Find the equation of the line that contains the given point and is perpendicular to the given line. Write the equation in slope-
intercept form, if possible. (5,1);y=-5/2x+3
1 answer:
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Answer:
y=4/3+19/3
Step-by-step explanation:
When it asks for perpendicular it means your focusing on the slope.
Perpendicular means opposite of the current slope, so flip it and change the sign (-3/4 changes to 4/3). Next you will use the equation (y-y1)=m(x-x1)
y1=the y value given
x1=the x value given
m=your slope
(y-1)=4/3(x+4) Since the x point is minus a negative we get to change the sign to a positive. Next distribute the 4/3 to each term in the parenthesis.
y-1=4/3(x)+4/3(4)
y-1=4/3x+16/3 Now we add the one to both sides.
+1 +1 The one isn't in teh correct format to just add so first imagine it as 1/1. Now to get the bottom to have a 3 like in 16/3 we just multiply the top and bottom by 3.
Now we can add this to the 16/3
We can now put this back into our equation.
y=4/3+19/3
Answer:
The difference between the greatest and the smallest angle of the triangle PBQ is 98°.
Step-by-step explanation:
The question is:
In a triangle ABC, angle B measures 64 ° and angle C measures 72°. The inner bisector CD intersects the height BH and the bisector BM at P and Q respectively. Find the difference between the greatest and the smallest angle of the triangle PBQ.
Solution:
Consider the triangle ABC.
The measure of angle A is:
angle A + angle B + angle C = 180°
angle A = 180° - angle B - angle C
= 180° - 72° - 64°
= 44°
It is provided that CD and BM are bisectors.
That:
angle BCP = angle PCH = 36°
angle CBQ = angle QBD = 32°
angle BHC = 90°
Compute the measure of angle HBC as follows:
angle HBC = 180° - angle BHC + angle BCH
= 180° - 90° - 72°
= 18°
Compute the measure of angle BPC as follows:
angle BPC = 180° - angle PCB + angle CBP
= 180° - 18° - 36°
= 126°
Then the measure of angle BPQ will be:
angle BPQ = 180° - angle BPC
= 180° - 126°
angle BPQ = 54°
Compute the measure of angle PBQ as follows:
angle PBQ = angle B - angle QBD - angle HBC
= 64° - 32° - 18°
angle PBQ = 14°
Compute the measure of angle BQP as follows:
angle BQP = 180° - angle PBQ - angle BPQ
= 180° - 14° - 54°
angle BQP = 112°
So, the greatest and the smallest angle of the triangle PBQ are:
angle BQP = 112°
angle PBQ = 14°
Compute the difference:
<em>d</em> = angle BQP - angle PBQ
= 112° - 14°
= 98°
Thus, the difference between the greatest and the smallest angle of the triangle PBQ is 98°.
