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The y-intercept of A is 7. A also passes through point (7, 2). (a) Find an equation of A in the form y = mx + c. (b) B is perpendicular to A and also has a y-intercept of 7. Write down the equation for B in the form y = mx + c.

(a) y-intercept = (0,7); other point = (7,2) ; gradient, m = change in y / change in x ; m = (0 - 7) / (7 - 2) => m = -7/5 ; y = mx + c (we know from the question that c=7) ; y = (-7/5)x + 7(b) gradient o...
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Answered by Oliver T. • Maths tutor
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Prove that the multiple of an even number and an odd number is always even.

2n is even, so (2n+1) is odd ; Multiplying even by odd gives: 2n(2n + 1) ; which is a multiple of 2, thus even * odd = even.
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Answered by Oliver T. • Maths tutor
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A person leaves their flat at 8:00am and travels to work at an average speed of 32 mph. They arrive at work at 9:15am. Calculate the distance they travel to work.

SUVAT equations give s = vt ; v = 32mph ; t = 1h 15mins = 1.25h ; s = 32 * 1.25 = 40 miles
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Answered by Oliver T. • Maths tutor
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Prove 2^(n+2) + 3^(2n+1) is a multiple of 7 for all positive integers of n by mathematical induction.

Let P(n) be the proposition that 2 n+2 + 3 2n+1 is a multiple of 7 for all positive integers of n. Let n=12 3 + 3 3 = 8 + 27 = 35 = 7(5)This is divisible by 7. Assume n=k2 k+2 + 3 2k+1 = 7m The above equatio...
EP
Answered by Eashan P. • Maths tutor
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Write x^2+6x+14 in the form of (x+a)^2+b where a and b are constants to be determined.

Completing the square is a method that can be used to solve the quadratic equation x^2+6x+14 in the form of (x+a)^2+b. The way we find a and b is as follows:For constant a , is found by halving the coefficie...
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Answered by Chara D. • Maths tutor
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