If we draw a rhombus OABC on a coordinate grid with one vertex at the point O (0,0)
and let its height be 1 then (using the Pythagoras theorem) the coordinates of the 4 points will be as follows:-
O = (0,0) , A = (1, 1), B = (sqrt2+ 1 , 1) , C = (sqrt2, 0)
Slope of the diagonal OB = 1 / (sqrt2 + 1)
Slope of the other diagonal AC = - 1 / (sqrt2 - 1)
Product of the slopes = - 1 / ( sqrt2 + 1)(sqrt2 - 1) = -1 / 1 = -1
This proves that the diagonals are perpendicular.
Do recall that squaring and the *radical sign* cancel each other out... like so:(

)

= a
When you put it that way, it isn't enough :P
(

)

= a
(

)

=?
so you start with
(

)

=

8x+1=25 <-- subtract 1 to both sides
8x=24 <- divide 8 to both sides
x= 3
To find out if it's an extraneous solution ask yourself: It mustn't result in a radical that I like to call... 'illegal'. Plug it into the radicand 8x+1 and make sure you get something that is not a negative number.... so, DO you get a negative number when you plug in x = 3 into the radicand?
(extraneous solution is a invalid solution)
x=3 not extraneous
Answer:
100
Step-by-step explanation:
Ratio is a fraction, so ratio of boys to girls would be written as [let boys be "b" and girls be "g"]:

Also, there are 250 more girls than boys, so we can write:
g = 250 + b
Lets substitute this into "g" of the ratio we wrote and cross mulitply and solve for b:

The number of boys = 100
Looks correct to me but i'm not 100% sure
1.75
2.15
3.105
4.90
these are the answers