Answer:
For f(x) = 2x + 3 and g(x) = -x 2 + 1, find the composite function defined by (f o g)(x)
(f o g)(x) = f(g(x))
= 2 (g(x)) + 3
= 2( -x 2 + 1 ) + 3
= - 2 x 2 + 5 Given f(2) = 3, g(3) = 2, f(3) = 4 and g(2) = 5, evaluate (f o g)(3)
Step-by-step explanation:
So firstly, we have to find f(x) when x = 8 and x = 0. Plug the two numbers into the x variable of the function to solve for their f(x):
Now that we have their y's, we can use the slope, aka average rate of change, formula, which is 
. Using what we have, we can solve it as such:
In short, the average rate of change from x = 0 to x = 8 is 5/21.
175000 / 100 = 1750 this step finds 1% of 175000
1750 x 4.5 = 7875 this step finds 4.5% of 175000
Commission for first house $7875
199000 / 100 = 1990 this step finds 1% of 199000
1990 x 4.5 = 8955 this step finds 4.5% of 199000
Commission for second house $8955
$7875 + $8955 = $16,830
Kensho's commission for this quarter is $16,830
Two ratios that are equivalent are the same in value. We call these equivalent ratios. To find an equivalent ratio multiply or divide both of the numbers by a common number (or same number), this would be the exact same when finding equivalent fractions as well.
<span>part A:
Let
t = total the liquid in the bottle including lemon juice and water
so t = lemon juice + water ( w = water, l = lemon juice) so t = l + w
but the bottle has 1 liter of water. and <span>60% lemon juice
</span>contains 60% lemon juice = 0.6, so l = 0.6t and w(water ) = 1 liter
t = l + w
substitute l = 0.6t and w = 1 into t = l + w
now you have equation
t = 0.6t + 1
part B:
from part A, you have equation t = 0.6t +1
solve for t
t = 0.6t +1
subtract 0.6t on both sides
t - 0.6t = 0.6t - 0.6t + 1
simplify
0.4t = 1
divide both sides by 0.4
0.4t/0.4 = 1/ 0.4
simplify
t = 2.5
2.5 liters is total including lemon juice and water
2.5 - 1(1 liter of water) = 1.5 <span>1 liter of lemon juice</span></span>
