Please help! im timed! ill give 20 more points if you're correct

san4es73 [151]

Step-by-step explanation:

Step 1: Determine an ordered pair

A solution of an equation just means that the point lies on the line. We can find any y-value when we plug in a specific x-value. For example, if we want to know what ordered pair lies at x=1, we just plug in y = -1/2(1) and solve for y which gives us -1/2. This gives us an ordered pair of (1, -1/2). We can continue to do this for any x value.

We can also reverse the order and plug in the y-value and get the x-value in order to accomplish the same goal but it's a bit harder.

Hope this helps!

6 0

1 year ago

Read 2 more answers

Find the partial fraction decomposition of the rational expression with prime quadratic factors in the denominator

SpyIntel [72]

$\dfrac{5x^4-7x^3-12x^2+6x+21}{(x-3)(x^2-2)^2}=\dfrac{a_1}{x-3}+\dfrac{a_2x+a_3}{x^2-2}+\dfrac{a_4x+a_5}{(x^2-2)^2}$
$\implies 5x^4-7x^3-12x^2+6x+21=a_1(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(a_4x+a_5)(x-3)$

When $x=3$ , you're left with

$147=49a_1\implies a_1=\dfrac{147}{49}=3$

When $x=\sqrt2$ or $x=-\sqrt2$ , you're left with

$\begin{cases}17-8\sqrt2=(\sqrt2a_4+a_5)(\sqrt2-3)&\text{for }x=\sqrt2\\17+8\sqrt2=(-\sqrt2a_4+a_5)(-\sqrt2-3)\end{cases}\implies\begin{cases}-5+\sqrt2=\sqrt2a_4+a_5\\-5-\sqrt2=-\sqrt2a_4+a_5\end{cases}$

Adding the two equations together gives $-10=2a_5$ , or $a_5=-5$ . Subtracting them gives $2\sqrt2=2\sqrt2a_4$ , $a_4=1$ .

Now, you have

$5x^4-7x^3-12x^2+6x+21=3(x^2-2)^2+(a_2x+a_3)(x-3)(x^2-2)+(x-5)(x-3)$
$5x^4-7x^3-12x^2+6x+21=3x^4-11x^2-8x+27+(a_2x+a_3)(x-3)(x^2-2)$
$2x^4-7x^3-x^2+14x-6=(a_2x+a_3)(x-3)(x^2-2)$

By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that $a_2x^4=2x^4$ and $a_3(-3)(-2)=6a_3=-6$ . These alone tell you that you must have $a_2=2$ and $a_3=-1$ .

So the partial fraction decomposition is

$\dfrac3{x-3}+\dfrac{2x-1}{x^2-2}+\dfrac{x-5}{(x^2-2)^2}$

7 0

2 years ago

Dibuje la gráfica de la ecuación 2x + 3y = 6

Llana [10]

Answer:

y=3-3/2

Step-by-step explanation:

8 0

2 years ago

A football team lost five yards on each of two consecutive plays. Find the total change in yardage.

maria [59]

Answer:

The change is a loss of 10 yards, so -10 yards.

Step-by-step explanation:

The total change in yardage after 2 plays is the sum of the yardage of each play.

What lost yardage means?

Lost yardage means negative yardage.

Imagine that in a Buffalo Bills game, Devin Singletary lost 2 yards on his first carry. So his total yardage is -2.

If in the next carry he gets 3 yards, his total yardage is 1. If he loses 1, his total yardage is -3.

First play

Loss of 5 yards.

So the first play counts for -5 yards.

Second play

Loss of 5 yards.

So the second play counts for -5 yards.

Total

-5 - 5 = -10

The change is a loss of 10 yards, so -10 yards.

8 0

2 years ago

Find an equation perpendicular to x=1 and passing through (8,-9)

valina [46]

Answer:

$y=-9$

Step-by-step explanation:

We want to find an equation of a line that's perpendicular to x=1 that also passes through the point (8,-9).

Note that x=1 is a vertical line since x is 1 no matter what y is.

This means that if our new line is perpendicular to the old, then it must be a horizontal line.

So, since we have a horizontal line, then our equation must be our y-value of our point.

Our y-coordinate of our point (8,-9) is -9.

Therefore, our equation is:

$y=-9$

And this is in standard form.

And we're done!

3 0

2 years ago