1.
When you have the length of two sides and the angle between them, the triangle is totally determined. This is, there is only one segment that can complete the triangle: its length and position is totally fixed.
Answer:
15.59 feet
Step-by-step explanation:
We need to find BC and CD
First find BC
We can use the Pythagorean theorem
AB^2 + BC^2 = AC^2
11^2 + BC^2 = 13^2
121 + BC^2 =169
Subtract 121 from each side
121-121+BC^2 = 169-121
BC^2 = 48
Take the square of each side
sqrt(BC^2 ) = sqrt( 48)
BC = 6.92820323
then we need to find CD
We can use the Pythagorean theorem
CD^2 + DE^2 = CE^2
CD^2 + 5^2 = 10^2
CD^2 + 25 =100
Subtract 25 from each side
CD^2 + 25-25 =100-25
CD^2 = 75
Take the square of each side
sqrt(CD^2 ) = sqrt( 75)
BC = 8.660254038
BD = BC +CD
= 6.92820323 + 8.660254038
15.58845727
131 3/4 ⇒ 115 5/8 ⇒ 5 2/3
Subtract 131 3/4 by 115 5/8.
131 3/4 ⇒ 131 6/8
131 6/8 - 115 5/8 = 16 1/8
Now add 16 1/8 + 5 2/3 and this will give you how much weight she lost in all.
16 1/8 ⇒ 16 3/24
5 2/3 ⇒ 5 16/24
16 3/24 + 5 16/24 = 21 19/24
Felice lost 21 19/24 pounds in all.
The space diagonal will have length ...
... d = √(1² +4² +2²) = √(1 +16 +4) = √21
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This can be found using the Pythagorean theorem. A drawing can help. Find the length of any face diagonal, then use that length as the leg of a right triangle whose hypotenuse is the space diagonal and whose other leg is the edge length not used in the first calculation.
5(x-2)(x+4)>0 For this to be true, both parenthetical terms must be both positive or both negative.
x<-4 and x>2
x=(-oo,-4),(2,+oo)
