Answer:
[tex]A=\frac{C^2}{4\pi ^2}[/tex]
Step-by-step explanation:
Recall to find the circumference of a circle the formula is [tex]C=\pi d[/tex] or [tex]C=2\pi r[/tex]. We will also need the formula for the area of a circle which is [tex]A=\pi r^{2}[/tex]. Since the area formula is in terms of r we will use the second formula for circumference.
We start by solving for r in the Circumference formula.
[tex]C=2\pi r\\\frac{C}{2\pi } =r[/tex]. We input this value of r into the area formula.
[tex]A=\pi r^{2} \\A=\pi (\frac{C}{2\pi })^2\\A=\pi (\frac{C^2}{4\pi ^2 })\\A=\frac{C^2}{4\pi ^2}[/tex]
The formula for the area of a circle in terms of its circumference is A = (C²) / (4π), by substituting the expression for the radius r = C / (2π) into the area formula A = πr².
Explanation:The student has asked how to use the formula for the circumference of a circle to write a formula for the area of a circle in terms of its circumference. The formula for the circumference (C) of a circle is C = 2πr, where π (pi) is approximately 3.14159 and r is the radius of the circle.
To write the formula for the area (A) in terms of the circumference, we first solve the circumference formula for r: r = C / (2π). Then we substitute this expression for r into the formula for the area of a circle, which is A = πr². This gives us A = π (C / (2π))², simplifying, we get A = (C²) / (4π).
Thus, the formula for the area of a circle in terms of the circumference is A = (C²) / (4π).
if f(x)=x squared + 3x+5 what is f(a+h)
Answer:
a² + 2ah + 3a + 3h + 5 + h²
Step-by-step explanation:
to evaluate f(a + h) substitute x = a + h into f(x)
f(a + h)
= (a + h)² + 3(a + h) + 5 ← distribute
= a² + 2ah + h² + 3a + 3h + 5
Answer options are A,B,C. Please help ASAP!!
I think the answer is
1) B
2) C
3) A
hopes this helps ;)
he table shows the total cost for different numbers of jackets. Number of Jackets 2 5 7 Total Cost ($) 46.50 116.25 162.75 What is the cost of 3 jackets?
Answer:
$69.75
Step-by-step explanation:
2 jackets cost $46.50 and 5 jackets cost $116.25
The different between 5 and 2 is 3.
So the cost of 3 jackets would be =$116.25 - $46.50
= $69.75
I am a two digit odd number less than fifty. The sum of my digits is seven and my root is 5. What number am I?
Answer: 25
Step-by-step explanation:
The ages of Anjali and Aditya are in the ratio 3: 4.Eight years later sum
of their ages will be 44 years. What are their present ages
Answer:
12 years and 16 years
Step-by-step explanation:
their ages are in the ratio 3 : 4
let Anjali = 3x and Aditya = 4x ← present ages
In 8 years then
Anjali = 3x + 8 and Aditya = 4x + 8, hence
3x + 8 + 4x + 8 = 44 ← sum of their ages in 8 years
7x + 16 = 44 ( subtract 16 from both sides )
7x = 28 ( divide both sides by 7 )
x = 4
Anjali is 3x = 3 × 4 = 12 years old and Aditya = 4x = 4 × 4 = 16 years old
Solve. |x+5|>12 Help it would be great
Answer:
x < - 17 or x > 7
Step-by-step explanation:
Inequalities of the form | x | > a always have solutions of the form
x < - a or x > a
For | x + 5 | > 12, then
x + 5 < - 12 or x + 5 > 12 ( subtract 5 from both sides of the inequalities )
x < - 17 or x > 7
Which polygon has the most sides?
Answer:
It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.
Step-by-step explanation:
hope this helped
victoria invited 260 people to her quinceanera party. 76 guest rode in corvettes and the rest rode in 23 suburbans. how many guest rode in each suburban
Answer:
8 guest rode in each suburban .
Step-by-step explanation:
As given
victoria invited 260 people to her quinceanera party.
76 guest rode in corvettes and the rest rode in 23 suburbans.
As 76 guest rode in corvettes .
Thus
Number of guest rode in suburbans = 260 - 76
= 184 peoples
Let us assume that the number of guest rode in each suburban be x.
Total suburbans are 23.
Than the equation becomes
x × 23 = 184
[tex]x = \frac{184}{23}[/tex]
x = 8
Therefore 8 guest rode in each suburban .
NO ONE CAN Answer this!!!
Jaylan makes limeade using 3/4 cup water for every 1/5 cup of lime juice. Wanchen makes limeade using 2/3 cup of water for every 1/6 cup lime juice. Find the unit rates of water (cups) per lime juice. Whose limeade has a weaker lime flavor? Explain.
Jaylan : Water/Juice=(3/4)/(1/5)=15/4
Wanchen : Water/Juice=(2/3)/(1/6)=4/1 or 16/4
Wanchen has a weaker lime flavor because there is more water in her mixture than Jaylan's limeade. Both have the same amount of lime juice (assuming ratio), and Wanchen has more water, making Wanchen have the limeade that has the weaker lime flavor.
solve equation for x
Question
solve equation for x
Answer:
-3/2Step-by-step explanation:
1/4 - 2/3x = 3/4 - 1/3x
1/4 - 3/4 = 2/3x - 1/3x
-2/4 = 1/3x
x = -2/4 : 1/3
x = -2/4 * 3
x = -6/4 semplified -3/2
What's the distance between the points (–9,2) and (–4,2)?
Final answer:
The distance between the points (–9,2) and (–4,2) is 5 units, calculated as the absolute difference between the x-coordinates since the y-coordinates are equal.
Explanation:
The distance between the points (–9,2) and (–4,2) can be found using the distance formula, which is derived from the Pythagorean theorem. For two points (x1, y1) and (x2, y2) the distance is given by √((x2 - x1)² + (y2 - y1)²). However, because the y-coordinates of the points are the same, we can simplify this to the absolute value of the difference between the x-coordinates.
In this case, the distance is |(–4) - (–9)|, which simplifies to 5 units. There's no need to calculate a square root because there is no vertical change between the points.
WILL MARK AS BRAINLIEST IF CORRECT!
What is the distance between (0,0) and (3,4)
a. 5
b. 4
c. 3
d. 2
Answer:
Your answer is A:5
The graph shows a proportional relationship between the number of kilometers traveled by a bicycle (y) and the number of minutes (x).
PLS HELP ASAP! WILL GIVE BRAINLIEST TO CORRECT ANSWER!
Answer:
0.33 Km/Min
Step-by-step explanation:
Which basic geometric term has exactly one dimension?
A. Point
B. Plane
C. Line
D. Angle
Answer: Option 'C' is correct.
Step-by-step explanation:
We need to find which has one dimension.
Since Point is undefined term with no size or dimension, but in two dimensional it is found in ordered pair i.e. (x,y)
Plane is also an undefined term with length and width but no thickness, so, it is two dimensional.
Angle is undefined term formed by tow lines or rays diverging from a common vertex, so it is two-dimensional.
But Line is also undefined term with length only but there is no width or thickness.
So, Line has exactly one dimension.
Hence, Option 'C' is correct.
I'm super confused... Can someone help me?
Answer:
Second choice
Step-by-step explanation:
Multiply numerator by numerator and denominator by denominator
(2a+10)a
a^2(a^2+2a-15)
Cancel a from a^2
(2a+10)
a(a^2+2a-15)
Factor: 5-3=2 and 5(-3)=-15. a^2+5a-3a-15=0. Group: a(a+5)-3(a+5)=(a-3)(a+5)
Factor: 2*a+2*5=2(a+5)
Cancel out (a+5)
2/(a(a-3))
Find the slope of the line. Write your answer in simplest form.
Answer:
1/6
Step-by-step explanation:
The rise is 1 and the run is 6
A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation x3+6x2 can be used to find x. What are the dimensions of the party-favor bag? Use a graphing calculator and a system of equations to find the answer.
Answer:
[tex]x=3.783[/tex]
Step-by-step explanation:
We are given equation of volume
[tex]V=x^3+6x^2[/tex]
now, we can are given
volume is 140 in^3
we can set 140
and then we can solve for x
[tex]x^3+6x^2=140[/tex]
so, we can draw graph of these two functions
[tex]y=x^3+6x^2[/tex]
[tex]y=140[/tex]
and then we can find intersection point
we can see that intersection point is (3.783,140)
so,
[tex]x=3.783[/tex]
Answer:
The length is 5 inches, the width is 2 inches, and the height is 14 inches.
Step-by-step explanation:
Don’t mind the writing. Just trying to see if this is right?
Answer:
Step-by-step explanation:
Yep you are 100% correct grate job!!
solve the system by adding or subtracting:
-3x-3y=9
3x+8y=6
Answer:
x=-6, y=3
Step-by-step explanation:
I will use elimination to eliminate the x variable.
Add the two equations.
-3x-3y=9
3x+8y=6
-------------------
5y = 15
Divide each side by 5
5y/5 = 15/5
y=3
Now we need to find x
3x+8y=6
Substitute y=3
3x+8*3 =6
3x+24=6
Subtract 24 from each side
3x+24-24 = 6-24
3x = -18
Divide each side by 3
3x/3 = -18/3
x=-6
x < 4 and x > -3: I need this in interval notation please.
x > -3 and x < 4
in interval notation
[tex]x\in(-3,\ 4)[/tex]
>; < - a open circle on the number line and the parenthesis ( or )
≥; ≤ - a filled-in circle on the number line and the parenthesis [ or ]
A model is created to show 5 thousands blocks, 4 hundreds blocks, and 9 ones blocks. How would this number be written in standard form?
Answer: 5,409
Step-by-step explanation: Five thousand blocks is equivalent to 5,000. Four hundred blocks is equivalent to 400. Nine ones is equivalent to 9. In standard form, this number is five thousand four hundred and nine (5,409).
43.017 round to the nearest hundredth
Answer:
43.02
Step-by-step explanation:
Note the hundredth place value (underlined and bolded): 43.017
Look at the place value directly to the right of the one you are solving for (thousandth place value). It is a 7. Because 7 is greater than 5, round up
43.017 rounded to the nearest hundredth is 43.02
~
Answer:
43.02
Step-by-step explanation:
tens ones. tenths hundredths thousandths
4 3 . 0 1 7
The one is in the hundredths place, so we need to look at the 7
7>= 5 so we need to round the 1 up to 2
43.017 rounds to 43.02
Anna, Ivan and Elena are running for class president. On Thursday night Anna had 20% of the votes, Ivan had 35% of the votes and Elena had 45% of the votes. On Friday, final votes were added to the counts and all of them favored Elena. If in the end Anna had 16% of all votes, what percent of the voters chose Ivan?
Answer:
28%
Step-by-step explanation:
On Thursday night Anna had 20% of the votes, Ivan had 35% of the votes and Elena had 45% of the votes. You can take the number of total votes on Thursday equal to 100, then Anna had 20 votes, Ivan had 35 votes and Elena had 45 votes.
Let x be the number of votes added on Friday. All of them favored Elena, then Elena in total had 45+x votes and the number of all votes became 100+x. In the end Anna had 16%, then
100+x - 100%,
20 - 16%.
Write a proportion:
[tex]\dfrac{100+x}{20}=\dfrac{100}{16},\\ \\16(100+x)=2000,\\ \\1600+16x=2000,\\ \\16x=400,\\ \\x=25.[/tex]
Find the percent of the voters that chose Ivan:
125 - 100%,
35 - y%.
Write a proportion:
[tex]\dfrac{125}{35}=\dfrac{100}{y},\\ \\125y=35\cdot 100,\\ \\y=\dfrac{35\cdot 100}{125}=\dfrac{35\cdot 4}{5}=7\cdot 4=28\%.[/tex]
The Rawlins family has travelled 600 km on their vacation. This has taken them 8 hours. If they continued at the same rate, how long will it take them to complete their journey if the total distance to be travelled is 2100 km?
A. 20 hours
B. 28 hours
C. 26 hours
D. 12 hours
Answer:
B. 28 hours
Step-by-step explanation:
GIVEN :- Time taken by family to travel 600 km is 8 hours
CALCULATIONS :-
To calculate the time to travel 2100 km, we need to calculate distance traveled in 1 hour
Distance traveled in 1 hour = 600 km ÷ 8
= 75 km
Time required to travel 2100 km = 2100 ÷ 75
= 28 hours
Therefore time required to travel 2100 km is 28 hours.
Final answer:
The Rawlins family, traveling at a speed of 75 km/hour, will take a total of 28 hours
Explanation:
To determine the travel time for the remaining distance of the Rawlins family's journey, we use the formula
time = distance / speed. First, we need to find the family's speed during their trip. They have travelled 600 km in 8 hours, so their speed is
600 km / 8 hours = 75 km/hour.
Next, we calculate the time it would take to travel the total distance of 2100 km at this speed. So,
time = 2100 km / 75 km/hour. Upon performing the calculation, we get 28 hours. Therefore, if they continue at the same speed, the total travel time for the entire journey would be 28 hours.
A 10.5 ounce package costs $2.98 a 27.8 ounce package costs $8.99 which is the better deal based on the unit price...
Zoe babysat for x+3 hours yesterday.she earned x-2 dollars per hour.write a polynomial expression that represents the amount Zoe earned
Answer:
y=3x+2
Step-by-step explanation:
The total amount Zoe earned from babysitting is represented by the polynomial expression (x + 3) * (x - 2), which expands to [tex]x^2+x-6[/tex]
Explanation:To find the total amount that Zoe earned, it is necessary to multiply the time she worked by how much she earned per hour. Zoe worked for x + 3 hours yesterday and earned x - 2 dollars per hour. Therefore, the polynomial expression to represent the total amount she earned is (x + 3) * (x - 2). This can be expanded by using the distributive property, to give the polynomial: [tex]x^2[/tex] + x - 6.
So, the amount Zoe earned can be represented by the polynomial expression [tex](x+3)*(x+2)[/tex]
Learn more about Polynomial Expression here:https://brainly.com/question/29272918
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please help. What is the value of x?
screenshot below
Answer:
25
Step-by-step explanation:
Since the triangle is equilateral, all the sides have the same measures.
You can set any two sides equal to each other, and solve for x.
4x-30 = 2x + 20
4x = 2x + 50 add 30 to both sides
2x = 50 subtract 2x from both sides
x = 25 divide both sides by 2
You can plug x into the expressions and compare the sides to make sure its correct.
Calculate the difference between the compound interest and simple
interest on ₹20,000 in 2 years at 8% per annum.
Answer: ₹128
Step-by-step explanation:
To work out the simple interest, you need to work out 8% of ₹20,000 for 2 years, which is 1.08 * ₹20,000 = ₹21,600 in the first year and ₹23,200 in the second year
To work out the compound interest, you need to work out 8% of the new value
1st year: ₹21,600
2nd year: 8% of ₹21,600 = ₹23,328
The difference is ₹23,328 - ₹23,200 = ₹128
Estimate the sum or difference. Use the benchmarks,0, 1/2, and 1.
23/40- 11/30
A.0
B.1
C.1/2
Answer:
A. 0
Step-by-step explanation:
23/40 is approximately 1/2.
11/30 is approximately 1/2.
Sine 1/2 - 1/2 = 0, then 23/40 - 11/30 is approximately 0.
By converting the given fractions to a common denominator and performing subtraction, the result falls closest to the benchmark of 0. Hence, the estimated sum or difference of 23/40 and 11/30 is 0.
Explanation:The given problem is 23/40 - 11/30 and the student has to estimate the result using the benchmarks 0, 1/2, and 1.Steps to resolve the problem:
First, convert both fractions to a common denominator. The smallest number that both 40 and 30 divide into evenly is 120. Therefore, we multiply 23/40 by 3/3 to get 69/120, and 11/30 by 4/4 to get 44/120.Then, subtract the fractions: 69/120 - 44/120 = 25/120.Here, 25/120 is close to 1/4.The benchmark that is closest to 1/4 is 0. So, the estimated sum or difference would be 0.
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Which set represents a pythagorean triple
A) 1, 2, 3
B) 9, 12, 16
C)30, 40, 50
D)38, 44, 49
Please help!
Answer:
30, 40, 50 which is choice C
Step-by-step explanation:
Square the smaller two values (30 and 40)
30^2 = 900
40^2 = 1600
then add those results
900+1600 = 2500
Notice how 50^2 = 2500 as well. This shows us that 30^2 + 40^2 = 50^2 is a true equation. Both sides lead to the same result 2500. Therefore, a triangle with sides 30, 40, 50 is a right triangle. This is based on the 3-4-5 pythagorean triple, just each side has been multiplied by 10.
The set that represents a Pythagorean triple is 30, 40, 50. Hence, the correct option is C.
Pythagorean triples are sets of three numbers that satisfy the Pythagorean theorem, a² + b² = c², where a, b, and c are the lengths of the sides of a right triangle. To determine which set represents a Pythagorean triple, we need to check if the set's numbers satisfy this theorem.
Looking at the options:
A) 1, 2, 3 does not form a Pythagorean triple.
B) 9, 12, 16 does not form a Pythagorean triple.
C) 30, 40, 50 does form a Pythagorean triple because 30² + 40² = 900 + 1600 = 2500 = 50².
D) 38, 44, 49 does not form a Pythagorean triple.
Therefore, the set that represents a Pythagorean triple is C) 30, 40, 50.