Algebra Answers

A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?

How many solutions over the complex number system does this polynomial have?

2x^4 – 3x^3 – 24x^2 + 13x + 12 = 0

The profit made by a business in 2018 was triple that made in 2019. The profit made in 2020 was R 3 million less than the profit made in 2019. If the total profit in these 3 years was R 67 million, what was the profit made in 2020? 

Give one example with justification

a. Children in early primary school have a problem with handling formal arthimetic

X+X

Which point on the number line shows 3/2?, what misconception a learner may have when choosing the incorrect answer?

Give a rational function which has a domain of all numbers except 15

The value of a used car is now 5,600 euros. What was the value of the car three years ago when it has dropped 16% annually?

Consider the following examples in real-world situations that describe a correspondence between phenomena:

• The total cost for repairing a cell phone is R320 for parts plus R50 per hour for labour.

• Siphokazi sells 70% alcohol-based hand sanitisers. She earns R230 a week and receives a commission of 15% of her sales.

• The amount by which your savings will grow in a year depends on the interest offered by the bank.

• The area of a circle depends on the radius of the circle.

• A rental van costs R230 per day plus R4,30 per kilometre.

(a) Express each situation in functional words. For example, the income tax is a function of the total income. (8)

(b) For each situation, indicate the dependent and independent variables. (5)

(c) Write the two variables as an ordered pair, and write the function using the notation 𝑦=(𝑥). (5)

(d) Explain the meaning of a function in your own words. Illustrate with your own specific example. (2)

Given the function :f (x)=-x^2+9 and g (x)=6-2x.Draw f and g on the same system of axes