Answer:
constant of variation = 3
Step-by-step explanation:
we know that b varies jointly with c and d
so:
b∝c∝d
and b varies inversely with e, so
b∝
and i will call the constant of variation k, this way we can make an equation for b in the following form:
this satisfy that b varies jointly with c and d (if b increases, c and d also increase) and inversely with e (if b increases, e decreases)
we know that when b is 18, c is 4, d is 9, and e is 6:
substituting this in our equation for b:
and we solve operations and clear for the constant of variation k:
the constant of variation is 3.
Problem 1
<h3>Answer: False</h3>
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Explanation:
The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.
So,
f(x) = x+1
f( g(x) ) = g(x) + 1 .... replace every x with g(x)
f( g(x) ) = 6x+1 ... plug in g(x) = 6x
(f o g)(x) = 6x+1
Now let's flip things around
g(x) = 6x
g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)
g( f(x) ) = 6(x+1) .... plug in f(x) = x+1
g( f(x) ) = 6x+6
(g o f)(x) = 6x+6
This shows that (f o g)(x) = (g o f)(x) is a false equation for the given f(x) and g(x) functions.
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Problem 2
<h3>Answer: True</h3>
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Explanation:
Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.
For example, let
f(x) = 1/(x+2)
g(x) = -2
The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.
So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).
Answer:
y= 2x + 10
Step-by-step explanation:
The variable depends on the $2 so, the green box should be 2
I think that jeremy should learn how to do his own math
Answer:
18
Step-by-step explanation:
180-160 = 20 which equals the exterior angle
the sum of exterior angles is 360 so 360/20 = the number of sides as there is an exterior angle for every side
360/20 = 18
