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2 years ago

7

Solve the inequality −8≤8+y

1 answer:

Tcecarenko [31]2 years ago

6 0

Answer: -16 ≤ y

Step-by-step explanation: All we need to do is subtract 8 on both sides.

Hope this helped! :)

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A man buys furniture that has a list price of $255. He is allowed a discount of 12% but must pay a sales tax of 3% on the cost.

andriy [413]

I find it easiest to subtract and add the percentages to make a multiplier, then use that.

After the man's discount, he pays (100% - 12%) = 88% of the list price. After tax, he pays (100% + 3%) = 103% of the discounted price.

The amount he actually pays is $255×0.88×1.03 = $231.13.

The best choice is ...
(B) $231.13

7 0

3 years ago

Read 2 more answers

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

Carmen is making gift boxes for her friends. It takes her 10 minutes to pack a 4-pound treat box, and it takes her 15 minutes to

Darya [45]

Answer:

(5.2) for sure

Step-by-step explanation:

4 0

2 years ago

Uhm help please no links -^-

devlian [24]

Answer:

<u>x = 58</u>

Step-by-step explanation:

180 - 148 = 32

32 + 90 + x = 180

122 + x = 180

180 - 122 = x

x = 58

Have a nice day!

6 0

2 years ago

Read 2 more answers

What is -five sixths time six fifths

s2008m [1.1K]

Answer:

-five sixths= -5/6

six fifths= 6/5

times= multiplication

so , -5/6 x 6/5 = -1

(both sixes get cancelled and the fives also get cancelled to get -1/1 = -1)

8 0

3 years ago