Algebra Answers

Q2)

A) Kofi and Ama are brother and sister. Two times kofi's age plus five is the same as Ama's age. Ama is 17. How old is Kofi? First write a linear equation and then solve it.

C)

h(X)=ax^3-x^2-5x+b, where a and b are constants. For h(X) divide by (X+2) the remainder is 40 and for h(X) divided by (x-2) the remainder is 36. Find the value of a and b.

B) find the coefficient of x^3 in the expansion (2x^3-5x^3+2x-1)(3x^3+2x^2-9x+7)

A)

The polynomial g(X)=3x^3-2x^2-12x+8

(I) using the factor theorem, show that (X+2) is a factor of g(X)

(II) factorize g(X) completely

A system of equations is given below, 𝑡𝑥 + 2𝑦 + 3𝑧 = 𝑎 2𝑥 + 3𝑦 − 𝑡𝑧 = 𝑏 3𝑥 + 5𝑦 + (𝑡 + 1)𝑧 = 𝑐 Where 𝑡 is an integer and 𝑎, 𝑏, 𝑐 are real constants. The system does not have a unique solution, but it is consistent. Show that 𝑎 + 𝑏 = 𝑐.

In a certain country, the annual tax on a motor vehicle depends on the mass of the empty vehicle and the number of wheels. The tax is composed of R2 per year for every kg of the empty mass and R60 per wheel. Set up a formula that can be used to calculate the tax on any vehicle.

A group of four friends built a table and sold it to earn R rands. They will split their earnings equally. Write an equation that represents the amount of money each friend gets 

Supposed that you and your friends are in Landmark. Your mother gave you 

P1,000 to buy something for your birthday. You really want to buy bag for 

yourself as a gift, but they are all very expensive. You are now looking for items 

on sale. Then you found one store that has a large sign that reads: all items 

are currently 75% off. This sounds like great news. The original price of the 

bag is ₽1, 500. Does your money enough to buy that bag? What is the fraction 

of the amount of the bag?

Find the approximate value of ³√0.99 up to 4 decimal places.

(i) If 4𝑒 𝑥 − 3𝑒 −𝑥 ≡ 𝑃𝑠𝑖𝑛ℎ 𝑥 + 𝑄𝑐𝑜𝑠ℎ 𝑥, determine the values of 𝑃 and 𝑄. (ii) Solve the equation 𝑐𝑜𝑠𝑒𝑐ℎ 𝑦 = −0.4458, correct to 4 significant figures