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Solve this simultaneous equation: 2 + 5y = 3x, x + y = 6

step 1 - rearrange equation 2 to make x/y the subject how? example: subtract y from both sidesx = 6 - y step 2 - substitute x = 6 - y into equation 1. how? where x is in the equation put in (6 - y)2 + 5y = 3...
PW
Answered by Phoebe W. Maths tutor
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Solve the equation 3(x+1) = 21

When solving an equation with brackets, it is often easiest to expand the brackets first.3(x+1) = 21becomes...3x + 3 = 21Now this looks like an equation we know how to solve(minus three from both sides)3x + ...
JM
Answered by James M. Maths tutor
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Solve the equation 5m-2=16-4m

Our ultimate goal is to figure out what m equals.The most important thing to remember is that whatever you do to the left you also do to the right.Let us start by adding 4m to both sides: 5m+4m-2=16-4m+4 ---...
LW
Answered by Lara W. Maths tutor
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Let (x + 3) be a factor of the polynomial P(x) = x^3 + ax^2 - 7x + 6. Find a and the other two factors.

Firstly, (x - c) is a factor of a polynomial P(x) if and only if there exists a polynomial Q(x) such that P(x) = (x - c)Q(x), where c is a real or complex constant. Therefore, we can write: P(x) = x^3 + ax^2...
Answered by Maths tutor
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Let n be a positive integer. Find the continuous functions f:ℝ->ℝ with the property that integral from 1 to x of f(ln(t)) dt=x^n ln(x) for all positive real numbers x.

Differentiating the integral equation with respect to x we obtain: f(ln(x))=nx n-1 ln(x)+x n-1 =x n-1 =x n-1 (nln(x)+1) , for any positive real number x.Let ln(x)=t , thus x=e t and f(t)=e t(n-1) (nt+1) , fo...
Answered by Maths tutor
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