Step-by-step explanation:
a) Give two pairs which are in the relation
and two pairs that are not.
As stated before, a pair
is equal mod m (written
) if
. Then:
- x=0 and y=4 is an example of a pair

- x=0 and y=1 is an example of a pair

b) Show the
is an equivalence relation.
An equivalence relation is a binary relation that is reflexive, symmetric and transitive.
By definition
is a binary relation. Observe that:
- Reflexive. We know that, for every m,
. Then, by definition,
. - Symmetry. It is clear that, given x,y and m such that
, then
. Therefore 
- Transitivity. Let x,y,z and m such that
and
. Then,
and
. Therefore:
.
In conclusion,
defines an equivalence relation.
The dog house consists of two geometric objects, triangular prism and rectangular prism.
First, find the surface area of triangular prism
The triangular prism consists of
base of triangle (b) = 3 ft
height of triangle (h) = 2.5 ft
height of prism or length of rectangle (l) = 4 ft
side of triangle or width of rectangle (w) = 2.5 ft
Now, calculate the area
area of tp = area of two triangle + area of 2 rectangle
area of tp = (2 × 1/2 × b × h) + (2 × l × w)
area of tp = (2 × 1/2 × 3 × 2) + (2 × 4 × 2.5)
area of tp = 6 + 20
area of tp = 26 ft²
Second, find the surface area of rectangular prism
The rectangular prisms consists of
length (l) = 3 ft
width (w) = 4 ft
height (h) = 2 ft
Now, calculate the area
area of rp = area of back and front rectangle + area of left and right rectangle
area of rp = (2 × l × h) + (2 × w × h)
area of rp = (2 × 3 × 2) + (2 × 4 × 2)
area of rp = 12 + 16
area of rp = 28 ft²
Third, add both of the area
area = area of tp + area of rp
area = 26 + 28
area = 54 ft²
The area of the dog house is 54 ft²
Answer:
70 easyily
Step-by-step explanation:
Max mart is $1.25 for an orange, and megmart is $1.125 for an orange. So megmart has the best deal and the difference is $.125
Answer:
i think 10th: √ 50 ≈ 7.1 100th: √ 50 ≈ 7.07
Step-by-step explanation: