1. Select all of the true statements.
A. Pi is the area of a circle of radius 1.
B. Pi is the area of a circle of diameter 1.
C. Pi is the circumference of a circle of radius 1.
D. Pi is the circumference of a circle of diameter 1.
E. Pi is the constant of proportionality relating the diameter of a circle to its circumference.
F. Pi is the constant of proportionality relating the radius of a circle to its area.
Answers
We want to see which of the given statements about the number pi are true.
The correct options are: a, d, and e.
First, let's talk a little bit about the number pi.
The irrational number pi is defined as the quotient between a circle's circumference and its diameter.
So if we know that a circle has a diameter D, the circumference of that circle is given by:
C = pi*D
Now let's analyze each option to see which ones are true.
a) "Pi is the area of a circle of radius 1."
The area of a circle of radius R is given by:
A = pi*R^2
So if the radius of this circle is R = 1. we have:
A = pi*1^2 = pi
So the area of this circle is pi, thus the statement is true.
b) "Pi is the area of a circle of diameter 1."
The diameter is twice the radius, so the radius of this circle is 0.5, we know that pi is the area of a circle of radius 1, not a circle of radius 0.5, so this is false.
c) "Pi is the circumference of a circle of radius 1."
The circumference of a circle of radius R is given by:
C = pi*2*R
If the radius is equal to 1 we have R = 1, then:
C = pi*2*1 = 2*pi
The circumference of this circle is 2*pi, not pi, so this is false.
d) "Pi is the circumference of a circle of diameter 1."
We know that the circumference of a circle of diameter D is:
C = pi*D
So if D = 1, we have:
C = pi*1 = pi
So the circumference of this circle is equal to pi, thus, this statement is true.
e) "Pi is the constant of proportionality relating the diameter of a circle to its circumference."
A proportional relation is:
y = k*x
where k is the constant of proportionality.
The relation between the circumference is given by:
C = pi*D
So yes, pi is the constant of proportionality, this is true.
F) "Pi is the constant of proportionality relating the radius of a circle to its area."
The area equation is:
A = pi*R^2
note that the radius is squared, so this is not a proportional relation, then the statement is false.
Finally, we can conclude that the true statements are:
a, d, e.
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Related Questions
PLEASE HELP I WILL GIVE BRAINLYEST
-8x+-20=
Answers
Answer:
− 8 x- 20,
x = - 5/2
Step-by-step explanation:
rewrite 20 as 4 times 5,
and rewrite 8 as 4 times 2
= -4 times 2x - 4 times 5
= -4 (2x + 5)
Write the sentence as an equation.
251 is the same as 139 less than the product of a and 233
Answers
Answer:
251 = 139 < 233a
I hope that this is correct and that it helps you
Please help me I beg of you :(
Answers
Answer: 125 minutes to make tests for five classes, $2388 in two months, and 4800 women to 3,600 men
1 class: 25 minutes
5 classes: [tex]25[/tex] × [tex]5[/tex] [tex]= 125[/tex] minutes
[tex]\frac{3582}{3}=\frac{x}{2}[/tex]
[tex]\frac{7164}{3}=\frac{3x}{3}[/tex]
[tex]2,388 = x[/tex]
[tex]x= 2,388[/tex]
[tex]\frac{8}{6}=\frac{x}{3600}[/tex]
[tex]\frac{28,800}{6} =\frac{6x}{6}[/tex]
[tex]4,800=x[/tex]
[tex]x=4,800[/tex]
Which set of numbers are integers but not whole numbers or natural numbers?
PLEASE HURRYYYYY!!!!!
Answers
Integers, whole numbers and natural numbers are numbers without decimal points.
The set of number that are integer but not whole or natural number is:
[tex]\{-2, -3, -4\}[/tex]
As stated above that three set of numbers do not contain decimal point;
However, the difference between them is that; a negative number without a decimal point is referred to as an integer
From the given set: only [tex]\{-2, -3, -4\}[/tex] fit into the description of an integer, because
It does not have a decimal pointAnd it is negativeRead more about set of numbers at:
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round 2.52 to the nearest tenth
Answers
Answer:
2.5
Step-by-step explanation:
Answer:
2.50
Step-by-step explanation:
the tenths place is right after the ones place and before the hundreths place.
in 2.52, 5 is in the tenth's place. It's value is 5/10. The number in the hundreths place is 2, 2 is less than 5 so we round down. 2.52 becomes 2.50
3/4 - 1/2 PLEASE HELP
Answers
Answer: 1/4
Step 1: Convert to percents.
3/4 = 75%
1/2 = 50%
Step 2: Subtract.
75% - 50% = 25%
Step 3: Convert to fraction.
25% = 1/4
Hope this helps!
What is the solution to 0.3(12x - 16) = 0.4(12-3x)?
Answers
Answer:
x=2
Step-by-step explanation:
Answer:
x = 2
EXPLANATION:
expand the parenthesis. and then add like terms (put the x's on one side) and then dived to get x on its own!
Which number is an irrational number?
a. 5.38
b. V19
c. -V16
d. -10
Answers
Answer:
I think the Answer is B. √19
I hoped this helpful for you
thank you ☺️☺️
Any other ways this could be written?
Answers
Answer:
what could be written?
Answer:
The correct answer is 7¹⁰
Step-by-step explanation:
I think you wrote 1.7 because i wrote 1. 7¹⁰
but I meant that 1. as the first question i was answering, sorry if I wasn't clear
Yvette uses 6 grams of tea leaves of make 24 fluid ounces of tea. Last week she made 288 fluid ounces of tea. How many grams of tea leaves did Yvette use to make tea last week?
Answers
Answer:
72 grams of tea leaves.
Step-by-step explanation:
288/24=12
12*6=72
Please help ASAP!!!!!!
YOU ALSO GET ALOT OF POINTS!!!!
First to answer (correctly) will get brainliest!!!
A 2-column table with 4 rows. Column 1 is labeled x with entries 5, 3, negative 1, negative 2. Column 2 is labeled y with entries 6, 2, negative 6, negative 8. On a coordinate plane, a line goes through points (negative 2, 4) and (0, negative 4). Linear functions are expressed by data in a table and by a graph. Select all that apply. The slope is the same for both functions. The function expressed in the graph has a steeper slope than the function in the table. The y-intercept is the same for both functions. The table and the graph express an equivalent function.
Answers
Answer:
The function expressed in the graph has a steeper slope than the function in the table.
The y-intercept is the same for both functions.
Step-by-step explanation:
Answer:
B & CStep-by-step explanation:
Need help ASAP please
Answers
Answer:
63.75
Step-by-step explanation:
Answer:
21.25
Step-by-step explanation:
1/4 = 0.25 or 25%
because 0.25 is less than one, dividing will acually be mutiplying. So we have to mutiply to divide. 8*0.25 = 21.25.
answer is 21.25
A bottle of power drink costs $2.25. Which graph represents the relationship between the number of bottles and the total cost?
Answers
Answer: it’s c
Step-by-step explanation:
edg 2020
Answer:
C-the third picture!!
Step-by-step explanation:
8. 2|x - 7| =-4
What is the solution to this absolute value equation
Answers
The answer is there is no solution.
Answer:
No solutions
Step-by-step explanation:
2 | x - 7 | = -4 We need to isolate the absolute value, so in order to do that we need to divide 2 from both sides of the equation.
| x - 7 | = -2
Absolute values can not be equal to a negative number.
Therefore, your answer is no solutions.
What is the y-intercept of the line y + 11 = –2(x + 1.5)?
Answers
Answer:
-14
Step-by-step explanation:
y + 11 = -2(x + 1.5)
y = -2(x + 1.5) - 11
y = -2x - 3 - 11
y = -2x - 14
Answer:
for the y-intercept, i got -14
Step-by-step explanation:
Which of the following is the sum of all the odd integers between 5 and 102?
A. 2592
B. 2597
C. 2601
D. 2603
Answers
Answer:
2601
Step-by-step explanation:
The integers between 5 and 102 are
7, 9, 11, 13, 15, 17,19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101
The sum of the odd intergers between 2 and 105 can be calculated as follows
= (N + 1/2)^2
= (101 + 1 /2) ^2
= (102/2)^2
= 51^2
= 2601
Hence the sum of the odd intergers between 5 and 102 is 2601
What scale factor is required to dilate triangle abc to make it congruent to triangle efd
Answers
Answer:
And so, in fact, we can perform a series of similarity transformations that map to . And so, the answer is yes, triangle would need to be dilated by a scale factor of three, rotated, and then reflected.
Step-by-step explanation:
9. Which of the following equations represents a line with a positive slope and a
negative y intercept?
O y = 3.5x
O y = 7.5x – 2
O y = 1/4x +7
O y = -5x – 8
Answers
the slope is 7.5
the y-intercept is -2
If f(x)=x²+3x-2
find f(-2)
Answers
Answer:
f(- 2) = - 4
Step-by-step explanation:
To evaluate f(- 2) substitute x = - 2 into f(x) , that is
f(- 2) = (- 2)² + 3(- 2) - 2 = 4 - 6 - 2 = - 4
Value of f(-2) is -4
Given that;
f(x) = x²+3x-2
Find;
Value of f(-2)
Computation:
Given that;
f(x) = x²+3x-2
By putting x = -2
f(-2) = (-2)² + 3(-2) - 2
f(-2) = 4 - 6 - 2
f(-2) = 4 - 8
f(-2) = -4
So, -4 is the correct answer to the given equation.
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Distributive property of 48-16
Answers
Answer:
Ok, split the numbers into their addends, 16= 10+6, and 48= 40+8. Now distribute: (10+40)+(8+6)=(50)+(14)=64.
if not good, don't guess!
Step-by-step explanation:
Simplify the expression -3÷(-2/5)
Answers
Answer:
15/2 would be the simplified answer
Step-by-step explanation:
Answer:
15/2
(Decimal: 7.5)
Step-by-step explanation:
What is the perimeter of this triangle?
Answers
Answer:
45
Step-by-step explanation:
Nancy has a shelf over her bed where she keeps her four stuffed teddy bears. How many ways can she arrange the four bears?
Answers
Answer:
16
Step-by-step explanation:
I believe you just multiply 4 by 4 !
please help i’ll mark branliest
Answers
Answer:
45 degrees or choice D
Step-by-step explanation:
angles of a triangle will always amount to 180 when added
60+75+x=180
135+x=180
x=45
Answer:
45
Step-by-step explanation:
Triangle sum theorem states that all interior angles of a triangle = 180
Therefore, 60 + 75 + x = 180
Can you pleassee help need it asap.
3(9x8)-139
Answers
Answer: 77 :)
Step-by-step explanation:
Answer:
3*72-139
216-139
77
you just multiple the parenthesis first
please help! i need help ASAP much appreciated
Answers
Answer:
Plz check in step by step
Step-by-step explanation: Hong Kong Island is the second-largest island of the territory, the largest being Lantau Island. Its area is 78.59 km2 (30.34 sq mi), including 6.98 km2 (2.69 sq mi) of land reclaimed since 1887 and some smaller scale ones since 1851.
Harry's dog weighs 10 3/8 pounds. What is the weight of Harry's dog written as a decimal?
Answers
Answer:
10.375
Step-by-step explanation:
You can tell that 10 is going to be before the decimal because it's already a whole number, so all you have to do is figure out what 3/8 is as a decimal! In case you didn't know, to change a fraction to a decimal, you divide the numerator (the top number) by the denominator (the bottom number). In this case, you need to divide 3, the numerator, by 8, the denominator. 3/8 = 0.375.
So, put the 10 in front of the decimal point and you're done...the answer would be 10.375!
Have great day :3
Grandma Annie is 80 years old. This is 20 years less than 4 times the age of Ashley. How old is Ashley?
Answers
Answer:
Annie is 25.
Step-by-step explanation:
Work backwards. 80+20=100. 100÷4=25. Annie is 25. Let's check:
25x4=100
100-20=80
The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?
Answers
Answer:
70°
Step-by-step explanation:
In an isosceles triangle the 2 base angles are congruent , thus
base angle = [tex]\frac{180-40}{2}[/tex] = [tex]\frac{140}{2}[/tex] = 70°
Unscramble the letters below to form a math word:
MEANLOMPCETY
