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4 years ago

Solve the system of linear equations below.

Mathematics

1 answer:

sergiy2304 [10]4 years ago

6 0

Answer:

Step-by-step explanation:

Let's use the addition/elimination method to solve this. If we multiply the first equation through by -1 we can eliminate the x terms. Doing that gives us:

-x + 3y = 3

x + 3y = 9

The x's subtract each other away leaving us with

6y = 12 so

y = 2.

Now we will plug in 2 for y in either of the original equations to solve for x:

x + 3(2) = 9 and

x + 6 = 9 so

x = 3

The coordinate for the solution is (3, 2) or x = 3, y = 2

The second choice down is the one you want.

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HELP PLEASE !

olchik [2.2K]

Answer:

b=2

Step-by-step explanation:

Changing the y-intercept would move the graph down or up.

So we have the equation $y=\frac{-2}{3}x+5$ .

We want to move the graph down 3 units. We want the y-intercept to be 3 units lower than what is was. Since 5-3 is 2, then the new y-intercept is 2.

The equation would then be $y=\frac{-2}{3}x+2$ .

So b=2.

7 0

3 years ago

If the area of a rectangle is x^2+7x+12, what is the expression for the perimeter?

Cerrena [4.2K]

Length = 13 = (x + 3)

Width = 14 = (x + 4)

x2 + 7x + 12 = area of the rectangle

can be factored into

(x + 3)(x + 4)

Let L = one of the factors (x + 3)

Let W = the other factor (x + 4)

If x = 10 then

(10 + 3) = 13 = L

(10 + 4) = 14 = W

Checking this can be checked a couple of ways

Plug x = 10 into the original equation

x2 + 7x + 12

102 + 7(10) 12 = 100 + 70 + 12 = 182 = Area

Multiplty the factors

L x W = 13 x 14 = 182 = Area

I hope you find this useful if you have any questions please send me a message.

3 0

3 years ago

Nola hiked down a trail at a steady rate for 10 minutes. Her change in elevation was -200 feet. Then she continued to hike down

DedPeter [7]

The <em><u>correct answer</u></em> is:

The faster rate is when she hiked down 200 feet in 10 minutes.

Explanation:

The rate of change is given by the change in y over the change in x; in this case, the change in elevation over the change in time.

For the first part of the hike, the change in elevation was -200 and the change in time was 10; this gives us a rate of change of -200/10 = -20.

For the second part of the hike, the change in elevation was -300 and the change in time was 20; this gives us a rate of change of -300/20 = -15.

She hiked downhill faster during the first part of the hike, at 20 feet per minute.

8 0

3 years ago

7x+49=2x+94 solve for x

Illusion [34]

Answer: x=9

Step-by-step explanation:

7x=2x+45

5x=45

x=9

4 0

3 years ago

Read 2 more answers

The quotient of (x^3+3x^2-4x-12)/(x^2+5x+6)

Elis [28]

Answer: The quotient is (x-2).

Step-by-step explanation:

Since we have given that

$f(x)=(x^3+3x^2-4x-12)\\\\and\\\\g(x)=x^2+5x+6\\\\So,\ \frac{\left(x^3+3x^2-4x-12\right)}{\left(x^2+5x+6\right)}$

Now, we have to find the quotient of the above expression.

So, here we go:

$Factorise\ (x^3+3x^2-4x-12)\\\\=\left(x^3+3x^2\right)+\left(-4x-12\right)\\\\=-4\left(x+3\right)+x^2\left(x+3\right)\\\\=\left(x+3\right)\left(x^2-4\right)$

Now, we will divide the above simplest form with g(x):

$\frac{\left(x+3\right)\left(x^2-4\right)}{\left(x+2\right)\left(x+3\right)}\\\\=\frac{x^2-4}{x+2}\\\\=\frac{\left(x+2\right)\left(x-2\right)}{x+2}\ using\ (a^2-b^2)=(a+b)(a-b)\\\\=x-2$

Hence, the quotient is (x-2).

6 0

3 years ago

Read 2 more answers