The area of a right triangle is 50. One of its angles is 45. Find the lengths of the sides and hypotenuse of the triangle.
The triangle is right and the size one of its angles is 45; the third angle has a size 45 and therefore the triangle is right and isosceles(2 sides are equal) . Let x be the length of one of the sides and H be the length of the hypotenuse. Area = (1/2)square of x = 50 , solve for x: x = 10 We now use Pythagoras theorem to find H: sq(x) + sq(x) = sq(H) Solve for H: H = 10 sqrt(2)
An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost?
Lets consider 100 which is easy to understand, as an instrument store gives 10% discount we will get 10 Off thus julie pays 90 , while going back to school she gets 15% more on 90 thus discount will be 90*15/100 = 13.5 is the off thus 90-13.5 = 76.5 will the amount which will be payed for 100. Now julie would have payed $306. If 100 is the before discount for 76.5 then how much is for 306 = 306*100/76.5 = $400 Thus the original cost price = $400
Find the equation of the line that passes through the points (–2, 4) and (1, 2).
equation of line is given by y=mx+c or y=mx+b where m is the slope( change in y axis to the change in x axis) c or b is the y intercept. intercept is the point where it touches the axis. example x intercept is x the point where the line touches x axis . thus we can find the respective intercepts by making other zero. we are given two points on the graph through which line passes through thus according to the definition of slope it is the difference between y and x axis x1= -2 , x2 = 1 , y1=4, y2=2 m = (y2-y1)/(x2-x1) = (2-4)/(1-(-2)) = -2/3 As the line passes through these points we can use any of the two points to find b lets take (1,2) now we have equation as y=-2/3x+b by substituting the value of x as 1 and y as 2 : 2 = -2/3(1) +b b = 8/3 Thus y=-2/3x+8/3 3y=-2x+8