Unusual notation. I won't fuss with it.
a. We have isosceles PRT, so angle RPT = angle RTP.
By the definition of angle bisector, angle MTP = angle MTF, and angle MPT = angle MPU.
We have m angle RTP = m angle MTF + m angle MTP = 2 m angle MTP
Similarly, m angle RPT = 2 m angle MPT
2 m angle MTP = 2 m angle MPT
angle MPT = angle MPT
That's the first part.
b. That makes MPT isosceles.
c. 2x+124=180
2x = 56
x = 28 degrees
MTP = 28 degrees
d. We have angle RPT=angle RTP=56 so PRT=180-2(56)=68 degrees
PUT = 180 - UTP - UPT = 180 - 28 - 56 = 96 degrees
Bad drawing, PUT looks acute.
angle PRT = 68 degrees, angle PUT = 96 degrees
Let n be the number of lbs of nuts.
Let r be the number of lbs of raisins.
9n + 3r = 60 * 5 = 300 .............(1)
n + r = 60
n = 60 - r ...............(2)
Plugging the expression for n in (2) into (1) we get:
9(60 - r) + 3r = 300
which expands to:
540 - 9r + 3r = 300 .............(3)
Simplifying and rearranging (3) we get:
-6r = -240
Therefore r, the weight of raisins = 40 lbs
and the weight of nuts is 60 - 40 = 20 lbs
Answer:
12241.025
Step-by-step explanation:
Twelve thousand, two hundred and forty one point zero, two, five
