Given mCT=26 and m/CAT =124° find the length of CA, the radius in Circle A. Use
π = 3.14 in your calculation and round to the nearest tenth.
Answers
Answer:
[tex]\text{length of \textit{CA}} \ = \ 12.0 \ \ \ (\text{nearest tenth})[/tex]
Step-by-step explanation:
Radian measure is the ratio of the length of a circular arc to its radius.
A radian is the measurement of the central angle which subtends an arc whose length is equal to the length of the radius of the circle.
In the case of the unit circle, as shown in the figure below, one radian is the angle of the sector with a radius of 1 and circular arclength of 1.
Following this definition, the magnitude, in radians, of one complete revolution of a unit circle is the circumference of the unit circle divided by its radius, [tex]\displaystyle\frac{2\pi}{1}[/tex] or [tex]2\pi[/tex]. Thus, [tex]2\pi[/tex] radians is equal to [tex]360^{\circ}[/tex] degrees. Alternatively, one radian is equal to [tex]\displaystyle\frac{180^{\circ}}{\pi} \ \approx \ 57.296^{\circ} \ \ \ (3 \ d.p.)[/tex].
Since radian measure is defined as the ratio of the arc length of a sector to its radius, hence
[tex]\displaystyle\frac{s}{r} \ = \ \theta \\\\ s \ = \ r\theta[/tex]
where [tex]s[/tex] is the arclength, [tex]r[/tex] is the radius, and [tex]\theta[/tex] is the central angle, in radians.
Therefore, the length of CA is
[tex]\displaystyle\frac{s}{\theta} \ = \ r \\ \\ r \ = \ \displaystyle\frac{26}{124^{\circ} \ \times \ \displaystyle\frac{\pi}{180^{\circ}} \ \text{rad}} \\ \\ r = \displaystyle\frac{26 \ \times \ 45}{31 \ \times \ 3.14} \\ \\ r\ = \ 12.0 \ \ \ \ \left(\text{nearest tenth}\right)[/tex]
Related Questions
The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?
Answers
Answer:
Step-by-step explanation:
Comment
This can be done as a proportion. A proportion is 2 equal ratios. If you know three parts of the proportion then you can solve for the 4th.
Proportion
31 wrecks/1085 cars = 7 wrecks / x cars
Solution
31 wrecks/1085 cars = 7 wrecks / x cars Cross Multiply
31 * x = 1085 * 7 Simplify the right
31 * x = 7595 Divide both sides by 31
31 * x/31 = 7595/31
x = 245
Answer 7 wrecks means 245 cars have passed the intersection
A line of best fit was drawn for 16 data points. What is the maximum number
of these data points that may not actually be on the line?
OA. 14
OB. 13
O C. 15
OD. 16
Answers
The maximum number of data points that may not actually be on the line is 16. so, the correct option is D.
How to find the line of best fit?We know that a line of best fit is basically a straight line drawn for a given data that may or may not pass through data points.
It is given that the line is drawn for 16 data points.
Hence, the line may or may not pass through all these 16 points.
Therefore, the maximum number of data points that may not actually be on the line is 16.
so, the correct option is D.
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The stock of Company A gained 6% today to $87.45. What was the opening price of the stock in the beginning of the day?
Answers
The opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have:
The stock of Company A gained 6% today to $87.45.
Let x be the opening price of the stock in the beginning of the day.
(x + 0.06x) = 87.45
Because gained 6% today to $87.45
1.06x = 87.45
x = $82.5
Thus, the opening price of the stock at the beginning of the day was $82.5 and the stock of Company A gained 6% today to $87.45.
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The repeating decimal z=0.142857142857142857 as fraction
Answers
Answer:
[tex] \frac{1}{7} [/tex]
Simplify: √64(6z-7)² (square root over entire equation)
Answers
[tex]\sqrt{64(6z-7)^2}=\sqrt{64}\cdot\sqrt{(6z-7)^2}=8\cdot |6z-7|=8|6z-7|[/tex]
yo
24
yx
SECTION B
(a) Identity element;
(b) Inverse of 3 and -5 under *
Range y
[30 marks]
Answer all the questions in this section. All questions carry equal marks.
1. A binary operation is defined on the set of real numbers, R, by x + y = x + y + 10.
Find the:
X
x
Inverse
Answers
Answer:
Sike
Step-by-step explanation:
That's the wrong number only 123
What are m and b in the linear equation y=2x+8
Answers
Answer:
m=2 and b=8
Step-by-step explanation:
this is a linear equation, which takes on the formula of y=mx+b
therefore in the equation y=2x+8, 2 is the m, and 8 is the b
Determine the next three terms in the following sequence: Negative 1, one-half, negative one-fourth, StartFraction 1 Over 8 EndFraction,____, ____, ____,... a. StartFraction 1 Over 12 EndFraction, StartFraction 1 Over 24 EndFraction, StartFraction 1 Over 48 EndFraction b. StartFraction 1 Over 16 EndFraction, StartFraction 1 Over 32 EndFraction, StartFraction 1 Over 64 EndFraction c. Negative StartFraction 1 Over 12 EndFraction, StartFraction 1 Over 24 EndFraction, Negative StartFraction 1 Over 48 EndFraction d. Negative StartFraction 1 Over 12 EndFraction, StartFraction 1 Over 24 EndFraction, Negative StartFraction 1 Over 48 EndFraction
Answers
The next three terms will be -1/16, 1/32, and -1/64. Then the correct option is B.
What is the geometric sequences?Let a be term and r be the common ratio. Then the geometric sequences will be
[tex]\rm a_n = a_{n -1} \cdot r[/tex]
The sequence is given below.
-1, 1/2, -1/4, 1/8,....
The common ratio will be -1/2.
Then the next three terms will be
a₅ = a₄ x (-1/2)
a₅ = (1/8) x (-1/2)
a₅ = -1/16
a₆ = a₅ x (-1/2)
a₆ = (-1/16) x (-1/2)
a₆ = 1/32
a₇ = a₆ x (-1/2)
a₇ = (1/32) x (-1/2)
a₇ = -1/64
Then the next three terms will be -1/16, 1/32, and -1/64.
Then the correct option is B.
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Answer:
C
Step-by-step explanation:
Max is going to order a breakfast platter at The Breakfast Club. He can choose one style of eggs, one type of meat, and one kind of toast. The following table shows the options available to him.
Breakfast platter
Egg options Fried, Scrambled, Poached, Hard boiled
Meat options Bacon, Sausage, Ham, Steak
Toast options White, Wheat, Rye
How many different breakfast platters could Max create?
Answers
the answer is 48
Step-by-step explanation:
since there are 4 egg options 4 meat options and 3 bread options. so u multiply this.
4×3×4=48
help me pleaseeeeeeeeeeee i need the answer fast because it is limited
i will mark as brainiest
Answers
Answer:
D
Step-by-step explanation:
Original area = x * x = x^2
New area = x ( x +3.5) = x^2 + 3.5x <====the underlined is the increase in area
What is the point of intersection of the lines represented by these equations
Jy = -2x + 2
y = x - 4
A. (-2, 2)
B. (1, -3)
c. (2,-2)
D. (3,-4)
Answers
To find the point of intersection of two lines, we can use substitution to find the x and y coordinates.
Solving the QuestionWe're given:
[tex]y = -2x + 2[/tex][tex]y = x - 4[/tex]Use substitution to find x:
[tex]-2x + 2=x-4\\-2x=x-6\\-3x=-6\\x=2[/tex]
Use substitution to find y:
[tex]y=x-4\\y=2-4\\y=-2[/tex]
AnswerThe point of intersection is (2,-2).
Based on the graph of g (x), on which intervals
are the function's values positive? Select all that
apply.
Answers
Answer:
[tex]\text{A}) \text{ } -\infty < x < 3\\\\\text{C}) \text{ } -1 < x < 2\\\\[/tex]
Step-by-step explanation:
The graph lies above the x-axis for these intervals.
If BC is 1
CD is 2
DA is 3
AB is 4,
what is EF?
Answers
The length of the side EF will be 1 unit, approximately.
The complete figure is attached below.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The figure is given below.
The length of EF will be
EF = CF – CE
Then the value of CF will be
CF = BC × cos 30
CF = 2 × 0.866
CF = 1.732
Then the value of CE will be
CE = BC × cos 42
CE = 1 × 0.743
CE = 0.743
Then we have
EF = 1.732 – 0.743
EF = 0.989 ≈ 1
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Is 7/7 a proper fraction, an improper fraction, a mixed number, or decimal fraction?
None of these choices are correct.
O a decimal number
an improper fraction
O a mixed number
O a proper fraction
Answers
The difference between two numbers is -1 and their sum is 1. Find the two numbers.
Answers
Answer:
Let the no. be X and Y
X - Y = (-1)
X + Y = 1
X = (-1)+ Y
X = 1 - y
- 1.+ y = 1 - y
Y + Y = 1 + 1
2y = 2
Y = 1
X = 0
Answer:
x = 0 (first number), y = 1 (second number)
Step-by-step explanation:
x will represent the first number, and y will represent the second.
x - y = -1
x + y = 1
Now, it's time to get y by itself in one equation so that we can substitute.
x - y = -1 (subtract x from both sides)
-y = -1 - x (multiply both sides by -1)
y = x + 1
Plug in x + 1 for y in the second equation.
x + x + 1 = 1 (combine the x with the x)
2x + 1 = 1 (subtract 1 from both sides)
2x = 0 (divide both sides by 2)
x = 0
Since x = 0, we can plug 0 in for x into any equation to solve for y.
0 + y = 1
y = 1
Brainliest, please :)
Analia is a school district manager. Here are some details about two schools in her district for the last school year:
School A School B
Number of students 300030003000 400040004000
Number of teachers 190190190 380380380
Graduation rate 86\%86%86, percent 90\%90%90, percent
Budget per student \$10{,}500$10,500dollar sign, 10, comma, 500 \$10{,}000$10,000dollar sign, 10, comma, 000
% of students in sports club 62\%62%62, percent 68\%68%68, percent
Number of sports medals won 999 777
SAT average 120012001200 105010501050
SAT range (max-min) 900900900 700700700
Analia wants to know which school has higher athletic achievements relative to the SAT average.
1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
% of students in sports club divided by SAT average
(Choice B)
B
Graduation rate divided by SAT average
(Choice C)
C
Number of sports medals won
(Choice D)
D
Number of sports medals won divided by SAT average
2) Determine which school has higher athletic achievements relative to the SAT average, according to the two definitions. Did you get the same result for both definitions?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes. According to both definitions, School A has higher athletic achievements relative to the SAT average.
(Choice B)
B
Yes. According to both definitions, School B has higher athletic achievements relative to the SAT average.
(Choice C)
C
No. The definitions have opposite results.
Answers
Answer is in this link:
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he table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.
Answers
The height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have given a table:
Time height
2 8
4 12
6 16
8 20
10 24
The slope of the line = (12-8)/(4-2) = 4/2 = 2
The value of the slope is positive we can say, the height of water increases as time passes.
Thus, the height of water increases by 2 inches per minute option first "The height of the water increases 2 inches per minute" is correct.
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the answer is A: The height of the water increases 2 inches per minute.
hope this helped :)
Dan sold 40 concert tickets in 5 days.
Each day he sold 3 tickets MORE than the
previous day. The number of tickets he
sold on the third day is?
Answers
Step-by-step explanation:
The number of tickets sold by Dan the first day is x.
Tickets sold on the 2nd day: x+3
on the 3rd day: x+6
on the 4th day: x+9
on the 5th: x+12
Since the total of tickets sold by Dan is 40:
x+(x+3)+(x+6)+(x+9)+(x+12)=40
5x+30=40
5x=10
x=2
number of tickets sold on the third day: 8
Solve x:
3x + 99x= 1224
10 pts
Answers
Reason
Combine like terms
3x + 99 x = 1224
102x = 1224
Now solve for x
Divide both sides by 102
x= 12
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3x + 99x = 1,224}\\\\\large\textbf{COMBINE the LIKE TERMS}\\\\\mathsf{(3x + 99x) = 1,224}\\\mathsf{3x + 99x = 1,224}\\\mathsf{\bold{102x} = 1,224}\\\\\large\textbf{DIVIDE 102 to BOTH SIDES}\\\\\mathsf{\dfrac{102x}{102} = \dfrac{1,224}{102}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\mathsf{x = \dfrac{1,224}{102}}\\\\\mathsf{x = 12}\\\\\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 12}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
If f(x) = 3x-2 and g(x) = x+²,
find f(g(x)).
f(g(x)) = [?]
Simplify your answer as much as possible.
Answers
Answer:
x
Step-by-step explanation:
[tex]f(g(x)) = 3(\frac{x+2}{3} )-2\\= x + 2 - 2\\= x[/tex]
Each point has been reflected over the x-axis or y-axis.
Select the axis over which each point has been reflected.
Answers
The reflection is
x-axisx-axisy-axisWhat is reflection over axis?A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. In this case, the x axis would be called the axis of reflection.
For reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.
and, for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the y value the same.
So, by considering the above value rules the reflection of the given points as follows over respective axis.
E(7, 1) ⇒ (7, -1)
Here, the reflection is over x-axis because the y value is changing
F(-3, 5) ⇒ (-3, -5)
Here, the reflection is over x-axis because the y value is changing
G(6, -2) ⇒ (-6, -2)
Here, the reflection is over y-axis because the x value is changing.
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Quick please!
Will give brainliest
100 points
3(4j + 7 + 2j) or 3(6j +7) b. Use the distributive property to create an equivalent expression.
Answers
Answer:
3(4j + 7 + 2j)
12j + 21 + 6j
12j + 6j + 21
18j + 21 ----- (1)
3(6j +7)
18j + 21 --------(2)
eq 1 = eq. 2
both are equal
What is 43.808 in written form
Answers
Answer:
fourty-three.(point) eight zero eight
Step-by-step explanation:
hope it helps...
Hope this helps!
height of 24cm with a radius of 7cm. What is the total surface area of the cone?
Answers
Answer:
the answer to this problem is 703.7 in^2
Which of the following is a correctly written algebraic equation?
2 + 0.2x
5b - 5x + 2
a - 3x=0
3(x/5)
Answers
An investor decides to invest some cash in an account paying 13% annual interest, and to put the rest in a stock fund that ends up earning 7% over the course of a year. The investor puts $1300 more in the first account than in the stock fund, and at the end of the year finds the total interest from the two investments was $1270. How much money was invested at each of the two rates? Round to the nearest integer.
Answers
A percentage is a way to describe a part of a whole. The investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Le the amount that is put into the account is x, while the amount that is invested in the stock market is y. Given the investor puts $1300 more in the first account than in the stock fund, therefore, the equation can be written as,
x - y =1300
x = 1300 + y
Also, at the end of the year the total interest from the two investments was $1270. Therefore, we can write,
0.13x + 0.07y = 1270
Substitute the value of x from the above,
0.13(1300 + y) + 0.07y = 1270
169 + 0.13y + 0.07y = 1270
0.20y = 1101
y = 5505
substitute the value of y in the first equation,
x - y = 1300
x = 6805
Hence, the investment that was put in the account is 6805, while the amount that is invested in the stock is 5505.
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The number 900 is increased by 20% and then decreased by 20%. Find the new number.(the ans is 864 apparently:/ I need steps)
Answers
Step-by-step explanation:
if 900 is increased by 20% then
120/100×900=1080
Decreasing it by 20% then
80/100×1080=864
Giraffe Jack is 19 feet tall, and Ostrich Jim is 9 feet tall. A) What percent of Jack's height is Jim's height? B)What percent of Jim's height is Jack's height?
Answers
A percentage is a way to describe a part of a whole. Jim's Height is 47.37% of Jack's height.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Giraffe Jack is 19 feet tall, and Ostrich Jim is 9 feet tall.
A.) The percent of Jack's height is Jim's height,
Percentage = (Height of Jack/Height of Jim) × 100%
= 19/9 × 100%
= 211.11%
Hence, Jack's Height is 211.11% of Jim's height.
B.) The percent of Jim's height is Jack's height,
Percentage = (Height of Jim/Height of Jack) × 100%
= 9/19 × 100%
= 47.37%
Hence, Jim's Height is 47.37% of Jack's height.
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Answer:
211.11%
Step-by-step explanation:
Expand:
4(5x+5) - 3(2x + 4)
Answers
Answer:
14x + 8
Explanation:
⇒ 4(5x+5) - 3(2x + 4)
distribute inside parenthesis
⇒ 4(5x) + 4(5) - 3(2x) - 3(4)
multiply the variables
⇒ 20x + 20 - 6x - 12
collect like terms
⇒ 20x - 6x + 20 - 12
subtract like term
⇒ 14x + 8
4 x 5x = 20x
4 x 5. = 20
-3 x 2x = - 6x
-3 x 4 = - 12
Line them up, collect like terms & simplify
20x + 20 - 6x - 12
20x - 6x = 14x
20 - 12 = 8
Thus, answer is 14x + 8
Hope this helps!
Please help! Will give the brainliest :)
Answers
Answer: J. A translation of △XYZ to the right.
Step-by-step explanation:
I'll explain each bullet point one by one. A good hint is to pay attention to where the letters are.
-J is correct because the figure was shifted to the right.
-K is incorrect because if it was a reflection across the x-axis, the figure would be in Quadrant 3, or the bottom left.
-L is incorrect because if you pay attention to the letters, they are in the exact same place. If it was a reflection across the y-axis, the X' and Y' would switch places if you know what I mean.
-M is incorrect because if the figure was rotated 90°, point Z' would be furthest from the x-axis. In other words, the triangle would have been pointing up and not down.
-N is incorrect because if the figure was rotated 180° clockwise, the figure would have been in Quadrant 4, or the bottom right.
Given this information, the most appropriate answer is J.
I hope this helps! Pls give brainliest!! :)
