Answer:
We can describe FOIL using the distributive property of multiplication. For real numbers x, y, and z the distributive property of multiplication states that

Now let
, where v and w are real numbers.
Then 
Here, we can again use the distributive property of multiplication to get

Hence, it follows that

This is the method of FOIL (first: xv, outside: xw, inside: yv, last: yw)
For example, 
Answer:
1:2
Step-by-step explanation:
if the one side is twice the length that means that you need two of them to make the one thus the ratio 1 to 2
X² + x - 12 / x² - x - 20 ÷ 3x² - 24x + 45 / 12x² - 48x - 60
x² + x - 12 / x² - x - 20 * 12x² - 48x - 60 / 3x² - 24x + 45
<u>(x² + x - 12)(12x² - 48x - 60)</u>
(x² - x - 20)(3x² - 24x + 45)
<span><u>12x^4 - 48x³ - 60x² + 12x³ - 48x² - 60x - 144x² + 576x + 720</u>
</span>3x^4 - 24x³ + 45x² - 3x³ + 24x² - 45x - 60x² + 480x - 900
<span>
<u>12x^4 - 48x³ + 12x³ - 60x² - 48x² - 144x² - 60x + 576x + 720</u></span>
3x^4 - 24x³ - 3x³ + 45x² + 24x² - 60x² - 45x + 480x - 900
<u>12x^4 - 36x³ - 252x² + 516x + 720</u>
3x^4 - 27x³ + 9x² + 435x - 900
<u>12(x^4 - 3x³ - 21x² + 43x + 60) </u>
3(x^4 - 9x³ + 3x² + 145x + 300)
<u>4(</u><span><u>x^4 - 3x³ - 21x² + 43x + 60) </u>
</span><span> (x^4 - 9x³ + 3x² + 145x + 300)</span>
Answer:

Step-by-step explanation:
The equation
is a <em>linear equation</em>. By definition, the independent term on this equation (that is, the number that is not being multiplied by
) is the <em>y-intercept</em>, which is a fancy way of saying "the point where the line crosses the y-axis".
By looking at the equation, we know that our y-intercept is <em>c. </em>By looking at the graph, we can see that the y-intercept is -3. Therefore,
and we get the complete version of our linear equation:

Now, looking at the graph we can see that the point
lies on the line of the equation, which means that the point is a solution to our equation. All we have to do is replace
and
by the values of the given point (which are
and
, respectively), and then solve for
:

And we are done!
Answer:
y = -(3/7)x + 2
Step-by-step explanation:
(see attached)
recall that the slope-intercept form of a linear equation is
y = mx + b
where m = slope = given as -(3/7)
and b = y-intercept = 2
substituting these values into the eqation:
y = mx + b
y = -(3/7)x + 2