(x+2)(4+y)(5+6)(2+x)(4+0.5x)
combine like terms
(x+2) (4+y) (11) (x+2) (4+.5x)
11(x+2)^2 (4+y)(4+.5x)
distribute
11(x^2 +4x+2) (16+4y+2x+.5xy)
(11x^2+44x+22)(16+4y+2x+.5xy)
5.5 x^3 y + 22 x^3 + 66 x^2 y + 264 x^2 + 198 x y + 792 x + 176 y + 704
Answer:
16
Step-by-step explanation:
(6, 4, 4, 5, 1, 8, 10, 7, 8, 6, 6, 7, 5, 4, 6)
Lapatulllka [165]
<span>In a stem-and-leaf plot, </span><span>5| 4 means 54</span>
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
