Let
x-->volume of white vinegar you need to add to the mixture (measured in cups)
<span>then
the amount of the pure vinegar in the mixture will be -----> (10*0.1 + x) cups
t</span>he volume of liquid will be ---------> 10 + x
the concentration equation is-------> [(10*0.1 + x)/(10+x)]=0.50<span>multiply both sides by (10+x) and then simplify
</span>(10*0.1 + x)=(10+x)*0.50-----------> 1+x=5+0.50x-------> 0.50x=4
x=8
the answer is
<span>you need to add 8 of a cup of the pure vinegar to the mixture</span>
Answer:
c=56.3
Step-by-step explanation:
Sorry for the bad writing and diagram haha
Answer:
$50.08
Step-by-step explanation:
We use x to represent the price of the cheapest hat. Since the more expensive hat is twice the price of the cheaper one, we use 2x to represent it. Therefore x + 2x, or 3x, equals $75.12. Divide 75.12 by 3 to find x, which is 25.04. The more expensive hat is 2x, so we must multiply 25.04 by 2 to find the price of the more expensive hat.
Answer:
x = 1, y = 10
Step-by-step explanation:
y = -5x + 15 --- Equation 1
2x + y = 12 --- Equation 2
Substitute y = -5x + 15 into Equation 2:
2x + y = 12
2x - 5x + 15 = 12
Evaluate like terms.
15 - 3x = 12
Isolate -3x.
-3x = 12 - 15
Evaluate like terms.
-3x = -3
Find x.
x = -3 ÷ -3
x = 1
Substitute x = 1 into Equation 2:
2x + y = 12
2(1) + y = 12
2 + y = 12
Isolate y.
y = 12 - 2
y = 10
Answer:
Step-by-step explanation:
153•0.92^x is a decaying exponential function.
In theory these functions never reach zero.
Suppose that you were willing to change the problem to read:
"What value will x have to for the first number to come within 0.0001 of zero?" Solve 153•0.92^x = 0.0001.
To do this, take the common log of both sides, obtaining
log 153 + x*log 0.92 = log 0.0001
Note that log 0.0001 = -4; log 153 = 2.18469; and log 0.92 = -0.03621.
Then we have:
2.18469 + x(-0.03621) = - 4.
Isolate the 2nd term. To accomplish this, subtract 2.18469 from both sides, obtaining:
-0.03621x = -6.18469
Isolate x by dividing both sides by -0.03621:
x = 170.8
This tells us that as x approaches +179, the quantity 153·0.92x will be within 0.0001 of zero.