In Circle S with MRST=118 and RS=8 units, find the length of arc RT. Round to the nearest hundredth
Answers
Answer:
RT ≈ 16.48 units
Step-by-step explanation:
The measure of arc RT is calculated as
RT = circumference of circle × fraction of circle
= 2πr × [tex]\frac{118}{360}[/tex]
= 2π × 8 × [tex]\frac{118}{360}[/tex]
= 16π × [tex]\frac{118}{360}[/tex] ≈ 16.48 ( to the nearest hundredth )
The length of the arc RT is 8.23 units.
What are the properties of an arc?The characteristics of a circle's arc are:
Measured in linear measures like centimetres, inches, or metres, the arc length is the distance along the arc. It is proportionate to the angle that the arc and circle's centre make.The arc measure, which is expressed in degrees or radians, is the magnitude of the angle that is produced between the centre of the circle and the arc. It varies in accordance with the arc length.Since angle RST is 118 degrees, it subtends 118/360 = 0.3278 (rounded to four decimal places) of the full circumference of the circle. Therefore, the length of arc RT is:
length of arc RT = (0.3278) * (2 * π * radius)
where the radius is half the length of RS. Since RS is given as 8 units, the radius is 4 units. Substituting this into the formula, we get:
length of arc RT = (0.3278) * (2 * π* 4) = 2.0684 * π
Rounding to the nearest hundredth, we get:
length of arc RT ≈ 8.23 units.
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Related Questions
helpp me plz
thank you in advance
Answers
Answer:
1/4
Step-by-step explanation:
3 and 6 are both multiples of 3, so there is a 2/8 chance of spinning a multiple of 3, which can be simplified to 1/4.
When a number is decreased by 5%, the result is 20. What is the original number to the nearest tenth?
Answers
Step-by-step explanation:
so round up is b equal a plus 10....
the ratio of the number of Annes pencils to the number of jasons pencils is 4:3. Anne has 100 pencils how many pencils does Jason have
Answers
Answer:
Jason has 75 pencils.
Step-by-step explanation:
In order to get from 4 to 100, you must multiply by 25 (100/4 = 25). And in order to find the amount of pencils Jason has, you must have an equivalent ratio. So you have to also multiply 3 by 25, 3 * 25 = 75. Jason has 75 pencils.
PLEASE HELP! ITS DUE TODAY!
Answers
Answer:
D. Median
Step-by-step explanation:
I say this because is the average of the numbers
Find the zeros of the function f(x) = x^3 + 2x^2 -25x - 50 = 0
Answers
Answer:
x = -2, x= -5 , x= +5
Step-by-step explanation:
x^3 + 2x^2 -25x - 50 = 0
Factor by grouping
x^3 + 2x^2 -25x - 50 = 0
x^2(x+2) -25( x+2) = 0
(x+2) ( x^2 -25) =0
Using the zero product property
x+2 =0 x^2 -25 =0
x=-2 x^2 = 25
x= -2 Taking the square root of each side
x = ±5
76,45,64, 80, 92
Calculate the sample standard deviation
Answers
Answer:
15.94490514
Step-by-step explanation:
First, work out the average, or arithmetic mean, of the numbers:
Count: 5(How many numbers)
Sum: 357(All the numbers added up)
Mean: 71.4(Arithmetic mean = Sum / Count)
Then, take each number, subtract the mean and square the result:
Differences:
4.6, -26.4, -7.4, 8.6, 20.6
(Every Number minus Mean)
Differences^2:
21.16, 696.96, 54.76, 73.96, 424.36
(Square of each difference)
Now calculate the Variance:
Sum of Differences2:1271.2(Add up the Squared Differences)
Variance:254.24(Sum of Differences2 / Count)
Lastly, take the square root of the Variance:
Standard Deviation:15.94490514 (The square root of the Variance)
14. What's 17/12 as a mixed number?
O A.15/12
O B.1 127
O C.1/12
O D.712
Answers
Answer:
A
Step-by-step explanation:
17/12 = 1 5/12
1×12+5=17
Find the infinite geometric sum of 4+2.4+1.44+...
Answers
Answer:
4+2.4=6.4+1.44=7.84
The infinite geometric sum of 4+2.4+1.44+... will be 10.
What is the common ratio?At each point in the sequence, you multiply or divide by the common ratio. Divide two sets of phrases that follow one another to find it. Whichever pair of terms is picked, as long as they appear next to one another in the sequence, is irrelevant.
It is given that, the sequence is 4+2.4+1.44+...
The sequence is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is obtained that the common ratio is,
r=2.4/4
r=0.6
The Sum of an infinite geometric sequence is,
S = a / (1-r)
S=4 / (1-0.6)
S=10
Thus, the infinite geometric sum of 4+2.4+1.44+... will be 10.
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The value of x in 5(8+x)=20
Answers
Answer:
x = -4
Step-by-step explanation:
5(8+x)=20
Divide each side by 5
5/5(8+x)=20/5
8+x = 4
Subtract 8 from each side
8+x-8 = 4-8
x = -4
The right answer is -4.
Please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Solve the equation shown below.
1/2x−6=4
x =−4
x=−2
x=10
x=20
Answers
Add 6 to both sides.
1/2x = 10
Multiple each side by 2/1 (reciprocal) to get x by itself.
x = 10 * 2/1
x = 20
Final answer: x = 20
Hope this helped!
Answer:
x = 20
Step-by-step explanation:
→Add 6 to both sides:
[tex]\frac{1}{2} x-6=4[/tex]
[tex]\frac{1}{2} x=10[/tex]
→Multiply both sides by 2:
x = 20
what is the square root of 345 to the 9th power
Answers
Answer:
[tex](\sqrt[2]{32})^{9}[/tex]=5931641.60152
Step-by-step explanation:
:)
QUICK What is the solution to this system of equations? 3.2 x + 0.5 y = 4.2. Negative 1.6 x minus 0.5 y = 3.4.
Answers
Answer:
The solution is x=4.75 and y = -22
Step-by-step explanation:
To find the solution to the system of equations, we will follow the steps below:
3.2x + 0.5y = 4.2 --------------------------------------------------------------------------(1)
-1.6x -0.5y = 3.4 ----------------------------------------------------------------------------(2)
add equation (1) and equation (2)
1.6x =7.6
Divide both-side of the equation by 1.6 to get the value of x
1.6x /1.6 =7.6/1.6
x =4.75
substitute x = 4.75 into equation (1) and solve for y
3.2(4.75) + 0.5y = 4.2
15.2 + 0.5y = 4.2
subtract 15.2 from both-side of the equation
15.2 - 15.2 + 0.5y = 4.2-15.2
0.5y = -11
Divide both-side of the equation by 0.5
0.5y/0.5 = -11/0.5
y = -22
The solution is x=4.75 and y = -22
Answer
x= 4.75 y=-22
Step-by-step explanation:
got it right on the unit test!!
Anybody know this pls help
Answers
Answer:
1. (-1/4,0)(1.5,0)
2.(-1/2,2)(6/4,2)
Step-by-step explanation:
just locate the numbers on the graph
(URGENT)Determine the cross product of the vectors: x x y
Answers
x x y = (13 i + 4 j - 9 k) x (- i + 7 j - 4 k)
Distribute the cross product:
x x y = 13*(-1) (i x i) + 4*(-1) (j x i) + (-9)*(-1) (k x i)
........... + 13*7 (i x j) + 4*7 (j x j) + (-9)*7 (k x j)
........... + 13*(-4) (i x k) + 4*(-4) (j x k) + (-9)*(-4) (k x k)
x x y = -13 (i x i) - 4 (j x i) + 9 (k x i)
........... + 91 (i x j) + 28 (j x j) - 63 (k x j)
........... - 52 (i x k) - 16 (j x k) + 36 (k x k)
By definition of the cross product, we have
i x i = j x j = k x k = 0
i x j = k
j x k = i
k x i = j
and for any two vectors x and y, the product is anti-symmetric:
x x y = -(y x x)
This makes the products on the "diagonal" vanish, and we can condense terms using the anti-symmetry property:
x x y = (4 + 91) (i x j) + (9 + 52) (k x i) + (63 - 16) (j x k)
x x y = 95 k + 61 j + 47 i
x x y = 47 i + 61 j + 95 k
Please help! I have not seen a correct answer yet :(
A standard six-sided die is rolled 6 times. You are told that among the rolls, there was one 1, two 2's, and three 3's. How many possible sequences of rolls could there have been? (For example, 3,2,3,1,3,2 is one possible sequence.)
Answers
Answer:
60 possible sequences.
Step-by-step explanation:
That would be 6! / 3! 2!
6*5*4*3*2*1
= ------------------
3*2*1*2*1
= 5*4*3
= 60.
plz help plzzz thank you
Answers
Answer:
rectangles
Step-by-step explanation:
convenient to use rectangles for the individual areas because they will combine horizontally and vertically to make larger rectangles with no gaps.
Determine the quotient of (7.7x10^-2) divided by (2.2x10^-2
Answers
Answer:
3.5 is your answer.
Step-by-step explanation:
(7.7x10^-2) divided by (2.2x10^-2
Just *Divide*
Hope this helps.
: )
What is the equation of the function that is graphed as line a ? y = - x + 1 y = 3 x - 1 y = 3 x + 1 y = 1/3x - 1
Answers
Answer:
The answer is option 2.
Step-by-step explanation:
Given that the equation of a straight line is y = mx + c where m represents gradient and c is the y-intercept which touches the y-axis.
By looking at the graph, we know that it is a positive gradient and it touches -1 at y-axis.
Answer:
y = x - 1is this for calvert homeshcool?the image of the circle x2+y2-2x+3y=8 after being reflected by the line y=2x-3 is----------------.pls anyone
Answers
Answer:
The image of the circle is 9·x² + 9·y² - 42·x + 33·y = 22
Step-by-step explanation:
We convert the equation to the form (x - h)² + (y - k)² = r²
Where:
(h, k) = Coordinates of the center of the circle
We therefore have;
x² + y² - 2·x + 3·y = 8 which gives;
x² - 2·x + 1 - 1 + y² + 3·y + (3/2)² - (3/2)² = 8
(x - 1)² + (y + 3/2)² - 1 - (3/2)² = 8
(x - 1)² + (y + 3/2)² = 8 + 1 + (3/2)² = 45/4
Therefore, the center = (1, -3/2) and the radius = √5 × 3/2
The line joining the centers of the actual (1, -3/2) and reflected circle (h, k) is bisected by the line of reflection, therefore the midpoint of the line is on the line of reflection with coordinates;
Midpoint between (1, -3/2) and (h, k) = [tex]\left (\dfrac{{h - 1}}{2}, \, \dfrac{k - 3/2}{2} \right )[/tex]
Which gives;
y = 2·x - 3 being equivalent to [tex]\dfrac{k - 3/2}{2} = 2\times\dfrac{{h - 1}}{2} - 3[/tex]
Which gives;
4·h -2·k -13 = 0.......(1)
Similarly the slope of the reflecting line is perpendicular to the line joining the centers of the actual and reflected circles
Therefore;
The slope of the line, y = 2·x - 3 = 2, hence we have;
[tex]\dfrac{\left ( \dfrac{k - 3/2}{2} \right ) + 3/2}{\left (\dfrac{{h - 1}}{2}-1 \right )} = \dfrac{1}{2}[/tex]
Which gives;
2·h -4·k -12 = 0.......(2)
Multiplying equation (2) and subtracting from equation (1) gives
4·h -2·k -13 - 2×(2·h -4·k -12) = 0
6·k + 11 = 0
k = -11/6
From which we have;
2·h -4×(-11/6) -12 = 0
Hence;
h = 7/3
Therefore, the center of the reflected circle = (7/3, -11/6)
The equation of the reflected circle is therefore;
(x - 7/3)² + (y + 11/6)² = 45/4
Which gives;
9·x² + 9·y² - 42·x + 33·y - 22 = 0
or x² + y² - 42/9·x + 33/9·y = 22/9.
Which of these graphs do not represent constant rates of change? Check all that apply.
Answers
Answer:
A,D
Step-by-step explanation:
I'm taking the test
The first and the fourth graph do not represent constant rates of change. Hence, option A and option D are correct.
What is a graph?
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
In the first and the fourth graph the function follows a curved graph because of it, it does not follow linearity. In the second and third graphs, the function follows a linear line, therefore, it shows a constant rate of change.
Hence, option A and option D are correct.
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solve this proportion x/14 6/21
Answers
Answer:
X=4
Step-by-step explanation:
Solution: x equals 4
x/14-(6/21)=0
1. Simplify 2/7
x/14- 2/7 is 0
It’s too much steps
Classify the triangle by its angles and by its sides.
Answers
Answer:
Acute and Scalene.
Step-by-step explanation:
By definition, an acute triangle is one that has three angles that are less than 90 degrees. This triangle falls under the category.
By definition, a scalene triangle is one that has three sides with different measurements. This triangle falls under the category.
Hope this helps!
Find the missing side. Be sure to show all of your work. Round to the nearest tenth
if necessary
Answers
Answer:
x=3.9 approximately
Step-by-step explanation:
Using Pythagorean theorem:
[tex]x^{2} + (5x)^{2} = 20^{2}[/tex]
[tex]x^{2} + 25x^{2} = 400[/tex]
26x^2 =400
x^2 = 15.3846
x=3.9
Equality Properties
Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of EqualityGeometry[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
a is a legb is another legc is the hypotenuseApplicationStep 1: DefineLet's define what the problem gives us:
We are given a right triangle, indicated by the square box inside the triangle, with side lengths 5x and x and a hypotenuse of 20.We can set these measurements equal to our variables defined above in our Pythagorean Theorem equation:
a = 5xb = xc = 20Step 2: WorkNow, we can substitute our variables and solve for x, which will help us find the side lengths as well:
[Pythagorean Theorem] Substitute in variables:[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\\end{aligned}[/tex][Order of Operations] Simplify:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\\end{aligned}[/tex][Simplify] Combine like terms:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\\end{aligned}[/tex][Equality Properties] Divide both sides by 26:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\\end{aligned}[/tex][Equality Properties] Square root both sides:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\\end{aligned}[/tex][Simplify] Evaluate:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\& = \frac{10 \sqrt{26}}{13}\end{aligned}[/tex][Evaluate] Approximate:
[tex]\displaystyle\begin{aligned}a^2 + b^2 & = c^2 \\(5x)^2 + x^2 & = 20^2 \\25x^2 + x^2 & = 400 \\26x^2 & = 400 \\x^2 & = \frac{200}{13} \\x & = \sqrt{\frac{200}{13}} \\& = \frac{10 \sqrt{26}}{13} \\& \approx \boxed{3.9} \\\end{aligned}[/tex]
∴ our x approximately equals 3.9.
Now we can use our value of x to solve for the missing triangle lengths:
Length of 5x:
Substitute in x:[tex]\displaystyle\begin{aligned}\text{Side Length} & = 5x \\& = 5(3.9) \\\end{aligned}[/tex]Evaluate:
[tex]\displaystyle\begin{aligned}\text{Side Length} & = 5x \\& = 5(3.9) \\& = \boxed{19.5}\end{aligned}[/tex]
∴ this particular side length has a length of 19.5.
Length of x:
Substitute in x:[tex]\displaystyle\begin{aligned}\text{Side Length} & = x \\& = \boxed{3.9}\end{aligned}[/tex]
∴ this particular side length has a length of 3.9.
Answer∴ the side lengths of this particular triangle are 19.5 and 3.9, respective to their variables 5x and x.
___
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Topic: Geometry
Unit: Triangles
a model of a plane is made using a scale of 1:5 if the real length of a plane is 20m what is the length of the model?
Answers
Answer:
4
Step-by-step explanation:
you must scale down to size- 1 m in real life = 5 (unit) in the model
20/5= 40
hope this helps :)
Answer:
4m
Step-by-step explanation:
1/5 of 20
297 miles in 11 gallons of gas what is the unit rate
Answers
Answer: 27 miles in 1 gallon
Step-by-step explanation:
297/11
The unit rate of 297 miles in 11 gallons will be 27 miles/gallons.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b, will be the denominator.
We will be used when division is not possible wholly
For example 4/2 is divisible so we write 2 instant of 4/2 while 1/3 is not divisible so we write 1/3 instant of 0.33.
Proportion is the relation of a variable with another. It could be direct or inverse.
The ratio is very useful to determine complex calculation where decimal number become tough to solve.
Given,
297 miles in 11 gallons
297 miles ⇔ 11 gallons
Divide by 11 on both sides
297/11 miles ⇔ 11/11 gallons
27 miles ⇔ 1 gallon
So, 27 miles in 1 gallon.
Hence unit rate is 27 miles/gallon will be correct.
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Which of the following is a characteristic of hyperbolic geometry?
A. There are an infinite number of lines parallel to a given line
through a given point.
B. There is exactly one line perpendicular to a given line through a
given point.
C. There is exactly one line parallel to a given line through a given
point.
D. There are an infinite number of lines perpendicular to a given line
through a given point.
Answers
Answer:
A
Step-by-step explanation:
Hyperbolic geometry is defined as a non-Euclidean geometry.
(invalidating the fifth postulate of Euclid's five fundamental postulates)
Choice B and D can be eliminated because this has nothing to do with perpendicular lines.
Choice C should be eliminated as well since that's exactly the fifth postulate of Euclid's five fundamental postulates
We are left with A by the process of elimination
Answer:
A. There are an infinite number of lines parallel to a given line through a given point.
Hope this Helps!
pick a pair of alternate exterior angles
Answers
Answer: angles 1 and 7
Can someone help me with this.?
Answers
Answer:
Below.
Step-by-step explanation:
To find the answer, you have to compare the two equations:
[tex]y=\frac{1}{10}x+60[/tex] and [tex]y=\frac{1}{5}[/tex]
So first, the graph looks different because the two slopes are different. The first one will be more vertical than the second one.
The second difference is the y - intercepts. The first equation starts at (0, 60) and the second starts at the origin.
Applying the translation (x, y) → (x – 3, y + 7) maps the point (–4, 7) onto the point ________. Question 16 options: A) (–7, 14) B) (14, –7) C) (7, –14) D) (14, 7)
Answers
Answer:
A
Step-by-step explanation:
(-4-3, 7+7)
(-7, 14)
Answer: A
Step-by-step explanation:
Line parallel to y-1=4(x+3) and passes through (4,32)
Answers
Answer:
y - 32 = 4(x - 4)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 1 = 4(x + 3) ← is in point- slope form
with slope m = 4
Parallel lines have equal slopes.
Using m = 4 and (a, b) = (4, 32), then
y - 32 = 4(x - 4) ← equation of parallel line