Please use the following image for the next 7 questions. Keep in mind
that because XY is tangent to circle M, XY and XM form a right angle. XY is tangent to circle M at point X.
XM = 12 and YM = 43.
Questions:
1. What is the area of circle M?
2. What is the circumference of circle M?
3. Find the length of XY.
4. Find the measure of angle M.
5. Find the area of triangle XYM.
6. Find the area of the minor sector that has been created as a part of triangle XYM.
7. Find the arc length of the minor arc from point C to the point where YM intersects with the circle.
Answers
Answer:
Step-by-step explanation:
1). Since, XM is the radius of the circle,
Therefore, area of the circle = [tex]\pi r^{2}[/tex]
= [tex]\pi (XM)^2[/tex]
= [tex]\pi (12)^2[/tex]
= 452.39 units²
2). Circumference of a circle = 2πr
= 2π(XM)
= 2π(12)
= 24π
= 75.40 units
3). By applying Pythagoras theorem in ΔYXM,
YM² = XY² + XM²
(43)²= (XY)² + (12)²
1849 - 144 = (XY)²
XY = 41.29 units
4). tan(∠M) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{XY}{XM}[/tex]
m∠M = [tex]tan^{-1}(\frac{41.29}{12} )[/tex]
= 73.79°
5). Area of ΔXYM = [tex]\frac{1}{2}(\text{Base)}(\text{Height})[/tex]
= [tex]\frac{1}{2}(41.29)(12)[/tex]
= 247.74 square units
6). Area of the minor sector created by ΔXYM = [tex]\frac{\theta}{360}(\pi r^2)[/tex]
= [tex]\frac{73.79}{360}(452.39)[/tex]
= 92.73 units²
Related Questions
I need help with this problem-
Answers
Answer:
wat
Step-by-step explanation:
which sequence is a geometric progression
a 2 4 6 8
b 1 1 2 3
c1 2 4 8
d1 3 5 7
Answers
9514 1404 393
Answer:
c 1, 2, 4, 8
Step-by-step explanation:
It can work well to look at the first differences.
a: 4 -2 = 2; 6 -4 = 2 ⇒ differences are 2, 2, 2
b: differences are 0, 1, 1
c: differences are 1, 2, 4
d: differences are 2, 2, 2
__
Sequences 'a' and 'd' have common differences that are constant. These are arithmetic sequences. Sequence 'b' is of no named type.
Sequence 'c' has first differences that have a common ratio, the same as the sequence itself. This is an indication the sequence is geometric. The ratios of values are 2/1 = 2; 4/2 = 2; 8/4 = 2, so the terms have a common ratio.
Sequence c is a geometric progression.
33. What does equal in the solution of the system of equations below? 33 – 4y - z= 14 2r + 3y - 32 = 17 x + 2y + x = 20 10 04 -10 O-4
Answers
9514 1404 393
Answer:
(a) 10
Step-by-step explanation:
Attached is a graphical solution using "substitution." An expression was written for z using the first equation, and it was substituted into the remaining two equations. This gave two equations in x and y, easily solved graphically.
We found x = 10, y = 3, so ...
z = 3(10) -4(3) -14 = 30 -12 -14 = 4
The whole solution is (x, y, z) = (10, 3, 4).
Help!!!
Given a room is 12 feet by 10 feet and we have a circular rug with a radius of 3 feet,
calculate the amount of floor left uncovered by the circular area rug in a rectangular
living room.
Answers
Answer:
Step-by-step explanation:
floor = 12*10 = 120 sq ft
rug = π[tex]r^{2}[/tex] = 9π
120-9π = 91.74 sq ft
The amount of floor left uncovered by the circular area rug in a rectangular living room is 91.74 ft²
What is Area?Area is the space occupied by a 2 dimensional figure.
The room is rectangular and its 12 ft by 10 ft. Therefore,
area of the room = lw
where
l = length
w = width
area of the room = 12 × 10 = 120 ft²
The rug is circular and its use to cover the room. Therefore,
area of rug = πr²
where
r = 3 ft
Therefore,
area of rug = 3.14 × 3² = 28.26 ft²
The amount of floor left uncovered by the circular area rug in a rectangular living room can be calculated as follows:
area uncovered = 120 - 28.6 = 91.74 ft²learn more on area here; https://brainly.com/question/1389611
what is the value of 9 (n + 2) - 5n when n =1/4
Answers
9514 1404 393
Answer:
19
Step-by-step explanation:
The evaluation is easier if we simplify the expression first.
9(n +2) -5n = 9n +18 -5n = 4n +18
For n = 1/4, this is ...
= 4(1/4) +18 = 1 +18
= 19
The value of the expression for n = 1/4 is 19.
a fuel mixture consists of 3 parts oil and 11 parts gasoline. the oil costs $0.75 per liter, and the gasoline costs $1.60 per liter. a mechanic makes 392 liters of the mixture. how much should he charge for 15% profit
Answers
Answer:
Total selling price= $663.82
Selling price per liter= $1.69
Step-by-step explanation:
Giving the following information:
Proportion of oil and gasoline:
Oil= 3/14= 0.21
Gasoline= 11/14= 0.79
The oil costs $0.75 per liter.
The gasoline costs $1.60 per liter.
First, we need to calculate the number of liters of oil and gasoline required:
Oil= 0.21*392= 82.32 liters
Gasoline= 0.79*392= 309.68
Now, the total cost to produce 392 liters:
Total cost= 82.32*0.75 + 309.68*1.6
Total cost= $577.23
Finally, the total and unitary selling price:
Total selling price= 577.23*1.15= $663.82
Selling price per liter= 663.82 / 392= $1.69
this zigzag crystal vase has a height of 10 inches. The cross sections parallel to the base are always rectangles that are 6 inches by 3 inches long.
If we assume the crystal itself has no thickness, what would be the volume of the vase? NO LINKS!!!
Answers
9514 1404 393
Answer:
180 in³
Step-by-step explanation:
V = Bh
V = (6 in × 3 in)(10 in) = 180 in³
The volume is the product of the cross section area (6 in × 3 in) = 18 in² and the height perpendicular to that cross section, 10 in.
Use the diagram to estimate the perimeter, rounding each number to the nearest hundred.
A parallelogram is shown. Two sides are labeled 5,534 feet. The other two sides are labeled 1,566 feet.
14,200 feet
16,000 feet
14,400 feet
14,000 feet
Answers
Answer:
14,000 feet.
Step-by-step explanation:
A parallelogram has 4 total sides and the opposite sides are characterized as having the same length. Therefore, If we are provided the lengths of two adjacent sides we can easily calculate the perimeter by multiplying these provided lengths by 2 and then adding them together. Since we are asked to round each number to the nearest hundred, it would be the following...
(5,500 * 2) + (1,500 * 2) = x
11,000 + 3000 = x
14,000 = x
Finally, we can estimate that the perimeter of the parallelogram is 14,000 feet.
If it takes 1074 digits to number the pages of a book starting with page 1. how many pages are in the book? The book has a total of pages.
Answers
Answer:
394 pagesStep-by-step explanation:
1- digit numbers:
1 to 9, number of digits = 92- digit numbers:
10 to 99, number of digits = 2(99 - 9) = 1803- digit numbers:
100 to 999, number of digits = 3(999 - 99) = 2700This is more than we have, but we know the number of pages is 3-digit.
Let it be x, then we have:
9 + 180 + 3(x - 99) = 10743(x - 99) = 1074 - 1893(x - 99) = 885x - 99 = 885/3x - 99 = 295x = 295 + 99x = 394I forgot a long time ago, What is the slope of the line?
See the image as the line doesn't go through -2 on the x nor -1 on the y
Answers
Answer:
[tex] - \frac{4}{5}[/tex]
Step-by-step explanation:
Line is passing through the points (-3, 1) & (2, - 3)
Therefore,
Slope of line
[tex] = \frac{ - 3 - 1}{2 - ( - 3)} \\ \\ = \frac{ - 4}{2 + 3} \\ \\ = - \frac{4}{5} [/tex]
Question is on the screenshot
Answers
V= πr^2 h
V= π(5)^2 (6)
V= 150π
Please can somebody help I am not very good at maths
Answers
Answer:
z = 3a + 4
Step-by-step explanation:
Add 4 to both sides
What percent of 0.2 gram of 32 mg
Answers
Answer:
625
Step-by-step explanation:
First, you have to convert 0.2 grams to mg. To do this, multiply 0.2 by 1000. This yield 200. Now 200 is what percent of 32.
200 * 100 / 32
= 625
Write the equation of the line that has the indicated slope and contains the indicated point. Express the final equation in standard form.
m = 1/2, (6, 9)
Answers
Answer:
[tex]x-2y=-12[/tex]
Step-by-step explanation:
Hi there!
1) Determine the equation of the line in slope-intercept form
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)
Plug in the slope [tex]\frac{1}{2}[/tex]
[tex]y=\frac{1}{2}x+b[/tex]
Plug in the given point (6,9) and solve for b
[tex]9=\frac{1}{2}(6)+b\\9=3+b[/tex]
Subtract 3 from both sides
[tex]9-3=3+b-3\\6=b[/tex]
Plug 6 back into [tex]y=\frac{1}{2}x+b[/tex]
[tex]y=\frac{1}{2}x+6[/tex]
2) Rearrange the equation into standard form
Standard form: [tex]Ax+By=C[/tex] where A, B and C are integers and A is typically positive
[tex]y=\frac{1}{2}x+6[/tex]
Multiply both sides by 2 to remove the fraction
[tex]2y=1x+12\\2y=x+12[/tex]
Subtract x from both sides to isolate 12 as C
[tex]2y-x=x+12-x\\2y-x=12\\-x+2y=12[/tex]
Multiply both sides by -1 to make A positive
[tex]x-2y=-12[/tex]
I hope this helps!
Multiply 12x2y4z(-4x3y6z2)
Answers
Answer:
[tex]-48x^5 y^{10} z^3[/tex] should be the answer
Step-by-step explanation:
Which function has a greater Y intercept
Answers
What is the complementary number of 16
I
Answers
Answer:
2
Step-by-step explanation:
A group of coins is shown below. What is the probability of drawing each type of coin?
Answers
Answer:
likely
Step-by-step explanation:
Please help me, and can you do it by a table math
Answers
Answer:
Yeah
Step-by-step explanation:
A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:
769 691 699 730 711 765 702 718 719 712 768 688 757 695 768 735 709 758 708 693 736 700 687 772 715
Required:
a. What are the range and standard deviation?
b. Use the Empirical Rule to establish an interval which includes about 95 percent of the observations.
Answers
Answer:
[tex]Range = 85[/tex]
[tex]\sigma = 28.71[/tex]
[tex]Interval = [666.78, 781.62][/tex]
Step-by-step explanation:
Given
The data for 25 undergraduates
Solving (a): Range and Standard deviation
The range is:
[tex]Range = Highest - Least[/tex]
From the dataset:
[tex]Highest = 772[/tex]
[tex]Least = 687[/tex]
So:
[tex]Range = Highest - Least[/tex]
[tex]Range = 772-687[/tex]
[tex]Range = 85[/tex]
The standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]
First, calculate the mean
[tex]\bar x = \frac{769 +691 +............+715}{25}[/tex]
[tex]\bar x = \frac{18105}{25}[/tex]
[tex]\bar x = 724.2[/tex]
So, the standard deviation is:
[tex]\sigma = \sqrt{\frac{(769-724.2)^2 +(691-724.2)^2 +(699-724.2)^2 +(730-724.2)^2 +............+(715-724.2)^2}{25}}[/tex]
[tex]\sigma = \sqrt{\frac{20604}{25}}[/tex]
[tex]\sigma = \sqrt{824.16}[/tex]
[tex]\sigma = 28.71[/tex]
Solving (b): The interval of the 95% of the observation.
Using the emperical rule, we have:
[tex]Interval = [\bar x - 2*\sigma, \bar x+ 2*\sigma][/tex]
[tex]Interval = [724.2 - 2*28.71, 724.2 + 2*28.71][/tex]
[tex]Interval = [666.78, 781.62][/tex]
What is the area of the triangle
Answers
Answer:
60m^2 is the answer im pretty sure
Step-by-step explanation:
yeah man thats it
Select the equation of a straight line that is parallel to the line 4y = 3x + 5
Answers
Answer:
One equation can be y = 3/4X +2
Step-by-step explanation:
Any equation that has a slope of 3/4 will be parallel to the line 4Y = 3X + 5 because the slope is the same. This can also be shown visually using any graphing calculator.
Which function is graphed on the coordinate plane below?
Answers
Answer:
f(x) = 2x - 6
Step-by-step explanation:
positive slope = 2
y- intercept = -6
Answer:A
Step-by-step explanation:
You are paid $25 per hour.
You work 7 hours a day.
You work 5 days a week.
How much is your total pay each week? $=
Answers
Answer:
The total pay would be $50, But there would also be tax to consider in this situation.
if the pictures cost .29 cents and you have 353 pictures how much would it could all together
Answers
Answer:
102.37
Step-by-step explanation:
.29*353=102.37
353 pictures times 0.29 per picture=102.37
What is the solution to the system of equations below?
y=-3x+9 and y-ſx-12
(21, 2)
(21, -10)
(-21, 16)
(-21, -26)
Answers
I tried every combination. there seems to be something wrong with the informations you gave.
the second equation contains errors, and none of these 4 points can be solutions to the first equation alone
PLEASE ANSWER!! Solve for angle Z using the Sine Law. Round to the nearest degree.
Answers
Answer:
Z = 51º
Step-by-step explanation:
sinZ/12.5 = sin76/15.5
multiply both sides by 12.5
sinZ = sin76/15.5 * 12.5
Use calculator
sinZ = 0.782496553448384
Z = arcsin 0.782496553448384
Use calculator again
Z = 51.48972926377471º
Rounded
Z = 51º
A line intersects the point (3,4) and has a slope of -2. Substitute the values into point-slope form.
Answers
9514 1404 393
Answer:
y -4 = -2(x -3)
Step-by-step explanation:
The point-slope form of an equation for a line through point (h, k) with slope m is ...
y -k = m(x -h)
You have (h, k) = (3, 4) and m = -2, so your equation is ...
y -4 = -2(x -3)
Which graph shows the point (-2, 3)?
A.
B.
C.
D.
Answers
the ratio of the measures of the angles in cat is 2:7:9. find the measure of the smallest angle.
Answers
Answer:
20º
Step-by-step explanation:
Total parts
2 + 7 + 9 = 18
Value of each part given 180º in a triangle
180 / 18 = 10º
Smallest angle
2 * 10 = 20º
Answer:
20
Step-by-step explanation:
Multiply each angle by x
2x: 7x: 9x
The sum of the angles in a triangle is 180
2x+7x+9x = 180
Combine like terms
18x = 180
Divide by 18
18x/18 = 180/18
x =10
The smallest angle is 2x
2x = 2(10) =20