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3 years ago

Solving systems of equations algebraically. y = x + 2 y= 3x -2 And SHOW YOUR WORK!!!!

Mathematics

1 answer:

matrenka [14]3 years ago

6 0

Answer:

x = 2

y = 4

Step-by-step explanation:

Since it gives you the "value" of y, just plug one of them into an equation:

y = x + 2

3x - 2 = x + 2

Now, subtract x from both sides:

3x - 2 = x + 2

-x - x

__________

2x - 2 = 2

Then, add 2 to both sides:

2x - 2 = 2

+ 2 + 2

________

2x = 4

Finally, divide both sides by 2:

2x = 4

x = 2

Now to get y, just plug in 2 for x in an equation:

y = x + 2

y = 2 + 2

y = 4

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The perimeter of a rectangle is 56 inches. The rectangle is 20 inches long. How wide is the rectangle?

Mamont248 [21]

Answer:

The answer is A 8 inches

Step-by-step explanation:

If the perimeter is 56 inches and it is 20 inches long, then you would multiply 20 by two and get 40, then you subtract 40 from 56 and get 16. Finally, you divide 16 by two and get 8. So, A 8 inches will be your answer.

5 0

3 years ago

Solve the equation: w^2+7w+12=0

polet [3.4K]

Hi there!
We are given the equation w² + 7w + 12 = 0, and we are told to solve it. Well, we can first take all the factors of 12 -
1 12
2 6
3 4
Now, take the sum of each factor pair -
1, 12 = 13
2, 6 = 8
3, 4 = 7
Find which factor pair adds up to 7, and we can see that 3 and 4 add up to seven, while also having a product of 12. Therefore, since the whole equation has addition signs, we can factor the equation w² + 7w + 12 into (w + 3)(w + 4) = 0. Next, using the Zero Product Property, we can set each term to zero.
w + 3 = 0
w = -3

w + 4 = 0
w = -4
Therefore, the solution to the equation w² + 7w + 12 = 0 is w = -3, -4. Hope this helped and have a great day!

7 0

3 years ago

Find the distance between the points (-5, -10) and (2, 4).

Basile [38]

i am certain that this is the answer

4 0

3 years ago

Read 2 more answers

Hillary is making a blanket for her mom. Three fourths of the blanket is green and the rest is yellow. Two thirds of the yellow

Leviafan [203]

Answer:

1/6

Step-by-step explanation:

Hillary is making a blanket for her mom.

Let the total blanket = 1

Three-fourths of the blanket is green and the rest is yellow.

The fraction for the rest(yellow portion) = 1 - 3/4

The Lowest Common Denominator is 4

Hence,

4 - 3 /4 = 1/4

Two-thirds of the yellow part has her name on it.

The fraction of the blanket that will have her name on it is calculated as

2/3 of 1 /4

= 2/3 × 1/4

= 1/6

4 0

3 years ago

Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficie

Dvinal [7]

For part (a), you have

$\dfrac x{x^2+x-6}=\dfrac x{(x+3)(x-2)}=\dfrac a{x+3}+\dfrac b{x-2}$
$x=a(x-2)+b(x+3)$

If $x=2$ , then $2=b(2-3)\implies b=-2$ .

If $x=-3$ , then $-3=a(-3-2)\implies a=\dfrac35$ .

So,

$\dfrac x{x^2+x-6}=\dfrac 3{5(x+3)}-\dfrac 2{x-2}$

For part (b), since the degrees of the numerator and denominator are the same, you first need to find the quotient and remainder upon division.

$\dfrac{x^2}{x^2+x+2}=\dfrac{x^2+x+2-x-2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}$

In the remainder term, the denominator $x^2+x+2$ can't be factorized into linear components with real coefficients, since the discriminant is negative $(1-4\times1\times2=-7)$ . However, you can still factorized over the complex numbers, so a partial fraction decomposition in terms of complexes does exist.

$x^2+x+2=0\implies x=-\dfrac12\pm\dfrac{\sqrt7}2i$
$\implies x^2+x+2=\left(x-\left(-\dfrac12+\dfrac{\sqrt7}2i\right)\right)\left(x-\left(-\dfrac12-\dfrac{\sqrt7}2i\right)\right)$
$\implies x^2+x+2=\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)$

Then you have

$\dfrac{x+2}{x^2+x+2}=\dfrac a{x+\dfrac12-\dfrac{\sqrt7}2i}+\dfrac b{x+\dfrac12+\dfrac{\sqrt7}2i}$
$x+2=a\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)+b\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)$

When $x=-\dfrac12-\dfrac{\sqrt7}2i$ , you have

$-\dfrac12-\dfrac{\sqrt7}2i+2=b\left(-\dfrac12-\dfrac{\sqrt7}2i+\dfrac12-\dfrac{\sqrt7}2i\right)$
$\dfrac32-\dfrac{\sqrt7}2i=-\sqrt7ib$
$b=\dfrac12+\dfrac3{2\sqrt7}i=\dfrac1{14}(7+3\sqrt7i)$

When $x=-\dfrac12+\dfrac{\sqrt7}2i$ , you have

$-\dfrac12+\dfrac{\sqrt7}2i+2=a\left(-\dfrac12+\dfrac{\sqrt7}2i+\dfrac12+\dfrac{\sqrt7}2i\right)$
$\dfrac32+\dfrac{\sqrt7}2i=\sqrt7ia$
$a=\dfrac12-\dfrac3{2\sqrt7}i=\dfrac1{14}(7-3\sqrt7i)$

So, you could write

$\dfrac{x^2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}=1-\dfrac {7-3\sqrt7i}{14\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)}-\dfrac {7+3\sqrt7i}{14\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)}$

but that may or may not be considered acceptable by that webpage.

5 0

3 years ago

Read 2 more answers