Search our library of homework questions

Top answers

All subjects

All levels

Solve these simultaneous equations: 3xy = 1, and y = 12x + 3

From first equation: 3xy = 1 => x = 1/(3y)Substitute expression for x into second equation: y = 12x + 3 => y = 12(1/3y) + 3 = 4/y +3Multiply through by y: y² = 4 + 3y => y²

Answered by Hallam M. • Further Mathematics tutor

2137 Views

A is the point (2,-5), B is the point (-1,4). (a) What is the gradient of the line passing through points A and B? (b) Does the point (-100,301) lie on the line passing through points A and B?

(a) let A be (x1,y1) and B be (x2,y2), Gradient = m = (y2-y1)/(x2-x1) m = (4- -5)/(-1-2) = 9/(-3) = -3 Gradient = -3
(b) equation of a straight line line: y = mx + c => y1 = ...

Answered by Hallam M. • Maths tutor

3059 Views

I don't quite understand when to use the perfect tense vs the imperfect, could you help me please? (making the assumption they understand the conjugation rules already)

The imperfect tense is used to express things that 'were' happening or 'used to' happen. They may have taken place over a short period of time (a few seconds), or a prolonged period of time (several years...

Answered by Tommy C. • French tutor

1367 Views

How is DNA replicated, and why is this method of replication important?

DNA is replicated in a semi-conservative manner, which means that both 'parental strands' are used as templates. This ensures that genetic information is passed onto offspring without any changes
(di...

Answered by Salima B. • Biology tutor

2338 Views

How do I integrate by substitution?

Let's take for example the integral 5x²(x³-4)⁴dx. This is very difficult and not at all nice to expand in terms of x, so we can effectively "create" a new variab...

Answered by Edward C. • Maths tutor

3155 Views