Adelivery truck is transporting boxes of two sizes: large and small. the combined weight of a large box and a small box is 75 pounds. the truck is transporting 70
large boxes and 65 small boxes. if the truck is carrying a total of 5075
pounds in boxes, how much does each type of box weigh?

large box weights 40 pounds & small box weights 35 pounds

Step-by-step explanation:

We can write 2 equations and solve simultaneous.

Let x be weight of large box and y be weight of small box

"The combined weight of a large box and a small box is 75 pounds.":

"The truck is transporting 70  large boxes and 65 small boxes. If the truck is carrying a total of 5075  pounds":

Now we can solve for x in the first equation, which is x = 75 -y

We now substitute this into the 2nd equation and solve for y:

Using y = 35 and plugging that into the 1st equation, we can solve for x:

Hence, large box weights 40 pounds & small box weights 35 pounds

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.

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x