Answer:
44. answer = a. (<)
45. answer = b. (>)
Step-by-step explanation:
To find the relation between the angles, we can use the law of sines in the triangle that contains both angles.
So for question 44, the angles mQRW and mRWQ are both in the triangle QWR, so we have:
10 / sin(mQRW) = 17 / sin(mRWQ)
sin(mQRW) / sin(mRWQ) = 10 / 17
The bigger the sine of the angle, the bigger the angle, so if the ratio between the sine of mQRW and sine of mRWQ is lesser than 1, the angle mQRW is lesser than the angle mRWQ (correct option: a.)
In the same way, in the question 45, the angles mRTW and mTWR are both in the triangle TWR, so we have:
15 / sin(mRTW) = 8 / sin(mTWR)
sin(mRTW) / sin(mTWR) = 15 / 8
If the ratio between the sine of mRTW and sine of mTWR is greater than 1, the angle mRTW is greater than the angle mTWR (correct option: b.)
Basically, the angle opposite to the greater side is the greater angle, and the angle opposite to the smaller side is the smaller angle.
Decrease because the arrow is pointing down
Answer: 52m cards
Step-by-step explanation:
First part of question says: Karen has m decks of cards.
If Karen has m deck of cards and each deck has 52 cards in it, the total number of cards that all that Karen will have will be 52 multiplied by the number of deck of cards Karen has:
= 52 * m
= 52m
Answer:
c.
Step-by-step explanation:
Turn each number into the product of it's prime factors.
32=16x2=2x2x2x2x2=2^5
48=24*2=6x4x2=2x3x2x2x2
Pick the highest number that occurs. In this case it is 2. Now we have to see how many times it appears in both. It appears 5 times in 32 and 4 times in 48. 4 is the highest number of times it appears in the numbers so:
2^4=2x2x2x2=16
The Greatest Common Factor (GCF) of 32 and 48 is 16.
