A wire 320 in. long is cut into two pieces. one piece is formed into a square and the other into a circle. if the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)? circle in square in
Answers
.. Acircle = c^2/(4π)
The area of a square can be computed from its perimeter (p) as
.. Asquare = (p/4)^2 = p^2/16
These are equal when
.. Acircle = Asquare
.. c^2/(4π) = p^2/16
.. c^2/p^2 = (4π)/16
.. c/p = (√π)/2
The total length is 320 inches, so ...
.. wire for circle = ((√π)/2)/(1 +(√π)/2)*320 in ≈ 150.3 in
.. wire for square = 320 in - wire for circle ≈ 169.7 in
_____
In the graph, (x, y) represents (circle wire, square wire).
The lengths of the two pieces of wire, when one is formed into a square and the other into a circle with equal areas, are approximately 186.3 inches and 133.7 inches respectively.
Explanation:To solve this problem, we first need to understand that the total perimeter of both the square and the circle made from the wire lengths equal to the original wire length, which is 320 inches. Suppose the length of the wire used for the square is 'a' and the length for the circle is 'b'. So, 'a + b = 320' inches.
Given that, the areas of both the square and the circle are equal. The area of a square is side^2 and the side of our square will be 'a/4' (since a square has four equal sides) and the area of a circle is πr^2, with the circumference being 2πr or 'b' in this case, so the radius is 'b / (2π)'.
Setting these two areas equal gives us the equation '(a/4)^2 = π * (b/ (2π))^2'. Solving this system of equations, we find that 'a' is approximately 186.3 inches and 'b' is approximately 133.7 inches.
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Related Questions
Dora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 12.
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In oder to join a yoga club there is a $100 annual fee and a $5 fee for each class ytouattend. Write an equation in slope-intercept form that models this situation.
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___
5 being the daily fee, and x being each day you attend. Multiply these.
Perform the indicated operation.
(w 3 + 64) ÷ (4 + w)
w² - 4w - 16
w² + 4w - 16
w² - 4w + 16
THE ANSWER IS:
w^2 - 4w + 16
The reason I included the correct answer in the question is that this question was not yet asked and I felt that some people might need to know this. Feel free to answer the question and get the points! :)
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Thanks for the points :)
w^2 - 4w + 16
tytytytytyty
WILL GIVE BRAINLIEST!!! 12 POINTS!!!!!!
The table below represents the height of a shot basketball, f(x), based on its horizontal position in relation to the basket, x.
x f(x)
-24 7
-20 12
-16 15
-12 16
-8 15
-4 12
0 7
If all quantities are in feet, what is the height of the basketball as it passes the hoop?
Answer: _____ feet
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_________________________________________________
Note: This is the value of "f(x)" when "x = 0" .
_________________________________________________
5.11 find the probability of a couple having a baby girl when their third child is born, given that the first two children were both girls. assume boys and girls are equally likely. is the result the same as the probability of getting all girls among three children?
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how do you solve FOIL problems for algebra 1
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These refer to the position of terms in the parentheses and the order they are multiplied.
Example:
(x+1)(x+2)
multiply first positions (far left)
(x*x)
then multiply the two outside
(x*2)
multiply inside terms
(1*x)
multiply last terms (far right)
(1*2)
Solution to example:
(x+1)(x+2)
(x*x)+(2*x)+(1*x)+(1*2)
combine terms
x^2+3x+2
Hope this helps! :)
The sum of the square of a positive number and the square of 3 more than the number is 45. what is the number?
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sum= add
more than= add
is= equal sign
square of= multiply the # by itself
x^2 + (x+3)^2= 45
x^2 + (x+3)(x+3)= 45
x^2 + x^2 + 3x + 3x + 9 = 45
combine like terms
2x^2 + 6x + 9= 45
subtract 9 from both sides
2x^2 + 6x= 36
reduce by dividing everything by 2
x^2 + 3x= 18
subtract 18 from both sides
x^2 + 3x - 18= 0
factor
(x+6)(x-3)= 0
x+6= 0
x= -6
x-3=0
x= 3
The question asks for the POSITIVE integer, so...
ANSWER: x= 3
Hope this helped! :)
The positive integer is [tex]3[/tex]
Let the number be [tex]a[/tex]
square of [tex]a = a^{2}[/tex]
Square of [tex]3[/tex] more than [tex]a[/tex] = [tex](3+a)^{2}[/tex]
[tex](3 + a)^{2} = (3+a)(3+a) = 9 + 3a + 3a + a^{2} = a^{2} + 6a + 9[/tex]
[tex]a^{2} + a^{2} + 9a + 9 = 45[/tex]
[tex]2a^{2} + 6a + 9 = 45[/tex]
Subtract 9 from both sides :
[tex]2a^{2} + 6a = 45 - 9[/tex]
[tex]2a^{2} + 6a = 36[/tex]
Divide through by 2
[tex]a^{2} + 3a = 18\\a^{2} + 3a - 18 = 0[/tex]
Factorize :
[tex]a^{2} + 6a - 3a - 18 = 0\\a(a + 6) - 3(a + 6) = 0\\a + 6 = 0\\or\\a - 3 = 0[/tex]
[tex]a = 3 ;\\or\\a = - 6[/tex]
since, a is a positive integer, then [tex]a = 3[/tex]
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Which best describes the function on the graph?
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3. what is a popular sunday activity for families in mexico city ? ( 1point )
A. vista the beach
b. visit the prado museum
c. stroll by the roman aqueduct
d. go to the chapultepec park
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A woman walks 100 yards east along a straight shoreline and then swims 30 yards south into the ocean on a line that is perpendicular to the shoreline. Using her starting point as the pole and the east direction as the polar axis, give her current position polar coordinates. Round the coordinates to the nearest hundredth. Express θ in degrees. (11.40, –88.28°) (104.40, –88.28°) (11.40, –16.70°) (104.40, –16.70°)
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Tan θ = 30/100
θ = 16.70, but since it is in an anticlockwise direction it will be -16.7
using Pythagoras theorem
a²+b²=c²
thus, c²=100²+30²
c = √(100²+30²)
= 104.40.
Therefore,the current position coordinates will be
(104.40, -16.70°)
Compare the domains of the logarithmic function f(x) and the square root function g(x).
Graph of f(x):
https://homelifetn.ignitiaschools.com/media/g_alg02_ccss_2016/9/al2_9_20a_media02.gif
https://homelifetn.ignitiaschools.com/media/g_alg02_ccss_2016/9/img_alg02u09c03q25d_02.gif
In two or more complete sentences, explain whether or not the domains of the two functions are the same.
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A rectangle has a a perimeter of 72 ft. The length and width are scaled by a factor 3.5.
What is the perimeter of the resulting rectangle?
Enter your answer in the box.
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P=2(L+w)
P=2L+2w
Here Perimeter, p= 72 ft
And scale factor of length and width=3.5 which means rectangle is enlarged.
So perimeter of rectangle= 3.5 x 72
P=252ft
Answer: 252 ft
We also know that the perimeter P of the rectangle is defined as:
P=2L+2W.
So P is directly proportional to L+W. This means that if L or W were to get bigger, P will get bigger, and if L or W were to get smaller P will get smaller.
The question also states that both L and W are scaled by the same factor of 3.5 .
This means the sum of the dimensions L+W is scaled by 3.5
It also means that the perimeter is upscaled by 3.5 as it is proportional to L+W.
P = 72 ft × 3.5 = 252 ft.
252 ft is the answer.
Imari went on a hike and recorded the number of each type of bird he saw. The circle graph shows the results of his count. Imari saw 42 sparrows. How many birds did he count in all? Enter your answer in the box. A pie chart depicting a count for bird species. Cardinals are at 13 percent, Sparrows are at 35 percent, Chickadees are at 23 percent, Blue Jays are at 8 percent, Woodpeckers are at 4 percent, and Robins are at 17 percent.Imari went on a hike and recorded the number of each type of bird he saw. The circle graph shows the results of his count. Imari saw 42 sparrows. How many birds did he count in all?
Answers
Answer: 120
Hope This Helps ^_^
Jackson currently has $35 in his bank account , he is saving $15 a week to eventually buy a new cell phone. He can represent the amount in his account with the equation y=15x+35.
I also need help answer the other questions to
Answers
Answer:
1. We have our function y = 15x + 35
a) Where the x represents the numbers of weeks since each week he is saving $15, which is the independent variable.
b) Where the y represents the total money he has, which is the dependent variable.
c) the slope is 15, as x increments, the slope goes up by 15.
d) The y-intercept is 35, because when x = 0, y = 35.
2. To create the table you have to find the value of y, knowing the values of x.
Using our function, when x = 0
y = 15(0) + 35
y = 0 + 35
y = 35
Using our function, when x = 1
y = 15(1) + 35
y = 15 + 35
y = 50
Using our function, when x = 2
y = 15(2) + 35
y = 30 + 35
y = 65
Using our function, when x = 3
y = 15(3) + 35
y = 45 + 35
y = 80
Using our function, when x = 4
y = 15(4) + 35
y = 60 + 35
y = 95
Using our function, when x = 5
y = 15(5) + 35
y = 75 + 35
y = 110
Yes, the table is proportional, because for each week, the value of his money is increasing by 15.
3. To create the graph, you can put the values of the table into the graph
And the graph is not proportional because to be proportional the relationship between “x” and “y” should be constant, meaning that, if “x” changes, “y” changes by the same percentage.
In this case our function has an intercept of 35 meaning that at week 0, he has $35 saved,
after a week: $50,
after two weeks: $65,
So, although is linear, is not proportional because when you double the weeks saved, you don't double the money saved.
Help please got to finish khan academy I’m really confused
Answers
= 64^(t^3)*(64^(-1/2))^t . . . . change the sum of exponents to a product
= 64^(t^3)*(1/√64)^t . . . . . . negative exponent signifies inverse, 1/2 power is sqrt
= 64^(t^3)/8^t . . . . . . . . . . . simplify
= (4^3)^(t^3)/8^t . . . . . . . . . .replace 64 with 4^3
= 4^(3t^3)/8^t . . . . matches the first selection only
Find the surface area of the rectangular solid.
l=16 in, w=13 in, h=15in.
Surface area is in inches and to the 2nd power.
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.. A = 2(LW +LH +WH)
.. = 2(LW +H(L +W))
.. = 2((16 in)(13 in) +(15 in)*(16 in +13 in))
.. = 2(208 in^2 +435 in^2)
.. = 1286 in^2
The surface area of the prism is 1286 in^2.
Need help with this too, all connected
Answers
#6 B. 6:2
#7 C. 25%
#8 If the veterinarian treats 50 dogs in a week, they would treat 10 reptiles in the same amount of time.
The lowest common denominator for the fractions 8/64 and 8/32 is ?
Answers
Final answer:
The lowest common denominator for the fractions 8/64 and 8/32 is 32. This is found by identifying 32 as the least common multiple of the denominators 64 and 32, allowing both fractions to be expressed with the same denominator.
Explanation:
Finding the Lowest Common Denominator
To find the lowest common denominator (LCD) for the fractions 8/64 and 8/32, you must identify the smallest number that both denominators can divide into without leaving a remainder. Both 64 and 32 can be divided by 32, so the LCD for these fractions is 32. It's important to understand that finding an LCD involves looking for the least common multiple (LCM) of the denominators. In this case, since 32 is a multiple of 64 (32x2=64), it serves as the LCM of 32 and 64, and consequently, the LCD of the fractions.
To further clarify, each fraction can be expressed with a denominator of 32. For 8/64, when we divide both the numerator and denominator by 8, we get 1/8. This fraction can then be converted to have a denominator of 32 through multiplication by 4 (1/8 * 4/4 = 4/32). Similarly, the fraction 8/32 is already expressed with the desired denominator.
By finding the LCD, it is easier to perform addition, subtraction, or comparison of fractions, as they will share the same denominator.
The lowest common denominator for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( \boxed{64} \).[/tex]
To find the lowest common denominator (LCD) for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \)[/tex], we need to determine the least common multiple (LCM) of the denominators 64 and 32.
Step 1: Find the prime factorization of each denominator:
[tex]- \( 64 = 2^6 \)[/tex]
[tex]- \( 32 = 2^5 \)[/tex]
Step 2: Determine the LCM by taking the highest power of each prime that appears in any factorization:
[tex]\[ \text{LCM} = 2^{\max(6, 5)} = 2^6 = 64 \][/tex]
Therefore, the LCD of the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( 64 \).[/tex]
Step 3: Verify that ( 64 ) is indeed the LCD:
[tex]- \( \frac{8}{64} = \frac{1}{8} \)[/tex]
[tex]- \( \frac{8}{32} = \frac{1}{4} \)[/tex]
Both fractions can be rewritten with a denominator of ( 64 ):
[tex]- \( \frac{1}{8} = \frac{8}{64} \)[/tex]
[tex]- \( \frac{1}{4} = \frac{16}{64} \)[/tex]
Therefore, ( 64 ) is the lowest common denominator for[tex]\( \frac{8}{64} \) and \( \frac{8}{32} \).[/tex]
Thus, the lowest common denominator for the fractions [tex]\( \frac{8}{64} \) and \( \frac{8}{32} \) is \( \boxed{64} \).[/tex]
What Is 7 minutes after 1? And what is 23 minutes after 4?
Answers
Answer: 7 minutes after 1 is 1:07 and 23 minutes after 4 is 4:23
Step-by-step explanation: Please mark me brainliest ✨
Good luck on whatever you’re working on!
What is the value of x? Enter your answer in the box. x = . Triangle G E H with segment E D such that D is on segment G H, between G and H. Angle G E D is congruent to angle D E H. E G equals 99.2 feet, G D equals 62 feet, D H equals left parenthesis x plus 2 right parenthesis feet, and E H equals 112 feet.
Answers
.. (x+2)/112 = 62/99.2
.. x +2 = 112*62/99.2 = 70
x = 68 . . . . feet
Answer:
The value of x is 68 ft.
Step-by-step explanation:
Given information: [tex]\angle GED\cong \angle DEH[/tex]
Bisector of an angle of a triangle theorem states that an angle bisector of a triangle divides the opposite side into segments that are proportional to the adjacent sides.
In triangle FEH, ED is an angle bisector
[tex]\frac{EH}{EG}=\frac{DH}{GD}[/tex]
[tex]\frac{112}{99.2}\times 62=x+2[/tex]
[tex]70=x+2[/tex]
[tex]70-2=x[/tex]
[tex]68=x[/tex]
Therefore the value of x is 68 ft.
Which is a possible number of distinct real roots for a cubic function? Select all that apply.
0
1
2
3
4
Answers
I don't know how to explain, but 3
Answer: The answer is 1 and 3.
Step-by-step explanation: We are to select the correct options about the number of real roots of a cubic function.
We know that there are three roots of a cubic function, out of which one must be real because the least number of real roots of an odd degree function is 1.
Also, if the second root is real, then the third one must also be real because the complex roots of a function occur in pairs.
Therefore, there is one real root or three real roots for a cubic function.
Thus, the answer is 1 and 3.
Genghis Motors wants to build cars and motorbikes on a budget. The company plans to spend at most $75000 and use at least 320 workers to build cars and motorbikes.
8000C+5500M≤75000 represents the number of cars C and motorbikes M the company can build by spending at most $75000.
52C+38M≥320 represents the number of cars and motorbikes the company can build by using at least 320 workers.
Can the company meet both of its expectations by building 4 cars and 6 motorbikes?
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8000*4 +5500*6 = 65000 ≤ 75000 . . . true
52*4 +38*6 = 436 ≥ 320 . . . . . . . . . . . . . true
Yes, the company can meet both its expectations by building 4 cars and 6 motorbikes.
Of course, another way to work this is to draw the graph and see if the offered point is in the feasible region. It is.
:)If Dani has 5,054 of a certain item and she needs to collect 6,000 of it, how much more does she need to reach her goal? :) Just for fun lol
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PLEASE HELP
Missi designed a stained glass window and made a scale drawing using centimeters as the unit of measurement. She originally planned for the length of the window to be 44 in. but decided to change it to 48 in. If the length of the window in her scale drawing is 4 cm, which statement about the change of scale is true?
A)One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale.
B)One cm represented 44 in. in the first scale, but now 1 cm represents 48 in. in the second scale.
C)One cm represented 1 in. in the first scale, but now 1 cm represents 1 in. in the second scale.
D)One cm represented 12 in. in the first scale, but now 1 cm represents 11 in. in the second scale.
Answers
Answer:
The correct answer is option A,
One cm represented 11 in. in the first scale, but now 1 cm represents 12 in. in the second scale
Step-by-step explanation:
The earlier planned length was [tex]44 in\\[/tex]
So the scale of the map was
[tex]\frac{44}{4} \\= 11\\1 cm = 11 in\\[/tex]
The second planned length was [tex]48 in\\[/tex]
So the second scale of the map was
[tex]\frac{48}{4} \\= 12\\1 cm = 12 in\\[/tex]
Thus, option A is correct.
banananana help me i need you
Answers
Pentagon; Regular
----------------------------
The second question shows something that obviously is not a square nor rectangle, so by process of elimination Parallelogram is your answer.
Parallelogram
Answer:
Banananana. How do you know that person?
Step-by-step explanation:
What is the equation of the exponential graph shown?
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Factor completely. a2+3a−28 Enter your answer in the box.
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PLS PLS PLS help I am rly confused
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Please help me! I don't know the answer.
Lines L and M are parallel. GEOMETRY
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The angle measure of ∠2 is equal to 38°.
m∠2 = 38°.
What are the corresponding angles?When two parallel lines are crossed by another line, comparable angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).
Given:
Lines L and M are parallel lines.
And the parallel lines are cut by a traversal line.
From the property of corresponding angles:
The angle measure of ∠2 is equal to 38°.
Therefore, m∠2 = 38°.
To learn more about the corresponding angles;
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Which measure describes how all of the values of a data set vary with a single number?
A) mean
B) median
C) mode
D) range
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hope this helps<3
Answer:
The answer is d. range.