Two chords measuring 18.64cm and 14.32cm intersect at a point on a circle at an angle of 114°26’. A third chord connects the noncommon endpoints of the chords to form a triangle. Find all the measurements of the triangle.
Answers
Answer:
third chord length is 27.8088 cm
Between III and I chord is \(27^\circ57'30''\)
Between III and II chord is \(37^\circ36'30''\)
Step-by-step explanation:
The calculation of measurements of the triangle is shown below:-
By Cosine rule
\(BC^2 = (14.32)^2 + (18.64)^2 - 2\times 14.32 \times 18.64 cos\114^\circ26'\\\\ BC^2 = 773.330156\\\\ BC = \sqrt{773.330156}\)
BC = 27.8088 (it is the length of third chord)
By Sin rule
\(\frac{Sin A}{BC} = \frac{Sin B}{14.32} \\\\ \frac{Sin114^\circ26'}{27.8088} = \frac{Sin B}{14.32} \\\\ Sin B = \frac{14.32114^\circ26}{27.8088}\)
After solving this we will get
Sin B = 0.468829
\(<B = Sin^{-1} 0.468829\\\\ <B = 27^\circ 57'30''\)
Therefore
\(<A + <B + <C = 180^\circ\)
\(<C = 180^\circ - 114^\circ26'-27^\circ57'30''\\\\ <C = 37^\circ36'30''\)
Now,
third chord length is 27.8088 cm
Between III and I chord is \(27^\circ57'30''\)
Between III and II chord is \(37^\circ36'30''\)
The same is to be considered
Related Questions
Andrei, Amit and Andrew were each asked to factor the term 20x^620x
6
20, x, start superscript, 6, end superscript as the product of two monomials. Their responses are shown below.
Andrei Amit Andrew
20x^6=(2x)(10x^5)20x
6
=(2x)(10x
5
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 2, x, right parenthesis, left parenthesis, 10, x, start superscript, 5, end superscript, right parenthesis 20x^6=(4x^3)(5x^3)20x
6
=(4x
3
)(5x
3
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 4, x, cubed, right parenthesis, left parenthesis, 5, x, cubed, right parenthesis 20x^6=(20x^2)(x^3)20x
6
=(20x
2
)(x
3
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 20, x, squared, right parenthesis, left parenthesis, x, cubed, right parenthesis
1) Which of the students factored 20x^620x
6
20, x, start superscript, 6, end superscript correctly?
Choose all answers that apply:
Choose all answers that apply:
(Choice A) Andrei
A
Andrei
(Choice B) Amit
B
Amit
(Choice C) Andrew
C
Andrew
(Choice D) None of the above
D
None of the above
Answers
Based on the given responses, the student who factored 20x^6 = (2x)(10x^5) correctly is Andrei. Therefore, the correct answer is (Choice A) Andrei.
Among the given responses, the student who factored 20x^6 = 20, x to the power of 6 correctly is Andrei. Andrei's factorization is (2x)(10x^5), which correctly represents the original term 20x^6. Therefore, the correct answer is (Choice A) Andrei.
Amit's factorization is (4x^3)(5x^3), which is incorrect because it breaks down the term into two factors with the same exponent, while the original term has an exponent of 6.
Andrew's factorization is (20x^2)(x^3), which is also incorrect as it does not accurately represent the original term 20x^6.
Hence, the only student who correctly factored 20x^6 = 20, x to the power of 6 is Andrei.
The right answer is A. Andrei who factored 20x^6 = (2x)(10x^5) correctly.
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Can someone help me on 3-6?
Directions: Find the volume of each figure. Round the nearest hundredth.
Answers
Using the formula of volume of a sphere and hemisphere, the volume of the figures are given as;
1. 2144.57 m³
2. 696.6 m³
3. 20569.1m³
4. 2637ft³
5. 56.5km³
6. 6381.79 in³
What is volume of sphere?The volume of a sphere is given as 4/3πr³
Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.
1. The volume of the sphere is;
v = 4/3 * 3.14 * 8³ = 2144.57m³
2. The volume of the sphere is;
v = 4/3 * 3.14 * (11/2)³ = 696.6m³
3. The volume of the sphere is;
v = 4/3 * 3.14 * 17³ = 20569.1m³
4. The volume of the hemisphere is;
v = 2/3 * 3.14 * 10.8³ = 2637ft³
5. The volume of the hemisphere is;
v = 2/3 * 3.14 * 3³ = 56.5km³
6. The volume of the hemisphere is;
v = 2/3 * 3.14 * (29/2)³ = 6381.79in³
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Which expression is NOT equivalent to the expression 8m + 12?
A - 1/2 (16m + 24)
B - 4 (2m + 3)
C - 2 (4m + 6)
D - 8 (m +12)
Answers
9514 1404 393
Answer:
D. 8 (m +12)
Step-by-step explanation:
One cannot factor the coefficient from the first term and apply that to both terms. The result is NOT equivalent.
8m +12 ≠ 8(m +12) = 8m +96
Determine the check digit for the UPCs that have these initial 11 digits. a) 73232184434 b) 63623991346 c) 04587320720 d) 93764323341
Answers
Answer:
The check digits
a) x₁₂ ≡ 5( mod 10 )
b) x₁₂ ≡ 2( mod 10 )
c) x₁₂ ≡ 0( mod 10 )
d) x₁₂ ≡ 3( mod 10 )
Step-by-step explanation:
Given the data in the question;
We know that the formula for determining the UPCs check is;
3x₁ + x₂ + 3x₃ + x₄ + 3x₅ + x₆ + 3x₇ + x₈ + 3x₉ + x₁₀ + 3x₁₁ + x₁₂ ≡ 0( mod 10 )
now we will substitute the given values to determine the value of the last bit
a)
73232184434
we substitute into the formula
3×7 + 3 + 3×2 + 3 + 3×2 + 1 + 3×8 + 4 + 3×4 + 3 + 3×4 + x₁₂ ≡ 0( mod 10 )
x₁₂ ≡ 5( mod 10 )
b)
63623991346
we substitute into the formula
3×6 + 3 + 3×6 + 2 + 3×3 + 9 + 3×9 + 1 + 3×3 + 4 + 3×6 + x₁₂ ≡ 0( mod 10 )
x₁₂ ≡ 2( mod 10 )
c)
04587320720
we substitute into the formula
3×0 + 4 + 3×5 + 8 + 3×7 + 3 + 3×2 + 0 + 3×7 + 2 + 3×0 + x₁₂ ≡ 0( mod 10 )
x₁₂ ≡ 0( mod 10 )
d)
93764323341
we substitute into the formula
3×9 + 3 + 3×7 + 6 + 3×4 + 3 + 3×2 + 3 + 3×3 + 4 + 3×1 + x₁₂ ≡ 0( mod 10 )
x₁₂ ≡ 3( mod 10 )
PLEASE HELP ME I WILL GIVE YOU 5 STAR RATING A THANKS AND BRAINLIEST RATINGGGGG
Answers
Answer:
It's the third choice.
Step-by-step explanation:
IF y varies inversely as x then y = k/x where k is a constant,
and k = xy
For the 3rd choice
-1 * -2/7 = 2/7
4 * 1/14 = 2/7 and
6 * 1/21 = 2/7
so, this is inverse variation.
Find the measure of x
Answers
Answer:
≈ 11,88
Step-by-step explanation:
Use trigonometry:
cos (62∘) = 8 / x
x = 8 / cos (62∘) ≈ 11,88
Solve for m∠PNM.
58
186
97
87
Answers
The calculated measure of m∠PNM is 87 degrees
How to calculate the meausre of m∠PNM.from the question, we have the following parameters that can be used in our computation:
The circle
Where, we have
PM = 360 - 64 - 122
Evaluate
PM = 174
Next, we have
m∠PNM = 1/2 * 174
So, we have
m∠PNM = 87
Hence, the measure of m∠PNM is 87 degrees
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The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answers
Answer:
Step-by-step explanation:
3.6*
It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2
For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.
We get
36 = s^2
Now, we need to get the square root of both sides, which gives us
s = √36 s = 6 cm
Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.
Therefore, the perimeter of the square is 24 cm.
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Select the correct answer. Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 years ago. If Jenna’s age is x, which equation represents the situation? How many solutions does the equation have? A. x + 5 = (5 − x) − 5, which has one solution B. x + 5 = (x + 5) − 5, which has infinitely many solutions C. x + 5 = (x + 5) − 5, which has no solution D. x + 5 = (5 − x) − 5, which has infinitely many solutions E. (x + 5) + 5 = (x + 5) + 5, which has infinitely many solutions
Answers
Answer: x + 5 = x
Step-by-step explanation:
Jenna's age Jessica's age
Today x x + 5
in 5 years x+5
5 years ago x + 5 - 5
Equality x + 5 = x + 5 - 5
=> x + 5 = x
The equation is x + 5 = x
That equation has not any solution, because it reduces to 5 = 0, which is an absurd.
So, the conclusion is that information given by Jenna is wrong.
It is logical: if the difference of the ages is 5, in five years Jenna will have 10 years more than what her sister had 5 years ago, no 5 as she told Jessica.
Joanna runs at an average speed of 7.5km/h. She runs 15km every day. What time did
she leaves her house if she arrives back at 8:30 am after her morning run?
Answers
how much she runs everyday: 15km
15km/7.5= 2 hours of running time everyday
She leaves at 8:30, comes back at ?
8:30+ 2:00= 10:30
Joanna arrives back at 10:30a.m.
Answer:
She might of left her home around 8:00 possibly.
Step-by-step explanation:
Hopefully this helps you.
Please give me brainliest if it is correct.
Thank you xx
By rounding to 1 significant figure, estimate
542.04 × 1.88
Answers
1.88 = 2
542 x 2 = 1084
By rounding to 1 significant figure 542.04 × 1.88 equal to 1019.0352
is 1019.
What is rounding off of numbers?We round off numbers to make them easier to remember and it also keeps their value approximately to the place it has been rounded off.
To round off any number to any place we'll look for the digit next to that place and if it is equal to or greater than 5 we'll add one to the previous digit and make all the digits after it zeroes and if the digit is less than 5 we do not add one to the preceding digit and simply make all the digit after it to zeroes.
Given we have to round off 542.04×1.88 = 1019.0352.
Now rounding off to one significant digit means we should have only one digit after the decimal place and the second digit after the decimal place is 3 which is less than 5.
∴ 1019.0352 rounded off to one significant digit is 1019.
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If I'm looking at buying a house for $450,000, and want my deposit to be
20%, how much do I need to have saved?
A) 50,000.00
B) Your deposit needs to be higher than 20%
C) 52,000.00
D)90,000.00
Answers
Answer: 90,000
Step-by-step explanation:
In the following image, segment BD bisects segment AC, and three triangles are similar: AABC~ AADB~ ABDC. Complete the two-column
proof of the Pythagorean theorem.
3: A. (AC)DC) + (AC)(CD) = (AC)AC) + (BC)BC)
B. (AC)(CD) + (AC)(AD) = (BC)BC) + (AB)AB)
C. (AB)(CB) + (AD)CD) = (AC)AC) + (BC)BC)
D. (AC)BC) = (AC)(AC) + (BC)BC)
5: A.angle bisector postulate
B. triangles
C. common line segment
D. segment addition postulate
Answers
1. The Fill ups are as follow:
AB² + BC² = AC. AD + AC. CD
2. Segment addition postulate
What is Pythagorean theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
Given:
BC/ AC = CD/ BC and AB/ AC = AD/ AB
Now, BC² = AC. CD and AB² = AC. AD
Using, Addition Property of Equality
AB² + BC² = AC. AD + AC. CD
and, AB² + BC² = AC (AD + CD) [factor]
AD + CD = AD (segment addition postulate)
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PLATO
i got it correct :)
HELP ME
Final exam guide due
Show work
Answers
The approximate height of the tree is given as follows:
45.6 ft.
What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
The altitude segment for this problem is given as follows:
14.5 ft.
The bases are given as follows:
5.2 ft and x ft.
Hence the value of x is given as follows:
5.2x = 14.5²
x = 14.5²/5.2
x = 40.4 ft.
Hence the height of the three is given as follows:
5.2 + 40.4 = 45.6 ft.
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#7 find the answer with the offering 20% discount
Answers
Given a discount of 20% and a manufacturer's coupon of $200, the price after the discount and coupon, (C ∘ D)(x), is 0.8x - 200.
What is a discount?A discount is an amount that reduces the price of a retail item.
Discounts are offered as rates and the discounted price is computed by multiplying the discount factor and the price.
Discount rate on offer = 20%
Discounting factor = 80% or 0.8 (100 - 20%)
Manufacturer's coupon off the price = $200
Let the price of the bureau = x
The price after the discount (discounted price) is given by D(x)
D(x) = 0.8x
The price after the coupon = C(x) = x - 200
The price after applying the discount and the coupon, (C ∘ D)(x) = 0.8x - 200
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Complete Question:Wilson's Warehouse sells a certain brand's bureau. They are offering a 20% discount in addition to accepting a manufacturer's coupon for $200 off. Let the price of the bureau be x. If the price after the discount is given by D(x) and the price after the coupon is C(x), find (C ∘ D)(x).
change 12 1/2% to a declmal and then to a fraction in its lowest terma
\(change 12 \: 1 \2 \: to \: a \: declmal \: and \: then \: to \: a \: fraction \: in \: its \: lowest \: terma \)
Answers
The lowest terma of this number is 1/8. If you use 1 divide by 8, you would get 0.125.
Hope it helps!
Does anyone know this answer??
Answers
Answer:
96.25%
Step-by-step explanation:
The empirical rule regarding mean and standard deviation is that
Around 68% of scores are between 40 and 60.Around 95% of scores are between 30 and 70.Around 99.7% of scores are between 20 and 80.Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find approximately 95/2 = 47.5% of the values
Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values
Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values
A group of campers and one group leader left a campsite in a canoe. They traveled at an average rate of 10 km/h. Two hours later, the other group leader left the campsite in a motorboat. He traveled at an average rate of 22 km/h.A. How long after the canoe left the campsite did the motorboat catch up with it?B. How long did the motorboat travel?
Answers
A .The canoe left the campsite did the motorboat catch up with it 3 hrs and 40 minutes
B . The motorboat travel at 1 hr 40 minutes
A group of campers and one group leader left a campsite in a canoe.
They traveled at an average rate of 10 km/h.
1st Group DATA:
rate = 10 km/h ; distance = x km ; time = d/r = x/10 hrs
Two hours later, the other group leader left the campsite in a motorboat.
He traveled at an average rate of 22 km/h.
Group Leader DATA:
rate = 22 km/h ; distance = x km ; time = d/r = x/22 hrs
A. How long after the canoe left the campsite did the motorboat catch up with it?
Group time - Leader time = 2 hr
x/10 - x/22 = 2
Multiply thru by 110 to get:
11x - 5x = 220
6x = 220
x = 110/3 = km
canoe total time = x/10 = (110/3)/(10) = 11/3 = 3 hrs and 40 minutes
B. How long did the motorboat travel?
motorboat time = x/22 = (110/3)/22 = 1 hr 40 minutes
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the product of a quarter of 3 more than a number a and 2 times a number b
Answers
Answer:
\( \frac{1}{4} (3a + 2b)\)
The expression from the given condition is 1/4(3a+4b).
We have given that,
The product of a quarter of 3 more than a number a and 2 times a number b.
What is the quarter?
The quarter means divided into four equal or corresponding parts.
Therefore we get the expression from the given condition is
1/4(3a+4b).
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The map shows an obstacle course at a school fair. The units are given in yards.
What is the total distance of
the obstacle course?
? yards
Start
(-40, -10)
Tire
Race
(-40, -30)
Finish
(10, 20)
Monkey
Bars
(40,20)
Rope
Climb
(40,-30)
Answers
The total distance of the obstacle course can be calculated by finding the distance between each pair of consecutive points and adding them up. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2).
Using this formula, we can calculate the distances between each pair of consecutive points as follows:
Start to Tire Race: distance = sqrt((-40 - (-40))^2 + (-30 - (-10))^2) = 20 yards
Tire Race to Rope Climb: distance = sqrt((40 - (-40))^2 + (-30 - (-30))^2) = 80 yards
Rope Climb to Monkey Bars: distance = sqrt((40 - 40)^2 + (20 - (-30))^2) = 50 yards
Monkey Bars to Finish: distance = sqrt((10 - 40)^2 + (20 - 20)^2) = 30 yards
Adding up all these distances, we get a total distance of 20 + 80 + 50 + 30 = 180 yards for the obstacle course.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Answer:
B. 3188.5 cubic inches.
Step-by-step explanation:
The volume of a cone is calculated using the following formula:
Volume = (1/3) * π * r² * h
Where:
π is the mathematical constant pi, approximately equal to 3.14.r is the radius of the base of the cone.h is the height of the cone.In this problem, we are given that r = 17 inches and S.h = 20 inches.
First we need to find height h.
py using Pythagorous theorem,we get
c²=a²+b²
here c= slight height and a is radius
20²=17²+b²
20²-17²=b²
111=b²
b=√(111)
Plugging these values into the formula, we get:
Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches
Therefore, the volume of the cone is 3188.5 cubic inches.
find all the fraction between 0 and 1
Answers
Answer:
Between 0 and 1 there is 12, between 1 and 2 there is 112=3/2, and so on. In fact, there are infinitely many fractions between any two whole numbers. Let's see why. Between 0 and 1 there are also 13, 14, 15, and any number that can be written as 1n where n is some whole number.
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-Dont let the Pirates get ya!
-Jaron, King of Carthya.
Finally! After nearly two weeks of manual labor in the Georgia summer heat, all of the moving boxes are unpacked and all of your things have a place. You and your three roommates, Alex, Payton, and Jordan, got so lucky in the real estate department. Your apartment is right in the heart of midtown and in walking distance from the Georgia Tech Engineering building where you take the majority of your classes. Everything is perfect! Well… except one crucial component. The four of you cannot seem to agree on an internet and cable provider!
You have narrowed the list of options down to a few of the best companies. All companies offer exactly what the four of you need to continue being top engineering students.The big difference? The price. Your roommates are math enthusiasts and engineering majors just like you, so you know you need to provide extensive evidence to each of them to help move the decision along.
SignoCable has a program where you are able to waive the installation fee and offers your cable for $210 per month.
Urban Cable is offering a special promotion. They are requiring a $320 installation fee upfront. The month to month payment will be $115 for the first 12 months. After the first year, the monthly fee will increase.
ITP Cable requires a lower installation fee than Urban Cable. After six months with this company, you would have paid $1081 since the beginning of the year, and $1257 after 7 months of paying.
MonstroPin Cable company’s installation fee is $100.50. The total payment in August is $59 more than three times the total payment in February.
You’ve decided it’s up to you to save you and your friends money by presenting them with a clear model of the out of pocket expense for all cable companies. Not only do you plan on making a visual representation for Alex, you will even write a proposal that analyses your findings for Payton and Jordan. You will provide them with indisputable evidence of which cable company will provide the most cost effective service. The service you guys choose now will dictate how fast you can register for classes, when you can stream Game of Thrones, and turn your papers in on time. Needless to say, this is an important decision!
Answers
Any help would be appreciated
Answers
Answer:
$8.25
Step-by-step explanation:
I don't know how to explain it to you but if I'm wrong tell me I'll try it aagain.
vardan's homework assignment contains 24 problems of 58 1/3 of them are geometry. how many geometry problems are there?
Answers
There are 14 Geometry problems in Vardan's homework assignment.
The number of geometry problems in Vardan's homework assignment, we need to calculate 58 1/3 percent of the total number of problems.
First, let's convert 58 1/3 percent to a decimal by dividing it by 100:
58 1/3 percent = 58.33/100 = 0.5833
Next, we multiply the decimal by the total number of problems:
Number of geometry problems = 0.5833 * 24
To calculate this, we can multiply 0.5833 by 24:
Number of geometry problems = 0.5833 * 24 = 14
Therefore, there are 14 geometry problems in Vardan's homework assignment.
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Help me ASAP please !!!! I attached a pic
Answers
how would I write an equation?
and what would my x and y represent?
Answers
The equation is x + y=z. X represents the number of hours for tutoring, and Y represents the total cost for the tutoring session. The equation does not represent direct variation, as the hourly rate is a fixed rate, not a variable rate.
How to write an equation for any data? To write an equation for any given data, first identify the independent and dependent variables in the data set. The independent variable is the variable that is changed or manipulated, while the dependent variable is the variable that is observed or measured. Once the independent and dependent variables have been identified, the equation can be written using the dependent variable in terms of the independent variable. For example, if the data set contains a set of values for the independent variable x and the corresponding values for the dependent variable y, then the equation can be written as y = f(x). The function f(x) represents the relationship between the two variables and can be determined by plotting the data points and finding the best fit line or curve. This line or curve is the equation that describes the data set.To learn more about equation refer to:
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HELPPPP ASAPP
The number of chapters read, y, after x days. The slope of the line is 5/4 and the y-intercept is 2. The slope of 5/4 means that....
A. Every 4 days, you read 5 chapters
B. Every 5 days you read 4 chapters
C. You started on chapter 4 out of 5 chapters
Answers
Zero(s) of multiplicity one:
Zero(s) of multiplicity two:
Zero(s) of multiplicity three:
Please look at photo for the full question. Thank you.
Answers
The zeros and the multiplicities are
Zero(s) of multiplicity one: x = 6Zero(s) of multiplicity two: x = 11Zero(s) of multiplicity three: x = -6 and x = -5How to determine the zeros and the multiplicitiesfrom the question, we have the following parameters that can be used in our computation:
f(x) = (x + 6)³(x - 11)²(x - 6)(x + 5)³
The power of each factor are the multiplicities
So, we have
Zero(s) of multiplicity one:
x - 6 = 0
Zero(s) of multiplicity two:
x - 11 = 0
Zero(s) of multiplicity three:
x + 6 = 0 and x + 5 = 0
When evaluated, we have
Zero(s) of multiplicity one:
x = 6
Zero(s) of multiplicity two:
x = 11
Zero(s) of multiplicity three:
x = -6 and x = -5
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What is eight hundred seven thousand, eight hundred twenty five in standard form?
Answers
so you should write 8 in a box then under the box write what place it is like hundredth and you do the same for the rest
8 0 7 , 8 2 5
hundred thousandth^ and so on^