Question

Got three questions need with .

Answer 1

14.

Center = (-7,4)

Radius = 7

15. 189 square yards

16. 84 square inches

Explanation:

14.

The standard form of a circle is given as:

`(x-h)^2 + (y-k)^2 = r^2`

Where

(h,k) is the center

and

r is the radius of the circle

Given, the circle equation in this problem as:

`(x+7)^2+(y-4)^2=49`

We re arrange this:

`(x-(-7))^2+(y-(4))^2=7^2`

Now, we clearly see that the center is (-7,4) and the radius is 7

Hence,

Center = (-7,4)

Radius = 7

15.

For simplicity, let the point at DE, where it makes the right angle, be the point "H".

DEF is the triangle.

So, we see now that:

DE = 21 yd

FH = 18 yd

DE is the base of the triangle and FH is the height of the triangle.

The area of a triangle is:

Area = 0.5 * base * height

So, we now find the area to be:

Area = 0.5 * 21 * 18 = 189 square yards

16.

Rhombus is a quadrilateral (figure with 4 sides) whose 4 sides have equal length.

The diagonal is the length from one corner to the opposite corner. So, a rhombus has 2 diagonals.

The area of the rhombus, in terms of diagonals, would be:

Area = (Diagonal1 * Diagonal2)/2

So, we multiply the 2 diagonal's length and divide the answer by 2.

We have:

Diagonal 1 = 12

Diagonal 2 = 14

Hence, area would be:

Area = (12*14)/2 = 84 square inches