Answers
The [tex]\angle[/tex]C is [tex]77^o[/tex] in the triangle ABC inscribed in the circle as evident from the figure.
A triangle is a polygon with three angles, three edges, and three vertices. It's one of the most introductory and abecedarian shapes in geometry.
Triangles can be classified by their side lengths, their angles, or their symmetry.
As the angle on the circumference is double the angle on the semicircle,
therefore,
[tex]\angle[/tex]B = [tex]\frac{110^o}{2}[/tex]
= [tex]55^o[/tex].
As the sum of a triangle is [tex]180^o[/tex],
So,
[tex]\angle[/tex]A + [tex]\angle[/tex]B + [tex]\angle[/tex]C = [tex]180^o[/tex],
Given that [tex]\angle[/tex]A = [tex]48^o[/tex],
[tex]48^o[/tex] + [tex]55^o[/tex] + [tex]\angle[/tex]C = [tex]180^o[/tex],
[tex]\angle[/tex]C = [tex]180^o[/tex] - [tex]48^o[/tex] - [tex]55^o[/tex],
[tex]\angle[/tex]C = [tex]77^o[/tex]
So, the [tex]\angle[/tex]C is [tex]77^o[/tex].
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Related Questions
Please help i'm really confused.
0! = 0
True
False
Answers
0! is defined to be 1
If a single die is rolled twice there are how many possible outcomes
Answers
Find the volume of a sphere with a great circle area of 201.06 square inches
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so, we know if we cut the sphere like a cantaloupe, in half, the circular inner-part of the cantaloupe will have an area of 201.6 in².
keeping in mind that, the radius of that circular section, is the same radius of the sphere, what is it anyway?
[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ -----\\ A=201.06 \end{cases}\implies 201.06=\pi r^2 \\\\\\ \cfrac{201.06}{\pi }=r^2\implies \sqrt{\cfrac{201.06}{\pi }}=r\\\\ -------------------------------[/tex]
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi \left( \sqrt{\frac{201.06}{\pi }} \right)^3}{3}\implies V=\cfrac{4\pi \left( \frac{\sqrt{201.06^3}}{\sqrt{\pi ^3}} \right)}{3} \\\\\\ V=\cfrac{4\pi \cdot \frac{\sqrt{201.06^3}}{\pi \sqrt{\pi }}}{3}\implies V=\cfrac{\frac{4\sqrt{201.06^3}}{\sqrt{\pi }}}{3}\implies V=\cfrac{4\sqrt{201.06^3}}{3\sqrt{\pi }}[/tex]
Final answer:
To find the volume of a sphere with a given great circle area, solve the equation 4πr² = 201.06 to find the radius, then use the formula V = (4/3)πr³ to calculate the volume. The volume is approximately 267.97 cubic inches.
Explanation:
To find the volume of a sphere with a given great circle area, we first need to find the radius of the sphere. The great circle area is equal to the surface area of the sphere, which is 4πr², where r is the radius of the sphere. In this case, the great circle area is 201.06 square inches, so we can solve the equation 4πr² = 201.06 to find the radius. Once we have the radius, we can use the formula for the volume of a sphere, V = (4/3)πr³, to calculate the volume.
First, let's solve the equation 4πr² = 201.06 for r:
4πr² = 201.06
r² = 201.06 / (4π)
r² ≈ 16.06
r ≈ √16.06 ≈ 4.01
Now that we have the radius, we can calculate the volume using the formula V = (4/3)πr³:
V ≈ (4/3)π(4.01)³ ≈ 267.97 cubic inches
For each example below, determine whether a positive, negative, or no cause and effect relationship exists.
1) Smoking and cases of lung cancer.
2) Amount of time spent at school each day and number of text sent per day
3) The number of licks taken and the size of the Tootsie Pop
Answers
#2 - No relationship.
#3 - Negative
A positive relation between two things means that they are proportional to each other. One affects the other thing.
1) Smoking and cases of lung cancer. This is positive. As smoking affects lungs and can cause lung cancer. So, with increased smoking comes the increased risk of lung cancer thus increasing cases of lung cancer.
2) Amount of time spent at school each day and number of text sent per day - These two events are independent of each other. They are not based on each other. Hence, no relationship here.
A negative relation implies that if one thing increases, the other decreases.
3) The number of licks taken and the size of the Tootsie Pop. This is negative. As the number of licks increases, the size of the pop decreases.
A multiple choice test has 9 questions each of which has 5 possible answers
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When the temperature is 68 F, the speed of the sound in air is approximately 343 meters per second. Approximately how many kilometers dose sound travel in five seconds?
Show all your work
Answers
We want to find how many kilometers sound will travel when the air is at 68 degrees in five seconds.
Step 1: Multiply 343 by five. (1 sec. to 5 secs.)343 * 5 = 1715
Step 2: Divide 1715 by 1000. (1 m. to 0.001 km)1715/1000 = 1.715 km/5 secs.
At a temperature of 68°, sound will travel 1.715 km in 5 seconds.
What does y=mx+b mean
Answers
m = rise/run = Δy/Δx = (y2-y1)/(x2-x1)
with (x1,y1) and (x2,y2) as points on the line. b is the quantity defined as the y-intercept, that is, the y-value of where the line crosses the vertical y-axis.
WZ and XR are diameters of circle C. The diagram is not drawn to scale.
What is the measure of convex arc upper ZWX?
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WZ + 41 = ZWX
From here, we must clear We must replace the value of WZ.
The value of WZ is given by
WZ=180
We have then:
ZWX = 180 + 41
ZWX = 221 degrees
Answer:
the measure of convex arc upper ZWX is:
ZWX = 221 degrees
The measure of convex arc upper ZWX is 180 degrees.
Explanation:The measure of convex arc upper ZWX can be found by considering the angles formed by the diameters WZ and XR. Since WZ and XR are diameters of the circle, they intersect at the center of the circle. The angle formed by the diameters at the center is a right angle, which means that arc upper ZWX is a semicircle. A semicircle has a measure of 180 degrees. Therefore, the measure of convex arc upper ZWX is 180 degrees.
A distribution reasonably well described by the normal curve has a mean of 60.00 with a standard deviation of 10.00 points. basing your prediction on the normal (z) curve, approximately what percent of the population would you predict will score within 10.00 points of the mean (between 50.00 and 70.00)?
Answers
The empirical rule states that 68% of data will fall within 1 standard deviation of the mean. 10 is the standard deviation, so anything within 10 points of the mean is within 1 standard deviation.
Answer:
68%
Step-by-step explanation:
Anyone know this geometry question?
Answers
∠JEK + ∠DFH = 90°
Find:
relationship, if any, of ∠JEK to angles CFL, HFG, LFE
Solution:
We note that ∠DFG = 90° = ∠DFH + ∠HFG, so ∠JEK ≅∠HFG.
We also note that ∠HFG and ∠CFL are vertical angles, so ∠JEK ≅∠CFL.
And ∠LFE and ∠DFH are vertical angles, so ∠JEK + ∠LFE = 90°.
Evaluating the choices, we find
A) false. The angles are not complementary, they are equal.
B) false. The angles are not equal, they are complementary.
C) false. The angles are not supplementary, they are equal.
D) TRUE. The angles are equal.
The appropriate choice is ...
D) ∠JEK ≅∠CFL
what are solutions to the equation sinx cosx = square root 3 over4
Answers
please help...
The radius of the planet is 4100 miles. Find the distance d to the horizon that a person can see on a clear day from a height of 1298 feet above the planet. (hint: use the conversion 1 mile = 5280 ft) Round your answer to the nearest 10th, and don't forget to convert feet to miles.
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[tex]1298ft*\frac{1mi}{5280ft}= \frac{59}{240} mi[/tex]
Next, we are going to set up a right triangle using the radius of the Earth and the distance above the planet.
The hypotenuse of our triangle will be the radius of the Earth + the distance above the planet. One of the legs of our triangle will be the radius of the Earth, and the other leg, [tex]d[/tex], will be the distance that a person will see on a clear day.
Using the Pythagorean theorem:
[tex]d^2= (\frac{984059}{240} )^2-4100^2[/tex]
[tex]d= \sqrt{(\frac{984059}{240} )^2-4100^2} [/tex]
[tex]d=44.9[/tex] miles
We can conclude that the distance, [tex]d[/tex], to the horizon that a person can see on a clear day from a height of 1298 feet above the planet is 44.9 miles.
I really need help with this!!
Answers
= wx/xy substitute
= 12/13 plug in wx
12 and xy= 13
What did the prince do whenever he found a girl who might be cinderella
Answers
Final answer:
When a prince in fairy tales finds a potential Cinderella, he typically engages in a quest to determine if she is the one, reflecting the theme of male heroism and romantic pursuit found in traditional literature and films.
Explanation:
The passage raises the theme of romantic endeavors and the traditional role of women in classical literature and film, typically anchored within the context of royalty and fairy tales. When the prince in such stories finds a girl that could potentially be Cinderella, typically he would engage in a quest to discover if she truly is the one - often symbolized by a glass slipper fitting or other identifying item. This quest underscores the narrative of countless romantic tales where the male lead seeks to find and often rescue his female counterpart, a concept reflected in various Disney princess movies.
In the greater realm of literature and films, the prince often represents the chivalrous savior. This tradition is evident in the series of princess-centric stories produced by Disney, where a common girl becomes royalty by marriage or starts as a princess whose ultimate happiness is achieved through romance. Although contemporary stories may showcase more agency in their female protagonists, the motif of the male hero remains prevalent.
Two trains leave towns 1250 km apart at the same time and travel toward each other. one train travels 10 km/hr slower than the other. if they meet in 5 hours, what is the rate of each train?
Answers
(n represents train A's speed)
A: n
B: n + 10
We know it is 5 hours, and total distance, so:
5(n) + 5(n + 10) = 1250
5n + 5n + 50 = 1250
10n = 1200
Divide:
n = 120
One train goes 120, the other goes 130
Mr. and Mrs. Yeager want to buy a home valued at $320,000. If they have 15% of this amount saved for a down payment, how much have they saved? a. $480 b. $4,080 c. $4,800 d. $48,000
Answers
Answer:
The correct answer is D
Step-by-step explanation:
I got it right on Edge.2020. Have a great day!
If they have 15% of this amount saved for a down payment, then they saved 48000 dollar.
So option D) $48,000 is correct.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that Mr. and Mrs. Yeager want to buy a home valued at $320,000.
If they have 15% of this amount saved for a down payment, then
15% =15/100=0.15
Therefore, we get;
0.15 (320000)=48000
If they have 15% of this amount saved for a down payment, then they saved 48000 dollar.
So option D) $48,000 is correct.
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How would you find the width of a golden rectangle if your givin the length?
Answers
Given the length, you would divide by 1.618 to find the width.
Edit: The exact value is [tex] \frac{ 1+\sqrt{5} }{2} [/tex], but 1.618 should suffice.
Look at the figure rectangle PQRS, find m angel P
Answers
Answer: [tex]144^{\circ}[/tex]
Step-by-step explanation:
In the given figure , we have given a parallelogram .
We know that the opposite sides and angles of a parallelogram are equal.
Thus from the given parallelogram PORS we have
[tex]\angle {Q}=\angle {S}\\\\\Rightarrow\ (4\alpha-12)^{\circ}=3\alpha^{\circ}\\\\\Rightarrow\ 4\alpha-12=3\alpha\\\\\Rightarrow 4\alpha-3\alpha=12\\\\\Rightarrow\ \alpha=12[/tex]
Also, the value of angle p is given by :-
[tex]\angle {P}=12\alpha^{\circ}\\\\\Riightarrow\ \angle {P}=12(12)^{\circ}\\\\\Riightarrow\ \angle {P}=144^{\circ}[/tex]
able below shows the relative frequencies of the color of cars bought last month by males and females. Which percentage represents the car bought most often? Male Female Total Blue Car 0.04 0.12 0.17 Black Car 0.08 0.06 0.13 White Car 0.11 0.20 0.31 Gray Car 0.02 0.09 0.11 Red Car 0.17 0.10 0.27 Total 0.43 0.57 1.00
Answers
Answer:
31%
Step-by-step explanation:
Answer:
31%
Step-by-step explanation:
You plan on financing a new road bike for $2,500. The bike shop offers a 13.5% APR for a 24 month loan. Use this information, and the table above, to determine the monthly payments. Round your answer to the nearest cent.
Answers
Given that the financing is for a new road bike of $2,500 and that the bike shop offers a 13.5% APR for a 24 month loan.
Thus, PV = $2,500; r = 13.5% = 0.135; t = 12 payments (since payment is made monthly); n = 2 years (i.e. 24 months)
Thus,
[tex]2500=P\left( \frac{1-\left(1+ \frac{0.135}{12} \right)^{-2\times12}}{ \frac{0.135}{12} } \right) \\ \\ =P\left( \frac{1-\left(1+ 0.01125 \right)^{-24}}{ 0.01125 } \right)=P\left( \frac{1-\left(1.01125 \right)^{-24}}{ 0.01125 } \right) \\ \\ =P\left( \frac{1-0.764531}{ 0.01125 } \right)=P\left( \frac{0.235469}{ 0.01125 } \right)=20.9306P \\ \\ \Rightarrow P= \frac{2500}{20.9306} =119.44[/tex]
Therefore, his monthly payment is $119.44
A 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours. Assuming the variables are directly related, how many hours would a 9-ounce candle be expected to burn?
18
27
33
45
Answers
to find the rate it burns:
20 ounce / 60 hours = 1/3 ounce per hour
divide 9 ounces by 1/3 ounce per hour to find total time:
9 / 1/3 = 27 hours
Answer:
B. 27.
Step-by-step explanation:
We have been given that a 20-ounce candle is expected to burn for 60 hours. A 12-ounce candle is expected to burn for 36 hours.
We know that a direct proportional equation is in form [tex]y=kx[/tex], where k represents constant of proportionality.
Let is find value of k by substituting [tex]x=20[/tex] and [tex]y=60[/tex] in above equation as:
[tex]60=k*20[/tex]
[tex]\frac{60}{20}=\frac{k*20}{20}[/tex]
[tex]3=k[/tex]
The equation [tex]y=3x[/tex] represents our given direct proportional relation.
Now, we will substitute [tex]x=9[/tex] to solve for y as:
[tex]y=3*9[/tex]
[tex]y=27[/tex]
Therefore, a 9-ounce candle would be expected to burn for 27 hours and option B is the correct choice.
Write an equation of a line containing (2, 1) and (3, 4) in point-slope form.
Answers
Your equation is:
(y₂ - y₁)/(x₂ - x₁) = Slope
Let:
(2,1) = (x₁,y₁)
(3,4) = (x₂,y₂)
Plug into corresponding numbers
(4 - 1)/(3 - 2) = 3/1
3/1 is your slope
hope this helps
Center c of the circle above has coordinates of (4, 3). what is the circumference of the circle?
Answers
C = 2 * pi * r = (2)(3.14)(3) = 18.8 or so
Slips of paper numbered 1 through 14 are placed in a hat. in how many ways can two numbers be drawn so that the sum of numbers is 12
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1 and 11
2-10
3-9
4-8
5-6
6-6
so there are 6 ways
Subtract. (4x^2+8x−2)−(2x^2−4x+3) Enter answer, in standard form
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A box contains 16 transistors, 5 of which are defective. if 5 are selected at random, find the probability that
a. all are defective. and. none are defective.
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Only one way of selecting the 5 defective transistors:
Number of ways of selections available = 6C5 = 16!/[5!*(15-5)!] = 4368
Probability they are all defective = Number of ways of selecting 5 defectives/Total number of ways possible = 1/4368 ≈ 0.000229
Part (b): None are defective
Total number of non defectives = 16 -5 = 11
Number of ways of selecting 5 non defective = 11C5 = 462 ways
Total number of ways possible = 16C5 = 4368
Probability of selecting 5 non defectives = 462/4368 = 11/104 ≈ 0.1058
A - all defective
B - none defective
[tex] \displaystyle
|\Omega|=\binom{16}{5}=\dfrac{16!}{5!11!}=\dfrac{12\cdot13\cdot14\cdot15\cdot16}{2\cdot3\cdot4\cdot5}=4368\\
|A|=1\\
|B|=\binom{11}{5}=\dfrac{11!}{5!6!}=\dfrac{7\cdot8\cdot9\cdot10\cdot11}{2\cdot3\cdot4\cdot5}=462\\\\
P(A)=\dfrac{1}{4368}\approx0.02\%\\
P(B)=\dfrac{462}{480480}=\dfrac{1}{1040}\approx0.1\% [/tex]
What is the value of y in the equation 2(3y + 6 + 3) = 196 − 16?
Answers
2(3y + 9) = 196
6y + 18 = 196
6y + 18 - 18 = 196 - 18
6y = 178
Divide both sides by 6
y = 178 / 6
y ≈ 29.667
What is the height of the trapezoid?
Answers
40 *2 = (10+6)*h
80/16 = h
5 unit = h
The square root of the sum of a number and 7 is 8. find the number
Answers
Possibility 1: 8 = sqrt(x+7) in which the answer is 57.
Possibility 2: 8 = sqrt(x) + 7, in which the answer is 1.
Hope this helps! I'm sorry if I get it wrong.
An integer greater than 1 that is not prime is called composite. if the two-digit integer n is greater than 20, is n composite?
Answers
eg 21 is composite and 23 is prime.