\(\frac{1}{18}\)
\(\frac{8}{81}\)
\(\frac{9}{2}\)
8
Correct answer is D
\(x \propto \frac{1}{y}\)
\(x = \frac{k}{y}\)
\(\frac{2}{3} = \frac{k}{9}\)
\(3k = 18 \implies k = 6\)
\(x = \frac{6}{y}\)
When y = \(\frac{3}{4}\),
x = \(\frac{6}{\frac{3}{4}}\)
= \(\frac{6 \times 4}{3}\)
= 8
Given that \(27^{(1+x)}=9\) find x
-3
\(\frac{-1}{3}\)
\(\frac{5}{3}\)
2
Correct answer is B
\(27^{(1+x)}=9\\
3^{3(1+x)}=3^2\\
3(1+x)=2\\
3+3x = 2\\
3x = -1
x = \frac{-1}{3}\)
Given that \(x = -\frac{1}{2}and \hspace{1mm} y = 4 \hspace{1mm} evaluate \hspace{1mm} 3x^2y+xy^2\)
-5
-1
4
11
Correct answer is A
\(x = -\frac{1}{2}, y = 4\\
3x^2y + xy^2\\
3\left[-\frac{1}{2}\right]^2 \times 4 \times + \left(\frac{-1}{2}\right)(4)^2\\
3\times \frac{1}{4} \times 4 -\frac{1}{2} \times 16\\
3-8 = -5\)
160o
140o
120o
100o
Correct answer is D
< T = < S = 50° (OS = OT)
< SOT = 180° - 2(50°) = 80°
< ROP = 80° (vertically opposite angle)
\(\therefore\) < OPQ = 180° - 80° = 100° (adjacent angles)
If the interior angles of hexagon are 107°, 2x°, 150°, 95°, (2x-15)° and 123°, find x.
\(57\frac{1}{2}^{\circ}\)
\(65^{\circ}\)
\(106^{\circ}\)
\(120^{\circ}\)
Correct answer is B
Sum of interior angle in a hexagon = (6 - 2) x 180°
= 720°
\(\therefore\) 107° + 2x° + 150° + 95° + (2x - 15)° + 123° = 720°
460 + 4x = 720 \(\implies\) 4x = 720 - 460
4x = 260° \(\implies\) x = 65°
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