Algebra Answers

If we know that the roots of the cubic equation x³ - 61x² -8000 = 0 are in G.P., then find the roots of the equation.

x>0, n>=1, prove that 1 + x + x² + .....+ x²ⁿ >= (2n+1)xⁿ

An employee of a big business company earns a gross annual salary of

₱450,000. What is the weekly, and monthly pay for this employee?

Solve each of the following problems. Follow Polya's four stages of problem solving in your solution.

1. An egg vendor broke all the eggs that he was delivering to a local store. He could not remember how many eggs there were in all. However, he did remember that when he tried to pack them into packages of 2, 3, 4, 5, and 6 he had one left over each time. When he packed them into packages of 7, he had another left over. What is the smallest number of eggs he could have had in the shipment?

2. Edwin has 100 baseball cards. He wants to place the cards in three stacks so that the second stack has twice as many cards as the first, and the third stack has twice as many cards as the second. How many cards will be in each stack? How many will be left over?

1. A box contains 3 red,10 white, 5 blue and 2 green balls identical in mass and shape. Find the ratio of the number of green ball to the total numbers of balls.

2. The number of goals scored by a famous footballer per match in a tournament are:

0,2,1 0,1,3,2,1,1,1,4,1,1,2,1 2,0,0,1,1,1,1,0,2,0,0,2,1,1,3

From this data, find the ratio of the number of matches where the footballer scored more than two goals to the total number of matches.

x - 3y + 6z = 21

3x + 2y - 5z = - 30

2x - 5y + 2z = -6

The sum of values of x

x, y

y, and z

z of the solution is

If a vertical and horizontal number line intersect perpendicularly, they form

right angles (of 90◦) with each other and a co-ordinate system of axes is formed, the horizontal line is called:

[1] Quadrants

[2] Y-axes

[3] Co-ordinates

[4] X-axes

A town has a population of 10000 and grows at 5% every year. What will be the population after 5 years, to the nearest whole number?

An element with mass 630 grams decays by

18.8% per minute. How much of the element

is remaining after 7 minutes, to the nearest

10th of a gram?