A workbench for a motorcycle is in the shape of parallelogram IJKL. The motorcycle is raised and lowered as the angles of the parallelogram change. Which statement is
correct?

ZJ and ZL are supplementary
ZJ and ZK are congruent.
65° K
ZJ and ZK are supplementary
ZI and ZL are congruent.

J and K are supplementary

Step-by-step explanation:

Given

The attached image

Required

The true statement

From the attached image, it is hard to determine the values of angles I and L as there are no enough information to determine their values.

However, J and K can be worked easily.

From the image

--- vertically opposite angles

And:

---- angle on a straight line

Substitute:

When two angles add up to 180, the angles are supplementary.

Hence, (c) is correct

the one that has a slope of 1/2 and is positive.

step-by-step explanation: 2 buckets 1 trip ; 4 buckets 2 trips and so on.

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