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 = \(\sqrt{\frac{27}{8}}\)
= (\(\frac{27}{8}\))\(\frac{1}{3}\)
= \(\frac{(3^3)^{\frac{1}{3}}}{(2^3)^{\frac{1}{3}}}\)
= \(\frac{3}{2}\)
Which of the following is not a probability of Mary scoring 85% in a mathematics test?
0.15
0.57
0.94
1.01
Correct answer is D
The probability not scoring 85% is = 1 - pro(scoring 85%)
= 1 - \(\frac{85}{100}\) = 1 - 0.85
= 0.15
not scoring would be less than 1
The bearing of Y from X is 060o and the bearing of Z from Y = 060o. Find the bearing of X from Z
300o
240o
180o
120o
Correct answer is B
No explanation has been provided for this answer.