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3 years ago

Solve the system of equations using substitution -3x + 2y = 12 x = 2y - 8

Mathematics

1 answer:

SCORPION-xisa [38]3 years ago

5 0

Answer:

(-2, 3)

Step-by-step explanation:

Given the system of equations:

-3x + 2y = 12

x = 2y - 8

You can 'substitute' the expression '2y - 8' for the value of 'x' in the first equation and solve for 'y':

-3(2y - 8) + 2y = 12

Distribute: -6y + 24 + 2y = 12

Combine like terms: -4y + 24 = 12

Subtract 24 from both sides: -4y + 24 - 24 = 12 - 24 or -4y = -12

Divide both sides by -4: -4y/-4 = -12/-4 or y = 3

Use y = 3 to solve for 'x':

x = 2(3) - 8 or 6 - 8

x = -2

(-2, 3)

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− 3 ( 7 − 2 x ) = − 1 − 4 x

Bogdan [553]

Answer:

5208

Step-by-step explanation:

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2 years ago

Find f if f′(x)=2x−3/x^4, x>0 and f(1)=2.

slavikrds [6]

$f'(x)=2x-\dfrac3{x^4}$
$\displaystyle\int f'(x)\,\mathrm dx=\int\left(2x-\frac3{x^4}\right)\,\mathrm dx$
$f(x)=x^2+\dfrac1{x^3}+C$

Given that $f(1)=2$ , we get

$2=1^2+\dfrac1{1^3}+C$
$2=2+C$
$\implies C=2$

so that

$f(x)=x^2+\dfrac1{x^3}$

8 0

3 years ago

How to use substitution to solve system of equations

svlad2 [7]

Answer: See explanation.

Step-by-step explanation:

Let's assume that you have a System of two equations. You can solve this System using the Substitution Method.

In order to use that method to solve the System of equations, you can follow the steps shown below:

Step 1: You must choose one of the equations of the system and solve for one of the variables. Let's call this new equation "Equation A"

Step 2: Then you must substitute"Equation A" into the other equation.

Step 3: Now you must solve for the other variable in order to find its value.

Step 4: Finally, you need to substitute the value of the variable obtained in the previous step, into the "Equation A" and then evaluate in order to find the value of the other varibale.

(Note: You can also substitute the value of the variable calculated in Step 3 into any original equation and solve for the other variable to find its value).

4 0

3 years ago

Melissa Costouras obtains a $3,000 loan for darkroom equipment. She makes six monthly payments of $511.18. Determine the APR.

nasty-shy [4]

Using the simple interest formula, it is found that the APR for the loan is of 4.472%.

<h3>What is the simple interest formula and when it is used?</h3>

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

$A(t) = A(0)(1 + rt)$

In which:

A(0) is the initial amount.

r is the interest rate, as a decimal.

The parameters for this problem are:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

We solve the equation for r to find the APR.

$A(t) = A(0)(1 + rt)$

$3067.08 = 3000(1 + 0.5r)$

$1 + 0.5r = \frac{3067.08}{3000}$

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

More can be learned about simple interest at brainly.com/question/25296782

#SPJ1

5 0

1 year ago

Point Z is translated right 1,done 8. Which is the coordinate pair for the translated point Z. A.(1.4) B.(1,-4) C.(4,-1) D.(-8,1

nikdorinn [45]

Assuming point Z is at the origin (0,0), you move from the origin over to the right one, and go down 8.
Therefore you would be at point (1,-8) answer D

7 0

3 years ago