what do the following two equations represent? please help 4x+2y= 10 4x-2y= -10 a) the same line b) distance parallel lines c) perpendicular lines d) intersecting, but not perpendicular lines

D

Step-by-step explanation:

The equations are

● 4x + 2y = 10 (1)

● 4x - 2y = -10 (2)

● 4x + 2y = 10

Add - 4x to both sides

● 4x + 2y -4x = 10 -4x

● 2y = 10 -4x

Divide both sides by 2

● 2y/2 = (10 - 4x)/2

● y = 5 - 2x

● y = -2x + 5 (1)

● 4x - 2y = -10

Add -4x to both sides

● 4x -2y -4x = -10 - 4x

● -2y = -10 - 4x

Divide both sides by -2

● -2y/-2 = (-10 -4x)/-2

● y = 10 + 2x

● y = 2x + 5 (2)

So the equation are

● y = 2x + 5

● y = -2x + 5

Graph them

The lines intersect at (0,5) but aren't perpendicular

So the answer is d

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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