PQRS is a cyclic quadrilateral. If ∠QPS = 75°, what is the size of ∠QRS?
180o
150o
105o
75o
Correct answer is C
< QPS = 75°
< QRS = 180° - 75° = 105° (opposite angles of a cyclic quadrilateral)
5cm
9cm
12cm
15cm
Correct answer is C
\(V= \frac{1}{2}\hspace{1mm}base\hspace{1mm}area\hspace{1mm}\times\hspace{1mm}height\\
120=\frac{1}{3}\times 5 \times 6 \times h; h = \frac{120}{10}=12cm\)
Evaluate \(\frac{log8}{log\left(\frac{1}{4}\right)}\)
-2
\(\frac{-3}{2}\)
\(\frac{1}{2}\)
4
Correct answer is B
\(\frac{log8}{log\frac{1}{4}}=\frac{log2^3}{log2^{-2}}=\frac{3log2}{-2log2}=-\frac{3}{2}\)
Find the value of x which satisfies the equation
5(x-7)=7-2x
x =2
x=4
x=6
x = 14
Correct answer is C
5(x - 7) = 7 - 2x
5x - 35 = 7 - 2x
5x + 2x = 7 + 35
7x = 42
x = \(\frac{42}{7}\)
= 6
Simplify \(\left(1\frac{2}{3}\right)^2 - \left(\frac{2}{3}\right)^2\)
\(2\frac{1}{3}\)
\(1\frac{1}{3}\)
1
\(\frac{3}{7}\)
Correct answer is A
\(\left(1\frac{2}{3}\right)^2 - \left(\frac{2}{3}\right)^2=\left(\frac{5}{3}\right)^2 - \left(\frac{2}{3}\right)^2\)
Difference of two squares
\(\left(\frac{5}{3}-\frac{2}{3}\right)\left(\frac{5}{3}+\frac{2}{3}\right)=\left(\frac{3}{3}\right)\left(\frac{7}{3}\right)\\
\frac{7}{3}=2\frac{1}{3}\)
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