HERES THE ANSWER AND EXPLINATION
⇒Associative property of Addition is applied for three real numbers.For, any three real numbers, A, B and C
≡A+B+C=A+(B+C)=(A+B)+C=(A+C)+B→→→Associative Property of Addition
that is , we can add any two numbers first and then the third number with them.
⇒Also, Commutative Property of Addition of two numbers says that for any two numbers , A and B
≡A+B=B+A
We have to find equivalent expression using Associative Property of the sum of set of three numbers
→→(13+15+20)+(20+47+18)
Answer Written by Jerry
→(20+13+15)+(20+47+18)
Answer Written by Layla
→(20+47+18)+(13+15+20)
The Expression Written by Keith and Melinda is Incorrect,because they haven't used the bracket Properly, as associative property says that you can add any two numbers first and then the third number among three numbers.
→→Number of Students who has applied the Associative property Correctly
Option B ⇒Two(Jerry, Layla)
As soon as I read this, the words "law of cosines" popped
into my head. I don't have a good intuitive feeling for the
law of cosines, but I went and looked it up (you probably
could have done that), and I found that it's exactly what
you need for this problem.
The "law of cosines" relates the lengths of the sides of any
triangle to the cosine of one of its angles ... just what we need,
since we know all the sides, and we want to find one of the angles.
To find angle-B, the law of cosines says
b² = a² + c² - 2 a c cosine(B)
B = angle-B
b = the side opposite angle-B = 1.4
a, c = the other 2 sides = 1 and 1.9
(1.4)² = (1)² + (1.9)² - (2 x 1 x 1.9) cos(B)
1.96 = (1) + (3.61) - (3.8) cos(B)
Add 3.8 cos(B) from each side:
1.96 + 3.8 cos(B) = 4.61
Subtract 1.96 from each side:
3.8 cos(B) = 2.65
Divide each side by 3.8 :
cos(B) = 0.69737 (rounded)
Whipping out the
trusty calculator:
B = the angle whose cosine is 0.69737
= 45.784° .
Now, for the first time, I'll take a deep breath, then hold it
while I look back at the question and see whether this is
anywhere near one of the choices ...
By gosh ! Choice 'B' is 45.8° ! yay !
I'll bet that's it !
Ur answer would be 56.6 degrees just subtract 33.5 from 90
