Answer:

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Step-by-step explanation:
I am not sure what your problem here is.
you understand the inequality signs ?
anyway, to get
6×f(-2) + 3×g(1)
we can calculate every part of the expression separately, and then combine all the results into one final result.
f(-2)
we look at the definition.
into what category is -2 falling ? the one with x<-2, or the one with x>=-2 ?
is -2 < -2 ? no.
is -2 >= -2 ? yes, because -2 = -2. therefore, it is also >= -2.
so, we have to use
1/3 x³
for x = -2 that is
1/3 × (-2)³ = 1/3 × -8 = -8/3
g(1)
again, we look at the definition.
into what category is 1 falling ? the one with x > 2 ? or the one with x <= 1 ?
is 1 > 2 ? no.
is 1 <= 1 ? yes, because 1=1. therefore it is also <= 1.
so we have to use
2×|x - 1| + 3
for x = 1 we get
2×0 + 3 = 3
6×f(-2) = 6 × -8/3 = 2× -8 = -16
3×g(1) = 3× 3 = 9
and so in total we get
6×f(-2) + 3×g(1) = -16 + 9 = -7
Answer:
y = 2x + 2
Step-by-step explanation:
To find the slope we do (Y1 - Y2)/(X1-X2) aka rise over run
So, m = (-4 - 2) / (-3 - 0)
m = 2
Now we have y = 2x +b
Notice one of our points is (0,2)
Since the x value of that point is 0, it is the y intercept.
In the slope intercept form b = y-intercept
Therefore b = 2
So, y = 2x + 2
F and U and C and K and then finally U
The solution of the given exponential equation is 0.688.
Given that Mike is working on solving the exponential equation 37ˣ = 12.
An exponential equation is an exponential equation where the power (or) part of the exponent is a variable.
firstly, we have to slve this equation is by converting it to logarithmic form. Any exponential equation can be transformed into an equivalent logarithmic equation as follows:
aˣ = y
logₐy = x
Now, we will apply this transformation to our equation and we get
log₃₇12=x
Further, we will apply the change of base formula so that solution is written in terms of base 10 logs:
x=log12/log37
So, this is an exact answer to given equation, but we can simplify it further by using decimal approximation of it using a calculator. Remember that these logs are base 10:
x≈1.079/1.568
x=0.688
Hence, the solution of the given exponential equation 37ˣ=12 is 0.688.
Learn more about exponential equation from here brainly.com/question/24162621
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