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Solve these simultaneous equations. 2x + y = 10 and 3x + 4y = 25.

2x + y = 10 (1) 3x + 4y = 25 (2) 1. Eliminate y. Method 1: (1) x 4: 8x + 4y = 40 (1') (1') - (2): 5x = 15 Method 2: Rearrange (1): y = 10 - 2x (1") Substitute (1") into (2): 3x + 4(10 - 2x) = 25 (3...
DD
Answered by Daisy D. • Maths tutor
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When should I use the quadratic formula?

If you're asked to solve a quadratic equation, you could factorise it, or you could use the quadratic formula. The quickest way is to factorise, but sometimes the numbers are too tricky to factorise, (if an ...
SM
Answered by Sarah M. • Maths tutor
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A right-angled triangle has base 10cm and height 4cm. What is the area of the triangle?

The first thing we should note here is that we are looking for the area, so we need to recall the formula for the area of a right-angled triangle: Area = (base x height) / 2 Next we can input our values give...
KS
Answered by Kirsty S. • Maths tutor
14330 Views

Use the chain rule to differentiate y=(x-3)^(-3)

Hint: the chain rule states that for y=u(x) ^a, the derivative will be dy/dx = dy/du * du/dxSo we just need to find dy/du and du/dx!In this case u(x)=x-3, so du/dx = 1.from y=u^(-3), dy/du = -3u^(-4).This me...
RT
Answered by Rosemary T. • Maths tutor
5766 Views

Solve the inequality x < 4 - |2x + 1|.

In order to deal with the modulus sign, we must take account of 2 possible cases: Case 1: |2x + 1| = (2x +1). In this case we can solve algebraicly, preserving the inequality sign, to get that x &lt; 4 -(2x ...
JC
Answered by Joe C. • Maths tutor
8572 Views