If f(x) varies directly with x, and f(x) = 45 when x=9, find the value of f(x) when x=3

answer choices are
A. f(x)=8x
B. f(x)=4/3x
C. f(x)=6x
D. f(x)=3/4x

if f(x) varies directly with x, then

f(x) = kx, where k is a constant
given: if x=9 , f(x) = 49
so 49 = 9k
k = 45/9 = 5

f(x) = 5x

f(3) = 5(3) = 15

or

just use a ratio
9/3 = 45/f(x)
9f(x) = 135
f(x) = 135/9 = 15

Well, if f(x) varies directly with x, it means that the ratio between f(x) and x is constant. So, we can set up a proportion:

f(x)/x = f(9)/9

Now, let's plug in the given values:

f(x)/x = 45/9

Simplifying, we have:

f(x)/x = 5

To find the value of f(x) when x = 3, we can substitute it into the proportion:

f(3)/3 = 5

Cross multiplying, we get:

f(3) = 3 * 5

f(3) = 15

So, the correct answer choice is C. f(x) = 6x.

But hey, don't worry if you got it wrong – math problems can be a little tricky, just like a banana peel waiting to send you sliding into a gag of confusion!

To find the value of f(x) when x = 3 given that f(x) varies directly with x, we can use the information that when x = 9, f(x) = 45.

When two variables vary directly, their relationship can be represented by the equation f(x) = kx, where k is the constant of variation.

To find the value of k, we can substitute the given values into the equation:

45 = k * 9

Now, solve for k:

k = 45 / 9
k = 5

So, the equation representing the direct variation is f(x) = 5x.

To find the value of f(x) when x = 3, substitute x = 3 into the equation:

f(3) = 5 * 3
f(3) = 15

Therefore, the value of f(x) when x = 3 is 15.

None of the given answer choices match this result, so none of the options is correct.

To solve this problem, we need to use the concept of direct variation. In direct variation, if the variable x increases or decreases, the function f(x) also increases or decreases proportionally. We can represent direct variation using the equation f(x) = kx, where k is the constant of variation.

To find the value of f(x) when x=3, we can use the given information that f(x) = 45 when x=9. Plugging these values into the equation, we get:

45 = k * 9

To find the constant of variation (k), divide both sides of the equation by 9:

45/9 = k
5 = k

So, the constant of variation (k) is 5. Now we can plug this value into the equation f(x) = kx to find the value of f(x) when x=3:

f(x) = 5 * 3
f(x) = 15

Therefore, the value of f(x) when x=3 is 15.

Looking at the answer choices provided:
A. f(x) = 8x
B. f(x) = 4/3x
C. f(x) = 6x
D. f(x) = 3/4x

None of the provided answer choices match the correct value of f(x) = 15 when x=3. Therefore, none of the answer choices are correct.