CPhill

I think that anyone who is a member can give you points....I just gave you a few!!!!

This parabola opens upward

The axis of symmetry for a parabola that opens upward (or downward ) will  always  be the average of the two x values whenever those two x values are associated with the same y value 

Thus...to find the average....add the x values and divide by 2

The axis of symmetry will  be found by adding the x coordinates of these points and dividing by 2......so

x  =  [ -3 + 11]  / 2

x  =  [ 8 ] / 2

x = 4   ⇒   axis of symmetry

Ellie and her friends go to the students union to see a band play. Tickets are £3 if purchased in advance or £5 if brought at the door. The total amount received from ticket sales was £11 500 and the amount received from tickets bought on the door was £3250. How many tickets were sold altogether

The number of tickets sold at the door  =  3250 / 5  =  650

The number of tickets sold in advance  =  [  11500 - 3250 ] / 3  = 2750

So.....the total number of tickets sold  =  650 + 2750   =  3400

We need to solve this

108  = - 6t^2 + 51t      rearrange as

6t^2 - 51t + 108  = 0       divide through by 3

2t^2 - 17t + 36  = 0        factor

(2t  - 9) (t - 4)  = 0

Set each factor to 0 and solve

2t -9 = 0                                         t - 4  =0

2t = 9                                             t = 4 sec

t = 9/2 sec = 4.5 sec

So...4 sec

We have 7 marbles  and 1 is red....so...the probability  =  1  / 7

If x and y are numbers such that 9^x-4^y=10 and 3^x-2^y=2, compute $3^x+2^y$

We can factor   9^x - 4^y   as   (3^x - 2^y) (3^x + 2^y)  

So 

 (3^x - 2^y) (3^x + 2^y)   = 10

( 2) ( 3^x + 2^y)  = 10         divide both sides by 2

3^x + 2^y  =    5

I think this is correct

The smallest four-digit number  is  C(1000, 1)  = 1000

The second smallest  = C(14, 4) = C(14, 10)  =  1001

Here :   https://www.desmos.com/calculator/kkpdlglglo