Answer:
Step-by-step explanation:
![\frac{x^{3} }{\sqrt[6]{x}}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E%7B3%7D%20%7D%7B%5Csqrt%5B6%5D%7Bx%7D%7D)
Answer:
Step-by-step explanation:
<span>
If BA is d units the CB must be 2d units. B is on the x-axis, 2d units
right of C so its coordinates are (2d, 0). A is d units above B at (2d,
d). </span>
Answer: A) 30 cards
<u>Step-by-step explanation:</u>
1. 52 cards
2. subtract red suit cards: 52 - 26 = 26
3. add back the hearts: 26 + 13 = 39
4. remove the 3 remaining jacks, 3 remaining queens, & 3 remaining kings: 39 - 9 = 30
There are 30 cards remaining
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! :)
