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Prove algebraically that the straight line with equation x - 2y = 10 is a tangent to the circle with equation x^2 + y^2= 20

rearrange line equation: x=10 + 2ysubstitute into circle equation: (10+2y) 2 + y 2 =20expand: 4y 2 +20y +20y + 100 + y 2 = 20 collect terms: 5y 2 + 40y +100 = 20move all to one side: 5y 2 + 40y + 80=0divide ...
AB
Answered by Annabel B. • Maths tutor
12515 Views

Expand and simplify 6x^2(x-1)(x+2)

First we need to use the rules of BIDMAS (brackets, indices, division, multiplication, addition, subtraction)So we must deal with the brackets of the function first(x-1)(x+2)To expand these brackets we use F...
EP
Answered by Emily p. • Maths tutor
3339 Views

Expand and simplify: 3(4x+1)-5(3x-2)

3(4x+1)-5(3x-2)= 12x+3-15x+10= -3x+13 or 13-3x
CB
Answered by Charlotte B. • Maths tutor
4486 Views

Solve (5-x)/2= 2x-7

Our first objective is to have all the x terms on one side of the equation and all the non x terms on the other side. The division of the left member of the equation by 2 is our first problem to solve. We ha...
LP
Answered by Leonardo P. • Maths tutor
7214 Views

How do you solve the quadratic X^2 - 8X + 15 = 0 ?

First factorise (using a "farmer's field", will draw this on whiteboard):=> (X-3)(X-5) = 0Hence using the zero rule (one of the brackets must be equal to 0 if the product is 0),either X-3 = 0 OR...
SJ
Answered by Simone J. • Maths tutor
3018 Views