Find the \(n^{th}\) term of the sequence 2 x 3, 4 x 6, 8 x 9, 16 x 12...
2\(^n\) x 3(n + 1)
2\(^n\) x 3n
2\(^n\) x 3\(^n\)
2\(^n\) x 3\(^n - 1\)
Correct answer is B
2 x 3, 4 x 6, 8 x 9, 16 x 12,...
2\(^1\) x 3 x 1, 2\(^2\) x 3 x 2, 2\(^3\) x 3 x 3, 2\(^4\) x 3 x 4,.... 2\(^n\) x 3n
(3x + 2)(1 - x)
(3x + 2)(2x + 1)
3\((x + 2)^2\)
3(x + 1)(1 - x)
Correct answer is D
\((x + 2)^2\) - \((2x + 1)^2\)
= \((x^2 + 4x + 4) - (4x^2 + 4x + 1)\)
= \(x^2 \) + 4x + 4 - 4 \(x^2 \) - 4x - 1
= -3 \(x^2 \) + 3
= 3 - 3 \(x^2 \)
= 3(1 - \(x^2 \))
= 3(1 + x)(1 - x)
Solved the equation \(2x^2 - x - 6\) = 0
x = \(\frac{-3}{2}\) or 2
x = -2 or \(\frac{3}{2}\)
x = -3 or 2
x = 3 or -2
Correct answer is A
\(2x^2 - x - 6\) = 0
\(2x^2 - 4x + 3x - 6\) = 0
2x(x - 2) + 3(x - 2) = 0
(2x + 3) (x - 2) = 0
Either; 2x + 3 = 0 or x - 2 = 0
x = \(\frac{-3}{2}\) or x = 2
Find the value of x for which \(\frac{x - 5}{x(x - 1)}\) is defined
0 or 5
-5 or 5
-11 or 5
0 or 1
Correct answer is A
The expression \(\frac{x - 5}{x(x - 1)}\) is defined whten
x(x - 5) = 0.38
either x = 0 or x - 5 = 0
Hence, x = 0 or x = 5
The total surface area of a hemispher is 75\(\pi cm^2\). Find the radius.
5.0 cm
7.0 cm
8.5 cm
12.0 cm
Correct answer is A
Total surface area of hemisphere is
3\(\pi r^2\) = 75\(\pi cm^2\)
\(r^2\) = \(\frac{75 \pi}{3 \pi}\)
\(r^2\) = 25
r = \(\sqrt{25}\)
r = 5cm