Consider the following set of equations: equation c: y = 2x + 8 equation d: y = 2x + 2 which of the following best describes the solution to the given set of equations? (4 points) no solution one solution two solutions infinite solutions

y = 2x+8 start with the first equation

2x+2 = 2x+8 replace y with 2x+2

2x+2-2x = 2x+8-2x subtract 2x from both sides

2 = 8 ... we end up with a false equation

Since the last equation is false, this means there are no solutions.

this means the system is inconsistent. The graph would show two parallel lines that never intersect

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 figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation: