9514 1404 393
Answer:
- DE ≈ 9.49, EF ≈ 8.06, FD ≈ 14.87
- obtuse scalene triangle
Step-by-step explanation:
For finding side lengths, it is convenient to work with the differences of the coordinates.
DE = E(-1, -3) -D(8, -6) = (-9, 3)
EF = F(-2, 5) -E(-1, -3) = (-1, 8)
FD = D(8, -6) -F(-2, 5) = (10, -11)
Then the lengths are ...
DE = √((-9)² +3²) = √90 = 3√10 ≈ 9.49
EF = √((-1)² +8²) = √65 ≈ 8.06
FD = √(10² +(-11)²) = √221 ≈ 14.87
The lengths are all different and the largest angle is obviously more than 90°, so the triangle is an obtuse scalene triangle.
Answer:
Step-by-step explanation:
Given that there are three variables satisfying the equation
Here each x is given to be a positive integer
i.e. solution set for each of the variable can be any integer from 1 to 20 at most.(because if two other integers are 1 each third has to be 20)
Hence solution set can be of the form
If x1 =1, there are 20 solution sets
If x1 =2,there are 19
...
If x1 =20 there is 1 set
Hence total solutions can be
Answer:
Step-by-step explanation:
reading_rate: 2.5R = 1250
R = 1250/2.5 = 500 pages/hr or ( 1 hr)/(500 pages)
Solve for hr?
=( 1 hr)/(500 pages) * 1250 pages
now, cancel out pages and we are left with hours
= 1250/500 hours
= 2.5 hours
So, first add 1.75 and 1.15 together. the answer? 2.9, add a zero, 2.90. then subtract 2.90 off of 5, the answer is 2.1.
Answer:
1)m=9ft and n=10ft
2) p=10cm and r=18cm
3) s=4mi and t=8mi
Step-by-step explanation:
1)
Finding 3rd angle:
F= 180-(90+60)
= 180-150
=30
Now using law of sines to find sides m and n
m/sinD = 5/sinF
m= sin60(5/sin30)
= 8.66
= 9
n/sinE= 5/sin30
n= sin90(5/sin30)
= 10
hence m=9ft and n=10ft
2)
Finding 3rd angle:
F= 180-(90+60)
= 180-150
=30
Now using law of sines to find sides p and r
p/sinF = 21/sinE
p= sin30(21/sin90)
= 10.5
= 10
r/sinD= 21/sin90
r= sin60(21/sin90)
= 18.18
=18
hence p=10cm and r=18cm
3)
Finding 3rd angle:
F= 180-(90+60)
= 180-150
=30
Now using law of sines to find sides s and t
s/sinF = 3√6/sinD
s= sin30(3√6/sin60)
= 4.24
= 4
t/sinE= 3√6/sinD
t= sin90(3√6/sin60)
= 8.48
= 8
hence s=4mi and t=8mi !
