Answer:
x = 16
m<Y = 34°
Step-by-step explanation:
∆XYZ is an isosceles ∆. An isosceles ∆ has two equal sides, as well as the bases of the isosceles triangle are congruent. In this case, therefore:
<X = <Z
(6x - 23)° = (4x + 9)
Solve for x
6x - 23 = 4x + 9
Collect like terms
6x - 4x = 23 + 9
2x = 32
Divide both sides by 2
x = 16
m<Y = 180° - (m<X + m<Z) (sum of ∆)
m<Y = 180 - ((6x - 23) + (4x + 9))
Plug in the value of x
m<Y = 180 - ((6(16) - 23) + (4(16) + 9))
m<Y = 180 - (73 + 73)
m<Y = 34°
A. X ~ N(66, 6.25)
b.
Using a standard normal probability table to find probability values for the z-scores, we get:
P(65 < X < 69) = 0.1554 + 0.3849 = 0.5403
c. z= 0.524 and -0.524
1.31 = X - 66
X = 67.31
When z = -0.524, X = 64.69.
P(64.69 < X < 67.31) = 0.4
There is a not so well-known theorem that solves this problem.
The theorem is stated as follows:
"Each angle bisector of a triangle divides the opposite side into segments proportional in length to the adjacent sides" (Coxeter & Greitzer)
This means that for a triangle ABC, where angle A has a bisector AD such that D is on the side BC, then
BD/DC=AB/AC
Here either
BD/DC=6/5=AB/AC, where AB=6.9,
then we solve for AC=AB*5/6=5.75,
or
BD/DC=6/5=AB/AC, where AC=6.9,
then we solve for AB=AC*6/5=8.28
Hence, the longest and shortest possible lengths of the third side are
8.28 and 5.75 units respectively.
Answer:
ten thousands place
Step-by-step explanation:
6 tens of thousands = 60,000
5 thousands= 5,000
3 hundreds= 300
60,000
+ 5,000
<u>+ 300</u>
<u>6</u>5,300
