Step-by-step explanation:
csc x / (cot x + tan x)
Write in terms of sine and cosine.
(1 / sin x) / [(cos x / sin x) + (sin x / cos x)]
Multiply top and bottom by sin x.
1 / [cos x + (sin²x / cos x)]
Multiply top and bottom by cos x.
cos x / (cos²x + sin²x)
Use Pythagorean identity.
cos x / 1
cos x
Answer: 16 men
32 women
38 children
Step-by-step explanation:
Let x represent the number of men in the group.
Let y represent the number if women in the group.
Let z represent the number of children in the group.
A group of 86 people consist of men women and children. This means that
x + y + z = 86 - - - - - - - - - - - - 1
There are twice as many women than there are men. It means that
x = y/2
There are 6 more children than there are women. This means that
z = y + 6
Substituting x = y/2 and z = y + 6 into equation 1, it becomes
y/2 + y + y + 6 = 86
multiplying through by 2, it becomes
y + 2y + 2y + 12 = 172
5y = 172 - 12 = 160
y = 160/5 = 32
x = y/2 = 32/2
x = 16
z = y + 6 = 32 + 6
z = 38
9514 1404 393
Answer:
see below
Step-by-step explanation:
The y-coordinates of the points are the same, so the distance between those points will be the difference of the x-coordinates. The first number line shows those x-coordinates plotted properly. It can be used to find the difference between them.
If you cut the rectangle (the wall) diagonally, you get two congruent triangles. The measurements of the sides of one the triangles is 8, 15 and x. There is a pythagorean triples 8, 15, 17 so x has to be 17. if you dont know the triple you can do a^2 + b^2 = c^2 8^2 + 15^2 = c^2 c = 17
the diagonal of wall should be 17
