If you plot the points given on a coordinate plane you see that this is a hyperbola that is is horizontal in nature, meaning it opens side to side, not up and down. We can determine the center of it by taking the point equidistant from the vertices, which is (4, 5), the h and k of our center, respectively. Also, the equation looks like this when it is horizontal:
. a is the distance between the center and the vertices, so our a = 2, and c is the distance between the center and the foci, so our c = 3. We need to find b now, using Pythagorean's theorem.
and
. Now we have everything we need to rewrite the equation:
Answer:
{∅, {a}, {b}, {a,b}}
Step-by-step explanation:
The value of power of a set is generalized by using the formula,
Power of a set (P) = 2^n where n is the number of element in the set.
Given two distinct elements a and b say;
A = {a,b}
n(A) = 2 i.e the number of elements in the set is 2. Therefore the power of the set will be 2^n which gives 2^2 = 4.
P(A) = 4 means there are 4 subsets of the given set. Subsets are sets of elements that can be found in the set. The subsets of element A will be;
{∅, {a}, {b}, {a,b}} which gives 4 elements in total.
Note that empty set ∅ is always part of the subset of any given set
Answer:
Small flags = 108
large flags= 47
Step-by-step explanation:
Step one:
given
let the number of small lag be x
and big flags be y
so
3.5x+6.5y= 683.5----------1
x+y=155------------------------2
Step two:
from eqn 2 x= 155-y
put x= 155-y in eqn 1
3.5(155-y)+6.5y= 683.5
542.5-3.5y+6.5y=683.5
collect like terms
3y=141
divide by 3
y= 141/3
y=47
Step three:
put y= 47 in eqn 2
x+47=155
x= 155-47
x=108
