Question

What is the circumference of a circle with a radius of 2.2 in terms of pi?
Answer
What is the perimeter of triangle PQR with vertices P(-2, 9), Q(7, -3), and R(-2, -3) in the coordinate plane?
Answer
You're tiling a kitchen floor that is 10 ft wide and 12 ft long. How many square yards of tile do you need?
Answer
The diameter of circle Z is 5 in. What is its area in terms of pi?
Answer
Points A (-10, -6) and B (6, 2) are the endpoints of line AB. What are the coordinates of point C on line AB such that AC is 3/4 the length of line AB?
Answer
thats not right, sorry
Answer
How can you use a straightedge and a compass to construct an angle that is both congruent and adjacent to a given angle?
Answered by GPT 3.5
The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference and r is the radius.

Given that the radius is 2.2, we can substitute the value into the formula and calculate the circumference:
C = 2π(2.2) = 4.4π

Therefore, the circumference of a circle with a radius of 2.2 is 4.4π (or approximately 13.823 in terms of pi).
Answered by GPT 3.5
To find the perimeter of a triangle given its vertices in the coordinate plane, you can use the distance formula.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Let's calculate the distances between each pair of vertices.

For PQ:
d₁ = √((7 - (-2))² + (-3 - 9)²)
= √(9² + (-12)²)
= √(81 + 144)
= √225
= 15

For QR:
d₂ = √((-2 - 7)² + (-3 - (-3))²)
= √((-9)² + 0²)
= √81
= 9

For RP:
d₃ = √((-2 - (-2))² + (-3 - 9)²)
= √(0² + (-12)²)
= √144
= 12

Now, we can sum up the distances to find the perimeter of triangle PQR:

Perimeter = PQ + QR + RP
= 15 + 9 + 12
= 36

The perimeter of triangle PQR is 36 units.
Answered by GPT 3.5
To calculate the amount of square yards of tiles needed to tile a kitchen floor, you need to convert the measurements from feet to yards and then calculate the area.

The area of the kitchen floor can be found by multiplying the width and length:

Area = Width * Length

Given that the width is 10 ft and the length is 12 ft, we can plug in the values:

Area = 10 ft * 12 ft
= 120 square feet

Next, we need to convert the area from square feet to square yards. Since 1 yard is equal to 3 feet, we know that 1 square yard is equal to 9 square feet (3 ft x 3 ft = 9 sq ft).

Therefore, to convert 120 square feet to square yards, we divide by 9:

Area in square yards = 120 sq ft / 9
= 13.333 sq yd (rounded to three decimal places)

Therefore, you would need approximately 13.333 square yards of tile to cover the kitchen floor.
Answered by GPT 3.5
The formula to calculate the area of a circle is given by:

A = πr²

Given that the diameter of circle Z is 5 inches, we can find the radius by dividing the diameter by 2.

r = d/2 = 5/2 = 2.5 inches

Now, we can substitute the radius value into the formula:

A = π(2.5)²
= π(6.25)
= 6.25π

Therefore, the area of circle Z in terms of pi is 6.25π square inches.
Answered by GPT 3.5
To find the coordinates of point C, we need to determine the position of C along the line AB such that AC is 3/4 the length of AB.

First, let's find the length of line AB using the distance formula.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

For AB:
d_AB = √((6 - (-10))² + (2 - (-6))²)
= √((16)² + (8)²)
= √(256 + 64)
= √320
≈ 17.89

Now, we can find the position of C such that AC is 3/4 the length of AB.

Using the section formula, the coordinates of point C can be found as:

x_C = (1 - 3/4) * x_A + 3/4 * x_B
y_C = (1 - 3/4) * y_A + 3/4 * y_B

Plugging in the coordinates of points A and B:

x_C = (1 - 3/4) * (-10) + 3/4 * 6
= (-1/4) * (-10) + 3/4 * 6
= (10/4) + (18/4)
= 28/4
= 7

y_C = (1 - 3/4) * (-6) + 3/4 * 2
= (-1/4) * (-6) + 3/4 * 2
= (6/4) + (6/4)
= 12/4
= 3

Therefore, the coordinates of point C on line AB such that AC is 3/4 the length of AB are (7, 3).
Answered by GPT 3.5
I apologize for the confusion. Let's correct the calculations.

To find the coordinates of point C, we can use the formula:

x_C = (1 - 3/4) * x_A + (3/4) * x_B
y_C = (1 - 3/4) * y_A + (3/4) * y_B

Plugging in the coordinates of points A and B:

x_C = (1 - 3/4) * (-10) + (3/4) * 6
= (1/4) * (-10) + (3/4) * 6
= (-10/4) + (18/4)
= 8/4
= 2

y_C = (1 - 3/4) * (-6) + (3/4) * 2
= (1/4) * (-6) + (3/4) * 2
= (-6/4) + (6/4)
= 0/4
= 0

Therefore, the correct coordinates of point C on line AB such that AC is 3/4 the length of AB are (2, 0).
Answered by GPT 3.5
To construct an angle that is both congruent and adjacent to a given angle, you can use a straightedge and compass as follows:

1. Start with the given angle, let's call it angle ABC.

2. Place the compass at point A and draw an arc that intersects both rays of angle ABC. Make sure to keep the compass radius large enough so that the arcs intersect both rays.

3. Without changing the compass radius, place the compass at point B and draw an arc that intersects the first arc you drew. Label the point where the arcs intersect as D.

4. Use the straightedge to draw a line passing through points A and D. This line creates an angle, angle ADE, which is congruent to angle ABC.

5. Angle ADE is also adjacent to angle ABC since they share a common side, the line segment AD.

By following these steps, you can use a straightedge and compass to construct an angle that is both congruent and adjacent to a given angle.