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.
If you want to learn more, you can read:
https://brainly.com/question/7135052
Related Questions
Mae Ling earns a salary of $360 plus a 8.0% commission on sales at a gift shop. How would she make in a week if she sold $4,900 worth of merchandise.
PLEASE HELP I WILL MARK BRAINLIEST PLEASEE
Answers
4,900 x .08 = 392
392 + 360 = 752
answer
757
Step-by-step explanation:
I just know made a A on the test
retail store purchases a couch for $600 and marks it up 25% to sell. How much is the retailer asking for the couch?
Answers
Answer:
$750
Step-by-step explanation:
To find the new price, multiply the original price by 1.25, since there is a 25% increase in the price:
600(1.25)
= 750
So, the retailer is asking for $750 for the couch
At the end of the day, Mr. Díaz drains the pool. The equation
y = -50x + 300 can be used to find y, the number of gallons of
water left after draining the pool for x minutes. Graph the
equation. How long does it take to drain the pool? Explain.
Answers
Answer: 6 minutes.
Step-by-step explanation: You can use a graphing calculator to see the exact graph, but you're trying to figure out what value of x gives you a y of 0. -50 times 6 is 300, plus 300 equals 0.
The graph of the equation y = -50x + 300 is a straight line, and plotted below. The time it take the pool to drain, according to this equation, is 6 minutes.
How do we make graph of a function?Suppose the considered function whose graph is to be made is f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values f(x) are plotted on the vertical axis.
They are together plotted on the point
(x,y) = (x, f(x))
This is why we usually write the functions as:
y = f(x)
For this case, we're specified that:
y = the number of gallons of water left after draining the pool for x minutes.The relationship between x and y given is: y = -50x + 300Take two different values of x, let it be 0 and 1.
Then, the value of y we get is:
Case 1: x = 0:[tex]y = -50x + 300\\y = -50 \times 0 + 300\\y = 300[/tex]
Thus, one point on the equation y = -50x + 300 is (0,300)
Case 2: x = 1:[tex]y = -50x + 300\\y = -50 \times 1 + 300\\y = 300 - 50 = 250[/tex]
Thus, another point on the equation y = -50x + 300 is (1,250)
Plot these points taking x on horizontal and y on vertical axis. Then join those two points by a straight line. This is the graph of the considered equation as equation of type [tex]y = mx +c[/tex] is a straight line's equation and for straight line, two of its points are sufficient to plot it.
The graph is given below.
Since we know that:
y = number of gallons of water left after draining the pool for x minutes,
so when the pool drains of fully, there will be no water left, or y = 0.
Putting y = 0 in the equation y = -50x + 300, we get:
[tex]y = -50x + 300\\0 = -50x + 300\\\\\text{Adding 50x on both the sides}\\\\50x = 300\\\\\text{Dividing both the sides by 50}\\\\x = \dfrac{300}{50}= 6[/tex]
Thus, when y= 0, we get x = 6, so when the fully filled pool is drained for 6 minutes, the whole pool gets drained (for this case).
Thus, the time it take the pool to drain, according to this equation, is 6 minutes. The graph of the equation y = -50x + 300 is given below.
Learn more about graphing functions here:
https://brainly.com/question/14455421
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HELP PLS UHM 15 POINTS AND Brainliest
Answers
Answer:
(0,2)
Step-by-step explanation:
The intercept is the part of the line touching the quadrat.
Answer:
B (0,2)
Step-by-step explanation:
Because if its on the red line on the y axis its 2.
Find the answer for x.
Answers
Answer:
x=25
Step-by-step explanation:
since this is a triangle you would add up all the measure of this and set it equal to 180. 90 is the side with the box. so it would be 2x+15+x+90=180 then solve for x and you would get your answer.
Solve for x: −2(x + 3) = −2x − 6 NEED HELP PLZ:(
A: 0
B: 3 C:All real numbers
D:No solution
Answers
Answer:
The answer is C:All real solutions
Step-by-step explanation:
here are the steps in case u need them :)
Step 1: Simplify both sides of the equation.
−2(x+3)=−2x−6
(−2)(x)+(−2)(3)=−2x+−6(Distribute)
−2x+−6=−2x+−6
−2x−6=−2x−6
Step 2: Add 2x to both sides.
−2x−6+2x=−2x−6+2x
−6=−6
Step 3: Add 6 to both sides.
−6+6=−6+6
0=0
Answer:
C: All real numbers.
Step-by-step explanation:
-2 ( x + 3 ) = -2x -6
-2 times x, -2 times 3
-2x -6 = -2x -6
Add 6
-2x -6 +6 = -2x -6 +6
-2x = -2x
same as....
0 = 0
Please help me find the equivalent fractions!
Answers
Answer:
7/9 = 14/18
4/10 = 16/40
3/12 = 9/36
8/10 = 4/5
12/16 = 6/8
18/21 = 6/7
Step-by-step explanation:
Answer:
7/9 is equivalent to 14/18
4/10 is equivalent to 16/40
3/12 is equivalent to 2/8
8/10 is equivalent to 4/5
12/16 is equivalent to 6/8
18/21 is equivalent to 6/8
The graph shows a proportional relationship. Which equation matches the graph?
Answers
Answer is y=2x because when you look at graph it’s clear
Answer: y=2x
Step-by-step explanation:
what property is 4x + 8 = 28
Answers
Answer:
x=5
Step-by-step explanation:
4x + 8 = 28,
it's rather straight forward,
you would subtract 8 from the left side,
doing the same on the right.
now you have
4x = 20
x= 20/4
x=5
hope this helps.
What is the solution to the equation 1/2x+3=2/3x+1
Answers
Answer: x=12
Step-by-step explanation: because I’m smart and in middle school
Jacob's job pays him $12.50 per hour. Which equation can be used to find Jacob's salary,
y, if he works for x hours? *
(5 Points)
A. y = x/12.50
B.y = 12.50 + x
.
C.y = 12.50 - x
D.y = 12.50x
Answers
Answer:
D
Step-by-step explanation:
BECAUSE the number of hrs he works his salary multiplies
hope this helps..
the value of 1 by 3- 1 by 2=
Answers
Answer:
the value of 1 by 3- 1 by 2 is 1
Step-by-step explanation:
it is one because 1 by 3 is 1*3
that equals to 3
then you do 1 by 2 (aka 1*2)
then it is 3-2 which equals to 1
Credit card A is running a promotion where they will charge 0% interest for the first year, and then 0.8% compounded continuously after that. Credit card B has an interest rate of 0.7%, also compounded continuously. If you are going to make a $500 purchase and plan to not make a single payment for 2.5 years, which credit card should you go with? Write the equation showing the total balance at the end of 2.5 years for that card. How much money invested at 5% compounded continuously for 3 years will yield $820
Answers
Answer: 0.1
Step-by-step explanation:
your going to substact credit card a and b and then what ever you get will be your answer
1. − p + 6p ≤ 4 + 6p
Answers
Step-by-step explanation:
-p + 6p <_ 4 + 6p
5p <_ 4 + 6p
-4 <_ p
-4 less than or equal to p
PLEASE HELP I DONT UNDERSTAND WILL GIVE LIKE 20 POINTS
Answers
Answer:
Step-by-step explanation:
11/4 <3
Answer:
11/4
Step-by-step explanation:
Hope this helps!
I’ve tried but I don’t know what it is please help
Answers
Answer: x=11
Step-by-step explanation:
I got this by 126-49=77. Then I divided 77 by 7 and got 11.
PLEASE HELP I AM BEING TIMED!
In the Diagram Angles B and C are_____?
Options: Right
Similar
Congruent
Obtuse
Answers
HELP PLS. What information do you need to graph a linear function?
Answers
Explain how do you know whether the relationship between two quantities is a proportional relationship. *
Answers
Two quantities have a proportional relationship if they can be expressed in the general form y = kx, where k is the constant of proportionality. In other words, these quantities always maintain the same ratio. That is, when you divide any pair of the two values, you always get the same number k.
The expression 3/8z + 1 factored is
Answers
Answer:
Factored out is 1/8
Step-by-step explanation:
3z+8/8
Select all that apply.
Which of the following name an angle in the drawing?
Answers
Answer:
ECB and CDE
Step-by-step explanation:
the others arent the same
You are buying packages of beads to make bracelets. Each package costs $3 plus 7% tax. You have a gift card for $15, and you plan to use only the gift card to pay for the beads. Which function c(p) represents the total cost, where p represents the number of packages of beads you purchase? What is a reasonable domain?
A. c(p) = 3.21p − 15; {0, 1, 2, 3, 4}
B. c(p) = 3.21p; all nonnegative integers
C. c(p) = 0.07(3p − 15); all nonnegative integers
D. c(p) = 1.07(3p); all nonnegative integers
Answers
Answer:
A
Step-by-step explanation:
You must multiply the number your buying by the price then you need to multiply by 1.07 because you need 7% or .07 to get the tax but you want to add that to the old number so you need a 1 in front so the answer is c(p) = 1.07(3p) however you still need the $15 gift card so instead you add the 7% into the three dollars you are multiplying by the number then subtract the 15 dollars because you aren't really paying. The reasonable domain is 0 1 2 3 4 because the number 5 would be over the 15 dollar limit.
Simplify. - (2b - 4)
Show work
PLEASE HELP
Answers
Answer:
-2b+4
Step-by-step explanation:
we are multiplying by a negative 1 in the expression.
-1(2b-4)
-2b+4
*negative multiplied by a negative makes a positive
Hope this helps!
The point Q (5,3) is translated 2 units left. What are the coordinates of the resulting point Q
Answers
Answer:
(3,3)
Step-by-step explanation:
Since it's to the left, and not up or down at all, the y-value does not change. The x-value, however, is affected. Since it's to the left, it is decreasing in value by 2 points. If it were to the right, it would increase in value to (7,3), since it'd be going further away from (0,0).
Answer:
Q = (3,3)
Step-by-step explanation:
Moving the point left moves the x value down 2.
5-2=3
Therefore, Q = (3,3)
V = 1/3 πr^2h
Pls help
Answers
If your solving for a different letter then tell me. Thanks
Andy's phone plan charges $0.45 per text message plus a $20 monthly fee. Jeff's plan charges $0.20 a text plus an additional $35 monthly fee. Which equation can be used to determine when the phone plans will cost the same based on the number of texts?
Answers
Answer:
20+0.45x=35+0.20x
Step-by-step explanation:
From the information given, you can say that Andy's plan cost would be equal to Jeff's plan cost and then solve for the number of text to find when the phone plans will cost the same:
20+0.45x=35+0.20x, where x is the number of texts
Now, you can solve for x:
0.45x-0.20x=35-20
0.25x=15
x=15/0.25
x=60
According to this, the equation that can be used to determine when the phone plans will cost the same based on the number of texts is 20+0.45x=35+0.20x.
A number is in expanded form: (9 x 10) + (6 x 1) + (2 x 1/100) + (3 x 1000) What is the number is standard form?
Answers
Answer:
96.023 is the answer yeah
1:Write 2 whole numbers that are less than 941,020
Answers
Answer:
900,000500,000Step-by-step explanation:
There are lots of numbers that are less than 941,020
( Exactly 941,019 without Negative Numbers )
( If Negative Numbers are involved, it's infinity )
Hope this helps! <3
Answer:
5 and 9303 (Those are just examples)
Step-by-step explanation:
You can choose any number that is below 941,020, and hs no decimal places, so 0, 6, 930, and 90493 all work.
Using Oliver’s table, how can you find the unit rate?
Answers
Answer:
Is there a table I can see if I'll be able to help
Answer:
Oliver’s table indicates that for every increase of 2 strides, the distance he travels increases by 7 feet. So, the change in distance divided by the change in stride gives the unit rate.
Step-by-step explanation:
This Is The Sample AnswerQUESTION 1, Saturday, October 10th, 2020
I have some geometry questions today. Please include your thoughts or reasoning with your answer. Please ignore the answer I selected for it was not an purpose. Thanks!
Answers
Answer:
Hi in my opinion ur answer means option 2 SAS is correct
Answer:
SASStep-by-step explanation:
The triangles have one side congruent, one side common = congruent and the angle between them congruent
It is Side, Angle, Side = SAS