Bosco

Real numbers x and y satisfy    

x + xy = 250y    

x - xy = -240y    

Enter all possible values of x, separated by commas.     

First thing to do is just add them together.    

  x + xy  =    250y    

  x – xy  =  –240y    

2x          =     10y          ——>>     x = 5y    

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Three red and two blue balls are placed in a hat. A ball is chosen at random and not replaced. A second ball is chosen at random. What is the probability that both balls chosen will be blue.    

The 1st ball probability is 2 / 5   

If the first ball is blue, there's only one blue ball in the hat, so ...    

The 2nd ball probability is 1 / 4    

Probability of both happening is (2 / 5) x (1 / 4)  =  2 / 20  =  1 / 10    

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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.    

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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.    

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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    

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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    

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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    

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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    

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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    

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