Answer:
In the given figure the point on segment PQ is twice as from P as from Q is. What is the point? Ans is (2,1).
Step-by-step explanation:
There is really no need to use any quadratics or roots.
( Consider the same problem on the plain number line first. )
How do you find the number between 2 and 5 which is twice as far from 2 as from 5?
You take their difference, which is 3. Now splitting this distance by ratio 2:1 means the first distance is two thirds, the second is one third, so we get
4=2+23(5−2)
It works completely the same with geometric points (using vector operations), just linear interpolation: Call the result R, then
R=P+23(Q−P)
so in your case we get
R=(0,−1)+23(3,3)=(2,1)
Why does this work for 2D-distances as well, even if there seem to be roots involved? Because vector length behaves linearly after all! (meaning |t⋅a⃗ |=t|a⃗ | for any positive scalar t)
Edit: We'll try to divide a distance s into parts a and b such that a is twice as long as b. So it's a=2b and we get
s=a+b=2b+b=3b
⇔b=13s⇒a=23s
If you are asking which ratio is equivalent to 8 then it is neither. They are both simplified to 3:1. 54/18= 3, 18/6= 3. If you were asking if they were equivalent to each other the answer is yes.
Answer:
Olivia is 24 years old
step by step
because Olivia is 20 years old and Mike is 4 years older than her so Olivia is 24 years old
Answer:
The y-intercept should be 8.
Step-by-step explanation:
Question
2,4,8,16 recursive form
Answer:
The first term is 2, and each term after that is twice the previous term, so the equations are:
a sub1 = 2
a sub n = 2a sub n-1, for n>1
