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Tysm it seems so easy now haha

x^2  - y^2  = (x + y) (x - y)

We need   to have   (52)(48)

It's obvious that x must be < 52....because,if not, ...... y is positive.... and adding them together would produce  more than 52

So x must either be  50 or 48

Notice that if x  = 50 and y  = 2, we have

(50 + 2)  (50 - 2)  =

(52) (48)   !!!!

Tysm! :D

If we "anchor" any one person in a seat, there are  8! arrangements of the other peoeple that are possible = 40320  arrangements

If we "anchor"  the mathematicians in any 4 consecutive positions there are 4! = 24 arrangements of them that are possible

And the other people can be arranged  in 5!  = 120 ways

So....the total number of ways that the mathematicians can be seated is  24 * 120  = 2880  ways

So....the probability that all 4 math majors sit in consecutive seats  is      2880 / 40320  = 1/14 ≈  7.14%

Thanks, Rarinstraw  !!!

EDIT: Included Question 2

Question 1: Simplify the expression: \((2-3i)(4+2i)\)

For this, we'll use the FOIL method.

2*4=8

8+__+__+__

2*2i=4i

8+4i+__+__

-3i*4=-12i

8+4i-12i+__

-3i*2i=-6i²

(I'm assuming i=sqrt(-1))

8+4i-12i+6=14-8i

Option S is your answer

Question 2: Simplify the expression: \((3x^4+9x^3-7x+15)+(-6x^4-8x^2+5x-3)\)

This is adding like terms.

First, let's start with x^4

3-6=-3

-3x⁴+9x³-8x²+__+__

There were only one x^3 and x^2 in the expression, so we know that part for sure.

Now, to the x term.

-7+5=-2

-3x⁴+9x³-8x²-2x+__

Now, to the normal numbers.

15-3=12

Final answer: -3x⁴+9x³-8x²-2x+12

Hope this helped!

Here's one way to do it, ACG..but maybe not the best...sorry I can't provide a pic...!!

Draw angle bisectors to A, B and C

Where these bisectors meet is the incenter of the triangle....and this will  be the center of the circle....call this point, O

Now...looking at the circle, FE, FD and DE  form chords within the circle....and any chord passing through O will be a diameter....but none of these chords will pass through O....and any chord in a circle not passing through the center will intercept an arc on the circle that is  less than 180°

Thus....inscribed angles FDE, EFD and and FED will intercept arcs that will be less than 180°....so each of their measures will be less than  (1/2)  of 180°  =   less than 90°

So...triangle DEF is acute because each of its angles measure < 90°

I hope that helps ....!!!

Good Job!!!!.

Note.....   ⁿ√a^m   =  a^m/n  .... so.....

⁵√w³  is equivalent to    w^3/5  =  ( w^1/5 ) ³  ⇒​   "D"

Second one

Let the width be, W

So the length is 10 more than this  = W + 10

And 

Area  = W * L  =  W (W + 10)  = f(W)

Awe, thanks GingerAle, I certainly tried my best on that solution.

Thanks CPhill!

Thanks!! 

You can do adults = x

and say students = 45 - x

this is just easier

i hope this helps

gavin

gcd(a,b)=168- this means that a=a₁*168, b=b₁*168, where a₁ and b₁ are coprime.

gcd(a,c)=693, meaning that a=a₂*693, c=c₁*693, where a₂ and c₁ are coprime.

168=2³*3*7, 693=3²*7*11 gcd(168, 693)=3*7=21. Therefore gcd(b,c)>=21. To prove that 21 is the smallest possible value of gcd(b,c) i have to find an example-

a=lcm(168, 693)=5544, b=168, c=693.

check:

gcd(a,b)=gcd(5544,168)=gcd(168*33, 168)=168*gcd(33,1)=168

gcd(a,c)=gcd(5544,693)=gcd(693*8,693)=693*gcd(8,1)=693

gcd(b,c)=gcd(168,693)=21.

All you need to do is work out the volume of each cone then sort them by volume, starting with the least.

CHB can you please clarify?

Don't worry, I have sorted it out finally:

It is:

Adults = x

Students  = y

So x + y = 45

x = 45 - y....(1)

Adult tickets are R375 and Student Tickets are R200, which means that 375x + 200y = 9875....(2)

So then just sub (1) into (2) and do the sum.

Students are 40 and Adults are 5.

Thanks Chris :)

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Screech..................

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And quit giving yourself points for your B U L L S H I T questions!!!

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