Asquare is inscribed in a circle. if the area of the square is 9 in2, what is the ratio of the circumference of the circle to the perimeter of the square? answer should be put like this: c°/p^

Given the formula for the area of a square is:

A=s2 where A is the Area and s is the length of the side of the square, we can find the length of one side of the square by substituting and solving:

9 in2=s2

√9 in2=√s2

3 in=s

s=3 in

Using the Pythagorean Theorem we can find the length of the squares diagonal which is also the diameter of the circle:

The Pythagorean Theorem states:

a2+b=c2 where a and b are legs of the triangle and c is the hypotenuse of the right triangle. In this case, both legs of the triangle are sides of the square so the are both the same length. Substituting and solving gives:

(3i n)2+(3i n)2=c2

9 in2+9 in2=c2

9 in2×2=c2

√9 in2×2=√c2

√9 in2√2 in=c

3 in√2=c

c=3√2 in

We can now find the perimeter of the square and the circumference of the circle.

Formula for Perimeter of a square is:

p=4s where s is the length of a side of the square.

Substituting and calculating p gives:

p=4×3 in

p=12 in

Formula for the circumference of a circle is:

c=2πr where r is the radius of the circle.

Or,

c=dπ where d is the diameter of the circle. Remember: d=2r

Substituting and calculating c gives:

c=3√2π in

We can then write the ratio of the circumference to perimeter as:

3√2π in12 in⇒

3√2π in124 in⇒

√2π4

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form