Determine whether quadrilateral abcd with vertices a(–4, –5), b(–3, 0), c(0, 2), and d(5, 1) is a trapezoid.

step 1: find the slope of ab. the slope of ab is .

step 2: find the slope of dc. the slope of dc is .

step 3: find the slope of bc. the slope of bc is .

step 4: find the slope of ad. the slope ad is .

the quadrilateral is a trapezoid because .

We are given a quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).

Step 1:

We find the slope of side AB.

with vertices A(-4,-5) and B(-3,0)

Hence, the slope of two points (a,b) and (c,d) is calculates as:

So, the slope of AB is:

Hence slope AB=5.

Step 2:

Now we have to find the slope of DC.

with vertices D(5,1) and C(0,2)

So, the slope of DC is:

Hence slope AB=-1/5.

Step 3:

slope of BC with vertices B(-3,0) and C(0,2) is:

Step 4:

slope of AD with vertices A(-4,-5) and D(5,1) is:

As we know that parallel sides have same slope.

As slope of BC=AD.

Hence AD is parallel to BC.

and the slope of two opposite sides are not equal hence the two sides are not parallel.

Hence, the given quadrilateral ABCD is a trapezoid. ( since it has a pair of opposite sides which are parallel and a pair of non-parallel opposite sides)

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

f(x)=2/3x-8, which give g(x) the greatest value.

step-by-step explanation: