Let's solve the equation 2k^2 = 9 + 3k
First, subtract each side by (9+3k) to get 0 on the right side of the equation
2k^2 = 9 + 3k
2k^2 - (9+3k) = 9+3k - (9+3k)
2k^2 - 9 - 3k = 9 + 3k - 9 - 3k
2k^2 - 3k - 9 = 0
As you see, we got a quadratic equation of general form ax^2 + bx + c, in which a = 2, b= -3, and c = -9.
Δ = b^2 - 4ac
Δ = (-3)^2 - 4 (2)(-9)
Δ<u /> = 9 + 72
Δ<u /> = 81
Δ<u />>0 so the equation got 2 real solutions:
k = (-b + √Δ)/2a = (-(-3) + √<u />81) / 2*2 = (3+9)/4 = 12/4 = 3
AND
k = (-b -√Δ)/2a = (-(-3) - √<u />81)/2*2 = (3-9)/4 = -6/4 = -3/2
So the solutions to 2k^2 = 9+3k are k=3 and k=-3/2
A rational number is either an integer number, or a decimal number that got a definitive number of digits after the decimal point.
3 is an integer number, so it's rational.
-3/2 = -1.5, and -1.5 got a definitive number of digit after the decimal point, so it's rational.
So 2k^2 = 9 + 3k have two rational solutions (Option B).
Hope this Helps! :)
The answer is 93 to 31 :)
Answer:
ST = 12 units
Step-by-step explanation:
As RA is parallel to ET, the angle in R is equal to the angle in T, and the angle in A is equal to the angle in E, so the triangle RAS is similar to the triangle SET.
If RT is 21 units, we have that RS + ST = 21 -> RS = 21 - ST
Using a rule of three with the sides of the triangle (as they are proportional), we have:
RS / ST = AR / ET
(21 - ST) / ST = 6 / 8
4 * (21 - ST) = 3*ST
84 - 4*ST = 3*ST
7*ST = 84
ST = 12 units
We know that
g=3
r=2
b=5
total marbies=g+r+b------> 3+2+5----> 10
a) <span>probability that the first marble is red
P(red)=r/total marbies------------> 2/10-----> 1/5
b) </span><span>probability that the second marble is blue
in this case total marbles-------> 9
P(blue)=b/total marbles----------> 5/9
c) </span><span>the probability that the first marble is red and the second is blue
(1/5)*(5/9)=1/9
the answer is
1/9</span>
