If \(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\), find the value of x.
x = -4
x = 2
x = -2
x = 4
Correct answer is A
\(25^{1 - x} \times 5^{x + 2} \div (\frac{1}{125})^{x} = 625^{-1}\)
\((5^2)^{(1 - x)} \times 5^{(x + 2)} \div (5^{-3})^x = (5^4)^{-1}\)
\(5^{2 - 2x} \times 5^{x + 2} \div 5^{-3x} = 5^{-4}\)
\(5^{(2 - 2x) + (x + 2) - (-3x)} = 5^{-4}\)
Equating bases, we have
\(2 - 2x + x + 2 + 3x = -4\)
\(4 + 2x = -4 \implies 2x = -4 - 4\)
\(2x = -8\)
\(x = -4\)
Express \((0.0439 \div 3.62)\) as a fraction.
\(\frac{21}{100}\)
\(\frac{21}{1000}\)
\(\frac{12}{1000}\)
\(\frac{12}{100}\)
Correct answer is C
\((0.0439 \div 3.62)\)
= 0.01213
\(\approxeq\) 0.012
= \(\frac{12}{1000}\)
\(\frac{\pi h}{3} (2R + r)\)
\(2R + r + \frac{\pi h}{3}\)
\(\frac{\pi h}{3} (2R^2 + r + 2r)\)
\(\frac{2R^2}{3} \pi h\)
Correct answer is A
\(V = \frac{\pi h}{3} (R^2 + Rr + r^2)\)
\(V = \frac{\pi R^2 h}{3} + \frac{\pi Rr h}{3} + \frac{\pi r^2 h}{3}\)
\(\frac{\mathrm d V}{\mathrm d R} = \frac{2 \pi R h}{3} + \frac{\pi r h}{3}\)
= \(\frac{\pi}{3} (2R + r)\)
43.7% loss
13.2% gain
13.2% loss
43.7% gain
Correct answer is C
Cost price of the car = N 1,250.00
Selling price = N 1,085.00
Loss = N (1250 - 1085)
= N 165.00
% loss = \(\frac{165}{1250} \times 100%\)
= 13.2% loss
1080°
1260°
2160°
1800°
Correct answer is B
Since each interior angle = 140°;
Each exterior angle = 180° - 140° = 40°
Number of sides of the polygon = \(\frac{360°}{40°}\)
= 9
Sum of angles in the polygon = 140° x 9
= 1260°