Determine whether y varies directly with x. if so, find the constant of variation and write the equation. x | y -2 | -4 -4 | -8 -16 | -32 a. no b. yes; k=-2 and y=-2x c. yes; k=1/2 and y=1/2x d. yes; k=2 and y=2x

The correct option is d.

Step-by-step explanation:

If y varies directly with x, then y is directly proportional to x.

             .... (1)

Where, k is constant of variation.

From the given table it is clear that the value of y is -4 at x=-2.

Put x=-2 and y=-4 in equation (1).

Divide both sides by -2.

The value of k is 2. Put this value in equation (1), to find the relation between x and y.

At x=-4,

At x=-16,

All the points of the table satisfy the equation. It means y is directly proportional to x, the constant of variation is 2 and required equation is y=2x.

Hence option d is correct.

cut 138 centimeters off

step-by-step explanation:

250-112 = 138

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180