Exercise 10

By solving the following system of equations: [ begin{cases} cfrac{2}{x} – cfrac{1}{y} = 2 \[.5em] cfrac{1}{x} + cfrac{2}{y} = 11 end{cases} ] we obtain that (frac{x}{y}) equals to: (cfrac{4}{3}) (cfrac{3}{4}) (cfrac{1}{12}) (-cfrac{16}{5}) (-cfrac{26}{23}) Try to solve it before checking the answer. Answer (cfrac{4}{3}) Step by Step Solution Multiplying both equations by (x): (2 – cfrac{x}{y} […]

Exercise 9

If the sum of three numbers in arithmetic progression is 30 and their product is 510, what is the largest of these three numbers? 7 10 13 17 14 Try to solve it before checking the answer. Answer 17 Step by Step Solution Let these numbers be (a_1), (a_2) and (a_3), and let (d) be […]

Exercise 8

The sum of the values of (x) that cancel the expression (2x^2 – 4x – 16) is: (-4) (-2) (2) (4) (8) Try to solve it before checking the answer. Answer (2) Step by Step Solution We are being asked for the sum of the roots of the equation: ( 2x^2 – 4x – 16 […]

Exercise 7

If the radius of a circle measures 6, what is the perimeter of the square inscribed in such circle? (12 sqrt{2}) 12 24 36 (24 sqrt{2}) Try to solve it before checking the answer. Answer (24 sqrt{2}) Step by Step Solution The diagonal of the square is a diameter of the circumference, which measures 12. […]

Exercise 6

If (L_1)   and   (L_2) are parallel lines, what is the measure of angle (alpha?) (300^{circ}) (270^{circ}) (210^{circ}) (90^{circ}) (110^{circ}) Try to solve it before checking the answer. Answer (270^{circ}) Step by Step Solution Let’s draw the line (L) that is parallel to (L_1) and (L_2), and that passes through the vertex of the […]

Exercise 5

If (f(x) = x (x – 1)), then ( f(-x) ) equals to: (f(x)) (-f(x)) (f(1 – x)) (f(x + 1)) (f(x – 1)) Try to solve it before checking the answer. Answer (f(x + 1)) Step by Step Solution Indeed: [begin{aligned}f(x) &= (-x) ( (-x) – 1 )\[.5em]&=(-x) (-x -1)\[.5em]&=(-x) (-1) (x + 1)\[.5em]&=x […]

Exercise 4

If: [ x = 4^{ frac{k}{3} + 2L } left( sqrt[3]{4} right)^{ – (K + 4L) } left( 16^{ 1 – frac{L}{3} } right), ] then (x) equals to: If   ( x = 4^{ frac{k}{3} + 2L } left( sqrt[3]{4} right)^{ – (K + 4L) } left( 16^{ 1 – frac{L}{3} } right) ), […]

Exercise 3

A car travels at 10 miles per hour (mph) for one hour, doubles its speed in the second hour, and continues doubling its speed every hour thereafter. If the vehicle keeps this rate of change, what speed will it be traveling at during the seventh hour? 3200 mph 1280 mph 640 mph 320 mph 256 […]

Exercise 2

The expresion: [ begin{aligned} &frac{1}{2} – left[ frac{1}{2} – left{ frac{1}{4} – left( 2 cdot left( frac{1}{2} right) – frac{1}{4} right) right} right. \[.5em] &hspace{9em} left. + frac{1}{2} – left( – frac{1}{4} right) right] end{aligned} ] [ frac{1}{2} – left[ frac{1}{2} – left{ frac{1}{4} – left( 2 cdot left( frac{1}{2} right) – frac{1}{4} right) right} […]

Exercise 1

The greatest common multiple of 5 and 25 that is greater than 25 and lower than 100 is: 100 25 75 50 95 Try to solve it before checking the answer. Answer 75 Step by Step Solution The common multiples of 5 and 25 greater than 25 and lower than 100 are 50 and 75. […]