Select all the statements that are true.
The radius of a circle is twice its diameter.
To find the diameter of a circle, divide its circumference by π.
The circumference of a circle is greater than its diameter.
The circumference of a circle is twice its radius.
To find the diameter of a circle, multiply its radius by two.
No, only one triangle can be drawn with the given conditions.
This is because in a triangle, the length of each side and the measure of each angle determines the shape and size of the triangle. Two sides and the angle between them are known as the SSS (side-side-side) condition of a triangle.
In the given conditions, we have two sides of length 5 inches and 6 inches and the included angle is 45°. This information determines the shape and size of the triangle uniquely, so only one triangle can be drawn with these conditions.
Therefore, no matter how we arrange these sides and angle, only one triangle can be formed.
Statements 2 and 5 are true.
Why?? Explain!!!!
Statement 2, "To find the diameter of a circle, divide its circumference by π," is true because the formula for finding the circumference of a circle is C=πd, where C is the circumference and d is the diameter. Solving this formula for d, we get d=C/π, which means that to find the diameter, we must divide the circumference by π.
Statement 5, "To find the diameter of a circle, multiply its radius by two," is also true. The definition of the diameter of a circle is the distance across the circle passing through its center. Since the radius of a circle is the distance from the center to any point on the circle's edge, multiplying the radius by 2 gives us the diameter. Therefore statement 5 is also true.
The other statements are false. The first statement is false because the diameter of a circle is twice its radius, not the other way around. The third statement is false because the circumference of a circle is equal to π times its diameter, not greater than it. The fourth statement is false because the circumference of a circle is equal to 2π times its radius, not twice its diameter.
Thanks!! Faybelle you are the best!!!!
You're welcome! It's my pleasure to help you out!
What is the diameter of a circle with a circumference of 84.78 inches? Use 3.14 for π. Enter your answer in the box.
The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter.
We are given that the circumference is 84.78 inches, and π is approximately 3.14.
Substituting these values into the formula, we get:
84.78 = 3.14d
Dividing both sides by 3.14, we get:
d = 84.78/3.14
Simplifying this expression, we get:
d ≈ 27
Therefore, the diameter of the circle is approximately 27 inches.
So the diameter is 27?? Are you sure!!!!!!!!!!!!
Yes, that's correct!
We know that the circumference of the circle is 84.78 inches, and we use the formula for the circumference of a circle, which is:
C = πd
where C is the circumference, and d is the diameter.
Substituting the given values, we get:
84.78 = 3.14d
Dividing both sides by 3.14, we get:
d ≈ 27
So, the diameter of the circle is approximately 27 inches.
A mountain bike tire completes 20 revolutions and travels 136 feet. Rounded to the nearest inch, what is the diameter of the bike’s tire? Use 3.14 for π. Enter your answer in the box.
Each revolution of the wheel corresponds to the circumference of the tire. So, the distance traveled in 20 revolutions is equal to 20 times the circumference of the tire.
Let d be the diameter of the tire, then the circumference of the tire is πd.
So, the distance traveled in 20 revolutions is:
20 x πd
We are given that this distance is 136 feet. So, we can write an equation:
20 πd = 136
Dividing both sides by 20π, we get:
d = 136 / (20 π)
We can simplify this expression by using 3.14 for π:
d = 136 / (20 x 3.14)
d ≈ 2.17
Rounding this to the nearest inch gives:
d ≈ 2 inches
Therefore, the diameter of the bike tire, rounded to the nearest inch, is 2 inches.
Are you sure/???????
I apologize for the mistake in my previous response. After recalculating using the correct formula, the correct answer is:
If each revolution covers a distance of 136 feet, then 20 revolutions cover a distance of:
20 x 136 = 2720 feet
The circumference of the tire is the distance covered by one revolution, so we can find the circumference by dividing the distance traveled by the number of revolutions:
C = distance / # of revolutions = 2720 / 20 = 136 feet
Now we can use the formula for circumference to find the diameter:
C = πd
Substituting the value we just found for C, we get:
136 = πd
Dividing both sides by π, we get:
d = 136/π
Using the value of π as 3.14, we get:
d = 43.312 inches
Rounded to the nearest inch, the diameter of the bike tire is 43 inches.
I apologize for any confusion caused by my earlier mistake and thank you for bringing it to my attention.
Can more than one triangle be drawn with the following conditions?
A. side lengths of 5 inches and 6 inches with an included angle of 45° between those two sides
Can a triangle be drawn with a side length of 3 inches with angles at each end measuring 90° and 89°? Explain.
No, it is not possible to draw a triangle with a side length of 3 inches and angles at each end measuring 90° and 89°.
To see why this is true, let's use the triangle inequality theorem. According to this theorem, in any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's assume that we can draw a triangle with a side length of 3 inches and angles at each end measuring 90° and 89°.
The sum of the angles in any triangle is always 180°, so the third angle must measure:
180° - 90° - 89° = 1°
Now, the side opposite the 89° angle must be longer than the side opposite the 1° angle (because the 89° angle is larger), so the length of the third side must be less than 3 inches.
However, this contradicts the triangle inequality theorem, which says that the sum of the lengths of any two sides must be greater than the length of the third side. In this case, the sum of the lengths of the two smaller sides is 3 inches (the length of the given side), which is not greater than the length of the third side.
Therefore, it is not possible to draw a triangle with a side length of 3 inches and angles at each end measuring 90° and 89°.