Harlon wrote the equation a=18(x^2+1) to find the area of a rectangle that has a length of x^2+1 and a width of 18. he solved for x and got x= ±√(a/18 -1). which of the following is an equivalent equation for x?

a. x= ±√(a-18/18)
b. x= ±√(a+18/18)
c. x= ±√(a-36)
d. x= ±√(a+36)

To solve for x in the equation for the area which was given to be , A = 18(x^2 + 1), we divide both sides of the equation by 18 first.

                                A/18 = x^2 + 1

Then, we subtract 1 from both sides of the equation,

                                A/18 – 1 = x^2

Then, we simplify the expression in the left side of the equation,

                              (A – 18)/18 = x^2

And finally, obtain the square root from both sides of equation,

                             Sqrt ((A-18)/18) = x

The expression equivalent to this is letter A. 

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 formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0