ΔHGE and ΔFGE are congruent by the Angle-Side-Angle Congruence Theorem (ASA).
<em><u>Recall:</u></em>
- A segment that divides an angle into equal parts is known as an angle bisector.
- Two triangles are congruent by the ASA Congruence Theorem if they share a common side and have two pairs of congruent angles.
In the diagram given, Angle bisector, GE, divides ∠HEF into congruent angles, ∠HEG ≅ ∠GEF.
Also divides ∠FGH into congruent angles, ∠HGE ≅ ∠FGE.
Both triangles also share a common side, GE
<em>This implies that: ΔHGE and ΔFGE have:</em>
two pairs of congruent angles - ∠HEG ≅ ∠GEF and ∠HGE ≅ ∠FGE
a shared side - GE
Therefore, ΔHGE and ΔFGE are congruent by the Angle-Side-Angle Congruence Theorem (ASA).
Learn more about ASA Congruence Theorem on:
brainly.com/question/82493
Answer:
3200 ft-lb
Step-by-step explanation:
To answer this question, we need to find the force applied by the rope on the bucket at time 
At 
After seconds, the weight of the bucket is 
Since the acceleration of the bucket is the force on the bucket by the rope is equal to the weight of the bucket.
If the upward direction is positive, the displacement after seconds is 
Since the well is 80 ft deep, the time to pull out the bucket is 
We are now ready to calculate the work done by the rope on the bucket.
Since the displacement and the force are in the same direction, we can write
Use and 
![=\left[63 t-0.2 t^{2}\right]_{0}^{36}](https://tex.z-dn.net/?f=%3D%5Cleft%5B63%20t-0.2%20t%5E%7B2%7D%5Cright%5D_%7B0%7D%5E%7B36%7D)
Pick any two points
(0, 3), (-1,9)
Find slope (y2-y1)/(x2-x1)
(9-3)/(-1-0) = 6/-1 = -6
Y = -6x + b
Plug in a point
3 = 0 + b, b= 3
Final equation: y = -6x + 3
Answer:
k = 6.5
Step-by-step explanation:
y = 2x + c is given. Thus, we know immediately that the slope of this line is m = 2. If (k, 10) is a point on this line, then the following must be true:
10 = 2(k) + c, and
-3 + 2(0) + c
or
10 = 2k + c
c = -3
Thus, 10 = 2k + -3 becomes 13 = 2k, so that k = 6.5
Answer:
0.54 is the sales tax.
Step-by-step explanation:
2.25 x 3 = 6.75
When trying to do percentages move the decimal place to the right 2 times.
6.75 x 0.08= 0.54.
