Answer:
You can prove this statement as follows:
Step-by-step explanation:
An odd integer is a number of the form
where
. Consider the following cases.
Case 1. If
is even we have:
.
If we denote by
we have that
.
Case 2. if
is odd we have:
.
If we denote by
we have that 
This result says that the remainder when we divide the square of any odd integer by 8 is 1.
Answer:
14, 16
Step-by-step explanation:
The prime factorization of 224 is 2⁵ × 7. To make it a perfect square, we need the bases to have an even exponent, therefore we divide it by 2 × 7 = 14 to get 16.
Answer:
90 degree rotation in the clockwise direction.
Step-by-step explanation:
Point A transforms to A'
- that is x coordinate: 2 ---> 3
and y coordinate 3 ---> -2
So the rotation is clockwise from Quadrant1 to Quadrant 4.
The slope of OA = 3/2 and the slope of OA' = -2/3.
The product of these slopes = 3/2 * -2/3 = -1 so the lines are perpendicular - that is the line has passed through an angle of 90 degrees.
A similar result occurs if we consider points B, C and D.
Answer:

Step-by-step explanation:
Carrie has 2 meters of ribbon. She cuts off pieces of ribbon that are 5/10 meter, 1/10 meter, and 7/10 meter
Lets add all the cut of pieces and subtract it from 2 meters

Now we subtract 13/10 from 2 meters

To subtract , make the denominator same

7/10 meter is the remaining piece of ribbon