7. the coordinates of the vertices of a rectangle are go
i by
r(-3,-4), e(3, 4), c(4,4), and t(4-4). plot these points
on the coordinate plane at the right and connect them to
draw the rectangle. then connect points e and t to form
diagonal et.
a. use the pythagorean theorem to find the exact
length of et.
b. how can you use the distance formula to find the
length of et? show that the distance formula gives
the same answer

a. By Pythagorean Theorem:

b. By Distance Formula:

Step-by-step explanation:

The given rectangle has vertices R(-3,-4), E(-3, 4), C(4,4), and T(4-4).

The points have been plotted on the coordinate plane as shown in the attachment.

a. Using the Pythagoras Theorem;

We substitute the side lengths to obtain:

Take positive square root to obtain:

b. The distance formula is given by:

The endpoints of ET are at E(-3,4) and T(4,-4).

Using the distance formula;

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

300pi

step-by-step explanation: