Which of the following pairs of inequalities is represented on the number line?
\(x<-2 and x\ge1\)
\(x\ge -2 and x>1\)
\(x\le -2 and x\ge1\)
\(x< -2 and x>1\)
Correct answer is C
No explanation has been provided for this answer.
\(\frac{m}{2}-3\le 10\)
\(\frac{m}{2}-3\ge 10\)
\(\frac{m-3}{2}\ge10\)
\(\frac{m-3}{2}\le10\)
Correct answer is C
Total number of mangoes = m
Amina ate 3 mangoes \(\implies\) Remainder = m - 3
Shared equally with Uche \(\implies \frac{m - 3}{2}\)
\(\frac{m - 3}{2} \geq 10\)
2cm
5cm
8cm
15cm
Correct answer is B
Volume of water after 9 seconds = \(5\pi \times 9 = 45\pi cm^3\)
Volume of cylinder = \(\pi r^2 h\)
\(\therefore \pi r^2 h = 45\pi\)
\(\pi \times 3^2 \times h = 45\pi\)
\(\implies 9h = 45 \)
\(h = 5 cm\)
(where h = height of the water after 9 secs)
24cm
36cm
72cm
144cm
Correct answer is B
Area = \(\frac{1}{2} \times base \times height\)
\(height : base = 1 : 3\)
\(\implies base = 3 \times height\)
Let height = h;
Area = \(\frac{1}{2} \times 3h \times h = 216\)
\(3h^2 = 216 \times 2 = 432\)
\(h^2 = \frac{432}{3} = 144\)
\(h = \sqrt{144} = 12.0 cm\)
\(\therefore base = 3 \times 12 = 36 cm\)
A car travel at x km per hour for 1 hour and at y km per hour for 2 hours. Find its average speed
\(\frac{2x + 2y}{3}kmh^{-1}\)
\(\frac{x + y}{3}kmh^{-1}\)
\(\frac{x + 2y}{3}kmh^{-1}\)
\(\frac{2x + y}{3}kmh^{-1}\)
Correct answer is C
Travelled x km/h for 1 hour \(\therefore\) traveled x km in the first hour.
Traveled y km/h for 2 hours \(\therefore\) traveled 2y km in the next 2 hours.
Average speed = \(\frac{x + 2y}{1 + 2}\)
= \(\frac{x + 2y}{3} kmh^{-1}\)
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