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ABC, DEF and PQRS are parallel lines. BEQ is a straight line. Angle ABE = 60° Angle QER = 80° Work out the size of the angle marked x. Give reasons for each stage of your working.

Angles ABE and EQR are alternate interior angles. This means they are the same thus angle EQR = 60˚. We know that the sum of the interior angles of a triangle is equal to 180˚ and we know that angle QER = 80...
JP
Answered by Juliana P. • Maths tutor
8822 Views

Solve this set of simultaneous equations: 5x+3=3y 9x+9=6y

Firstly, you need to understand that the two equations are interlinked, therefore the x and the y variables are the same values in both equations. To make things easier, we can number both equations. What we...
RJ
Answered by Ryan J. • Maths tutor
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For what values of k does the line y=kx-1 have two distinct points of intersection with the circle (x-2)^2+(y-3)^2=2?

sub y=kx-1 into circle equation, get (k^2+1)x^2-(8k+4)x+18=0for 2 distinct solutions need b^2-4ac>0, ie -8k^2+64k-56>0iff k^2-8k+7<0complete the square: intersections of equation in k satisfy(k-4)^2...
CB
Answered by Christopher B. • Maths tutor
5832 Views

Solve x^2 = 4(x – 3)^2

x 2 = 4(x-3) 2 x 2 = 4(x-3)(x-3) - showing that these are double bracketsx 2 = 4(x 2 - 6x + 9) - expanding the double bracketsx 2 = 4x 2 - 24x + 36 - multiplying the 4 by the expression inside to remove the ...
EL
Answered by Emily L. • Maths tutor
4216 Views

Expand the following equations

a. x(x+4)b. 3x(x+4)c. (x+8)(x+3)d. (x+7)^2
KS
Answered by Kane S. • Maths tutor
3771 Views