Answer:
Answer for 9: C. 36
Answer for 10: G. 6
Answer for 12: F
Step-by-step explanation:
Answer: Phoebe have 48 apples.
Explanation:
It is given that Pru, Piper, and Phoebe share apples in the ratio 5:3:4. If Pru has 24 more apples than Piper.
Let the total number of apples be x.
The sum of the ratios is,
Therefore the number of apples shared by Pru, Piper, Phoebe are 
respectively.
It is given that Pru has 24 more apples than Piper, so
Since phoebe have 
appels,
Therefore, Phoebe have 48 apples.
Let,
f(x) = -2x+34
g(x) = (-x/3) - 10
h(x) = -|3x|
k(x) = (x-2)^2
This is a trial and error type of problem (aka "guess and check"). There are 24 combinations to try out for each problem, so it might take a while. It turns out that
g(h(k(f(15)))) = -6
f(k(g(h(8)))) = 2
So the order for part A should be: f, k, h, g
The order for part B should be: h, g, k f
note how I'm working from the right and moving left (working inside and moving out).
Here's proof of both claims
-----------------------------------------
Proof of Claim 1:
f(x) = -2x+34
f(15) = -2(15)+34
f(15) = 4
-----------------
k(x) = (x-2)^2
k(f(15)) = (f(15)-2)^2
k(f(15)) = (4-2)^2
k(f(15)) = 4
-----------------
h(x) = -|3x|
h(k(f(15))) = -|3*k(f(15))|
h(k(f(15))) = -|3*4|
h(k(f(15))) = -12
-----------------
g(x) = (-x/3) - 10
g(h(k(f(15))) ) = (-h(k(f(15))) /3) - 10
g(h(k(f(15))) ) = (-(-12) /3) - 10
g(h(k(f(15))) ) = -6
-----------------------------------------
Proof of Claim 2:
h(x) = -|3x|
h(8) = -|3*8|
h(8) = -24
---------------
g(x) = (-x/3) - 10
g(h(8)) = (-h(8)/3) - 10
g(h(8)) = (-(-24)/3) - 10
g(h(8)) = -2
---------------
k(x) = (x-2)^2
k(g(h(8))) = (g(h(8))-2)^2
k(g(h(8))) = (-2-2)^2
k(g(h(8))) = 16
---------------
f(x) = -2x+34
f(k(g(h(8))) ) = -2*(k(g(h(8))) )+34
f(k(g(h(8))) ) = -2*(16)+34
f(k(g(h(8))) ) = 2
Answer:
The exterior angle to the vertex P, measuring 90°
Step-by-step explanation:
The sum of the internal angles of any triangle needs to be equal 180 degrees. So, we can write two equations:
mP = mQ + mR
mP + mQ + mR = 180°
Substituting (mQ + mR) by mP in the second equation, we have:
mP + mP = 180°
mP = 90°
this right angle is the bigger angle in the triangle, because the sum of all three angles needs to be 180°.
Each exterior angle is the supplementary angle of the respective internal angle, so the bigger the internal angle, the smaller the external angle.
So if the bigger internal angle is mP = 90°, the smaller exterior angle is 180 - 90 = 90°.
