homework 2 central angles & arc measures answers

Unit 10: circles homework 2: central angles & arc measures

The central angle (127 degrees) is the angle at point K

The measures of JL and JML are 127 and 233 degrees, respectively

From the complete question, we have:

JL = 127 degrees.

The sum of angles at a point is 360 degrees

So, we have:

JML + 127 = 360

Subtract 127 from both sides

Hence, the measures of JL and JML are 127 and 233 degrees, respectively

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Related Questions

I have already done Number one but I need help with 2. Please help when you find time to!

Step-by-step explanation:

Area of a triangle = 1/2 x base x height

Area of a rectangle = width x length

Surface area of square based pyramid = area of base + 4 × area of triangle

⇒ SA = (6 × 6) + 4(1/2 × 6 × 14)

         = 36 + 168

         = 204 yd²

Surface area of a cuboid = 2 × base area + 2 × end area + 2 × side area

⇒ SA = 2(10 × 6) + 2(6 × 3) + 2(10 × 3)

         = 120 + 36 + 60

         = 216 mm²

Extra credit question

Surface area of a triangular based prism = base area + 2 × triangle area + 2 × side areas

base area = 3 × 10 = 30 mm²

triangle area = 1/2 × 3 × 2 = 3 mm²

side area = 10 × 2.5 = 25 mm²

⇒ total SA = 30 + (2 × 3) + (2 × 25)

                 = 30 + 6 + 50

                 = 86 mm²

❍ Concept : -

We can solve these questions by using the formulas of area of triangle and rectangle, which will make our work easier. So, we know that,

[tex] \blue{ \underline{ \boxed{ \begin{array}{cc} \sf1. ~Area_{Triangle} = \dfrac{1} {2} \times b \times h \qquad \: \: \: \: \: \: \: \\ \\ \\ \sf2. \: Area_{Rectangle} = Length \times Breadth \end{array}}}} \\ \\ [/tex]

Using these formulas and figuring out the number of triangles and rectangles in each shape, we will solve this question.

✰ Solution : -

1. In this square pyramid, if we closely observe, we will get to know that there are 1 rectangle and 4 triangular faces. Thus,

[tex]\sf \hookrightarrow Area=6 \times 6 + 4( \dfrac{1}{2} \times 6 \times 14) \\ \\ \\ \sf \hookrightarrow Area=36 + 168 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {204 \: yd}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ [/tex]

2. Now, here, we can use the formula of total surface area for cuboid, i.e.

TSA = 2( lb + bh + hl )

[tex]\sf \hookrightarrow Area=2(10 \times 6 + 6 \times 3 + 10 \times 3) \\ \\ \\ \sf \hookrightarrow Area=2(60 + 18 + 30) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=2 \times 108 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {216 \: mm}^{2} \: \: \qquad \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

Extra Credit Question.

Here, we can find out the total surface area by finding,

Base area i.e. length x breadth ( B.A. )

Side area i.e. length x breadth ( S.A. )

triangular area = 1/2 x b x h ( T.A. )

TSA = BA + 2 x S.A. + 2 x T.A.

[tex]\sf \hookrightarrow Area=(10 \times 3) + 2(10 \times 2.5) + 2(\dfrac{1}{2} \times 3 \times 2) \\ \\ \\ \sf \hookrightarrow Area= 30 + 2 \times 25 + 2 \times 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=30 + 50 + 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {86 \: mm}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

The box-and-whisker plot below represents some data set. What is the minimum value of the data?

minimum value is: the left whisker

box an whisker plot: left line is the minimum, first part of the box is Q1, where the box has a middle line it is called Median, the other end of the box is Q3, the right line is called the maximum whisker.

Hope this helps

Hong has a bookcase with 8 shelves. There are k books on each shelf. Using , write an expression for the total number of books.

Answer: total books = 8k

k = books on each shelf

total books = bookcases * shelves per bookcase * books per shelf (k)

total books = 1 * 8 * k

total books = 8k

To find the total number of books, take the number of shelves and multiply by the number of books on each shelf

The total number of books is 8k

A‌ ‌drink‌ ‌recipe‌ ‌calls‌ ‌for‌ ‌papaya‌ ‌juice‌ ‌and‌ ‌water.‌ ‌This‌ ‌equation‌ ‌represents‌ ‌the‌ ‌proportional‌ ‌relationship‌ ‌between‌ ‌the‌ ‌number‌ ‌of‌ ‌milliliters‌ ‌of‌ ‌papaya‌ ‌juice‌ ‌(‌p‌)‌ ‌and‌ ‌water‌ ‌(‌w‌)‌ ‌in‌ ‌the‌ ‌recipe.‌ ‌ ‌5‌p‌‌ ‌=‌ ‌85‌w‌ ‌ ‌Enter‌ ‌the‌ ‌number‌ ‌of‌ ‌milliliters‌ ‌of‌ ‌water‌ ‌used‌ ‌for‌ ‌1‌ ‌milliliter‌ ‌of‌ ‌papaya‌ ‌juice.‌ ‌

1/17 mL of water

Divide both sides by 85.

5p/85 = 85w/85

For 1 mL of papaya juice, p = 1.

1/17 mL of water is used for 1 mL of papaya juice.

Lillie and Adam are simplifying the expression 643 Whose reasoning is correct?

The first one

"Only Lillie is correct" that's the right answer.

64^2/3 = 16

Help pls!!!!!!!!! ddddddddddddddd

what is the volume of a sphere if its radius is 30

About 113,097.34 units

           The volume of a sphere can be found with the equation V = [tex]\frac{4}{3}[/tex]πr³ when r is the radius.

V = [tex]\frac{4}{3}[/tex]πr³

V = [tex]\frac{4}{3}[/tex]π(30)³

V ≈ 113,097.34 units

James has 3 blue candies and 3 green candies. 3 people come in and take 2 candies. What is the probability that they do not take 2 candies of the same color? ~ pls solve, i'm really confused

33.3333333333

we see that there are 6 candies in total

we also see that there is a 50% chance that someone will take out 3 candies of the same color,

50/3 = 16.66666666666667

so the chance of getting 2 marbles of the same color is 16.66666666666667 + 16.66666666666667 which is 33.3333333333

I hope I could help

The equation to model Exponential Decay is: y = a[1 – r) y= total amount a= starting amount r= the growth rate as a decimal t= number of growth periods Question 1 (1 point) Sarah takes 550 mg of an antibiotic. Every hour, her body breaks down 25% of the remaining drug. How much will be left after 12 hours? Guys help me please I really don’t understand this

I will give some hints. We know most values, we have to solve for y as that is the remaining amount.

y = We have to find.

a = 550 mg (She takes this much)

r = 0.25 (This is 25% as a decimal, don't forget to subtract 1)

t = 12 (This is because over the 12 hours, each hour it breaks down so (12 hours total * 1 hour periods) gives us 12 periods.

I hope this helps!

I NEED THE ANSWER |(-2+1)*3)|

The answer is 3

add -2+1 first equal -1 flip -1 to positive equal 1. Multiply 3*1 and that equals 3

Find the length of the third side. If necessary, round to the nearest tenth. 6 8 there also a right angle

See below ↓

Given side lengths :

This question can be solved in two ways :

Hope it helps~

Giovanni drops a rock from the Leaning Tower of Pisa in Italy. The height in feet (h) of the falling rock above the ground is given by the following equation, where t represents the time, in seconds. h = -16t2 + 186 Approximately how long will it take the rock to reach the ground?

It would take about 3.4 seconds for the rocks to reach the ground.

An equation is an expression t hat shows the relationship between two or more numbers and variables.

Let h represent the height of the rock above the ground after t seconds . Given the equation:

h = -16t² + 186

The rock would reach the ground at h = 0, hence:

0 = -16t² + 186

t = 3.4 seconds

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Which statement accurately describes the contents of the two boxes in the image? A. The box on the top consists of a mixture while the box on the bottom consists of a pure substance. B. Both boxes consist of pure substances. C. The box on the top consists of a pure substance while the box on the bottom consists of a mixture. D. Both boxes consist of mixtures. ​

The statement that describes the content of the two boxes is that the box on the top contains a pure substance , while the one on the bottom contains a mixture .

A pure substance often refers to a specific element such as nitrogen , helium , etc. that has not been modified or mixed with others.

On the other hand, a mixture includes two or more elements mixed.

The first box contains only nitrogen , which is a pure substance .

Different from the first box , this box contains two types of substances carbon and oxygen , which is why particles have two different colors . This means the content is a mixture .

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its literally 15 points How do i find lateral area? dont answer in a confusing way please i just need to understand this :(

There are many areas but

Area of square is L × W

where you multiply both length × width you get the answers squared

Area of a cube is L × W × H

this is where you multiply all length × width × height and get the answer cube

An equilateral triangle with side lengths equal to 12 StartRoot 3 EndRoot units is inscribed in a circle. Half a side length of the equilateral triangle is 6 StartRoot 3 EndRoot units, so the apothem is units long and the radius of the circle is units long. Each segment of the circle has an area equal to the difference between the areas of the sector and triangle, or ( π − StartRoot 3 EndRoot) units2.

The apothem (x) is 11.62 units, the radius of the circle is 12 units, and the area of each segment is 48π − 23.25√3 square units.

It is a locus of a point drawn equidistant from the center . The distance from the center to the circumference is called the radius of the circle .

An equilateral triangle with side lengths equal to 12√3 units is inscribed in a circle .

And half a side length of the equilateral triangle is 6√3 units.

The apothem (x) is units long and the radius of the circle will be

x² = (9√3)² - (6√3)²

x² = 243 - 108

And the radius of the circle will be

[tex]\begin{aligned} \cos 30 &= \dfrac{6\sqrt3}{r}\\\\\dfrac{\sqrt3}{2}&= \dfrac{6\sqrt3}{r}\\\\r &= 12 \end{aligned}[/tex]

Each segment of the circle has an area that will be

Area = the difference between the areas of the sector and triangle

Area = the areas of the sector - the areas of the triangle

The area of the sector will be

[tex]\rm Sector's \ area= \dfrac{120}{360} \pi *12^2 \\\\Sector's \ area= 48\pi[/tex]

The area of the triangle will be

[tex]\rm Triangle's \ area = \dfrac{1}{2*3} * 11.62 * 12\sqrt3\\\\Triangle's \ area = 23.25\sqrt3[/tex]

Then the area of each segment will be

Segment area = 48π − 23.25√3

More about the circle link is given below.

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I need help Imagine that you designed a firework. When the firework first explodes, it splits into eight sparkles. Each of those sparkles then explodes and splits into eight new sparkles. How many sparkles would the second explosion produce? Explain how you determined your answer.

Just including the second explosion, each of the 8 sparks bursts into 8, that means 8 sparks were produced 8 times, or 8x8

1 sparkle Burst it produces 8 sparkles so you say 8×8×8×8×8×8×8×8

What is the volume of this figure? 6004 in³ 6624 in³ 9936 in³ 10,488 in³

The volume of the figure is the amount of space in the figure

The volume of the figure is 10488 cubic inches

The figure is a composite figure , and it contains:

The volume (V1) of the rectangular prism is:

V1 = Length * Width * Height

V1 = 18 in * 23 in * 16 in

V1 = 6624 cubic inches

The volume (V2) of the triangular prism is:

V2 = 0.5 * Base * Width * Height

V2 = 0.5 * 23 in * 16 in * 21 in

V2 = 3864 cubic inches

Add the volumes of both figures

V =  V1 + V2

V = 6624 cubic inches + 3864 cubic inches

V = 10488 cubic inches

Hence, the volume of the figure is 10488 cubic inches

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The answer is D: 10488

A gas station sells motor oil in 2-liter bottles. The gas station sold 6 bottles of oil each day for 8 days. How many liters of motor oil did the gas station sell in these 8 days?

Two liters are in each bottle, so that means they sold 12 bottles of oil each day. Multiply that with 8 days to get the answer:

12 × 8 = 96

Ninety-six liters.

10. Jacinto Corado rented a minivan for 4 days in Tampa, Florida, for $88.00 a day plus $0.20 a mile for all miles over 200. He drove 75, 120, 85, and 140 miles on the days rented. He paid a CDW fee of $18.50 per day and $61.83 for gasoline.

75+120+85+140=420. Take away the 200 he was allowed. Leaves 220

220*.20 =44

gas is set at 61.83

Sum each of those.

352+44+74+61.83= $531.83

) Which expression represents the SUM of n and 12?

the "sum of" means we add.

So the sum of n and 12 means we add n and 12:-

12+n (both  of these expressions mean the same thing)

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Joslynn makes $8.25 per hour babysitting. If she made $123.75 last week, then how many hours did she work last week?

We already know that Joslynn makes $8.25 per hour.

123.75 divided by 8.25= worked hours

123.75 divided by 8.25 = 15 hours

So last week Joslynn worked 15 hours to make $123.75.

Find the area of triangle

So we see one large triangle, that can be split into two triangles split by the thin dotted line:

Let us find the other leg of the First triangle which also happens to be the height of the larger triangle, using the Pythagorean theorem

     [tex]a^2+b^2=c^2\\a^2 + 11^2 = 26^2\\a^2 = 26^2-11^2=555\\a=23.56[/tex]

Thus the height of the entire triangle is 23.56 which also happens to be one of the legs of the Second triangle

      [tex]a^2+b^2=c^2\\a^2+(23.56)^2=42^2\\a^2 = 1764-555=1209\\a = 34.77[/tex]

Having found the other leg of the Second Triangle , we can find the base of the larger triangle is:

     -->  34.77 + 11 = 45.77

The height as found in the first initial step is 23.56 thus the area is

   Area = [tex]\frac{1}{2}*b*h=\frac{1}{2}*23.56*45.77=539.17[/tex]

Hope that helps!

Number 5? Pre Cal- A small airplane is cruising at an airspeed of 235 kph heading in a direction of 45° (measured from the positive z-axis). The wind is blowing at 60kph in a direction of 120°. Find the resulting direction and groundspeed of the airplane to the nearest whole number.

four friends earned $5.20 for washing a car They shared the money equally how much did each friend get.

We need to figure out how much each friend gets out of the 5.20 so we will have to divide :)

5.20/4 = $1.30

Have an amazing day!!

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Which choices are in the solution set of the equation below? Check all that apply. 4x = 30 A. 8 B. 7.5 C. 8.5 D. 7 E.6.5

Help me please I’m struggling with this subject :/

I believe the answer is 135 square feet.

so 10x12=120. 10x3=30 and you divide the triangle by 2 so 30/2=15. 120+15=135

well, we don't know the cost of the carpet, however hmmm we know the cost of the carpet is 4 bucks per ft², which means we need to know how many ft² the Randall family is going to use in the first place hmmmm, Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ a=12\\ b=15\\ h=10 \end{cases}\implies \begin{array}{llll} A=\cfrac{10(12+15)}{2} \\\\\\ A=\cfrac{10(27)}{2}\implies A=135~ft^2 \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{per~ft^2}{(4)}~~\stackrel{area~in~ft^2}{(135)}\implies \stackrel{\$}{540}\impliedby \textit{total cost}[/tex]

A teacher used the change of base formula to determine whether the equation below is correct. (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = 3 Which statement explains whether the equation is correct? The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = log (2 times 10) times log (4 times 8) times log (10 times 4). = log (20) times log (32) times log (40). =3 The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = StartFraction log 10 Over log 2 EndFraction times StartFraction log 8 Over log 4 EndFraction times StartFraction log 4 Over log 10 EndFraction. = StartFraction log 8 Over log 2 EndFraction. = 3 The equation is correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = StartFraction log 10 Over log 2 EndFraction times StartFraction log 8 Over log 4 EndFraction times StartFraction log 4 Over log 10 EndFraction. = StartFraction log 8 Over log 2 EndFraction. = 4. The equation is not correct since (log Subscript 2 Baseline 10) (log Subscript 4 Baseline 8) (log Subscript 10 Baseline 4) = log StartFraction 10 Over 2 EndFraction times log eight-fourths times log four-tenths. = log 5 times log 2 times log 0. 4. = negative 0. 8.

The solution to the problem is correct and the correct option from the given options is B.

A log function is a way to find how much a number must be raised in order to get the desired number.

[tex]a^c =b[/tex]

can be written as

[tex]\rm{log_ab=c[/tex]

where a is the base to which the power is to be raised ,

b is the desired number that we want when power is to be raised ,

c is the power that must be raised to a to get b.

For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.

The given logarithmic problem can be solved in the following manner , therefore,

[tex]\rm log_210\ log_48\ log_{10}4\\\\[/tex]

Using the logarithmic properties , we can write,

[tex]=\rm \dfrac{log10}{log2}\cdot \dfrac{log8}{log4}\cdot \dfrac{log4}{log10}\\\\[/tex]

Now cancelling out the values we will get,

[tex]=\rm \dfrac{log2^3}{log2}\\\\=\rm \dfrac{3log2}{log2}\\\\= 3[/tex]

Thus, the solution to the problem is correct and the correct option from the given options is B.

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If x=3, y=-2, z=-1 ,find the value of 3x-4y+z I really need help

Since, x=3, y=-2, z=-1

We can Substitute:

3(3)-4(-2) + -1

9 -4(-2)+-1

Determine if there was a percent increase or decrease in the number of trench coats sold, and by how much. (Round your answer to the nearest tenth. ) a. The percentage of trench coats sold decreased by 0. 8%. B. The percentage of trench coats sold increased by 0. 8%. C. The percentage of trench coats sold decreased by 23. 3%. D. The percentage of trench coats sold increased by 23. 3%.

The percentage of trench coats sold increased by 23. 3%. therefore, option D is correct .

A percentage is a minimum number or ratio that is measured by a fraction of 100.

First, we need to subtract the final from the initial , then divide the difference by the initial , then multiply your answer by 100 to get the percentage

the final is 127, and the initial is 103

127 - 103 = 24

24/103 = 0.233

0.233 x 100

Thus, The percentage of trench coats sold increased by 23. 3%.

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Assume that f(x) = 2x^2 + 4. The function f(x) + k, where k is a constant, is represented by the graph below. what effect did adding k have on the graph of f(x)‽​

The effect  of adding k on the graph of f(x) will shift the curve upward by k units on the xy-plane.

Given the parent function of the given graph expressed as  f(x) = 2x^2 + 4.

If this function is represented as f(x)+k, the addition of the constant "k" shows hat the  function f(x) has been shifted vertically upward s by a factors of 'k'

Hence the effect  of adding k on the graph of f(x) will shift the curve upward by k units on the xy-plane.

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