Answer:
x = -2.
Step-by-step explanation:
2 ln(x + 3) = 0
ln(x + 3) = 0
Now ln 1 = 0 so
x + 3 = 1
x = -2.
Answer:
2nd option
Step-by-step explanation:
It's direct because it's equation is y = -1/2x
That means it passes through the point (0, 0), making it an example of direct variation.
Answer:
8.25
Step-by-step explanation:
Plug in 8.25 where x is. Then according to PEMDAS you add everything up in the parenthesis then multiply the sum of that by 7/3.
From all this information we can come up with a few equations to work with...
first we have that the worth of each coin times the number of those coins all added together equals 4.65
here I have n = nickels, d = dimes, and q = quaters
then we are told that there are "three more quarters than dimes"
which translates to the equation
or
we are also told that there are "twice as many nickels as quarters"
this translates to
to solve for quarters, we plug in d (in terms of q) and n (in terms of q) into the first equation we created.
then we distribute and start trying to solve for
then add like terms
then add 0.30 to both sides
then divide both sides by 0.45
therefore our answer is B) 11 quarters
Step OneFor convenience f(x) = y
y = -(1/2) sqrt(x + 3) Interchange x and y
x = -(1/2) sqrt(y + 3) Multiply both sides by -2
(-2x) = sqrt(y + 3) Square both sides
4x^2 = y + 3 Subtract 3 from both sides
4x^2 -3 = y
f-1(x) = 4x^2 - 3
GraphsThe original graph is in blue
The inverse is red.
Green Line y = x : explained below.
CommentInverses have a very strange property. It acts as a check.
If you perform the following operation
f-1(f(x)) you are left with x
In this case f-1[-1/2 sqrt(x + 3)]= 4(-1/2 * sqrt(x + 3))^2 - 3
f-1 (-1/2sqrt(x+3)) = 4 (1/4 (x+3) - 3
f-1(-1/2sqrt(x + 3)) = x+ 3 - 3 = x
I've included this because I think you have to put the same restriction on f-1(x) as you do on f(x) which is that for f(x) x ≥ -3
This last assertion could be incorrect, but I don't think so.
The answer is f-1(x) = 4x^2 - 3 <<<<<
answer first box and
x≥-3 for the second box. <<<<<<
answer for the second box.Let me know if these are correct. I'm not sure about the restrictions.