Find the value of p if \(\frac{1}{4}\)p + 3q = 10 and 2p - q = 7
4
3
-3
-4
Correct answer is A
\(\frac{1}{4}\)p + 3p = 10...(1)
2p - \(\frac{1}{3}\)q = 7...(2)
Multiply equation (2) by 3 to clear fraction
3 x 2p - 3 x \(\frac{1}{3}\)q = 3 x 7
6p - q = 21
6p - 21 = q....(3)
substituting 6p - 21 for q in (1)
\(\frac{1}{4}\)p + 3(6p - 21) = 10...(4)
Multiply equation (4) by 4 to clear fraction
4 x \(\frac{1}{4}\)p + 4 x 3(6p - 21) = 4 x 10
p + 12(6p - 21) = 40
p + 72p - 252
73p = 292
p = \(\frac{292}{73}\)
= 4
Describe the shaded portion in the diagram
P' \(\cap\) Q \(\cap\) R'
(P' \(\cap\) R)' \(\cap\) R
P' \(\cap\) Q \(\cap\) R
(P \(\cap\) Q)' \(\cap\) R
Correct answer is A
No explanation has been provided for this answer.
A trader bought 100 oranges at 5 for N40.00 and 20 for N120.00. Find the profit or loss percent
20% profit
20% loss
25% profit
25% loss
Correct answer is D
Cost price CP of the 100 oranges = \(\frac{100}{5}\) x N40.00
selling price SP of the 100 oranges = \(\frac{100}{20}\) x N120
= N600.00
so, profit or loss per cent
= \(\frac{SP - CP}{CP}\) x 100%
= \(\frac{600 - 800}{800}\) x 100%
= \(\frac{-200}{800}\) x 100%
Hence, loss per cent = 25%
22\(\frac{1}{2}\)km
30km
33\(\frac{1}{2}\)km
45km
Correct answer is A
R \(\alpha\) D2
R = D2K
R = 4 Litres when D = 15cm
thus; 4 = 152k
4 = 225k
k = \(\frac{4}{225}\)
This gives R = \(\frac{4D^2}{225}\)
Where R = 9litres
equation gives
9 = \(\frac{4D^2}{225}\)
9 x 225 = 4d2
D2 = \(\frac{9 \times 225}{4}\)
D = \(\sqrt{9 \times 225}{4}\)
= \(\frac{3 \times 15}{2}\)
= 22\(\frac{1}{2}\)km
\(\frac{2}{15}\)
\(\frac{2}{5}\)
\(\frac{2}{3}\)
\(\frac{4}{5}\)
Correct answer is B
Let x represent the entire farmland
then, \(\frac{2}{5}\)x + \(\frac{1}{3}\)[x - \(\frac{2}{3}x\)] + M = x
Where M represents the part of the farmland used for growing maize, continuing
\(\frac{2}{5}\)x + \(\frac{1}{3}\)x [1 - \(\frac{2}{3}x\)] + M = x
\(\frac{2}{5}x + \frac{1}{3}\)x [\(\frac{3}{5}\)] + M = x
\(\frac{2}{5}\)x + \(\frac{1x}{5}\) + M = x
\(\frac{3x}{5} + M = x\)
M = x - \(\frac{2}{5}\)x
= x[1 - \(\frac{3}{5}\)]
= x[\(\frac{2}{5}\)] = \(\frac{2x}{5}\)
Hence the part of the land used for growing maize is
\(\frac{2}{5}\)