E^2x -2e^x -8=0 => e<span>^(2x) -2e^x -8=0
Temporarily replace e^x with y.
Then (y)^2 - 2y - 8 = 0. Factors are (y-4) and (y+2).
Roots are y = 4 and y= -2.
Now remembering that we temporarily replaced e^x with y, we let
y=4 = e^x. We need to solve for x. Taking the natural log of both sides, we get:
ln 4 = x (answer)
We have to discard the other root (y= -2), because we cannot take the ln of a negative number.
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Answer:
The total weight of his purchase is 1.08 pounds
Step-by-step explanation:
To find the total weight of his purchase, we sum the weight of each of his purchases.
He purchased:
4/9 pound of peanut.
7/11 pounds of raisins
Total:
The least common multiple between 9 and 11 is 99.
Then
The total weight of his purchase is 1.08 pounds
Answer:
Let S = price of sweater
Let P = price of pants
S + P = 89.47 because that was the total spent
S = P - 8.53 because the sweater is 8.53 less than pants
Substitute P-8.53 in place of S in the
1st equation and solve for P
P - 8.53 + P = 89.47
2P - 8.53 = 89.47 add 8.53 to both sides
2P = 89.47 + 8.53
2P = 98.00 divide both sides by 2
P = 98.00/2
P = $49.00
S = P - 8.53
S = 49.00-8.53
S = $40.47
A sweater costs $40.47 and the pants cost $49.00
When applying indirect proofs, we assume the negation of the conclusion is true, and show that this assumption would lead to nonsense, or contradiction.
In our case we assume a is not smaller than 7, that is we assume a≥7.
a≥7 then, multiplying both sides by 3:
3a≥21, then, adding both sides 7:
3a+7≥28,
which is a contradiction because 3a+7 is smaller than 28.
So our assumption is wrong, which means the opposite of it is correct.
Answer: assume a≥7
