Yay, love these ones.
First of all, (4x-+3)(-2x-5) is the same as (4x-3)(-2x-5)
So the method for solving these can be remembered by FOIL.
F= Firsts O= Outsides I= Insides L= Lasts
In other words everything is multiplied by everything, for example:
4x * -2x and -3 * -5 <span>is the firsts of the brackets multiplied and last of the brackets mulitplied
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4x * -5 and 3 * -2x is the outsides of the brackets multiplied and the insides of the brackets multiplied
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The SUM of FOIL is then added:</span><span>
</span><em>4x*-2x = -8x^2</em>
<em>-3*-5= 15</em>
<em>4x*-5=-20x</em>
<span><em>3*-2x=-6x</em>
</span><span>-8x^2 -20x -6x + 15 = 0
-8x^2 -26x + 15 = 0
So the factored of (4x-3)(-2x-5) <u /><em>=</em> -8x^2 -26x + 15 = 0
So then you graph that equation on your given grid
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The answer is... Just use a calculator
First time 23 words
after week 26 words
after two weeks 29 words
so after 1 week Alfred is faster on 3 words
so after 4 weeks he could type 35 words per minute
Hi there!
a. 8x^2 - 1
(x^2 - 4x + 5) + (7x^2 + 4x - 6)
= x^2 + 7x^2 - 4x + 4x - 1
= 8x^2 - 1
b. 5x^2 + 7x - 7
(7x^2 + 4x - 6) - (2x^2 - 3x + 1)
= 7x^2 + 4x - 6 - 2x^2 + 3x - 1
= 7x^2 - 2x^2 + 4x + 3x - 6 - 1
= 5x^2 + 7x -7
Hope this helps!
Hello,
The rate of change is the slope (rise/run, y/x). To find that, we use the equation (y2-y1) over (x2-x1). It means take the second "y" and subtract it from the first "y" and the same to "x". If I plug in the numbers, it would be (3-6) over (5-4), and after you subtract, the answer simplifies to: -3/ 1 which is -3. Yay! We got the slope (rate of change) done.
Now let's find the y-intercept by using the formula of point-slope form,
y-y1= m (slope) (x-x1). This is saying you "y" is subtracted from the first
"y" of the points which equals the slope (m) times the quantity of "x" subtracted by the first "x" of the points.
Let's plug the numbers in: y-6 = -3 (x-4). Let's distribute -3 to the parenthesis, and after that it should simplify to: y-6 = -3x + 12. To get "y" by itself, add 6 to both sides: y = -3x +18. We have finally found the slope-intercept equation for those two points (4,6) and (5,3). To then find the y-intercept in this equation, it would be the 18, because -3 is the slope, so that makes 18 the y-intercept.
In conclusion, the rate of change is -3 and the y-intercept is 18.
I hope this helps!
May
