t = -2 and 3
t = 2 and -3
t = 2 and 3
t = -2 and -3
Correct answer is C
For collinear points (points on the same line), the slopes are equal for any 2 points on the line.
Given (-1, t - 1), (t, t - 3), (t - 6, 3),
\(slope = \frac{(t-3) - (t-1)}{t - (-1)} = \frac{3 - (t-3)}{(t-6) - t} = \frac{3 - (t-1)}{(t-6) - (-1)}\)
Taking any two of the equations above, solve for t.
\(\frac{t - 3 - t + 1}{t + 1} = \frac{6 -t}{-6}\)
\(12 = (6 - t)(t + 1)\)
\(-t^{2} + 5t + 6 - 12 = 0 \implies t^{2} - 5t + 6 = 0\)
Solving, we have t = 2 and 3.
Find the variance of 1, 2, 0, -3, 5, -2, 4.
\(\frac{52}{7}\)
\(\frac{40}{7}\)
\(\frac{32}{7}\)
\(\frac{27}{7}\)
Correct answer is A
Mean, \(\bar{x} = \frac{1+2+0+(-3)+5+(-2)+4}{7} = \frac{7}{7} = 1\)
| \(x\) | \((x - \bar{x})\) | \((x - \bar{x})^{2}\) |
| 1 | 0 | 0 |
| 2 | 1 | 1 |
| 0 | -1 | 1 |
| -3 | -4 | 16 |
| 5 | 4 | 16 |
| -2 | -3 | 9 |
| 4 | 3 | 9 |
| Total (n) = 7 |
52 |
Variance = \(\frac{\sum (x - \bar{x)^{2}}{n}\)
= \(\frac{52}{7}\)
In how many ways can 9 people be seated on a bench if only 3 places are available?
1200
504
320
204
Correct answer is B
No explanation has been provided for this answer.
5.7\(ms^{-1}\)
6.0\(ms^{-1}\)
60.0\(ms^{-1}\)
77.5\(ms^{-1}\)
Correct answer is A
\(s = ut + \frac{1}{2}at^{2}\)
\(250 = 6u + \frac{1}{2}(12)(6^{2})\)
\(250 = 6u + 216 \implies 6u = 250 - 216 = 34\)
\(u = \frac{34}{6} \approxeq 5.7ms^{-1}\)
For what values of m is \(9y^{2} + my + 4\) a perfect square?
\(\pm {2}\)
\(\pm {3}\)
\(\pm {6}\)
\(+12\)
Correct answer is D
No explanation has been provided for this answer.