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photoshop1234 [79]
3 years ago
14

The difference of two numbers is 15. Five times the smaller is the same as 9 less than twice the larger. Find the numbers

Mathematics
1 answer:
Usimov [2.4K]3 years ago
6 0

Answer:

x= -13

y= -28

Step-by-step explanation:

To find the two numbers, write a system of equations with x as one number and y as another:

x-y=15

5x=2y-9

Use substitution to substitute one equation into another. Then solve for the variable.

x=15+y into 5x=2y-9

becomes

5(15+y) = 2y-9

75+5y = 2y- 9

75+3y= -9

3y = -84

y= -28

To find x, substitute y= -28 into one equation.

x - (-28) = 15

x+28 =15

x = 15-28

x=-13




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Step-by-step explanation:

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In Exercise, find the derivative of the function.<br> y = 3ex - xex
nevsk [136]

Answer:

the question is incomplete, the complete question is "find the derivative of the function y=3e^{x}-xe^{x}"

answer: \frac{dy}{dx}=(2-x)e^{x}.

Step-by-step explanation:

From the equation,  y=3e^{x}-xe^{x}, we approach the question using the differentiation of a product and differentiation of a sum simultaneously,

the differentiation of a sum is express as

f(x)=u(x)+v(x)+.....w(x) then

\frac{df(x)}{dx}=\frac{du(x)}{dx}+\frac{dv(x)}{dx}+...\frac{dw(x)}{dx}.\\

For the differentiation of a product we have

 f(x)=u(x)v(x), then

\frac{df(x)}{dx}=\frac{dv(x)}{dx}u(x)+\frac{du(x)}{dx}v(x)

hence if we go by the formula we arrive at

for   y=3e^{x}

let u(x)=3 hence du/dx=0 and

v(x)=e^{x} and \frac{dv(x)}{dx}=e^{x}

hence \frac{dy}{dx}=3e^{x}+0e^{x}\\\frac{dy}{dx}=3e^{x}---equation 1\\

Also for y=-xe^{x}\\\frac{dy}{dx}=-e^{x}-xe^{x}---equation 2.

if we add equation 1 and equation 2 we arrive at

\frac{dy}{dx}=3e^{x}-e^{x}-xe^{x}\\\frac{dy}{dx}=(3-1-x)e^{x}\\\frac{dy}{dx}=(2-x)e^{x}.

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Determine the solution to the following system of equations: x + y = -3x - y = 1
Zina [86]

Answer:

( -1,-2)

Step-by-step explanation:

x + y = -3

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Add the two equations together to eliminate y

x + y = -3

x - y = 1

------------------

2x = -2

Divide by 2

2x/2 = -2/2

x = -1

Now find y

x+y =-3

-1 +y = -3

-1+1 +y = -3+1

y = -2

( -1,-2)

5 0
3 years ago
Which expression is equivalent to the given expression?<br> (- 1/2 y + 1/4)
PSYCHO15rus [73]

Answer:

-\left(\dfrac{1}{2}y+\dfrac{1}{4}\right)=-\dfrac{1}{2}y-\dfrac{1}{4}=-\dfrac{1\cdot2}{2\cdot2}y-\dfrac{1}{4}=\dfrac{-2y}{4}-\dfrac{1}{4}=\dfrac{-2y-1}{4}\\\\=-\dfrac{2y+1}{4}

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2.0

3 votes

THANKS 4

Report

Step-by-step explanation:

4 0
4 years ago
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