If f(x) = x² + 5x and g(x) = 2x + 1, find f(5) + g(6).
since the triangle is right use the sine ratio to find x
sin65° = =
multiply both sides by x
x × sin65° = 22 ( divide both sides by sin65° )
x = ≈ 24.27 cm → d
triangle b is right
using the converse theorem of pythagoras.
if the square of the longest side in a triangle equals the sum of the squares of the other 2 sides then the triangle is right.
longest side squared = 36² = 1296
26² + 18² = 676 + 324 = 1000 ≠ 1296
hence triangle a is not right
longest side squared = 25² = 625
20² + 15² = 400 + 225 = 625 ← correct
hence triangle b is right
let w represent lizette's walking speed. then her running speed is w+6. the relationship between speed, time, and distance is
distance = speed × time
lizette ran for 1.5 hours, then walked for 3 hours. her total distance is
(w+6)·1.5 + w·3 = 18
4.5w + 9 = 18 . . . simplify
4.5w = 9 . . . . . subtract 9
w = 2 . . . . . . divide by 4.5
lizette's walking speed is 2 mph; her running speed is 8 mph.