$

For x = 5:

$y=\dfrac{4}{5}(5)-1=4-1=3\to(5;\ 3)$

Mark points on the coordinate plane and draw a line through these points.

astra-53 [7]3 years ago

4 0

Answer: The answer is the picture shown below

Step-by-step explanation:

To do this you will need to make a coordinate plane about 20 up and 20 down. So there is a formula that is y=mx+b which is called the slope intercept form and as you can see the problem given to you was already given in this formula. The variable m in the equation is the slope and slope is also known as rise (which basically means go up if positive and down if negative) over run (which is right if positive and left if negative) and as you can see in the equation the number 4/5 is the variable m. Since slope is rise over run 4 would be the rise and 5 would be the run, so you would go up 4 and right 5 because they are both positive. Now there is another variable that is b which would be the -1. In slope intercept formula b is the y intercept so -1 is where the line would cross the y axis. Now that you know all the parts to the slope you can put it together giving you the answer.

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A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associ

g100num [7]

Answer: the system of equations that could be used are

700x + 1700y = 21200

y = x + 4

Step-by-step explanation:

Let x represent the number of associates assigned to the case.

Let y represent the number of partners assigned to the case.

The daily rate charged to the client for each associate is $700 and the daily rate for each partner is $1700.

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3 years ago

3 times the difference of a number and 4 equals 12. Find the number.

Anna [14]

Answer:

Step-by-step explanation:

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3 years ago

Y″+ 5y′ + 6y = 3δ(t − 2) − 4δ(t −5); y(0) = y′′(0) = 0

Snowcat [4.5K]

Answer:

y(t) = 3u₂(t) [ $e^{-2t+4} - e^{-5t + 10)}$ ] - 4u₅(t) [ $e^{-2t+10)} - e^{-5t + 25)}$ ]

Step-by-step explanation:

To find - y″+ 5y′ + 6y = 3δ(t − 2) − 4δ(t −5); y(0) = y′(0) = 0

Formula used -

L{δ(t − c)} = $e^{-cs}$

L{f''(t) = s²F(s) - sf(0) - f'(0)

L{f'(t) = sF(s) - f(0)

Solution -

By Applying Laplace transform, we get

L{y″+ 5y′ + 6y} = L{3δ(t − 2) − 4δ(t −5)}

⇒L{y''} + 5L{y'} + 6L{y} = 3L{δ(t − 2)} − 4L{δ(t −5)}

⇒s²Y(s) - sy(0) - y'(0) + 5[sY(s) - y(0)] + 6Y(s) = 3 $e^{-2s}$ - 4 $e^{-5s}$

⇒s²Y(s) - 0 - 0 + 5[sY(s) - 0] + 6Y(s) = 3 $e^{-2s}$ - 4 $e^{-5s}$

⇒s²Y(s) + 5sY(s) + 6Y(s) = 3 $e^{-2s}$ - 4 $e^{-5s}$

⇒[s² + 5s + 6] Y(s) = 3 $e^{-2s}$ - 4 $e^{-5s}$

⇒[s² + 3s + 2s + 6] Y(s) = 3 $e^{-2s}$ - 4 $e^{-5s}$

⇒[s(s + 3) + 2(s + 3)] Y(s) = 3 $e^{-2s}$ - 4 $e^{-5s}$

⇒[(s + 2)(s + 3)] Y(s) = 3 $e^{-2s}$ - 4 $e^{-5s}$

⇒Y(s) = $\frac{3e^{-2s} }{(s + 2)(s + 3)} - \frac{4e^{-5s} }{(s + 2)(s + 3)}$

Now,

Let

$\frac{1}{(s+2)(s+3)} = \frac{A}{s+2} + \frac{B}{s+3} \\\frac{1}{(s+2)(s+3)} = \frac{A(s + 3) + B(s+2)}{(s+2)(s+3)}\\1 = As + 3A + Bs + 2B\\1 = (A+B)s + (3A + 2B)$