Answer:
A. x = 2 and BQ = 27
Step-by-step explanation:
The key to this problem is the fact that the centroid divides the median into segments in the ratio 2 : 1.
BM : MQ = 2 : 1
BM = 2·MQ
9x = 2(5x -1) . . . . . substitute the given expressions
9x = 10x -2 . . . . . . eliminate parentheses
0 = x -2 . . . . . . . . . subtract 9x
2 = x . . . . . . . . . . . .add 2
BQ = BM + MQ = 9(2) +5(2) -1
BQ = 27
Answer:
11.820 ft
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
The length of the ladder is the hypotenuse of a right triangle with 52° as the base angle. The side opposite is the height up the building where the top of the ladder rests. So, you have the relation ...
sin(52°) = height/(15 ft)
Multiplying by the denominator gives you ...
height = (15 ft)·sin(52°) ≈ 11.820 ft
Hope this helps
Answer:
36
Step-by-step explanation:
Carson had x number of apples to start with.
He gave 1/3 to Nathan. Now Carson has (2/3)x apples left.
He gave 1/2 of what was left to Nikki. Now Carson has (1/2)(2/3)x = (2/6)x = (1/3)x apples.
On the way home, he dropped 1/4, so he has 3/4 of the last amount he had, and the number is 9.
(3/4) * (1/3)x = 9
3/12 x = 9
1/4 x = 9
x = 36
Answer: He picked 36 apples.
Check:
Start with 36 apples.
Give 1/3 to Nathan. Now Carson has 24 apples.
Give 1/2 to Nikki. Now Carson has 12 apples.
Drop 1/4. 1/4 of 12 is 3. 12 - 3 = 9.
Hew only had 9 apples left, so 36 is correct.