Step-by-step explanation:
The point that partitions the segment in a ratio of 3:1 is located at :
Y = -9 + [¾ × (7-(-9)]
= -9 + (¾ × 16)
= -9 + 12
= 3
the coordinates are (2, 3)
The point that partitions the segment in a ratio of 1:3 is located at :
X = 2 + [¼×(2-2)]
= 2 + (¼×0)
= 2+0
= 2
the coordinates are (2, -5)
Ken has 1 of his money. He spends 1/5 so he still has 4/5 of the original amount of money. He has 4/5 and he spends $21and ends up with 1/2 of his money. 4/5 = 8/10 and 1/2 = 5/10.This means that $21 is 8/10-5/10 of his original amount of money. so $21 is 3/10 of his original amount of money. 21/3*10=70. His original amount of money is $70. This means that 1/2 of his money is $35. So Ken has $35 left.
<span>rotation of 180° about the origin is correct. Changing the signs of both x and y rotates 180 degrees.
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In this triangle by applying Pythagoras theorem.
H²=B²+P²
18²=15²+P²
324=225+p²
324-225=P²
√99=p
9.94
Answer:
Step-by-step explanation:
-5(n^3 - n^2 - 1) + n(n^2 - n)
-5n^3 + 5n^2 + 5 + n^3 - n^2
-4n^3 + 4n^2 + 5 <===
(n^2 - 1)(n + 2) - n^2(n - 3)
n^2(n + 2) - 1(n + 2) - n^3 + 3n^2
n^3 + 2n^2 - n - 2 - n^3 + 3n^2
5n^2 - n - 2 <===
n^2(n - 4) + 5n3 - 6
n^3 - 4n^2 + 5n^3 - 6
6n^3 - 4n^2 - 6 <===
2n(n^2 - 2n - 1) + 3n^2
2n^3 - 4n^2 - 2n + 3n^2
2n^3 -n^2 - 2n <===
putting them in order based on the coefficient n^2 is :
6n^3 - 4n^2 - 6
2n^3 - n^2 - 2n
-4n^3 + 4n^2 + 5
5n^2 - n - 2