Find the values of x and y that make the quadrilateral a parallelogram.

See below.

Step-by-step explanation:

In a parallelogram, opposite sides are to be equal, otherwise the sides cannot be parallel.

Therefore,

Parallelogram means opposite sides equal and parallel to each other

So

Done!

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is