First combine like terms:
14d+-2d=12d
Then do -84 divided by 12 = -7
D= -7
For the mix you need 60 Ib of nuts and raisins, and 60 lb of mix will sell for $300.
Let <em>x</em> be the weight of nuts and <em>y</em> the weight of raisins needed for the mix.
Total weight = <em>x</em>+<em>y</em> = 60, so <em>y</em> = 60 - <em>x</em>
Total value = 6<em>x</em> + 3<em>y</em> = 300. From the above, we can substitute the <em>y</em> for 60 - x:
Total value = 6<em>x</em> + 3(60 - <em>x</em>) = 300, which we can simplify to:
6<em>x</em> + 180 - 3<em>x</em> = 300, and simplify again to:
3<em>x</em> = 120, and again to:
<em>x</em> = 40. We can now calculate<em> y</em> from the first equation y = 60 - <em>x</em>, so:
y = 20.
40 lb of nuts and 20 lb of raisins. Check:
40 lb x $6/lb = $240, and 20 lb x $3/lb = $60, $240 + $60 = $300.
True; this statement is true.
<h3>
Answer: B) y = -x</h3>
==============================================
Work Shown:
g(x) = x^2-2
g(-2) = (-2)^2-2
g(-2) = 2
Saying (-2, g(-2)) is the same as saying (-2, 2)
---------------
g(x) = x^2-2
g(1) = 1^2 - 2
g(1) = -1
Saying (1, g(1)) is the same as saying (1, -1)
---------------
Let's find the slope of the line through (-2,2) and (1,-1)
m = (y2 - y1)/(x2 - x1)
m = (-1-2)/(1-(-2))
m = (-1-2)/(1+2)
m = -3/3
m = -1
Now turn to point slope form to find the equation
y - y1 = m(x - x1)
y - 2 = -1(x - (-2))
y - 2 = -(x + 2)
y - 2 = -x - 2
y-2+2 = -x-2+2 ... add 2 to both sides
y = -x
You could use the other point (1,-1) and you'd get the same answer. The slope m = -1 is the same each time.
