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Solve the simultaneous equations 2x + y = 18 and x - y = 6

2x + y = 6x - y = 6x = 6 + y => 2(6 + y) + y = 18 => 12 + 3y = 18 => 3y = 6 => y = 2x - (2) = 6 => x = 8x = 8, y = 2

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FInd the equation of the line tangent to the graph g(x)=integral form 1 to x of cos(x*pi/3)/t at the point x=1

This problem requires us to find out the equation of the tangent line, which has form y=mx+q.M is the angular coefficient or slope of the line and can be evaluated through the derivative of the function ...

Answered by • Maths tutor

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There are 16 hockey teams in a league. Each team played two matches against each of the other teams. Work out the total number of matches played.

16 teams. Therefore, 1 team plays (16-1)x2=30 matches in a season. Total matches played = 30+28+26+...+2+0. 16 teams so total number of matches = 16 x (30+0)/2 =240Or each team plays 30 matches. 30x16=480...

Answered by James D. • Maths tutor

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Given that 2log2(x+15) -log2(x) = 6, show that x^2-34x+225=0

As we know nlog(a) is the same as log(a)^n, we can rearrange the equation to log2(x+15)^2 -log2(x) = 6. Also, we know that log(a) - log(b) is equal to log(a/b), so we can fu...

Answered by Rafey A. • Maths tutor

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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?

first combine into one ratio by finding lowest common multiple between common category so houses:flats:bungalow = 14:8:5. then for every 5 bungalows to every 14 houses so 50/5 = 10 and 10 x 14 = 140. so t...

Answered by • Maths tutor

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