Answer:
ASA
ΔFGH ≅ ΔIHG ⇒ answer B
Step-by-step explanation:
* Lets revise the cases of congruence
- SSS ⇒ 3 sides in the 1st Δ ≅ 3 sides in the 2nd Δ
- SAS ⇒ 2 sides and including angle in the 1st Δ ≅ 2 sides and
including angle in the 2nd Δ
- ASA ⇒ 2 angles and the side whose joining them in the 1st Δ
≅ 2 angles and the side whose joining them in the 2nd Δ
- AAS ⇒ 2 angles and one side in the first triangle ≅ 2 angles
and one side in the 2ndΔ
- HL ⇒ hypotenuse leg of the first right angle triangle ≅ hypotenuse
leg of the 2nd right angle Δ
* Lets prove the two triangles FGH and IHG are congruent by on of
the cases above
∵ FG // HI and GH is transversal
∴ m∠FGH = m∠IHG ⇒ alternate angles
- In the two triangles FGH and IHG
∵ m∠FHG = m∠IGH ⇒ given
∵ m∠FGH = m∠IHG ⇒ proved
∵ GH = HG ⇒ common side
∴ ΔFGH ≅ ΔIHG ⇒ ASA
* ASA
ΔFGH ≅ ΔIHG
Since both terms have the same variable to the same power, you can simply add the coefficients...
14x^7
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Answer:
Og(x) is shifted 4 units left and 6 units down from f(x).
Step-by-step explanation:
To understand how the parent function is transformed, you have to look at a few things.
Firstly, is there a negative sign in front? If there is, then the function is flipped around the y-axis
Second, on the part where the x is included (in this case it is x+4) you have to see if there is a negative sign in front of this. If this is the case, then the formula is flipped around the x-axis
<em>Third, If the part with the x is being added to, then the graph is being translated to the left that many units. If it is being subtracted from, then it is being translated to the right that many units (in this case it is </em><u><em>x+4</em></u><em>, so we move to the left 4 units) ((it is the opposite of what would be common sense, I know))</em>
<em>Lastly, if the whole thing is being added to, move up that many units. If it is subtracted from, move down that many units (in this case it is 1/x+4 </em><u><em>- 6)</em></u><em> (( this one does follow common sense))</em>
There are other factors, such as leading coefficients (on just the x part or the whole thing) and other stuff I'm sure I don't remember )
For more information: https://mathhints.com/parent-graphs-and-transformations/
This is a geometric sequence with first term 1 and common ratio -1/2. r=-1/2.
a(n) = a(1)*(r)^(n-1).
Check: If n=2 our formula must return -1/2. Does it?
a(2) = 1(-1/2)^(2-1) = (-1/2)^1 = - 1/2. Yes.
a(3) should be 1/4. Is it? a(3) = (-1/2)^(3-1) = 1/4 Yes.
Then a(8) = (-1/2)^(8-1) = (-1/2)^7 = -1 / 2^7 = -1/128 (answer)
