Algebra Answers

if xyz = 1,then prove that 1/xyz^-1 + 1/xzy^-1 + 1/ yzx^-1 =1

Answer using the Venn Diagram.

1. In a certain supermarket 100 people were ask on the preferred brand of shampoo they like to be use:

6 preferred palmolive, sunsilk, dove
14 preferred palmolive and sunsilk
16 preferred palmolive and dove
15 preferred sunsilk and dove
34 preferred palmolive
42 preferred dove
50 preferred sunsilk


How many people preferred:

a. Exactly two types of brand?
b. At most 3 types of brand?
c. At least 2 types of brand?
d. None of the 3 brand?
e. Palmolive brand only?
f. Sunsilk brand only?
g. Dove and Sunsilk brand?
h. Dove or Sunsilk brand?
i. Palmolive or Sunsilk brand?
j. Dove and Sunsilk brand?

Find the Domain and Range:

f(x)= - square root -2x+3

f(x) = x^2 + x+2 / X^2 -x-2

what are the roots of x^3-2x^2-x+2=0?

A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 meters, assuming the width to be x, form an equation in x and solve it to find the value of x.

A plot 110 meters long and 80 meters broad is to be covered with grass leaving 5 meters all around. Find the area to be laid with grass.

The length of a rectangle is twice it's width. If the length of its diagonal is 16√5cm, find its area.

what are the zeros of the equation -x^3+5x^2-17x+13

Andrew has been doing archery for a number of years. While training, he noticed that when he draws the arrow, the bow is in the shape of a conic section. Determine the equation of this conic section given that the distance between his hands when he draws the arrow is 0.5 m and that the cor is attached to the bow at points (-2,-) and (-2,4). In addition, in a Cartesian coordinate system, his bow is open to the right.

A worker in a factory is paid Rs 2 per hour for normal work and double the rate for overwork. Write down the an expression for his one weeks earnings in which he worked 40 hours out of which x hours was overtime.