Answer:
f(g(9)) = 945/16
Step-by-step explanation:
To find f(g(x)), you have to substitute g(x) wherever there is an x in f(x).
g(x) = x + 3/4
f(x) = x² - 4x - 3
f(g(x)) = (x + 3/4)² - 4(x + 3/4) - 3
f(g(x)) = x² + 3/2x + 9/16 - 4x + 3 - 3
f(g(x)) = x² - 5/2x + 9/16 + 3 - 3
f(g(x)) = x² - 5/2x + 9/16
Now, put a 9 wherever there is an x in f(g(x)).
f(g(9)) = (9)² - 5/2(9) + 9/16
f(g(9)) = 81 - 5/2(9) + 9/16
f(g(9)) = 81 - 45/2 + 9/16
f(g(9)) = 117/2 + 9/16
f(g(9)) = 945/16
You can solve this in 2 easy steps: 1, multiply 44.55 by .17 (44.55 * .17 = 7.57) then adding the number you get to 44.55 (44.55 + 7.57 = 52.12). Your answer is D.
Answer:
-sinx
Step-by-step explanation:
a trig identity that is crucial to solving this problem is: sin^2 + cos^2 = 1
with knowing that, you can manipulate that and turn it into 1 - sin^2x = cos^x
so 1-sin^2x/sinx - cscx becomes cos^2x/sinx - cscx
it is also important to know that cscx is the same thing as 1/sinx
knowing this information, cscx can be replaced with 1/sinx
(cos^2x)/(sinx - 1/sinx)
now sinx and 1/sinx do not have the same denominator, so we need to multiply top and bottom of sinx by sinx; it becomes....
cos^2x
---------------------
(sin^2x - 1)/sinx
notice how in the denominator it has sin^2x-1 which is equal to -cos^2x
so now it becomes:
cos^2x
--------------
-cos^2x/sinx
because we have a fraction over a fraction, we need to flip it
cos^2x sinx
---------- * ----------------
1 - cos^2x
because the cos^2x can cancel out, it becomes 1
now the answer is -sinx
100 divided by 3. i know this because you are spitting the amount to each person
