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
To have a remainder 3, we take away 3 from each number first.
<u>Take away 3:</u>
224 - 3 = 221
250 - 3 = 247
302 - 3 = 299
<u>Prime factorisation of each of the numbers:</u>
221 = <span>13 x 17
247 = 13 x 19
299 = 13 x 23
<u>Find HCF:</u>
HCF = 13
Answer: The largest number that can be divided is 13.</span>
Answer:
x = 5/7
Step-by-step explanation:
(7^x)^4) = 7^2 * 7^3 / 7^3x
1. Simplify the expression
(7^x)^4) becomes 7^4x
7^2 * 7^3 becomes 7^5
7^5/7^3x becomes 7^5 - 7^3x
Your new equation: 7^4x = 7^5 - 7^3x
2. Since the bases(7) are the same set the exponents equal to each other
4x = 5 - 3x
3. Combine like terms
4x + 3x = 5
7x = 5
4. Divide both sides by 7 to get x by itself
x = 5/7
Answer:
Step-by-step explanation:
look, area = length x width
so that means that the area of this rectangle is
= 11 1/2 * 8
= 23/2 * 8
= 23 * 4 (simplified)
= 92 in^2