Answer:
The ratio in which the line x-y-2=0 divides the line joining A(3,-1) and B(8,9) is in the ratio 2:3
Step-by-step explanation:
Let (x, y) be the coordinates of point of intersection.
Hence x=(a*8+1*3)(a+1) = (8a+3)/(a+1)
and
y = {a*9+1*(-1)}/(a+1)=(9a-1)/(a+1)
Since this point lies on the line x-y-2=0
Hence (8a+3)/(a+1)-(9a-1)/(a+1)-2=0
i.e. 8a+3–9a+1–2(a+1)=0
Or 8a+3–9a+1–2a-2=0
i.e.-3a+2=0
Hence a=2/3
hence the ratio in which the line x-y-2=0 divides the line joining A(3,-1) and B(8,9) in the ratio 2/3:1
i.e. 2:3
9514 1404 393
Answer:
A∩B = {2, 23}
Step-by-step explanation:
The intersection of two sets is the list of elements common to both.
2 is found in both
12, 19 are only in set A
23 is found in both
29 is only in set A
34, 40, 45 are only in set B
The intersection of the two sets is {2, 23}.
Basically the Remainder theorem states that the remainder of dividing a polynomial P(x) by (x - a) is given by P(a).
So for example if we divide x^ 2 - 2x + 7 by x - 2 the remainder will be
2^2 - 2(2) + 7 = 7..
If the remainder is 0 then the divisor will be a factor of the polynomial. This is the Factor Theorem and can be used to test if a given polynomial has a factor x-a.
Answer:
n= 4f/5+90
Step-by-step explanation:
f= 5(n−90)
/4 (simplify)
f * 4=5(n−90) (multiply 4 on both sides)
4f=5(n−90) (regroup)
4f/5
=n−90 (divide 5 on both sides)
4f/5
+90=n (add 90 to both sides)
