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2 years ago

6

Write 3x + y < 8 in Slope Intercept form.

1 answer:

tekilochka [14]2 years ago

5 0

Answer:

y<-3x+8

Step-by-step explanation:

We are given 3x+y<8. There is exactly one step to put this in slope-intercept form, y=mx+b form where the equal sign can be an inequality sign. Our goal is to isolate y.

To do in 3x+y<8, we will just need to subtract 3x on both sides giving us y<-3x+8.

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Josie left an $8.00 tip restaurant. How many was her total bill, if the tip was 20% of the total?

givi [52]

Answer: $48
If she tipped $8.00 then the original bill was $40, and the total was $48

6 0

2 years ago

Consider the following differential equation to be solved by undetermined coefficients. y(4) − 2y''' + y'' = ex + 1 Write the gi

kompoz [17]

Answer:

The general solution is

$y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

+ $\frac{x^2}{2}$

Step-by-step explanation:

Step :1:-

Given differential equation y(4) − 2y''' + y'' = e^x + 1

The differential operator form of the given differential equation

$(D^4 -2D^3+D^2)y = e^x+1$

comparing f(D)y = e^ x+1

The auxiliary equation (A.E) f(m) = 0

$m^4 -2m^3+m^2 = 0$

$m^2(m^2 -2m+1) = 0$

$(m^2 -2m+1) this is the expansion of (a-b)^2$

$m^2 =0 and (m-1)^2 =0$

The roots are m=0,0 and m =1,1

complementary function is $y_{c} = (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x$

<u>Step 2</u>:-

The particular equation is $\frac{1}{f(D)} Q$

P.I = $\frac{1}{D^2(D-1)^2} e^x+1$

P.I = $\frac{1}{D^2(D-1)^2} e^x+\frac{1}{D^2(D-1)^2}e^{0x}$

P.I = $I_{1} +I_{2}$

$\frac{1}{D^2} (\frac{x^2}{2!} )e^x + \frac{1}{D^{2} } e^{0x}$

$\frac{1}{D} means integration$

$\frac{1}{D^2} (\frac{x^2}{2!} )e^x = \frac{1}{2D} \int\limits {x^2e^x} \, dx$

applying in integration u v formula

$\int\limits {uv} \, dx = u\int\limits {v} \, dx - \int\limits ({u^{l}\int\limits{v} \, dx } )\, dx$

$I_{1}$ = $\frac{1}{D^2(D-1)^2} e^x$

$\frac{1}{2D} (e^x(x^2)-e^x(2x)+e^x(2))$

$\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

$I_{2}$ $= \frac{1}{D^2(D-1)^2}e^{0x}$

$\frac{1}{D} \int\limits {1} \, dx= \frac{1}{D} x$

again integration $\frac{1}{D} x = \frac{x^2}{2!}$

The general solution is $y = y_{C} +y_{P}$

$y= (C_{1}+C_{1}x) e^0x+(C_{3}+C_{4}x) e^x +\frac{1}{2} (e^x(x^2-2x+2)-e^x(2(x-1)+e^x(2))$

+ $\frac{x^2}{2!}$

3 0

2 years ago

Identify if the line has a positive or negative slope. Calculate the slope of the line 2y = x - 8

saul85 [17]

Answer: m = 1/2

Step-by-step explanation: To find the slope of the line, we would first put the equation in y = mx + b form to get y by itself on the left side.

So divide both sides by 2 to get y = 1/2x - 4.

Now the slope is the coefficient of the x term which is 1/2.

This is a positive slope.

3 0

2 years ago

Rodger bowled seven games last week. His scores are: 155, 165, 138, 172, 127, 193, 142. What is the median of Rodger's score?

Damm [24]

Answer

The median is 155

Step-by-step explanation:

You get the numbers from least to greatest then the middle number is your median.

3 0

2 years ago

What is the value of x in: 4x+3y=12 and 2x-3y=-30 *

NNADVOKAT [17]

Answer:

The value would be

Step-by-step explanation:

What is the value of x in: 4x+3y=12 and 2x-3y=-30 *

4x + 3y

The answer is x = 2 - 3y = 4

3y = 30

So 2x + 3y = 12 is

X = 3 - 3y/4

2x - 3y = 30

X = 15 + 3y/2

Hope it help : ) Please Rate it for me!

Have a Great Day and Winter Break!

6 0

2 years ago