Let A be some subset of a universal set U. The "complement of A" is the set of elements in U that do not belong to A.
For example, if U is the set of all integers {..., -2, -1, 0, 1, 2, ...} and A is the set of all positive integers {1, 2, 3, ...}, then the complement of A is the set {..., -2, -1, 0}.
Notice that the union of A and its complement make up the universal set U.
In this case,
U = {1, 2, 3, 6, 10, 13, 14, 16, 17}
The set {3, 10, 16} is a subset of U, since all three of its elements belong to U.
Then the complement of this set is all the elements of U that aren't in this set:
{1, 2, 6, 13, 14, 17}
Answer:
(4x-5)(4x+5)
Step-by-step explanation:
16x^2 - 25
Rewriting
(4x)^2 - 5^2
We recognize that this is the difference of squares
a^2 - b^2 = (a-b) (a+b)
(4x)^2 - 5^2 = (4x-5)(4x+5)
Answer:
Step-by-step explanation:
We have
Put the coordinates of the given points and check the inequality:
For (0; 5) → x = 0; y = 5
For (2; 4) → x = 2, y = 4
For (1; 3) → x = 1, y = 3
Since Emily is walking at a constant speed, we can solve this using proportions, equating ratios of distance/time.
The first ratio is 3/4 miles/1/4 hour
The second ratio is 1 mile/ x hour
Equating the two ratios: 3/4 / 1/4 = 1/x
3 = 1/x
x = 1/3 hour
4(2x +5) = (8x + 20)
8x =20 is an equivalent expression
