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Write x² + 4x -16 = 0 in the form (x+a)² - b = 0. Solve the equation giving your answer in surd form as simply as possible.

x² + 4x -16 = 0 (x+2)² -20 = 0 We note that the coefficient of x 2 is 1 and the coefficient of x is 4. Therefore we say the that square is (x+2). This leaves us with an additional 4 from this expansion. We m...
HH
Answered by Henry H. • Maths tutor
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When do we add and when do we multiply probabilities?

We add probabilities when the corresponding events are alternatives, e.g. P(rolling a 4 on a pair of dice) = P(rolling a 1 and a 3) + P(rolling a 2 and a 2). These are mutually exclusive events which can't h...
LW
Answered by Liora W. • Maths tutor
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C is a circle with equation x^2 + y^2 = 16. The point P = (3,√7) is on C. Find the equation of the tangent to C at the point P.

First, we note the centre of the circle is at the origin (0,0). Then we calculate the gradient of the line OP, the line connecting the origin to P. The gradient = change in y / change in x = (√7 - 0) / (3 - ...
DC
Answered by Daniel C. • Maths tutor
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y is inversely proportional to x. y = 0.04 when x = 80. Find the value of y when x = 32.

If y is inversely proportional to x. We know that y=k/x for some constant k. We need to find this constant before continuing. Looking at the information given to us in the question we know for one example th...
TT
Answered by Tyler T. • Maths tutor
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solve the simultaneous equations 8x + 2y = 48 , 14x + 6y = 94

Step 1) Rearrange the first equation to make y the subject: 8x + 2y = 48 , 2y = 48 - 8x , y = 24 - 4x. step 2) Sub y = 23 - 4x into the second equation: 14x + 6(24 -4x) = 94 , 14x + 144 - 24x = 94 Step 3) so...
HS
Answered by Harrison S. • Maths tutor
3260 Views