Answer: Choice A
g(x) = sqrt(2x)
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Explanation:
"sqrt(x)" is shorthand for "square root of x"
f(x) = 3x^2 is given
g( f(x) ) = x*sqrt(6) is also given
One way to find the answer is through trial and error. This would only apply of course if we're given a list of multiple choice answers.
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Let's start with choice A
g(x) = sqrt(2x)
g( f(x) ) = sqrt(2 * f(x) ) .... replace every x with f(x)
g( f(x) ) = sqrt(2 * 3x^2 ) .... plug in f(x) = 3x^2
g( f(x) ) = sqrt(6x^2 )
g( f(x) ) = sqrt(x^2 * 6)
g( f(x) ) = sqrt(x^2)*sqrt(6)
g( f(x) ) = x*sqrt(6)
We found the answer on the first try. So we don't need to check the others.
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But let's try choice B to see one where it doesn't work out
g(x) = sqrt(x + 3)
g( f(x) ) = sqrt( f(x) + 3)
g( f(x) ) = sqrt(3x^2 + 3)
and we can't go any further other than maybe to factor 3x^2+3 into 3(x^2+1), but that doesn't help things much to be able to break up the root into anything useful. We can graph y = x*sqrt(6) and y = sqrt(3x^2 + 3) to see they are two different curves, so there's no way they are equivalent expressions.
Answer:
After how many years is the fish population 60?
x=2.71 years
Step-by-step explanation:
The fish population increases by a factor of 1.5 each year. We have the equation that represents this situation
Where x represents the number of years elapsed f(x) represents the amount of fish.
Given this situation, the following question could be posed
After how many years is the fish population 60?
So we do and solve for the variable x
Observe the solution in the attached graph
Answer:
Therefore, the correct options are;
-P(fatigue) = 0.44
= 0.533
--P(drug and fatigue) = 0.32
P(drug)·P(fatigue) = 0.264
Step-by-step explanation:
Here we have that for dependent events,
From the options, we have;
= 0.533
P(drug) = 0.6
P(drug and fatigue) = 0.32
Therefore
P(drug and fatigue) = P(drug)×
= 0.6 × 0.533 = 0.3198 ≈ 0.32 = P(drug and fatigue)
Therefore, the correct options are;
-P(fatigue) = 0.44
= 0.533
--P(drug and fatigue) = 0.32
P(drug)·P(fatigue) = 0.264
Since P(fatigue) = 0.44 ∴ P(drug) = 0.264/0.44 = 0.6.
Answer:
JLP = 16 degrees.
Step-by-step explanation:
KNP = 90 degrees. KNP is the supplement of NPL which is a right angle
KPN + PNK + PKN = 180 degrees. All triangles have 180 degrees.
- KPN = 44 Given
- PNK = 90 1st step here
- PKN = ?
Find JKN
- 44 + 90 + PKN = 180
- 134 + PKN = 180
- PKN = 180 - 134
- PKN = 46
- JKN = 2*PKN The angle is bisected. PKN = 1/2 JKN
- JKN = 2*46 = 92
J + JKL + L = 180
56 + 92 + L = 180
148 + L = 180
L = 32
1/2 L = JLP
JLP = 16 degrees
Answer:
4096
Step-by-step explanation:
Lets start by applying a basic exponent rule. (a*b)^n is equal to a^n * b^n
Therefore,
((9(3/16)^-2)^3/2 = 9^3/2 * ((3/16)^-2)^3/2
Now lets focus on ((3/16)^-2)^3/2
(3/16)^-2 = 1/(3/16)^2 = (16^2/3^2)^3/2.
We can quickly eliminate the fractional exponent by plugging it into the numerator and the denominator and we get, 16^3/3^3 = 4096/27
So now we have, 9^3/2 * 4096/27
We can easily compute 9^3/2, which is (sqrt(9))^3, which is equal to 27.
Therefore, you have, 27*4096/27. The 27 cancels to give us a final answer of 4096