Mrs. Doggendorf drove 45 miles and used 3 3/4 gallons of gas. Her sister Kelly, drove 85 miles and used 8 2/3 gallons of gas. Which driver used fewer gallons of gas per mile

Mrs.Doggendorf has fewer gallons per mile

Step-by-step explanation:

Mrs.Doggendorf drove 45 miles and used 3 3/4 gallons of gas

The miles per gallon is

convert  3 3/4 gallons to simple fraction= 15/4 gallons

miles per gallon= 45/15/4

miles per gallon= 45*4/15

miles per gallon= 12 miles per gallon

gallons per mile= 1/12

Kelly, drove 85 miles and used 8 2/3 gallons of gas

convert 8 2/3 gallons to simple fraction= 26/3 gallons

miles per gallon= 85/26/3

miles per gallon= 85*3/26

miles per gallon=9.80 miles per gallon

gallons per mile= 1/9.80

Hence Mrs.Doggendorf has fewer gallons per mile

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.

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step-by-step explanation: