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ollegr [7]
2 years ago
6

A.) A $135 pair of shoes is on sale for 40% off. If the sales tax is 8%, what is the final price of the shoes? The shoes will co

st ______
b. A $35 jacket was markup by the store by 27%. What is the selling price of the jacket? The jacket will cost ______.
Mathematics
1 answer:
Reil [10]2 years ago
5 0

Answer:

a is 87.48.

Step-by-step explanation:

135x0.40=54

135-54=81

81x1.08= 87.48

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Which expression is equivalent to<br> (2^3)^-5
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Answer:

(2×2×2)×(2×2×2)×(2×2×2)×(2×2×2)×-(2×2×2)×(2×2×2)

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Mariulka [41]

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A

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mestny [16]

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Drag each graph to show if the system of linear equations it represents will have no
Annette [7]
Top left, none
middle, many
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3 years ago
1. (a) Solve the differential equation (x + 1)Dy/dx= xy, = given that y = 2 when x = 0. (b) Find the area between the two curves
erastova [34]

(a) The differential equation is separable, so we separate the variables and integrate:

(x+1)\dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x+1} \, dx = \left(1-\dfrac1{x+1}\right) \, dx

\displaystyle \frac{dy}y = \int \left(1-\frac1{x+1}\right) \, dx

\ln|y| = x - \ln|x+1| + C

When x = 0, we have y = 2, so we solve for the constant C :

\ln|2| = 0 - \ln|0 + 1| + C \implies C = \ln(2)

Then the particular solution to the DE is

\ln|y| = x - \ln|x+1| + \ln(2)

We can go on to solve explicitly for y in terms of x :

e^{\ln|y|} = e^{x - \ln|x+1| + \ln(2)} \implies \boxed{y = \dfrac{2e^x}{x+1}}

(b) The curves y = x² and y = 2x - x² intersect for

x^2 = 2x - x^2 \implies 2x^2 - 2x = 2x (x - 1) = 0 \implies x = 0 \text{ or } x = 1

and the bounded region is the set

\left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^2 \le y \le 2x - x^2\right\}

The area of this region is

\displaystyle \int_0^1 ((2x-x^2)-x^2) \, dx = 2 \int_0^1 (x-x^2) \, dx = 2 \left(\frac{x^2}2 - \frac{x^3}3\right)\bigg|_0^1 = 2\left(\frac12 - \frac13\right) = \boxed{\frac13}

7 0
2 years ago
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