Solution for f(g(5)):
The notation f(g(5)) or (f • g)(5) means that we first plug 5 into the function g(x), simplify, then plug the answer that we got to f(x). We will do this step-by-step:
Step 1: Plugging 5 to g(x)
Step 2: Plugging the answer to f(x)
ANSWER: f(g(5)) is equal to 3.
Domain:
For the function f(g(x)), we can find the domain by analyzing the domains of each individual functions separately and excluding certain values depending on the restrictions from the outermost function.
However, since both functions have all real numbers as its domain, we will not need to do any exclusion anymore.
ANSWER: The domain of the function is all real numbers.
Answer:
B
C
F
D
H
A
G
E
Step-by-step explanation:
Ok. They are trying to reconstruct the smaller looking triangle in the bigger triangle using angle A as the common angle.
The first statement is always the given.
Second they constructed line segment XY into the bigger triangle so that XY is parallel to BC.
Third, from the construction of the parallel lines we can now find corresponding angles that are congruent. This would be the use of F.
Since we have all three angles in triangle AXY and triangle ABC, then the construction of the smaller triangle we made inside the bigger triangle is similar to the bigger triangle. So we have the triangles are similar. You could say E or D here in my opinion. This is choice D.
Fifth the creation of those fractions of sides being equal comes from us knowing the corresponding sides of similar triangles are proportional. This is choice H.
Things looked cut off for the sixth thing so I can't fully read it, but it is possible a substitution has occured.
The seventh thing is a congruence statement which can be proven by a congruence postulate. The only one listed is SAS. So that is G.
The last thing, since the triangle construction is congruent to the smaller triangle then we know the smaller triangle is also similar to the bigger triangle since the bigger one is also similar to the construction we made. I really think E and D is interchangeable. Choice E goes here.
Answer:
The total commission is $8905
Step-by-step explanation:
The commission on first $80000 = 2%
The commission on next $80000 = 4%
The commission on the sales of more than $160000 = 5%
Now we have to calculate the total commission on the amount of $242100. Let divide the amount in three parts, $80000 + $80000 + $82100 = 242100
Now total commission = $80000×2% + $80000 ×4% + $82100×5%
Total commission = $8905
Answer:
22
Step-by-step explanation:
ST is y and SU is 2y-4.
Note that SU = ST + TU = y + 18
So we have 2y - 4 = y + 18
2y - 4 = y + 18
2y = y + 22
y = 22
So ST is 22.
:)
Answer:
I gave you most of the answer. I'll let you check my work and find the point using the solution.
Step-by-step explanation:
The first thing we do is we divide by negative one in the first equation to get
y = -x.
-3x + 3y = -36
Plug in y = -x and get
-3x + 3(-x) = -36
= -3x - 3x = -36
This equals -6x = -36
divide both sides by -6 and you get 6. 6 is your x value
Plug 6 back in to the second equation.
-3x + 3y = -36
-3(6) + 3y = -36
-18 + 3y = -36
3y = -18
y = -6
