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X is a prime number higher than the square of 5 and lower than the square of 7. What are the smallest and largest possible values for X?

The square of 5 is 25 and the square of 7 is 49. The prime numbers found between these 2 values are: 29, 31, 37, 41, 43 and 47. This means the smallest value fitting the criteria is 29 and the largest value ...
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Answered by Oana C. • Maths tutor
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a) Find the equation of the line that passes through (2,10) and (4,16) b) Find the point where the line in (a) intersects the line y=5x-2

a) y=3x+4 b) (3,13)
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Answered by Tutor94163 D. • Maths tutor
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Simplify 125 ^ -2/3

= (1/125) ^ 2/3 = (1/5) ^ 2 = 1/25 To find a number to a negative power, you invert it (flip it so that 125 becomes 1/125) To find (1/125) ^ 2/3, find the cube root of 1/125 (=1/5) and then square it (=1/25)
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Answered by Ewen R. • Maths tutor
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Prove that the composite function fg(2)=-26 where f(x)=3x+1 and g(x)=1-5x

Here, f(x) and g(x) are functions of x, whose output depends on the value of x. fg(2) means fg(x) where x=2. Firstly, calculate g(2) and use this answer as the new value of x for f(x). g(2)=1-5(2)=-9. f(-9)=...
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Answered by Alisha L. • Maths tutor
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Factorise fully 3a^3b + 12a^2b^2 + 9a^5b^3

The first step here is to find a common factor in each term. If we first look at the coefficients of each term we can see the first common factor is 3, so we can write that first outside of our brackets. 3.....
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Answered by Ellie G. • Maths tutor
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