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The point P has coordinates (3, 4) The point Q has coordinates (a, b) A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a

Perpendicular gradients multiply to give -1. The gradient of the perpendicular line (y=-3/2x+7/2) is -3/2 , so the gradient of PQ is 2/3. Using gradient formula change in y/ change in x :(4-b)/(3-a) = 2/3...

Answered by Lizzie D. • Maths tutor

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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

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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

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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

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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

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