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2 years ago

Solve the inequality for x. 5 is greater than or equal to 4x+9 . simplify as much as possible

Mathematics

2 answers:

gayaneshka [121]2 years ago

7 0

Answer:

For this we need to solve using the transposition method

Step-by-step explanation:

We need to shift variables and constants from the RHS to LHS sgregating the x. + becomes - and x becomes /

natima [27]2 years ago

5 0

Answer:

X ≤ - 1

Step-by-step explanation:

5 ≥ 4x + 9 ( subtract 9 from both sides )

- 4 ≥ 4x ( divide both sides by 4 )

- 1 ≥ x , then

x ≤ - 1

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Use the method of undetermined coefficients to find the general solution to the de y′′−3y′ 2y=ex e2x e−x

djverab [1.8K]

I'll assume the ODE is

$y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}$

Solve the homogeneous ODE,

$y'' - 3y' + 2y = 0$

The characteristic equation

$r^2 - 3r + 2 = (r - 1) (r - 2) = 0$

has roots at $r=1$ and $r=2$ . Then the characteristic solution is

$y = C_1 e^x + C_2 e^{2x}$

For nonhomogeneous ODE (1),

$y'' - 3y' + 2y = e^x$

consider the ansatz particular solution

$y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x$

Substituting this into (1) gives

$a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1$

For the nonhomogeneous ODE (2),

$y'' - 3y' + 2y = e^{2x}$

take the ansatz

$y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}$

Substitute (2) into the ODE to get

$b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1$

Lastly, for the nonhomogeneous ODE (3)

$y'' - 3y' + 2y = e^{-x}$

take the ansatz

$y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}$

and solve for $c$ .

$ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16$

Then the general solution to the ODE is

$\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}$

6 0

1 year ago

I need help please and thank you

Sphinxa [80]

The answer is I believe: 21

8 0

3 years ago

Simplify the algebraic expression. -2(x - 5) + 4(9 + x)

AnnZ [28]

Answer:

2x+46

Step-by-step explanation:

-2(x-5)+4(9+x), Multiply

-2x+10+36+4x, Combine like terms

Simplified= 2x+46

5 0

3 years ago

−(7 − 2x) + 7 = −7 solve for x

jekas [21]

First, remove the parentheses

-7+2x+7=-7

Cancel the equal terms.

2x+7=0

Subtract 7

2x= -7

Divide both sides by 2

Final answer is:

X= -3.5

3 0

3 years ago

Jason's piggy bank contained $5.70 in nickels and pennies. If there were 30 more pennies than nickels, how many of each did he h

ValentinkaMS [17]

Answer:

98 nickles and 128 pennies

Step-by-step explanation:

You probably can't read my hand writing but I spent like, 15 minutes on this. This is the correct answer, but I don't know how to explain how it is but I promise it is!

8 0

3 years ago