1st and 3rd and 4th are yes
2nd and 5th are totally incorrect
Cost for travelling 1 mile = 3.75
cost 2 miles = 5.25
cost 3 miles = 6.75
cost 4 miles = 8.25
rate of change = 1.5 dollars per mile
Answer:
1) f(g(2)) = 24
2) f(g(-1)) = -4
Step-by-step explanation:
1) GIven f(x) = x²+2x and g(x) = 2x
f(g(x)) = f(2x)
f(2x) = (2x)² + 2(2x)
f(2x) = 4x² + 4x
f(g(x)) = 4x² + 4x
f(g(2)) = 4(2)² + 4(2)
f(g(2)) = 16+8
f(g(2)) = 24
2) f(x) = x+1 and g(x) = 5x
f(g(x)) = f(5x)
f(5x)= 5x + 1
f(g(x)) = 5x + 1
f(g(-1)) = 5(-1) + 1
f(g(-1)) = -5+1
f(g(-1)) = -4
175 mL at 25% concentration of alcohol contains 0.25 (175 mL) = 43.75 mL of alcohol. If <em>v</em> is the amount of the 70% solution that you use, then that amount contains 0.7<em>v</em> mL of alcohol.
Mixing these two yields a total volume of 175 mL + <em>v</em>, and it contains 43.75 mL + 0.7<em>v</em> alcohol. You want to end up with a concentration of 45%, which means the ratio of the amount of alcohol to the total volume needs to be 0.45:
(43.75 mL + 0.7<em>v</em>) / (175 mL + <em>v</em>) = 0.45
Solve for <em>v</em> :
43.75 mL + 0.7<em>v</em> = 0.45 (175 mL + <em>v</em>)
43.75 mL + 0.7<em>v</em> = 78.75 mL + 0.45<em>v</em>
0.25<em>v</em> = 35 mL
<em>v</em> = 140 mL
