Please help, At a festival 2/7th of the number of girls was equal to 3/5th of the number of boys.
There were 165 fewer boys than girls, how many children were at the festival in all?

465

Step-by-step explanation:

Let the number of girls at the festival be g

Let the number of boys at the festival beb

The conditions are;

2/7 g = 3/5 b (i)

g-b= 165 (ii)make g the subject of the expression

g= 165 +b(iii)use this equation in (i)

2/7 (165 +b)= 3/5 b multiply both sides by 7

7*2/7(165+b) =3/5*7 b

2(165+b)=21/5 b multiply both sides by 5

5*2(165+b) = 21/5*5*b

10(165+b) = 21 b open brackets

1650 +10 b = 21 bcollect like terms

1650 = 21 b- 10 b

1650 = 11 b divide both sides by 11

1650/11 = 11b/11

150 = b = number of boys

Using equation (ii) where g-b =165  ;  g-150 =165 , g= 165+150 =315 number of girls

Total number of children at the festival = 150+315 =465

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.