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Find from student what the first step is (get a or b in terms of the other).
a = 2.8 x10^5 = 0.28x10^6
a + b = (0.28 + 1.6) x 10^6
= 1.88 x10^6
ii)
Know that a^x x b^y = ab^x+y
.: 2.8 x 1.6 = 4.48
10^5 x 10^6 = 10^11
a x b = 4.48x10^11

Answered by Jerry A.

Studies Classics and Spanish at Oxford, Somerville College

Firstly, get all of the x's onto one side of the equation and all of the numbers onto the other. To make it easier at the end, subtract the smaller value of x so that it doesn't become negative: 3x-10=12x-7 (-3x) -10=9x+7 (+7) -3=9x To get what a single value of x equals, divide -3 by 9. Then simplify the fraction (3/9 = 1/3) -3/9 = x = -1/3 (don't forget the negative sign!)

Answered by Emma L.

Studies Psychology at Leeds

To combine these two fractions into one, you have to multiply the equation by the denominators in order to make a common denominator: 5(x-5)/(x+1)(x-5) + 6(x+1)/(x+1)(x-5) Now that the denominators are the same, you can add the two numerators to eachother, and then expand the brackets: [5(x-5)+6(x+1)]/(x+1)(x-5) [5x-25+6x+6]/(x+1)(x-5) Now simplify the numerator: [11x-19]/(x+1)(x-5) (This is a GCSE question though I'd only want to tutor 11+ 13+ for now)

Answered by Emma L.

Studies Psychology at Leeds

Answer= **1/4**
7+6+11= 24
Green =6/24
Simplifies to 1/4, by division by 6.

(2x+3) (2x+1) = 4x^2 + 8x + 3
(2x-8) (x-4) = 2x^2 - 16x - 32
(4x^2+8x+3) - (2x^2-16x-32) = 1
2x^2 - 8x - 29 = 1
2x^2 - 8x - 30 = 0
x^2 - 4x - 15 = 0
Using the quadratic formula;
x = 6.36 or x= -2.36 to 2dp

Using factorisation, first we would have to look at the factors that multiply to make the last term, (-14). We know that they are +/- 7 and -/+2, and +/- 14 and -/+ 1, respectively. Now we have listed the factors, we have to see which pair adds to make the coefficent of x, which in this case is (-5). From these pairs, only (-7) and (+2) add to make (5).
This means that the quadratic equation factorises to become (x - 7)(x + 2) - notice here that when you multiply out these two brackets, using the FOIL method, you get the equation that you had started with.
Setting (x - 7)(x + 2) = 0, we can now find the roots. One of these brackets have to equal (0) in order for the euqation to be true. Here, we can easily see that setting x = 7 or x = -2 does the trick, and hence (7) and (-2) are roots of the equations.

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