The equation 4x2 – 24x + 4y2 + 72y = 76 is equivalent to (1) 4(x – 3)2 + 4(y + 9)2 = 76 (2) 4(x – 3)2 + 4(y + 9)2 = 121 (3) 4(x – 3)2 + 4(y + 9)2 = 166 (4) 4(x – 3)2 + 4(y + 9)2 = 436 i know the answer is choice 1 but how do you get to that answer?

Option 4 is correct.

The equation is equivalent to

Step-by-step explanation:'

Given equation:

First group the terms with x and those with y;

Next, we complete the squares.

We can do this by adding a third term such that the x terms and the y terms are perfect squares.

For this we must either add the same value on the other side of the equation or subtract the same value on the same side so that the equality is maintained.

⇒

or

Add 360 on both sides we get;

Simplify:

Therefore, the given equation is equivalent to

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.

75

step-by-step explanation:

you do x-29=46 (the number of cantaloupes sold)

in order to find x, you have to find what minus 29 equals 46, meaning you'd have to add 29 to 46.

29+46=75

if you replace x with 75, the equation looks like:

75-29=46

x=75