<span>If f(x) = 2x + 3 and g(x) = (x - 3)/2,
what is the value of f[g(-5)]?
f[g(-5)] means substitute -5 for x in the right side of g(x),
simplify, then substitute what you get for x in the right
side of f(x), then simplify.
It's a "double substitution".
To find f[g(-5)], work it from the inside out.
In f[g(-5)], do only the inside part first.
In this case the inside part if the red part g(-5)
g(-5) means to substitute -5 for x in
g(x) = (x - 3)/2
So we take out the x's and we have
g( ) = ( - 3)/2
Now we put -5's where we took out the x's, and we now
have
g(-5) = (-5 - 3)/2
Then we simplify:
g(-5) = (-8)/2
g(-5) = -4
Now we have the g(-5)]
f[g(-5)]
means to substitute g(-5) for x in
f[x] = 2x + 3
So we take out the x's and we have
f[ ] = 2[ ] + 3
Now we put g(-5)'s where we took out the x's, and we
now have
f[g(-5)] = 2[g(-5)] + 3
But we have now found that g(-5) = -4, we can put
that in place of the g(-5)'s and we get
f[g(-5)] = f[-4]
But then
f(-4) means to substitute -4 for x in
f(x) = 2x + 3
so
f(-4) = 2(-4) + 3
then we simplify
f(-4) = -8 + 3
f(-4) = -5
So
f[g(-5)] = f(-4) = -5</span>
Answer:
-2y
Step-by-step explanation:
Let's simplify step-by-step.
x−y−(x+y)
Distribute the Negative Sign:
=x−y+−1(x+y)
=x+−y+−1x+−1y
=x+−y+−x+−y
Combine Like Terms:
=x+−y+−x+−y
=(x+−x)+(−y+−y)
=−2y
<em>C</em>
Approximately 95% of data falls within 2 standard deviations (±2) of the mean.
<em>Explanation</em>
According to the empirical rule of normal distribution:
Approximately 68% of the data falls within ±1 standard deviation of the mean
2. Approximately 95% of the data falls within ±2 standard deviations of the mean
3. Approximately 99.7% of the data falls within ±3 standard deviations of the mean.
Therefore, among the given options, only option C adheres to the empirical rule of the normal distribution. Therefore, the option C is correct
If you times it the answer is going to be 1,200
Step-by-step explanation:
the point-slope form is
y - y1 = m(x - x1)
where (x1, y1) is a point on the line.
m is the slope of the line, which is always (in any form) the factor of x.
the parallel line has -2/8 as factor of x, which is therefore also the slope of our new line (after all, it has to be parallel, so it must have the same slope).
so, we have
y + 5 = -2/8 × (x - 4)
which can be simplified, of course, to
y + 5 = -1/4 × (x - 4)
