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Find an expression for the nth term of this sequence: 3 - 11 - 19 - 27 - 35 . The nth term of a different sequence is 2n^3 + 3. Write down the first 3 terms of this sequence.

First, the sequence is 3 - 11 - 19 - 27 - 35. Looking at it, we can observe that each element of the sequence is created by adding 8 to the previous. The first term is 3. The second term is 3 + 8...

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The equation of a curve is y = x^2 + ax + b where a and b are integers. The points (0,-5) and (5,0) lie on the curve. Find the coordinates of the turning point of the curve.

In the equation for our line we have 2 unknowns: a and b. However, we know that the line passes through two known points with x and y coordinates. Therefore, we can begin by substituting in our known x an...

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Show that (2x^2 + x -15)/(2x^3 +6x^2) * 6x^3/(2x^2 - 11x + 15) simplifies to ax/(x + b) where a and b are integers

As you begin the question, it is important to note that immediately multiplying the two fractions, while would eventually get you to the correct answer would take far too long in an exam scenario. Instead...

Answered by Joe O. • Maths tutor

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Solve the simultaneous equations x – 2y = 1 and x^2 + y^2 = 29.

Start by modifying the first equation and making a third x=2y+1x²= (2y+1)² x²=4y²+4y+1therefore, if we sub this 3rd equation into the 2nd equation we get :4y

Answered by Adamya P. • Maths tutor

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In a box, there is 1 more green pens than black pens. The probability of taking 2 black pens is 0.2 . How many pens are in the box?

g = b+8g+b = p = 2b+1(b/p) x (b-1)/(p-1) = 1/5(b^2 - b)/(p^2 - p) = 1/5sub in p= 2b+1(b^2 - b)/(4b^2 + 2b) = 1/55b^2 - 5b = 4b^2 + 2bb^2 -7b = 0b = 7 or b = 0 (cannot be 0 as 2 pens must be taken)p = 2(7)...

Answered by James L. • Maths tutor

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