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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...

Answered by • Maths tutor

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Describe the shape of, and bonding in, a molecule of benzene and explain why benzene does not readily undergo addition reactions.

Benzene is a planar, cyclical, hexagonal molecule, with the molecular formula C₆H₆. It consists of a ring of 6 carbon atoms with alternating single bonds and double bonds. The length...

Answered by • Chemistry tutor

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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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Explain how blood glucose levels are controlled and how this is an example of negative feedback mechanisms.

The pancreas detects rises in blood glucose levelsThis triggers pancreatic beta cells to secrete insulin, and inhibits alpha cells from secreting glucagonInsulin stimulates the uptake of glucose into cell...

Answered by Hannah L. • Biology tutor

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