All Answers 357501 Answers

I’m pretty sure the answer is 768 because you have 4 pairs so thats 4! ways to arrange and then you have to account for the fact that the two people in each pair can switch so thats x2 but that can be said for all four pairs so its *2^4 and then you have to account for the rotation cause it could be clockwise or counterclockwise so thats another *2. So the equation at the end is 4!*2*2^4 which is 768.

If each exterior angle of a regular n-gon is $9$ how many sides must the polygon have    

By theorem, the sum of all the exterior angles of any polygon is 360^o.    

Since one of the angles is 9^o, there must be 40 of them to come to 360^o.    

There are the same number of sides as angles, so there must be 40 sides.    

_.    

Suppose P is the point (5,3) and Q is the point (6,-3). Find point T such that Q is the midpoint of segment PT.    

Since Q is the midpoint, Q to P is the same distance as Q to T.    

To get from Q to P, aka from (6, –3) to (5, 3), you go left 1 and up 6    

To get from Q to T, go the same distances except in the other direction.    

So from (6, –3) go right 1 and down 6 to (7, –9) and that's where T is.    

_.    

What are the ordered pairs of the solutions for this system of equations?

f(x) = x^2 - 2x + 3    

f(x) = -6x     

I plotted them on Desmos and determined  (–1, +6)  &  (–3, +18)    

check answers    

(–1)²  –  (2)(–1)  +  3    

 +1          +2        +3  = +6                (–6) • (–1)  = +6    

(–3)²  –  (2)(–3)  +  3    

 +9          +6        +3  = +18               (–6) • (–3)  = +18    

_.    

The sum of two numbers is 11. Twice the first number minus the second number is 7  Find the numbers.​    

  a + b  =  11    

2a – b  =   7     

add the two equations together and "b" goes away    

3a  =  18                ——>   a  =  6    

6 + b  =  11            ——>   b  =  5    

_.    

if 5 choc ices cost 345 cents how muhc do 11 choc ices cost    

345 / 5  =  69 ¢ for one    

69 x 11  =  759 ¢  or  $ 7.59 for eleven    

_.    

A box of cereal contains 15 3/5 ounces of cereal.  If a bowl holds 2 2/5 ounces of    
cereal, how many bowls of cereal are in one box?    

box contains 78/5 oz     for simplicity convert this to 15.6    

bowl holds    12/5 oz     for simplicity convert this to   2.4    

15.6 / 2.4  =  6.5    

_.    

1. The hypotenuse of an isosceles right triangle is 14. How long is each leg of the triangle?    

     leg  =  14 / sqrt(2)  = (14) • sqrt(2) / 2  =  7 • sqrt(2)     = approx 9.899    

2. The hypotenuse of an isosceles right triangle is 14. What is the area of the triangle?    

     Area  =  (1 / 2) • base • height  =  (1 / 2) • (7 • sqrt(2)) • (7 • sqrt(2))  =  49 • 2  =  98    

_.    

x / r =  [ x + h ] / R

x (R / r ) = x + h

x (R/r) - x =  h

x [( R/r) - 1 ]   = h

x  =    h / [ (R/r) - 1 ]

H = x + h

H = h / [ (R/r) -1 ] + h

The answer is \(\sqrt{913}\).

I will post explanation soon it is very long:

Find the number of arithmetic sequences such that:    
* The arithmetic sequence contains three terms    
* All the terms are integers in \{0, 1, 2, \dots, 10\}    

* The sum of the terms is 9.     

The ones I find are     0, 3, 6  and of course  6, 3, 0

                                   1, 3, 5  and  5, 3, 1     

                                   2, 3, 4  and  4, 3, 2     

                                   3, 3, 3  if it counts

I can't think of any more.  I found seven of them.    

_.    

My question to CPhill:

How can one formulate the equation AB / BD = AC / DC without knowing the angles of triangle ABC?

Please describe how I can arrive at this final solution.

Thanks in advance for your answer!

I will not be available until April 27, 2025.

 !

To find the denominator, we have to find the total number of ways to choose the marbles. There are 13 ways to choose the first marble and 12 ways to choose the second marble, so the denominator is \(13\times12=156\).

To find the numerator, we have to find the number of ways that the first marble is green and the second marble is red. There are 7 ways to pick a green marble and then 6 ways to pick a red marble, so the numerator is \(7\times6=42\).

This means that the answer is \(\frac{42}{156}\), which simplifies to \(\boxed{\frac{7}{26}}\).

By the way, our usernames are very similar