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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

2914 Views

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

2972 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

2650 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

3832 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

7787 Views