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In a village the number of houses and the number of flats are in the ratio 7 : 4. The number of flats and the number of bungalows are in the ratio 8 : 5 . There are 50 bungalows in the village. How many houses are there in the village?

H:F F:B7:4 8:550 bungalows, so bungalows have been multiplied by 10 to get from 5 to 50. So now we have to do the same process to the flats so we multiply 8 by 10 to get 80 flats. Now we need to get to 80 fl...
IA
Answered by Isra A. • Maths tutor
8683 Views

The function f is defined by f (x) = e ^(x+2), where x is any real number. Find f ^-1(x) and state its domain.

y=e x+2 , we want to make x the subject, x+2=ln(y), x=ln(y)-2, now that x is the subject, the inverse of the function can be found by swapping the x and the y. Therefore the inverse function is y=ln(x)+2, th...
JC
Answered by Jacob C. • Maths tutor
4650 Views

2x^2-7x+3=0, solve the following for the two solutions of x

X=1/2X=3
AJ
Answered by Alireza J. • Maths tutor
2942 Views

Complete the square on the equation (x^2)-4x-3

x 2 -4x-3 First factorise into squared form and expand.(x-2) 2 =x 2 -4x+4Balance the equations.x 2 -4x+4 needs to be x 2 -4x-3This leads to(x-2) 2 -4-3 to get rid of the +4 from factorising.Leaving finally(x...
EM
Answered by Eddie M. • Maths tutor
5175 Views

Solve the following quadratic simultaneous equation: y = x + 4 and y = x^2 + 4x

Y = x + 4y = x 2 + 4x(as both are equal to y, they can be equated)So: x 2 + 4x = x + 4(Rearrange to make the equation equal 0 - subtract x and 4)x 2 + 3x - 4 = 0(factorise)(x + 4)(x - 1) = 0Therefore: x = -4...
JC
Answered by Julius C. • Maths tutor
6825 Views