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Solve the simultaneous equations 2x + 3y = 19 , 3x + y = 11

Rearrange to make the y component the subject3y = 19 - 2x , y = 11 - 3xMultiply the second equation by 33y = 33 - 9xEquate to each other19 - 2x = 33 - 9xRearrange7x = 14Divide by 7x = 2Substitute x=2 into...

Answered by David B. • Maths tutor

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Write x^2 + 4x + 18 in the form (x + a)^2 + b, where a and b are constants to be determined.

(x + 2)^2 + 14. a = 2, b = 14

Answered by Danqing H. • Maths tutor

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The functions f and g are such that f(x)=5x+2 and g(x)=-x-4. a) Find fg(x). b) Find ff(x). c) Solve fg(x) = ff(x).

a) fg(X) = 5(-x-4)+2 = -5x-20+2 = -5x-18b) ff(X) = 5(5x+2)+2 = 25x+10+2 =25x+12c) 25x+12=-5x-18 25x+5x=-18-12 30x=-30 x=-1

Answered by Maria A. • Maths tutor

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Differentiate sin^2(x)

sin(2x)

Answered by James P. • Maths tutor

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Find g(f(x)) where g(x)=2x+4 and f(x)=x^2+1.

With functions of functions you work from the inside out, so you substitute the function f(x) for the x in g(x). We know that f(x)=x²+1 and g(x)=2x+4. In this question you therefore replace the...

Answered by Georgina M. • Maths tutor

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