What is the average rate of change for the sequence shown below?

-1/2

Step-by-step explanation:

If you connected the dots here you would have a straight line.  The average rate of change for a straight line is also known as the slope.  Slope, by definition, is rise over run (although rise doesn't necessarily mean "up"; it could also mean down, as it does here).  From one point to the next in our graph, we go down 1 unit (-1) and to the right 2 units (+2).  Therefore, the slope of the line is -1/2.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

15

step-by-step explanation:

we are given the following expression and we are to solve it and find the product:

-13 × (-5)

solving the given expression in the standard order of solving a mathematical expression, beginning with the opening of brackets and then multiplying the terms and changing their signs.

-3 × -5 = 15 (answer is positive because when negative is multiplied with negative, it gives a positive answer)