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y = (x + 2)(x + 5)

steps as follows:x times x = x 2 2 times 5 = 102 times x = 2xx times 5 = 5xthen add these together:y = x 2 + 7x +10x = -2, -5; y = 0, 10
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Answered by Georgie L. • Maths tutor
3730 Views

Use the addition formulas: sin(x+y)=sin(x)*cos(y)+sin(y)*cos(x), cos(x+y)=cos(x)*cos(y)-sin(x)*sin(y) to derive sin(2x), cos(2x), sin(x)+sin(y).

sin(2x)=sin(x+x) =sin(x)cos(x)+cos(x)sin(x) =2*sin(x)*cos(x); cos(2x)=cos(x+x) =cos(x)cos(x)-sin(x)sin(x) =[cos(x)] 2 -[sin(x)] 2 Now let x+y=a and x-y=b, then x=(a+b)/2 and y=(a-b)/2. Then sin(a)=sin[(a+b)/...
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Answered by Ioana S. • Maths tutor
4840 Views

Why do you need simultaneous equations?

This is an example of a simultaneous equation - 2X + Y = 5X + 3Y = 10 You can think of X and Y as apples and oranges from a market. You know that if you buy 2 apples and 1 orange it cost £5, but this doesn’t...
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Answered by Amelia G. • Maths tutor
3558 Views

Raya buys a van for £8500 plus VAT at 20%.Raya pays a deposit for the van. She then pays the rest of the cost in 12 equal payments of £531.25 each month. Find the ratio (in simplest form) of the deposit Raya pays to the total of the 12 equal payments.

Raya buys a van for £8,500 x 1.2 = £10,200. Total of 12 equal payments = 12 x £531.25 = £6375. Raya's deposit = £10,200 - £6375 = £3825. Ratio of the deposit Raya pays : Total of the 12 equal payments = 3825...
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Answered by Andrew B. • Maths tutor
30731 Views

A ladder of length 4.5m is leaning against a wall. The foot of the ladder is 2.3m from the base of the wall. What is the angle the ladder makes with the wall?

This is an application of trigonometry. The right angle in this case is between the wall and the floor and the hypotenuse is the ladder. The angle between the wall and the ladder can using the sine of the an...
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Answered by Nicci F. • Maths tutor
6393 Views