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There are n sweets in a bag. 6 of the sweets are orange. The rest of the sweets are yellow. Hannah takes a sweet from the bag and eats it. Hannah then takes at another sweet. The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0

P(2 orange sweets) = P(orange sweet) * P(orange sweet)

(6/n) * (5/(n-1)) = 1/3

30/(n(n-1)) = 1/3

90 = n(n-1)

90 = n²-n

n...

Answered by Tim V. • Maths tutor

16432 Views

What is the quadratic formula and how do I use it?

The quadratic formula is a way of solving quadratic equations of the form: ax²+bx+c=0. By plugging in the values a,b and c into it, the solutions for x can be obtained:x = [-b +/- sqrt(b^2<...

Answered by Patrick M. • Maths tutor

4788 Views

Two points have coordinates (1,-6) and (-2,3). Find the equation of the line which joins them, and their midpoint.

To find the line's equation, you need the gradient and the y-intercept. The gradient is found using:

(y2-y1)/(x2-x1)

Or simply (change in y direction)/(change in x direction...

Answered by Kara V. • Maths tutor

7571 Views

Show that the following system of equations has an infinite number of solutions. x+y+2z = -2; 3x-y+14z=6; x+2y=-5

Substitute values of one equation into another.

(1) x+y+2z = -2; (2) 3x-y+14z=6; x+2y=-5 (3).

Substitute x in (1) and (2) from (3).

We get -y+2z=3 in (1).

Answered by Egidijus S. • Maths tutor

7774 Views

When the polynomial 3x^3 +ax+ b is divided by x−2 , the remainder is 2, and when divided by x +1 , it is 5. Find the value of a and the value of b.

Insert the negative values of the divisors and put them into the polynomial. x-2 -> P(2) = 34+2a+b=2 x+1 -> P(-1)=3(-1)+(-1)a+b=5. 22+2a+b=0 -8-a+b=0, then solve the simultaneous equa...

Answered by Egidijus S. • Maths tutor

18358 Views