Solve for x and y if x - y = 2 and x2 - y2 = 8
(-1, 3)
(3, 1)
(-3, 1)
(1, 3)
Correct answer is B
x - y = 2 ...........(1)
x2 - y2 = 8 ........... (2)
x - 2 = y ............ (3)
Put y = x -2 in (2)
x2 - (x - 2)2 = 8
x2 - (x2 - 4x + 4) = 8
x2 - x2 + 4x - 4 = 8
4x = 8 + 4 = 12
x = \(\frac{12}{4}\)
= 3
from (3), y = 3 - 2 = 1
therefore, x = 3, y = 1
If 9x2 + 6xy + 4y2 is a factor of 27x3 - 8y3, find the other factor.
2y + 3x
2y - 3x
3x + 2y
3x - 2y
Correct answer is D
27x3 - 8y3 = (3x - 2y)3
But 9x2 + 6xy + 4y2 = (3x +2y)2
So, 27x3 - 8y3 = (3x - 2y)(3x - 2y)2
Hence the other factor is 3x - 2y
Make Q the subject of formula if p = \(\frac{M}{5}\)(X + Q) + 1
\(\frac{5P - MX + 5}{M}\)
\(\frac{5P - MX - 5}{M}\)
\(\frac{5P + MX + 5}{M}\)
\(\frac{5P + MX - 5}{M}\)
Correct answer is B
p = \(\frac{M}{5}\)(X + Q) + 1
P - 1 = \(\frac{M}{5}\)(X + Q)
\(\frac{5}{M}\)(p - 1) = X + Q
\(\frac{5}{M}\)(p - 1)- x = Q
Q = \(\frac{5(p -1) - Mx}{M}\)
= \(\frac{5p - 5 - Mx}{M}\)
= \(\frac{5p - Mx - 5}{M}\)
Find the equation of a line parallel to y = -4x + 2 passing through (2,3)
y + 4x + 11 = 0
y - 4x - 11 = 0
y + 4x - 11 = 0
y - 4x + 11 = 0
Correct answer is C
By comparing y = mx + c
with y = -4x + 2,
the gradient of y = -4x + 2 is m1 = -4
let the gradient of the line parallel to the given line be m2,
then, m2 = m1 = -4
(condition for parallelism)
using, y - y1 = m2(x - x1)
Hence the equation of the parallel line is
y - 3 = -4(x-2)
y - 3 = -4 x + 8
y + 4x = 8 + 3
y + 4x = 11
y + 4x - 11 = 0
At what value of X does the function y = -3 - 2x + X2 attain a minimum value?
-1
14
4
1
Correct answer is D
Given that y = -3 - 2x + X2
then, \(\frac{dy}{dx}\) = -2 + 2x
At maximum value, \(\frac{dy}{dx}\) = O
therefore, -2 + 2x
2x = 2
x = 2/2 = 1