Suppose that y varies directly with x and inversely with z, and y = 20 when x = 15 and z = 3. write the equation that models the relationship. then find y when x = 6 and z = 6.

y = 4x/z , y = 4.

Step-by-step explanation:

Recall ; from Variation,

y ∞ x 1

y ∞ ¹/z 2

Now , combine equation 1 & 2 together, it metamorphosed to

y  =  kx/z 3

Remember, k is a constant and the value  must be find first

K = yz/x

  = (20 x 3) /15

  = 4

 To get the equation that models the relationship, we substitute for k in equation 3

y = 4x/z.

To find the value of y , substitute for the values of k, x and z

y = ( 4 x 6 )/6

  = ²⁴/₆

 = 4

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

a) 7x=7

step-by-step explanation: