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Prove that (2*a^2 + 7a + 3)/(a + 3) is an odd number for any positive integer number, a.

We see that the numerator is a quadratic, so we factorise it to obtain: (2 a + 1)(a + 3)/(a + 3) = 2 a + 1 Since a is a positive integer, we know that 2*a + 1 will always be an odd number.
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Answered by Nadia M. • Maths tutor
3810 Views

Find the length of the hypotenuse if the right angled triangle's other two sides are of length 5cm and 12cm.

Use of a^2+b^2=c^2 must be included in the answer. Furthermore the numbers must be put in the above equation to give: 5^2+12^2=c^2 This must then be solved to give: 169^0.5=c The answer can be found without ...
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Answered by Sarah W. • Maths tutor
3858 Views

4x^2 + 8x + 3 can be written in the form a(x + b)^2 + c where a, b and c are whole numbers. Work out the values of a, b and c.

Factorise 4x 2 + 8x + 3 = 4(x 2 + 2x + 3/4) divide the coefficient of x by 2: 2/2=1 Now x 2 +2x = (x+1) 2 -1 2 = (x+1) 2 -1 Hence, 4((x+1) 2 -1+3/4) = 4(x+1) 2 -1 which is of the form a(x + b) 2 + c So a=4, ...
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Answered by Donny W. • Maths tutor
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Outline the main differences between an artery and a vein? (6 marks)

An artery carries blood away from the heart. The blood is oxygenated with the exception of the pulmonary and umbilical artery. The vessel must cope with high pressure demands and therefore has thick, elastic...
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Answered by Katy B. • Biology tutor
3344 Views

When do we use the present tense?

We use the present tense when we're describing what we're doing now or something we do regularly . Examples: Je vais au cinema Je joue au foot Phrases we use with the present tense: maintenant - now en ce mo...
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Answered by Natasha A. • French tutor
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