2 Pints in a Quart
If the solutions are p and q, then the quadratic is (x-p)(x-q) = 0 or x2 - (p+q)x + pq = 0 Hope this is what the question meant!
Two ratios, p/q and r/s (q and s non-zero) are equal if p/q - r/s = 0.
If the two axes intersect at the point (p, q), then the equation is: (x -p)2/25 + (y - q)2/9 = 1
p and q
If (p, q) is any point on the line, then the point slope equation is: (y - q)/(x - p) = 2 or (y - q) = 2*(x - p)
The p and q variables in the Hardy-Weinberg equation represent the frequencies of the two alleles in a population. The equation is often written as p^2 + 2pq + q^2 = 1, where p and q represent the frequencies of the dominant and recessive alleles, respectively.
Assume the two numbers are P & Q, the equation is P + Q = 53, rearranging this gives Q = 53 - P
2 Pints in a Quart
If P varies directly with the square of Q then the equation would be in the form of P = kQ2, where k is the constant of variation so the new equation would be: P = 6Q2, so when Q = 12 we have P=6*122, or P = 864
If the solutions are p and q, then the quadratic is (x-p)(x-q) = 0 or x2 - (p+q)x + pq = 0 Hope this is what the question meant!
Two ratios, p/q and r/s (q and s non-zero) are equal if p/q - r/s = 0.
2p + 3q = 13, 5p - 4q = -2 Multiply the first equation by 4 and the second by 3 and add them, which gets rid of the q: 8p + 15p = 52 - 6, and 23p = 46, so p=2. Plug that into the first equation to find q: 4 + 3q = 13, so q=3. Test your answers in the second equation to be sure: 5(2) - 4(3) = 10-12 = -2. It checks. So p=2, q=3.
If the two axes intersect at the point (p, q), then the equation is: (x -p)2/25 + (y - q)2/9 = 1
A simultaneous equation
p and q
The values of p and q work out as -2 and 4 respectively thus complying with the given conditions.