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Maths
GCSE

How do you rationalize the denominator of a fraction?

Questions which ask for you to rationalize the denominator usually includes an integer and a square root of a number (x+sqrt(y)).We can use the following formula to our advantage: (a+b)(a-b)=a^2-b^2. ...

Answered by Maths tutor
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A different pattern is made using 20 straight lines and 16 arcs. The straight lines and arcs are made of metal. 20 straight lines cost £12 and the cost of one straight line: cost of one arc = 2:3. Work out the total cost of metal in the pattern.

First we need to find the cost of one arc from the information we already have about the arc (20 straight lines cost £12). To do this divide the £12 total cost by the number of lines 20.12 ÷ 20 = £0.60 ea...

RD
Answered by Ryan D. Maths tutor
7013 Views

(x+6) and (x+5) are the length and width, respectively, of a rectangle with area 20. Calculate the width of the rectangle.

(x+6)(x+5)=20. x2 + 11x +30=20. x2+ 11x + 10 = 0. (x+10)(x+1)=0 . x=-1 and x=-10. width= -10+5=-5 (invalid solution). width =-1+5= 4. Checking through: (-1+6)*(-1+5)=20.

Answered by Maths tutor
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Three points have coordinates A(-8, 6), B(4, 2) and C(-1, 7). The line through C perpendicular to AB intersects AB at the point P. Find the equations of the line AB and CP.

To find the equation of a line, we need; the gradient of that line and a point on that line. To find the gradient of a line, we require two points on the line which have been prov...

RD
Answered by Ryan D. Maths tutor
10183 Views

Expand the brackets (3x^2 + 6x + 7)(x - 3)

To help the student understand how to expand the brackets I would start by splitting the equation to:3x2(x - 3) + 6x(x - 3) + 7(x - 3)I then would ask the student to expand these brackets to:3...

JD
Answered by Jasmine D. Maths tutor
3206 Views

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