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Use factorisation to simplify the following expression (x^2-9)/(x^2-4x+3)

we simplify the top and bottom of the fraction separately. x^2-9 factorises to (x+3)(x-3) using the difference of two squares.x^2-4x+3 factorises to (x-1)(x-3). So the above formula simplifies to (x+3)/(x-1)
JL
Answered by Jack L. • Maths tutor
5147 Views

A right-angled triangle has one angle size 60 degrees, and hypotenuse of length 32cm. Calculate the length of the side opposite the 60 degree angle, to 3sf.

Firstly, we want to draw out the triangle. No matter what the question asks, just draw out all the information you're given so that you can see what the question is asking. We've been given a right angle tri...
BR
Answered by Benjamin R. • Maths tutor
7053 Views

A light bulb is to be put in the middle of a room defined by the coordinates (10,5), (10,25), (20, 5) and (20,25). At what coordinate should the light bulb be placed?

Firstly we should try to establish the geometry of the room, ie identify the lines in which the walls lay. Noticing that two of the points have the same x coordinate of x = 10 suggests that there must be a w...
TL
Answered by Taiwo L. • Maths tutor
3314 Views

Find the median, upper and lower quartiles of these numbers: 160, 390, 169, 175, 125, 420, 171, 250, 210, 258, 186, 243

Order the data:125, 160, 169, 171, 175, 186, 210, 243, 250, 258, 390, 420Find middle observation:[125, 160, 169, 171, 175, 186] | [210, 243, 250, 258, 390, 420]Median = (186 + 210)/2 = 198Find middle observa...
SL
Answered by Samuel L. • Maths tutor
4583 Views

Shape S is one quarter of a solid sphere. The volume of S is 576(pi)cm(^3). Find the surface area of S correct to 3 significant figures

Radius is the only property of a sphere that is used to define surface areas and volumes. We need to find what the radius is from the information that the question has given us. S is a quarter sphere, and we...
JW
Answered by Joe W. • Maths tutor
15017 Views