The answer to this question is 5a^2-6a+20+(-175a+102)over(5a^2+6a-9)
HOW TO SOLVE:
1) use x as a variable
2) the starting equation is:
4x + 3x + 5x = 18
3) add all the like terms on the left side of the equation:
12x = 18
4) Divide by 12 on both sides:
x=1.5
5) Find the lengths of the sides:
- 4x = 4(1.5) = 6
- 3x = 3(1.5) = 4.5
- 5x = 5(1.5) = 7.5
SO, the lengths of the sides of this triangle are: 6, 4.5, and 7.5
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
Answer:
(i) 15 m, 6 m/s
(ii) 90 m
Step-by-step explanation:
(i) For some acceleration (a) from rest, the distance covered (d) in time t is ...
d = (1/2)at^2
The distance covered by Ben in the 5 seconds he is accelerating is ...
d = (1/2)(1.2 m/s²)(5 s)² = 15 m
Of course, Ben's speed at that point is ...
s = (1.2 m/s²)(5 s) = 6 m/s
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(ii) When Ben has been walking 5 s, Alan has been walking 10 s, so Alan has covered (10 s)(4 m/s) = 40 m. Their distance difference of 40 -15 = 25 m is being made up at the rate of their speed differences: (6 m/s) -(4 m/s) = 2 m/s.
It will take (25 m)/(2 m/s) = 12.5 s additional time for Ben to catch Alan. In the 22.5 s that Alan has been walking before they meet, he will have walked ...
(22.5 s)(4 m/s) = 90 m . . . the distance OP
2x - 17?
= -17 +2x (using commutative property of addition, changing order and sum remains the same)
answer is A) -17 + 2x
