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f(x) = x^2 + 2x - 3. Where does the graph of the function f intersect the x-axis?

First, let's use the discriminant to check that the function actually does intersect the x-axis. b²-4ac = 4-(4 x -3) = 4+12 = 16, which is greater than 0, so we're fine.
T...

Answered by George M. • Maths tutor

3065 Views

James buys a new car for £1000. Every year the value of the car decreases by 3%. If James bought the car in 2017 what would the value of the car be in 2021?

First work out how many years have passed since the car was bought. 2017-2021 is 4 years. Write an expression for the cost of the car after n years. Cost = 1000 * 0.97

Answered by William G. • Maths tutor

2795 Views

How do you expand brackets?

Take the expression(x+2)(x+4). Expanding brackets essentially means multiplying them out to get a new expression. In this case, it will have the form x²+cx+d, where c and d are numbers to be de...

Answered by Jan A. • Maths tutor

3987 Views

Expand and simplify: 4(2x − 3) − 2(x − 5)

4(2x - 3) - 2(x - 5) [Remember that a negative multiplied by a negative makes a positive]
8x - 12 - 2x +10
6x - 2 [Check: can I simplify further?
2(3x -...

Answered by Rachel C. • Maths tutor

8256 Views

In a class there are 57 students. Of these 32 study Spanish, 40 study German and 12 students study neither. How many students study Spanish but not German?

The best approach to this problem is using a Venn Diagram. The first step to solving this problem is calculating the number of students who study Spanish or German or both. In the question we are given th...

Answered by Calum D. • Maths tutor

3857 Views