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! :)
Looks like the system is
We can eliminate 
by taking
so that 
, and
Substitute into this last equation and solve for 
:
Then
Plug these values into any one of the original equation to solve for :
Hence the solution is x = 4, y = -3, and z = 2.
Answer: 6
Step-by-step explanation:
1 2/10 x 5=6 hope this helps
Answer:
See below
Step-by-step explanation:
It's hard to see your photo but if that say m∠T than your answer would be
m∠ L.
The drawings are saying the the triangles are congruent which means all the interior angles of one triangle are congruent to the angles of the second triangle. m∠M = m∠J, m∠K = m∠E and m∠L = m∠T
Since you have two of the angles, you can also determine what m∠L and m∠T is equal to. The sum on all interior angles must be 180 degrees.
180 - 86 - 32 = 62
X 0 1 2 ...
y -2 -9 -16...
(y) decreases by 7/<span> (x) increases by 1, so slope =-7,
y- int=-2
this is equation c) y=-7x-2</span>
