The cost to rent a rug cleaner is $25 plus $15 per hour at Floors, Inc. At Rugs R Clean the rug cleaner costs $45 plus $7 per hour. Which inequality can be used to show how many hours you need to rent the rug cleaner so that Floors, Inc.'s charges will be same the charges at Rugs R Clean?

25 + 15x < 45 + 7x

Step-by-step explanation:

Given:

Floors, Inc. Fixed charges = $25

Floors, Inc. Variable charges = $15 per hour

R rug clean Fixed charges = $45

R rug Variable charges = $7 per hour

Computation:

Assume number of hour = x

Floors, Inc. total cost = 25 + 15x

R rug  total cost = 45 + 7x

So,

25 + 15x < 45 + 7x

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.

the answer is here: : )

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