On a coordinate grid, the coordinates of vertices p and q for polygon pqrs are p(1, 3) and q(−2, 3). what is the length of side pq of the polygon?2 units 3 units 4 units 6 units

The length of the side is the distance between the two points.  The distance between two points is:

d^2=(x2-x1)^2+(y2-y1)^2, so in this case:

d^2=(-3-3)^2+(2-2)^2

d^2=(-6)^2+0^2

d^2=36

d=√36

d=6 units.

Note we could have just observed that the y-coordinate did not change and know that the distance between the two points or the length of the sides was just the change in x:  3--3=6 units.

y = 0.77(x)

step-by-step explanation:

the jacket retains this value after 23% cut or retains 77% of original value. plug original 87 jacket price for x and the remaining value should be y.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15