Simplify: \(\frac{x^2 - y^2}{(x + y)^2} \div \frac{(x - y)^2}{(3x + 3y)}\)
\(\frac{x - y}{3}\)
x + y
\(\frac{3}{x - y}\)
x - y
Correct answer is C
\(\frac{x^2 - y^2}{(x + y)^2} \div \frac{(x - y)^2}{(3x + 3y)}\)
\(\frac{(x + y)(x - y)}{(x + y)(x + y)}\div \frac{(x - y)(x - y)}{3(x + y)}\)
= \(\frac{3}{x - y}\)
N94x + 6y)
N(6x + 4y)
N(24x + 12y)
N(12x + 24y)
Correct answer is B
4 oranges sell for Nx, 1 orange will sell for \(\frac{Nx}{4}\)
24 oranges will sell for: \(\frac{Nx}{4} \times 24\) = n6x
3 mangoes sell for Ny, 1 mango will sell for \(\frac{Ny}{3}\)
12 mangoes will sell for \(\frac{Ny}{3} \times 12\) = 4Ny
total money pay N6x + N4y = N(6x + 4y)
A sales boy gave a change of N68 instead of N72. Calculate his percentage error
4%
5\(\frac{5}{9}\)%
5\(\frac{15}{17}\)%
7%
Correct answer is B
% error = \(\frac{error}{\text{actual value}} \times 100\)
error = N72 - N68 = 4
actual value = N72
%error = \(\frac{4}{72} \times 100\)
= \(\frac{100}{18} = \frac{50}{9}\) = 5\(\frac{5}{9}\)%
If \(\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}\), find K
-2
-1
1
2
Correct answer is D
\(\sqrt{50} - K\sqrt{8} = \frac{2}{\sqrt{2}}\)
\(\sqrt{50} - \frac{2}{\sqrt{2}}\) = K\(\sqrt{8}\)
= \(\sqrt{2} \times 25 - \frac{2}{\sqrt{2}}\)
= K \(\sqrt{4 \times 2}\)
\(\frac{5\sqrt{2}}{1} - \frac{2}{\sqrt{2}}\) = 2K\(\sqrt{2}\)
\(\frac{5\sqrt{4} - 2}{\sqrt{2}} = 2K\sqrt{2}\)
\(\frac{10 - 2}{\sqrt{2}} = 2K \sqrt{2}\)
\(\frac{8}{\sqrt{2}} = \frac{2K\sqrt{2}}{1}\)
= 2k\(\sqrt{2} \times \sqrt{2}\) = 8
2k \(\sqrt{4}\) = 8
2k x 2 = 8
4k = 8
k = \(\frac{8}{4}\)
k = 2
If Un = n(n2 + 1), evaluate U5 - U4
18
56
62
80
Correct answer is C
Un = n(n2 + 1)
U5 = 5(2 + 1)
= 5(25 + 1)
= 5(26) = 130
U4 = 4(42 + 1) = 4(16 + 1)
= 4(17) = 68
U5 - U4 = 130 - 68
= 62