Hey, there! For this question, we can just start by plugging in the known values. 
can be rewritten as 
.
Combine like terms: 
If you add x to 
, x will become 
, which means that x/2 + x = 3/2x.
--> 
If you rearrange this, then your answer will be option b. Hope this helps.
Answer:
Step-by-step explanation:
Given a certain function 
, and then its inverse function 
, the following expression is valid:
where the expression
indicates the composite function.
In this problem, we have:
And then, its inverse function is
To verify that g(x) is the inverse of f(x), the following expression must be true:
Substituting the expression of g(x) into f(x), we find that:
So, g(x) is the inverse of f(x).
Think of the inequalities as equations in the form of y=Mx+b. Notice how choices C and D match the line shown in the graph if they are seen as linear functions. Now look at the inequality. Since the shaded region is below the line, y must be less than what is input. The correct answer must be choice D.
-R
P.S. if you found this helpful, plz leave a “thanks”. Thx!
9514 1404 393
Answer:
see below
Step-by-step explanation:
Reflection across the x-axis just changes the signs of the y-coordinates. Rotation -120° about B' is difficult to do by hand. The transformation rule for that is ...
(x, y) ⇒ (x·cos(-120°) +y·sin(-120°), -x·sin(-120°) +y·cos(-120°))
(x, y) ⇒ ((-(x-3) +(y+2)√3)/2 +3, (-(x-3)√3 -(y+2))/2 -2)
__
It looks like your problem is presented in GeoGebra, which makes reflection and rotation easy.
Answer:
x = 18
Step-by-step explanation:
First, let's find the ratios between the two triangles
We'll use AV and AC
372 ÷ 589 = 12/19
All of the sides of the smaller triangle are 12/19 of the bigger triangle
Now let's find x
We know that AU + UB = AB
So it's 20x + 108 + 273 = AB
12/19 of a bigger triangle side equals a small triangle side
(12/19)AB = AU
For this equation multiply both sides by 19/12 to isolate AB
(12/19)AB x 19/12 = AU x 19/12
AB = (19/12)AU
Now we have this
20x + 108 + 273 = (19/12)(20x + 108)
20x + 381 = (19/12)(20x + 108)
Distribute the 19/12
20x + 381 = 95/3x + 171
Move all like terms to one side
20x + 381 = 95/3x + 171
- 171 - 171
20x + 210 = 95/3x
- 20x - 20x
Don't forget about common denominators
210 = 95/3x - 60/3x
210 = 35/3x
Multiply both sides by 3
210 x 3 = 35/3x x 3
630 = 35x
Divide both sides by 35
630/35 = 35x/35
x = 18
