28: 1, 2, 4, 7, 14, 28
40: 1, 2, 4, 5, 8, 10, 20, 40
The common factors are 1, 2, and 4.
You can use a factor rainbow to help you find the factors (:
you cannot show too much "work"
basically, you remove what is common to all of the factors, and then put brackets, as it will be multiplied back in, remember that when you multiply exponents with the same base, its same as adding them, so subtract to remove...
you can seperate two of the variables , then factor, then subtract the last one from those two, because it cannot be factored out , as in part2 #2
Answer:
Y1 intercept = 2
(0,2) (3,-7)
m= (-7 - 2) / (3-0) =-9/3 = - 3
Then y = - 3x + 2
Y2 intercept = - 8
(0,-8) (3,-7)
m = (-7 - - 8) / (3-0) = 1/3
Then y= (1/3)x-8
The tangent line to <em>y</em> = <em>f(x)</em> at a point (<em>a</em>, <em>f(a)</em> ) has slope d<em>y</em>/d<em>x</em> at <em>x</em> = <em>a</em>. So first compute the derivative:
<em>y</em> = <em>x</em>² - 9<em>x</em> → d<em>y</em>/d<em>x</em> = 2<em>x</em> - 9
When <em>x</em> = 4, the function takes on a value of
<em>y</em> = 4² - 9•4 = -20
and the derivative is
d<em>y</em>/d<em>x</em> (4) = 2•4 - 9 = -1
Then use the point-slope formula to get the equation of the tangent line:
<em>y</em> - (-20) = -1 (<em>x</em> - 4)
<em>y</em> + 20 = -<em>x</em> + 4
<em>y</em> = -<em>x</em> - 24
The normal line is perpendicular to the tangent, so its slope is -1/(-1) = 1. It passes through the same point, so its equation is
<em>y</em> - (-20) = 1 (<em>x</em> - 4)
<em>y</em> + 20 = <em>x</em> - 4
<em>y</em> = <em>x</em> - 24