Problem 215
Check out the attached image. Line up the letters ABC and CDE so the first set of letters are over the second set of letters. Order is important here. Note how A corresponds to C (second C), B corresponds to D, and (the first) C corresponds to E.
We have this mapping:
A <--> C
B <--> D
C <--> E
This means...
Angle BAC corresponds to Angle DCE (red angles)
Angle ABC corresponds to Angle CDE (blue angles)
Angle BCA corresponds to Angle DEC (green angles)
It also means...
Side BC corresponds to Side DE (red sides)
Side AC corresponds to Side CE (blue sides)
Side AB corresponds to Side CD (green sides)
Check out the attached image which I hope clears up any confusion you may have. Often I think it helps to represent stuff like this in a visual way.
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Problem 216
Answer: True
Since triangle ABC is congruent to triangle DEF, this means that side AB is congruent to side ED. These are corresponding sides. Since AB = 6, this means ED = 6 as well.
Answer:
If the goal is to break the vases: 3/20 = 15.0% or 0.15
If the goal is to not break the vases: 17/20 = 85.0% or 0.85
Answer:
300 sheets
Step-by-step explanation:
if you divide 35 by 7, you get 5
then divide 1,500 by 5 to get 300.
Answer:
88
Step-by-step explanation:
Write the expression for the sum in the relation you want.
Sn = u1(r^n -1)/(r -1) = 2.1(1.06^n -1)/(1.06 -1)
Sn = (2.1/0.06)(1.06^n -1) = 35(1.06^n -1)
The relation we want is ...
Sn > 5543
35(1.06^n -1) > 5543 . . . . substitute for Sn
1.06^n -1 > 5543/35 . . . . divide by 35
1.06^n > 5578/35 . . . . . . add 1
n·log(1.06) > log(5578/35) . . . take the log
n > 87.03 . . . . . . . . . . . . . . divide by the coefficient of n
The least value of n such that Sn > 5543 is 88.
We can cancel out the y^4 on the top and bottom of the fraction.
this gives us...
(x^3)/3