In the same way that other functions can be combined, a series of transformations can be combined into a single function. For example, this statement for the functions shows one way to represent the rotation of a point 270° counterclockwise about the
origin followed by a translation 3 units to the left and 1 unit up: S(270, 2/6 31>(X)(-3. + 1).
Write a function to represent each series of transformations:
• rotation of 90 degrees counterclockwise about the origin, point, then a reflection across the x-axis
• reflection across the yaxis, then a translation o units to the right and b units up
• translation a units to the right and b units up, then a rotation of 180 degrees counterclockwise about the origin, then a
reflection across the yaxis

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

n=9

step-by-step explanation:

7 times a number = 7n

decreased by 13 = 7n-13

same as is =

5 times the number = 5n

increased by 5 = 5n+5

7n-13 = 5n+5

2n=18

n=9

vertical=18cm horizontal=18cm hypotenuse=25.5

step-by-step explanation: