The graph of the relation y = x2 + 2x + k passes through the point (2, 0). Find the values of k
zero
-2
-4
-8
Correct answer is D
y = x2 + 2x + k at point(2,0) x = 2, y = 0
0 = (2)2 + 2(20 + k)
0 = 4 + 4 + k
0 = 8 + k
k = -8
If y varies directly s the square root of (x + 1) and y = 6 when x = 3, find x when y = 9
8
7
6
5
Correct answer is A
y \(\alpha\) \sqrt{x + 1}\), y = k\sqrt{x + 1}\)
6 = k\(\sqrt{3 + 1}\)
6 = k\(\sqrt{4}\)
6 = 2k
k = \(\frac{6}{2}\) = 3
y = \(\sqrt{(x + 1)}\)
9 = 3\(\sqrt{(x + 1)}\)(divide both side by 3)
\(\frac{9}{3}\) = \(\frac{3\sqrt{x + 1}}{3}\)
3 = \(\sqrt{x + 1}\)(square both sides)
9 = x + 1
x = 9 - 1
x = 8
Find the values of k in the equation 6k2 = 5k + 6
{\(\frac{-2}{3}, \frac{-3}{2}\)}
{\(\frac{-2}{3}, \frac{3}{2}\)}
{\(\frac{2}{3}, \frac{-3}{2}\)}
{\(\frac{2}{3}, \frac{3}{2}\)}
Correct answer is B
6k2 = 5k + 6
6k2 - 5k - 6 = 0
6k2 - 0k + 4k - 6 = 0
3k(2k - 3) + 2(2k - 3) = 0
(3k + 2)(2k - 3) = 0
3k + 2 = 0 or 2k - 3 = 0
3k = -2 or 2k = 3
k = \(\frac{-2}{3}\) or k = \(\frac{3}{2}\)
k = (\(\frac{-2}{3}\), k = \(\frac{3}{2}\))
If p = (y : 2y \(\geq\) 6) and Q = (y : y -3 \(\geq\) 4), where y is an integer, find p\(\cap\)Q
{3, 4}
{3, 7}
{3, 4, 5, 6, 7}
{4, 5, 6}
Correct answer is C
p = (y : 2y \(\geq\) 6)
2y \(\leq\) 6
y \(\leq \frac{6}{2}\)
y = \(\leq\) 3
and Q = (y : y -3 \(\geq\) 4)
y - 3 \(\geq\) 4
y \(\geq\) 4 + 3
y \(\geq\) 7
therefore p = {3, 4, 5, 6, 7} and Q = {7, 6, 5, 4, 3....}
P\(\cap\)Q = {3, 4, 5, 6, 7}
If 2 log x (3\(\frac{3}{8}\)) = 6, find the value of x
\(\frac{3}{2}\)
\(\frac{4}{3}\)
\(\frac{2}{3}\)
\(\frac{1}{2}\)
Correct answer is A
2 log x (3\(\frac{3}{8}\)) = 6(divide both sides by 2)
\(\frac{2 log_x(3 \frac{3}{8})}{2} = \frac{6}{2}\)
\(\log_x \frac{27}{8} = 3\)
\(\frac{27}{8} = x^3\)
\(x^3 = \frac{27}{8}\)
x = \(\sqrt{\frac{27}{8}}\)
= (\(\frac{27}{8}\))\(\frac{1}{3}\)
= \(\frac{(3^3)^{\frac{1}{3}}}{(2^3)^{\frac{1}{3}}}\)
= \(\frac{3}{2}\)