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3 years ago

Justin is asked to solve the following system of linear equations using the elimination method.

Mathematics

1 answer:

romanna [79]3 years ago

3 0

Alright, lets get started.

Justin is asked to solve the linear equations using elimination method.

By using elimination method means we have to multiply some numbers in our given equations in such a way that the co-efficient of x or y become same in both equations so that we could add or subtract them to cancel one of the term either x or y.

So, given equations are :

$5x - 12 = 3$

$-20x + 14 y = 13$

See we have 5x in first equation and -20x in second equation.

So, we try to change 5x into 20 x by multiplying it with 4, both of the equations will have 20 x in common

Lets multiply 4 in first equation

$4 * (5x-12y) = 4 * 3$

$20x - 48y = 12$

Now both equations could be added and 20 x will be cancelled out and we could easily find the value of y then solve for x.

So, Justin should try to change 5 so that it will be cancels, so option B : Answer

Hope it will help :)

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Joan took her three children to the zoo. Admission is $7 each. The snack bar sells water for $2 per bottle and chips for $3 per

lys-0071 [83]

The expression for the total cost of their trip is 7 + 2x + 3y.

As per the question, assuming the number of bottles to be x and number of bags to be y. The equation will have one time fee of admission, product of cost of bottles and number of bottles and product of cost of bags and number of chips bags.

The one time fee and two products will be added to form the expression. Forming the equation now -

Expression = 7 + 2x + 3y

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11 months ago

Ally ran 5 miles in 6 minutes. Sami ran 6 mile. If ally ran at a faster rate than Sami ,in how many minutes could Sami have run

Veseljchak [2.6K]

Answer:6 minutes
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3 years ago

Read 2 more answers

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melomori [17]

2 is 2
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3 years ago

A school store buys pencils in bulk and sells them to students for a small profit. The school pays $2.00 for 100 pencils and sel

Valentin [98]

Answer:

1,000 pencils

Step-by-step explanation:

First, there are 10,000 cents in $100.

So divide 10,000 by 10.

1,000.

I hope this helps!

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3 years ago

Find the differential coefficient of <br><img src="https://tex.z-dn.net/?f=e%5E%7B2x%7D%281%2BLnx%29" id="TexFormula1" title="e^

Gemiola [76]

Answer:

$\rm \displaystyle y' = 2 {e}^{2x} + \frac{1}{x} {e}^{2x} + 2 \ln(x) {e}^{2x}$

Step-by-step explanation:

we would like to figure out the differential coefficient of $e^{2x}(1+\ln(x))$

remember that,

the differential coefficient of a function y is what is now called its derivative y', therefore let,

$\displaystyle y = {e}^{2x} \cdot (1 + \ln(x) )$

to do so distribute:

$\displaystyle y = {e}^{2x} + \ln(x) \cdot {e}^{2x}$

take derivative in both sides which yields:

$\displaystyle y' = \frac{d}{dx} ( {e}^{2x} + \ln(x) \cdot {e}^{2x} )$

by sum derivation rule we acquire:

$\rm \displaystyle y' = \frac{d}{dx} {e}^{2x} + \frac{d}{dx} \ln(x) \cdot {e}^{2x}$

Part-A: differentiating $e^{2x}$

$\displaystyle \frac{d}{dx} {e}^{2x}$

the rule of composite function derivation is given by:

$\rm\displaystyle \frac{d}{dx} f(g(x)) = \frac{d}{dg} f(g(x)) \times \frac{d}{dx} g(x)$

so let g(x) [2x] be u and transform it:

$\displaystyle \frac{d}{du} {e}^{u} \cdot \frac{d}{dx} 2x$

differentiate:

$\displaystyle {e}^{u} \cdot 2$

substitute back:

$\displaystyle \boxed{2{e}^{2x} }$

Part-B: differentiating ln(x)•e^2x

Product rule of differentiating is given by:

$\displaystyle \frac{d}{dx} f(x) \cdot g(x) = f'(x)g(x) + f(x)g'(x)$

let

$f(x) \implies \ln(x)$
$g(x) \implies {e}^{2x}$

substitute

$\rm\displaystyle \frac{d}{dx} \ln(x) \cdot {e}^{2x} = \frac{d}{dx}( \ln(x) ) {e}^{2x} + \ln(x) \frac{d}{dx} {e}^{2x}$

differentiate:

$\rm\displaystyle \frac{d}{dx} \ln(x) \cdot {e}^{2x} = \boxed{\frac{1}{x} {e}^{2x} + 2\ln(x) {e}^{2x} }$

Final part:

substitute what we got:

$\rm \displaystyle y' = \boxed{2 {e}^{2x} + \frac{1}{x} {e}^{2x} + 2 \ln(x) {e}^{2x} }$

and we're done!

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3 years ago