The giant circle challenge is finally here let’s all work together for this one
Answers
The measure of the angles are: ∠1 = 30°, ∠2 = 30°, ∠3 = 21°, ∠4 = 39°, ∠5 = 39°, ∠6 = 24°, ∠7 = 24°, ∠8 = 66°, ∠9 = 66°, ∠10 = 21°, ∠11 = 60°, ∠12 = 120°, ∠13 = 60°, ∠14 = 120°, ∠15 = 48°, ∠16 = 105°, ∠17 = 27°, ∠18 = 129°, ∠19 = 51°, ∠20 = 129° and ∠21 = 51°
How to determine the measure of the angles?The given parameters are:
AB = 78°
FE = 105°
ED = 27°
CD = 42°
Considering the semicircle ABCD, the measure of arc BC is:
BC = 180 - AB - CD
This gives
BC = 180 - 78 - 42
Evaluate
BC = 60°
Considering the semicircle A FED, the measure of arc A F is:
A F = 180 - FE - ED
This gives
A F = 180 - 105 - 27
Evaluate
A F = 48°
The angle 16 subtends arc FE.
So, we have:
∠16 = FE
This gives
∠16 = 105°
Similarly, the angles 15 and 17 subtend arcs A F and ED respectively.
So, we have:
∠15 = 48°
∠17 = 27°
Angles at the circumference are half the angles at the arc.
This means that:
∠1 = Arc BC/2
∠3 = Arc CD/2
∠4 = Arc AB/2
∠5 = Arc AB/2
∠6 = Arc A F/2
∠10 = Arc CD/2
So, we have:
∠1 = 60/2 = 30°
∠3 = 42/2 = 21°
∠4 = 78/2 = 39°
∠5 = 78/2 = 39°
∠6 = 48/2 = 24°
∠10 = 42/2 = 21°
The angle in a semicircle is 90 degrees.
This means that:
∠2 = 90°
The sum of angles in a triangle is 180 degrees.
This means that:
∠11 = 180 - ∠1 - ∠2
∠12 = 180 - ∠3 - ∠4
So, we have:
∠11 = 180 - 30 - 90 = 60°
∠12 = 180 - 21 - 39 = 120°
Vertical angles are equal.
So, we have:
∠13 = ∠11
∠14 = ∠12
This gives
∠13 = 60°
∠14 = 120°
The sum of angles in a triangle is 180 degrees.
This means that:
∠18 = 180 - ∠17 - ∠6
So, we have:
∠18 = 180 - 27 - 24 = 129°
Vertical angles are equal.
So, we have:
∠20 = ∠18
This gives
∠20 = 129°
Angle on a straight line equals 180°.
So, we have:
∠21 = 180 - ∠18
This gives
∠21 = 180 - 129° = 51°
Vertical angles are equal.
So, we have:
∠19 = ∠21
This gives
∠19 = 51°
The sum of angles in a triangle is 180 degrees.
This means that:
∠7 = 180 - ∠21 - ∠16
So, we have:
∠7 = 180 - 51 - 105
∠7 = 24°
The angle in a semicircle is 90 degrees.
This means that:
∠7 + ∠8 = 90°
So, we have:
24 + ∠8 = 90°
Subtract 24 from both sides
∠8 = 66°
The sum of angles in a triangle is 180 degrees.
This means that:
∠8 = 180 - ∠15 - ∠9
So, we have:
∠8 = 180 - 48 - 66
So, we have:
∠8 = 66°
Hence, the measure of the angles are:
∠1 = 30°, ∠2 = 30°, ∠3 = 21°, ∠4 = 39°, ∠5 = 39°, ∠6 = 24°, ∠7 = 24°, ∠8 = 66°, ∠9 = 66°, ∠10 = 21°, ∠11 = 60°, ∠12 = 120°, ∠13 = 60°, ∠14 = 120°, ∠15 = 48°, ∠16 = 105°, ∠17 = 27°, ∠18 = 129°, ∠19 = 51°, ∠20 = 129° and ∠21 = 51°
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Related Questions
Which equation represents a line that passes through (–9, –3) and has a slope of –6? y – 9 = –6(x – 3) y 9 = –6(x 3) y – 3 = –6(x – 9) y 3 = –6(x 9)
Answers
Answer:
Y+3=-6(x+9)
Step-by-step explanation:
Got it right on usa test prep
For their season opener, the freshman basketball team sold 90 tickets for a total of $334.
Adult tickets for the game cost $5 and student tickets cost $3. How many adult tickets
were sold ?
Answers
58 student tickets were sold
32+58=90
5(32)+3(58)=334
at which angles are the x and y coordinate on the unit circle exactly the same? give your answer in radians and degrees
Answers
Answer:
In radian :
[tex]\frac{\pi }{4} \ \text{and}\ \frac{5\pi }{4}[/tex]
In degree :
45° and 225°
Step-by-step explanation:
the x and y coordinate on the unit circle exactly the same at the angles :
In radian :
[tex]\frac{\pi }{4} \ \text{and}\ \frac{5\pi }{4}[/tex]
In degree :
45° and 225°
At those angles :
[tex]\left( x,y\right) =\left( \frac{\sqrt{2} }{2} ,\frac{\sqrt{2} }{2} \right) \ or\ \left( x,y\right) =\left( -\frac{\sqrt{2} }{2} ,-\frac{\sqrt{2} }{2} \right)[/tex]
Write the equation of the given line in slope-intercept form
Answers
Answer:
y = -3x -1
Step-by-step explanation:
Hi there!
We are given a line on a coordinate grid, with 2 marked points, (-1, 2) and (1, -4)
We can use these points to help find the equation of the line, which we can write in slope-intercept form
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
First, we need to find the slope of the line
The formula for the slope calculated from 2 points is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We have everything we need to find the slope, but let's label the values of the points to help avoid confusion.
[tex]x_1=-1\\y_1=2\\x_2=1\\y_2=-4[/tex]
Now substitute these values into the formula to find the slope
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-4-2}{1--1}[/tex]
Simplify
m=[tex]\frac{-4-2}{1+1}[/tex]
m=[tex]\frac{-6}{2}[/tex]
Divide
m= -3
The slope of the line is -3
We can substitute this into the formula.
Here's our line so far:
y = -3x + b
Now we need to find b
As the equation passes through the points (-1, 2) and (1, -4), we can use either one to find the value of b
Taking (-1, 2) for example:
Substitute -1 as x and 2 as y.
2 = -3(-1) + b
multiply
2 = 3 + b
Subtract 3 from both sides
-1 = b
Substitute -1 as b.
y = -3x - 1
Hope this helps!
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Find the solution of this system of equations
-2y = 48 + 6x
-6x + 9y = -84
Answers
-6x - 2y = 48 ——(1)
-6x + 9y = -84
-6x = -84 -9y ——(2)
Substitute (2) into (1):
(-84 -9y) -2y = 48
-84 -9y -2y = 48
-84 -11y = 48
-11y = 48 + 84
-11y = 132
y = - 12
Substitute y = -12 into (1):
-6x -2(-12) = 48
-6x + 24 = 48
-6x = 48 -24
-6x = 24
X = -4
ANS : y= -12, x= -4
help. I can't do maths again
Answers
Answer:
x ≈ 14.4 cm
Step-by-step explanation:
the third angle of the triangle = 180° - 40° - 46° = 94°
Using the Sine rule in the triangle
[tex]\frac{x}{sin46}[/tex] = [tex]\frac{20}{sin94}[/tex] ( cross- multiply )
x × sin94° = 20 × sin46° ( divide both sides by sin94° )
x = [tex]\frac{20sin46}{sin94}[/tex] ≈ 14.4 cm ( to the nearest tenth )
Answer:
14 cm (rounded to nearest whole number)
Step-by-step explanation:
Law of Sine:
[tex]\displaystyle \large{\dfrac{\sin A}{a} = \dfrac{\sin B}{b} = \dfrac{\sin C}{c} = 2R}[/tex]
a,b,c are side lengths.R is radius so 2R is diameter.A,B,C are angles.Given angles are:
40°, 46°Definition of Euclidean Triangle:
Sum of three interior angles equals 180°Find another angle:
40°+46°+B = 180°86+B = 180B = 180-86B = 94°So another angle is 94°.
To find:
Value of xDetermine:
A = 46°a = x cmB = 94°b = 20 cmTherefore:
[tex]\displaystyle \large{\dfrac{\sin 46^{\circ}}{x} = \dfrac{\sin 94^{\circ}}{20}}[/tex]
Multiply both sides by 20x:
[tex]\displaystyle \large{\dfrac{\sin 46^{\circ}}{x} \cdot 20x = \dfrac{\sin 94^{\circ}}{20} \cdot 20x}\\\displaystyle \large{20\sin 46^{\circ}= x\sin 94^{\circ}}[/tex]
Divide both sides by [tex]\displaystyle \large{\sin 94^{\circ}}[/tex]:
[tex]\displaystyle \large{\dfrac{20\sin 46^{\circ}}{\sin 94^{\circ}} = \dfrac{x\sin 94^{\circ}}{\sin 94^{\circ}}}\\\displaystyle \large{\dfrac{20\sin 46^{\circ}}{\sin 94^{\circ}} = x}[/tex]
Evaluate the expression, hence:
[tex]\displaystyle \large{x = 14.42...}[/tex]
Round to nearest whole number:
[tex]\displaystyle \large{x = 14}[/tex]
Therefore, the value of x is 14 cm.
PLS HELP
What is the median of this data set?
Answers
Answer:
$3.50
Step-by-step explanation:
add up all the x's and distribute them starting from the outside until you get to the middle. if there is an odd number of x's (which there isn't), the last x to be placed will be on the spot that is the median. If there is an even number of x's, and they both land on the same spot, that spot will be the median, and if they are next to each other, the median will be between them.
1
The point lies in which quadrant?
A
Quadrant I
B
Quadrant II
C
Quadrant III
D
Quadrant IV
Answers
Answer:
Step-by-step explanation:
Since you did not include what the point is that you are trying to label, I can only tell you which quadrant is which. The quadrants go from 1 to 4 in a counterclockwise direction, starting from the top right quadrant (or the +,+ quadrant). One easy way to remember which direction the quadrants go in is the letter C, as they follow the same path as that letter.
I included a diagram to help.
Hope this helps! :)
need help with the question
Answers
Answer:
14 pi
Step-by-step explanation:
Here,
Area = 49 pi
Pi r ^2 = 49 pi
r^2 = 49
r = 7m
Now,
Circumference = 2 pi r
=2*pi *7
=14 pi
Two speeds are in the ratio 12:5 . If the first speed is 8km/h . what is the second speed?
Answers
Write two ratios equal to each other :
12/5 = 8/x(second speed)
Cross multiply:
12x = 40
Divide both sides by 12:
X = 3.333 or 3 1/3 km/h
second speed = 3.33 ( as a decimal) or 3 1/3 ( as a fraction) km/h
6.
Use the Change of Base Formula to evaluate log base 4 20
Answers
Answer:
The answer with calculator would be 2.16096
5 If the standard deviation of a distribution 3.2, find the varience correct to the nearest whole number
Answers
Answer:
Step-by-step explanation:
variance = (S.D)^2
=3.2^2
=10.24
=10
therefore , varience of a distribution is 10
1. Which expression below represents
"k more than 8"?
A 8k
B 8+k
C 8-k
D 8/k
Answers
Answer:
B. 8+kStep-by-step explanation:
A variable is an undetermined number represented by a letter.
K is a variable.
The addition of more than is not a subtraction.
Therefore, the correct answer is B. 8+k.I hope this helps. Let me know if you have any questions.
Does this figure have symmetry?
E
CLEAR
CHECK
Yes, because if you fold it in half, both halves match up.
Yes, because if you rotate it 90 degrees, the figure carries
onto itself.
No, because if you fold it in half, both halves do not match
up
No, because if you rotate it 180 degrees, it does not carry
onto itself.
Answers
Answer:
The Letter E has 1 line of symmetry. (Horizontal)
Step-by-step explanation:
Yes, because if you fold it in half (horizontally), both halves match up.
PLEASEE HELPPP!! The figure below is made of 2 rectangular prisms.
What is the volume of this figure?
Answers
Answer:
176 cubic cm
Step-by-step explanation:
[tex](2 \times 8 \times 2) + (3 \times 6 \times 8) = 32 + 144 = 176[/tex]
Please show work thank you so much y’all
Answers
Answer:
a
Step-by-step explanation:
looked it up if u dondon't like the answer sorry
find x. the whole question is- To what angle of depression should the security camera be adjusted in order to have lens aimed at point P on the ground?
Answers
Answer:
Hence, the security camera be adjusted in order to have the lens aimed at point. P. on the ground at an angle of depression of. x∘=30∘
Step-by-step explanation:
help pls?!?!?
calculate the area of the following.
Answers
Answer:
580.4 cm^2 to the nearest tenth.
Step-by-step explanation:
If we draw a perpendicular line from the top right vertex to the base we split the figure into 2 triangles and a rectangle in the center.
Left side triangle:
base = √(28^2 - 20^2) (using Pythagoras theorem
= 19.600
So its area = 1/2 * 19.6 * 20 = 196 cm^2.
Right side triangle:
Base = √(30^2 - 20^2) = 22.361
Area = 1/2 * 22.361 * 20 = 223.61 cm^2
Rectangle:
Base of rectangle = 50 - 19.6 - 22.361 = 8.039.
Area = 8.039 * 20 = 160.78.
So the area of the whole figure
= 196 + 223.61 + 160.78
= 580.39 cm^2.
If a. sub n. is a geometric sequence with a. sub 1 is equal to 10. and a. sub 5 is equal to 810. , find r., the common ratio.
a. 1/3
b. 3
c. 81
d. 1/81
Answers
A geometric series is the sum of an unlimited number. The common ratio of the geometric sequence is 3.
What is geometrical series?A geometric series is the sum of an unlimited number of terms with a fixed ratio between them.
Given the value of a₁ is 10, while the value of a₅ is 810, therefore, the common ratio can be written as,
[tex]\dfrac{a_5}{a_4} \times \dfrac{a_4}{a_3} \times \dfrac{a_3}{a_2}\times \dfrac{a_2}{a_1} = r \times r \times r \times r\\\\\\\dfrac{a_5}{a_1} = r^4\\\\\\dfrac{810}{10} = r^4\\\\\sqrt[4]{81} = r\\\\r = 3[/tex]
Hence, the common ratio of the geometric sequence is 3.
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Reflect the triangle in the x-axis
Answers
I think this might helpful
Algebra 1 8.2 worksheet answers
Answers
The graphs and their functions/equations are all illustrations of quadratic functions.
What are the zeros of a function?The zeros of a function of a graph are the points where the line or curve of the graph crosses the x-axis
What is the axis of symmetry?The axis of symmetry of a graph is the line that divides the graph into equal halves
What is the vertex of a function?The vertex of a function is the minimum or the maximum point on the graph
The vertex of a quadratic function is minimum if it opens upward, otherwise the vertex is maximum
Using the above definitions, the solutions to the worksheet are:
Graph 1
Zeros: -4 and 0Axis of symmetry: x = -2Min or Max: MaximumVertex: (-2, 4)Graph 2
Zeros: 2Axis of symmetry: x = -2Min or Max: MinimumVertex: (-2, 0)Graph 3
Zeros: -3 and 3Axis of symmetry: x = 0Min or Max = MinimumVertex: (0, -9)Graph 4
Zeros: -5 and -3Axis of symmetry: x = -4Min or Max = MaximumVertex: (-4, -1)Graph 5
Zeros: 3 and 7Axis of symmetry: x = 5Min or Max = MinimumVertex: (5, -4)Graph 6
Zeros: NoneAxis of symmetry: x = 24Min or Max = MinimumVertex: (2, 5)Graph 7
Zeros: 1 and 5Axis of symmetry: x = 3Min or Max = MinimumVertex: (3, -4)Graph 8
Zeros: -2 and 0Axis of symmetry: x = -1Min or Max = MaximumVertex: (-1, 1)Graph 9
Zeros: 5Axis of symmetry: x = 5Min or Max = MinimumVertex: (5, 0)Read more about quadratic functions at:
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Which of the following is NOT a function?
A. {(3, 8), (3, 9)}
B. {(3, 6), (6, 12)}
C. {(3, 7), (7, 13)}
D. {(3, 16), (4, 31)}
Answers
Answer:
A. is NOT the function.
Step-by-step explanation:
In a function, 1 input (the 3) can not have two differnt ouputs (8 and 9) meaning that this is NOT a dunction.
I hope this helps! :)
How to tell the difference between permutation and combination?.
Answers
Answer:
Permutation is an arrangement of things where order of arrangement matters. The position of each thing in a permutation matters. Thus, Permutation can be associated with Position.
Combination is grouping/selection of things where order does not matter. Permutation can be considered as an ordered combination.
Who the answer so ez to find
Answers
Mee
increase 31 kg by 100%
Giving 100 points
The dot plot below shows the hourly rate of some babysitters in a city:
A number line is shown from 1 dollar to 5 dollars in increments of 1 dollar for each tick mark. The horizontal axis label is Dollar per hour. There are 4 dots above 2 dollars, 2 dots above 3 dollars, 3 dots above 4 dollars, and 1 dot above 5 dollars. The title of the line plot is Babysitting Rates.
Which statement best describes the shape of the data?
It is symmetric and has a peak at $5.00.
It is not symmetric and has a peak at $2.00.
It is a cluster from $1.00 to $5.00 and has gaps.
It is a cluster from $1.00 to $5.00 and has no gaps.
Answers
Answer:
It is not symmetric and has a peak at $2.00
Step-by-step explanation:
$2.00 has 4 dots while the others have less
in order for it to be symmetric:
1 and 5 would need the same amount2 and 4 would need the same amount3 could be whateverit is also not clustered from $1.00 to $5.00 because $1.00 has no amount
There are no gaps as $1.00 has no amount
Answer:
It is not symmetric and has a peak at $2.00
Step-by-step explanation:
hope i helped you very much
Two times a number added to the other number is 25. Three times the first numb
minus the other number is 20. Find the numbers.
Answers
Answer:
First number = 9
Second number = 7
Step-by-step explanation:
Let x be the first number and y be the second.
2x + y = 25
3x - y = 20
1) Add them together.
5x = 45
x = 9
2) Solve for y.
2(9) + y = 25
y=7
3) Check your work on the other equation.
3(9) - (7) = 20
27 - 7 = 20
20 = 20
Therefore the first number is 9 and the second number is 7.
What is 0.47 expressed as a fraction in simplest form?
(SHOW WORK)
Answers
Answer: 0.47 is equal to 47/100
Step-by-step explanation:
1.00=100 Is like pennies, if you have a hundred of them you have 1 dollar but since there’s only 47 it’s out of a hundred
Answer:
0.47 as a fraction equals 47/100
Step-by-step explanation:
Write 0.47 as
Multiply both the numerator and denominator by 10 for each digit after the decimal point.
[tex]\frac{0.47}{1}[/tex] = [tex]\frac{0.47 x 100 } {1x100}[/tex] = [tex]\frac{47}{100}[/tex]
So, 0.47 as a fraction in simpliest form equals 47/100
Type the correct answer in each box.
Ella rolls a dle and then flips a coin. The sample space for this compound event is represented in the table (H is heads and Tis tails). Complete
the table and the sentence beneath it.
Die
1
2.
3
4
5
6
heads
H-1
H-2
H-3
H-5
H-6
Coin
tails
T-1
T-3
T-4
T-5
The size of the sample space is
Hi
Answers
The size of the sample space would be { H-1 H-2 H-3 H-5 H-6 T-1 T-3 T-4 T-5 }.
What is the sample space for a random experiment?Sample space is the set of all possible outcome the considered random experiment can result to.
Thus, suppose we toss a coin, then tossing a coin is a random experiment, and the sample space is {'head', 'tail'}.
We ignore other outcomes like slant coin, or standing coin by assuming that coin is very thin to stand and always falls down.
Ella rolls a die and then flips a coin. The sample space for this compound event is represented in the table (H is heads and T is tails).
Die 1 2 3 4 5 6
Coin: heads H-1 H-2 H-3 H-5 H-6
tails T-1 T-3 T-4 T-5
The size of the sample space
= { H-1 H-2 H-3 H-5 H-6 T-1 T-3 T-4 T-5 }
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Answer:
hope this works for u
Step-by-step explanation:
What is the balance after 3 years on a CD with an initial investment of $1,800.00 and a 2.75% interest rate?
Answers
Answer:
$1952.62
Step-by-step explanation:
1,800(1+.0275)^3
= 1952.62
Which expression is equivalent to startfraction 4 a 4 over 2 a endfraction times startfraction a squared over a 1 endfraction?
Answers
The expression that is equivalent to [(4a + 4)/2a] * [a²/(a + 1)] after simplification is; 2a
How to Simplify Fractions?We want to simplify the expression;
[(4a + 4)/2a] * [a²/(a + 1)]
This expression can be further reduced to;
[(4a + 4)/2] * [a/(a + 1)]
Factorizing the numerator to get;
[(4(a + 1)/2] * [a/(a + 1)]
(a + 1) will cancel out to get;
2a
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