1. which describes the collection of all points in the same plane that are
8 1/2
inches from point t?
a.
circle t with radius
8 1/2
inches
b.
circle t with diameter
8 1 / 2
inches
c.
circle t with radius 17 inches
d.
a sphere with center t and radius
8 1 /2
inches
2. the advertised size of a pizza is the diameter of the pizza. which is closest to the area of the crust of a 15-inch pizza?
a.
707 square inches
b.
177 square inches
c.
225 square inches
d.
47 square inches
3. the area of a circle is 78.5 square feet. what is the circumference? select all that apply.
a.
5
π
feet
b.
10
π
feet
c.
20
π
feet
d.
15.7 feet
e.
31.4 feet
f.
62.8 feet
4. determine which pizza is the better buy: a 10-inch diameter pizza for $8.99 or a 6-inch diameter pizza for $5.
a.
10-inch diameter pizza for $8.99
b.
6-inch diameter pizza for $5
5. a circular marble tabletop has a diameter of 42 inches. if the tabletop costs $280, what is the price per square inch?
a.
$0.05
b.
$0.20
c.
$4.25
d.
$4.95
6. garrett wants to make a circular pond in his yard and put a low fence around the edge. what is the largest area pond garrett can make if he has 136 feet of fencing?
a.
21.66 square feet
b.
468.98 square feet
c.
1472.61 square feet
d.
14,519.36 square feet
me i dont know what pi means or how to do it pleazeee?

1. circle T with radius 8 1/2 inches ⇒ answer A

2.  The area of the crust of a 15-inch pizza is 177 inches²  ⇒ answer B

3. 10π feet and 31.4 feet  ⇒ answers B and E

4. The better buy is 10-inch diameter pizza for $8.99 ⇒ answer A

5. The price per square inch is $0.20

6. The largest area of the pond is 1472.61 feet² ⇒ answer C

Step-by-step explanation:

* Lets explain how to solve the problem

1.

- A circle is the set of all points in a plane that are a given distance  

 from a fixed point.  

- The given distance is the radius of the circle and the fixed point

 is its center

- A sphere is the set of all points in a space that are a given distance

 from a fixed point.

- The given distance is the radius of the sphere and the fixed point

 is its center

- A circle is 2-Dimensional, but a sphere is 3-Dimensional.

∵ The collection of all points in the same plane that means it is in a  

  2-D dimensional

∴ It is a circle

∵ The collection of all points in the same plane that are 8 1/2  

   inches from Point T

∴ The radius of the circle = 8 1/2 inches and its center is T

* circle T with radius 8 1/2 inches

2.

- The advertised size of a pizza is the diameter of the pizza

∵ The advertised size of a pizza is 15-inch pizza

∴ The diameter of the pizza is 15 inches

∵ The diameter = 2 × radius

∴ The radius = 15 ÷ 2= 7.5 inches

- The area of the circle = πr²

∴ The area of the crust = π(7.5)² = 176.7 ≅ 177 inches²

* The area of the crust of a 15-inch pizza is 177 inches²

3.

- The area of the circle is πr²

- The circumference of the circle is 2πr

- To find the circumference of the circle you must to find the radius

  of the circle from its area

∵ The area of the circle is 78.5 feet²

∵ The area of the circle = πr²

∴ πr² = 78.5 ⇒ divide both sides by π

∴ r² = 78.5/π ⇒ take √ for both sides

∴ r = √(78.5/π)

∵ The circumference of the circle = 2πr

∴ The circumference of the circle = 2π × √(78.5/π) = 31.407

* The circumference of the circle ≅ 31.4 feet

∵ 10π ≅ 31.4  

∴ The answer is 10π feet and 31.4 feet

4.

- To find which pizza is better buy, you must find the price per

  square inch the lowest price will be better

∵ The area of the circle is πr²

∵ r = 1/2 diameter

∵ The price of the 10-inch diameter pizza is $8.99

∵ The radius of it = 1/2 × 10 = 5 inches

∴ Its area = π(5)² = 25π inches²

∵ Its price is $8.99

∴ The price per square inch = 8.99 ÷ 25π ≅ $0.11

∵ The price of the 6-inch diameter pizza is $5

∵ The radius of it = 1/2 × 6 = 3 inches

∴ Its area = π(3)² = 9π inches²

∵ Its price is $5

∴ The price per square inch = 5 ÷ 9π ≅ $0.18

∴ The price of a 10-inch diameter < the price of 6-inch diameter

∴ The better buy is 10-inch diameter pizza for $8.99

5.

∵ The area of the circle is πr²

∵ r = 1/2 diameter

∵ The cost of the circular marble tabletop is $280

∵ Its diameter is 42 inches

∵ The radius of it = 1/2 × 42 = 21 inches

∴ Its area = π(21)² = 441π inches²

∵ Its cost is $280

∴ The price per square inch = 280 ÷ 441π ≅ $0.20

* The price per square inch is $0.20

6.

∵ The pond shaped a circle

- The length of the fence is the circumference of the pond

∵ The circumference of the circle = 2πr

∵ The length of the fence is 136 feet

∴ 2πr = 136 ⇒ divide the two sides by 2π

∴ r = 136/(2π) = 68/π

∵ The area of the circle = πr²

∵ π ≅ 3.14

∴ The area of the pond = 3.14(68/3.14)² = 1472.61

∴ The largest area of the pond is 1472.61 feet²

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

theres no picture: /

step-by-step explanation: