Algebra Answers

Simplify (2c+12)(12-2c)

(12/15 + 16/50) * (1 - 7/8)

convert 67.5% into simple fraction

8/49 × 7/24 ÷ − 2/14

The annual bonus given to the employees of a company is 5% of their taxable incomes . after the state and central taxes are deducted.The state tax 10% of taxable income. The central tax is 20% of taxable income after deducting the state tax. Formulate this situation for determining the bonus.as a linear system.

Find the roots of the equation 2x^3 - x^2 - 22x - 24 = 0 .if two of them are in the ratio 3:4 .

Let x_i belongs to R such that 0 < x_1<= x_2 <= ...<= x_n , n>= 2 and (1/1+x_1)+(1/1+x_2)+...+(1/1+x_n) = 1 .Then show that √x_1 + √x_2 + ..+ √x_n >= (n-1) [( 1/√x_1)+...+(1/√x_n) .

A new car is purchased for 17900 dollars. The value of the car depreciates at 13% per year. What will the value of the car be, to the nearest cent, after 7 years?

A CNC machine has been programmed to drill 10 blind holes in a piece of flat plate. Each hole has a
depth which increments from the previous one by an amount derived from an arithmetic progression
(AP).
Hole 1 has a depth of 2 mm.
Hole 10 has a depth of 29 mm.
 Calculate, using an analytical method, the common difference of the hole depths.
 Ignoring the pull back and repositioning times, calculate the total time spent cutting metal
if the spindle feed rate is set at 2 mm/sec.

Your manager asks you to work on the design of a 10-speed drilling machine which has a common
ratio of 1.38. The lowest speed is to be set at 200rev/min.
 Work out all the speeds.
 Plot them in a chart.
 Write down the general expression for the geometric progression (GP) which you have
used.
 If the design is changed to a 12 speed, calculate the highest speed using the GP formula.