A regular pentagon is inscribed in a circle as shown. 1. Find the measure of minor arc cut off by one of the diagonals.2. Find the length of the same minor arc in problem 16a, given the radius of the circle is 10 cm. Leave the answer is terms of pi.
Answers
SOLUTION:
Step 1:
we are to find the measure of minor arc cut off by one of the diagonals;
The sum of interior angles in a pentagon is:
[tex]\begin{gathered} (n-2)\text{ x 180} \\ (5-2)\text{ x 180} \\ 3\text{ x 180} \\ 540 \end{gathered}[/tex]Each interior angle of a regular pentagon is
[tex]\frac{540}{5}\text{ = 108}[/tex]So the size of the major arc can be gotten by the circle theorem; the angle at the centre is twice the angle at the circumference.
[tex]\text{The major arc = 2 x 108 = 216}[/tex]Then recall,
[tex]\begin{gathered} \text{The major arc + the minor arc = 360 (sum of angles at a point)} \\ 216\text{ + the minor arc = 360} \\ \text{The minor arc = 360 - 216} \\ \text{The minor arc =144} \end{gathered}[/tex]Step 2:
We are to find the length of the same minor arc in problem;
[tex]\frac{\theta}{360}\text{ x 2 }\pi\text{ r}[/tex]Where our angle (titan) is 144 and radius is 10
[tex]\begin{gathered} \frac{144}{360}\text{ x 2 x }\pi\text{ x 10} \\ \\ 8\pi \end{gathered}[/tex]So the length of the minor arc, given that the radius is 10 cm is 8 pi
Related Questions
Please look at picture! thank you!
Answers
Answer:
16
Step-by-step explanation:
write the equation for a3
a3 = a2 + 3(3) -> eq1
now find what is a2, write equation for a2
a2 = a1 + 3(2) -> eq2
you know a1=1, replace that into eq2
a2 = 1 + 3(2) = 1 + 6 = 7
replace a2 into eq1
a3 = 7 +3(3) = 7 + 9 = 16
help pleaseee !!
thank you !!!!!
Answers
The value of x for the given figure is 7.
According to the question,
We have the following information:
We have a figure where two parallel lines are cut by another line. Some of the measurements of angles are given.
Now, we know that angle made on a straight line is 180°.
So, we have the following expression:
∠4+118 = 180
∠4 = 180-118
∠4 = 62°
Now, we know that alternate interior opposite angles are equal. In this case, ∠4 and (8x+6) are alternate interior opposite angles.
(8x+6) = m∠4
8x+6 = 62
Subtracting 6 from both the sides:
8x = 62-6
8x = 56
x = 56/8
x = 7
Hence, the value of x for the given figure is 7.
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Solve the equation 5.9g + 4 = 3.9g + 12.
Answers
Rearranging an equation:
isolating for a variable (g)merge like terms and solveuse inverse operations[tex]5.9g+4=3.9g+12[/tex]
[tex]5.9g-3.9g=12-4[/tex]
[tex]2g= 8[/tex]
[tex]\frac{2g}{2} = \frac{8}{2}[/tex]
[tex]g = 4[/tex]
g = 4
Answer:
g=4
Step-by-step explanation:
5.9g+4=3.9g+12
-4 -4
5.9g= 3.9g+8
-3.9g -3.9g
2g=8
/2 /2
g=4
Elizabeth has
4 1/2 feet of material to make bookmarks. She will use 9 inches of material for each bookmark. How many bookmarks can Elizabeth make?
Answers
So she can make 6 bookmarks
The table shows our research activities of two students at an observatory how much does a student pay to use a telescope for 1 hour the supercomputer? for 1 hour?
Answers
Answer: Student 1 pays $23.5 to use a supercomputer and pays $14.1 to use a telescope
Step-by-step explanation:
Using cross multiply and divided method, we can find the unit rate or just dividing.
Student 1. 3 1
$70.5 x
70.5 x 1 = 70.5
70.5 ÷ 3 = $23.5
x = $23.5
5 1
70.5 x
70.5 x 1 =70.5
70.5 ÷ 5 = 14.1
x = $14.1
Student 1 pays $23.5 to use a supercomputer and pays $14.1 to use a telescope.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Using the cross multiply and divide method, we can find the unit rate or just divide.
Student 1. 3 1
$70.5 x
70.5 x 1 = 70.5
70.5 ÷ 3 = $23.5
x = $23.5
5 1
70.5 x
70.5 x 1 =70.5
70.5 ÷ 5 = 14.1
x = $14.1
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May I please get help with this where I have tried multiple times but still cannot find the right answers for them
Answers
Given a point with coordinates (x, y), to rotate 90º counterclockwise, the rule is:
[tex](x,y)\Rightarrow(-y,x)[/tex]In thisc ase, we have the point:
[tex](2,-1)[/tex]Applying the rule:
[tex](2,-1)\Rightarrow(1,2)[/tex]Jordan types at a constant rate of 40 words per minute. The number of words typed, y, is a function of the number of minutes spent typing Part A Which equation models this situation? 95 CV 40and how many words can he type in 7.5 minutes
Answers
To write the equation that represents the situatio, as y is in function of x, you multiply the rate by the number of minutes (x):
[tex]y=40x[/tex]In 7.5 minutes he can type:
[tex]y=40(7.5)=300[/tex]Which equations represent a linear function? Select two. a. y = x-1 b. y = – 4.5 C. 3x – 4y = 2 d. 5x2 = 10y e. y = 1/2x2 +6
Answers
Explanation
a linear function must have
dependent and independent variables, ( y and x in this case)and the exponent of the independent vairable must be 1, so
Step 1
Check
a)
[tex]a)\text{ y=x-1}[/tex]this is a linear function
b)
[tex]y=4.5[/tex]this is not a functin, this expression has not x
c)
[tex]3x-4y=2[/tex]this functin has x and y, and the exponent of x is 1, so, this is a linear function
d)
[tex]5x^2=10y[/tex]this function has x and y, but the exponent is 2, so this is not a linear function
e)
[tex]y=\frac{1}{2}x^2+6[/tex]this function has x and y, but the exponent is 2, so this is not a linear function
i hope this helps you
At the local pizzeria, a slice of pizza costs $3.00. if there are eight slices in one pizza . how much would two whole pizzas cost?
Answers
Answer:
48 dollars
Step-by-step explanation:
3 x 8 = 24
24 x 2 = 48
Two whole pizzas will cost forty-eight dollars
Answer:
48 dollars
Step-by-step explanation:
because for each slice is 3 dollars and there is 8 slices in 1 pizza so 8*3=24 so for 1 whole pizza its 24 dollars and because we want 2 we multiply it by 2 so 24*2= 48 so for 2 whole pizzas it equals 48 dollars.
A easier way, in 2 pizzas there is a total of 16 slices so 16*3= 48
11. What are the zeros for the following quadratic relation: *
y = 5x² - 1125
O x = 0
O x = 5,15
O x= -15,5
O x=-15, 15
Answers
Answer:
x=15,-15
Step-by-step explanation:
5x^2-1125=0
5x^2=1125
x^2=225
x=square root of 225
x=+15 or -15
What is 275 = 5 (1 - 6k)
Answers
Answer:k=-9
Step-by-step explanation:
275=5(1-6k)
55=1-6k
54=-6k
-9=k
x²+2x for x=-3 please hurry
Answers
Answer:
3
Step-by-step explanation:
x²+2x and x=-3
= (-3)² +2(-3)
= 9-6
=3
10x−1= 7 x + 26 7x+26
Answers
Answer:
x = - 27/179
Step-by-step explanation:
10x - 1 = 7x + 182x + 26
10x - 1 = 189x + 26
10x - 189x = 26 + 1
- 179x = 27
x = - 27/179
9. Use the Distributive Property to solve the
equation 28-(3x+4)= 2(x+6) +x.
WITH SOLUTION please
Answers
Answer:
x=2
Step-by-step explanation:
T= 2
28 - (3æ+4) = 2(r + 6) + *
We need to use the distributive property for the
right side.
28 - 3z -4 = 2a + 12 + z
28 -3z -4 = (2) (æ) + (2)(6) + æ)
From here we need to subtract 3æ from both side.
-3æ + 24 -3 = 3æ + 12 – 3¢
3æ + 24 = 3z + 12
6z + 24 = 12
Transfer +24 on the right side. (P.S. don't forget to
change the sign)
62 = 12 - 24
6 = - 12
Finally, divide both sides by -6
6x/-6 = -13/-6
x=2
I hope I helped you
your gross income is 4520.00 your deductions are FICA (7.65%), federal tax withholding (11.75%), and state tax withholding (8.5%). Your fixed expenses are 30% of your realized income. You saved 5 months' worth in an emergency fund, placing 75% in a 60-day CD at a 5.25% APR and the rest in a regular savings account at a 3.8% APR. How much is the total interest earned between both accounts in 60 days?
Answers
The total interest earned between both accounts in 60 days is $92.01.
What is the interest?Given gross income = $4520/ month
Deductions = FICA+federal withholding + state with holding
Deductions = 7.65%+ 11.75%+8.5%= 27.9%
Total deductions = 27.9% of 4520= $1261.08
Net income = Gross income - Deductins = 4520-1261.08= $3258.92
Now 30 % of these are fixed expenses
Fixed expenses = 30% of 3258.92= $977.676
Amount left for month = 3258.92-977.676= $2281.244
5 months worth = 5*2281.244= $11406.22
Total money in the emergency fund = $11406.22
Since 75% in CD, amount imvested = 75% of 11406.22= 8554.665
APR= 5.25%
Number of days = 60
A= P*(1+r) ^n
Assuming they compound daily
r= 0.0525/365= 0.0001438
n= 60
A= 8554.665*(1+0.0001448) ^60
A= $8628.81
Regular savings:
25% in RS, Amount invested = 25% of 11406.22= 2851.55
APR= 3.8%
Number of days = 60
A= P*(1+r) ^n
Assuming they compound daily
r= 0.038/365= 0.0001041
n= 60
A= 2851.55*(1+0.0001041) ^60
A= $2869.42
Total interest earned = (2869.42+8628.81) -11406. l22
= $92.01
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need help as soon as possible !!!!!!
Answers
The value of the variable x: 40
Angles of the polygon are :
3x = 120(2x + 10) = 90(2x + 5) = 85(2x - 15) = 65What is Polygon?An Indian blockchain scalability platform is called Polygon. It addresses Ethereum's problems with excessive costs, a subpar user experience, and a meager number of transactions per second. Creating a framework for Proof of Stake transactions is one approach taken to overcome these problems.Calculate the measure of angles as follows:
3x(2x + 10)(2x + 5)And
(2x - 15)Since we have,
Sum of angle measure = 360°
Thus: 3x + (2x + 5) + (2x + 10) + (2x - 15) = 360Opening the brackets:
3x + 2x + 5 + 2x + 10 + 2x - 15 = 360Adding the like terms:
9x + 15 - 15 = 3609x = 360x = 360/9x = 40Hence, The measure of the variable is 40.
And the angle measures are:
3 x 40 = 120°(2(40) + 5) = 80 + 5 = 85°(2(40)+ 10) = 80 + 10 = 90°(2(40) - 15) = 80 - 15 = 65°Therefore, the value of the variable x: 40
Angles of the polygon are :
3x = 120(2x + 10) = 90(2x + 5) = 85(2x - 15) = 65To learn more about Polygon click on the link
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may you please help me! Whether you can help or not I hope you are doing amazing!!the instructions at the top fully say " use the compass and straightedge to construct a segment congruent to WX with endpoint P."
Answers
Step Guide:
Step 1: Place your compass at W and extend it to X.
Step 2: Using the same length, place your compass at P and mark an arc.
Step 3: Using the straightedge, draw a line from P to meet the arc.
Step 4: Label the point of intersection of the line and the curve Q.
This gives segment PQ that is congruent to WX,
19) Given that f(x)x² - 8x+ 15x² - 25find the horizontal and vertical asymptotes using the limits of the function.A) No Vertical or Horizontal asymptotesB) No Vertical asymptotesHorizontal asymptote aty - 1Vertical asymptote at x = 5Horizontal asymptote at y = 1D) Vertical asymptote at x = -5Horizontal asymptote at y = 1
Answers
EXPLANATION
Since we have the function:
[tex]f(x)=\frac{x^2-8x+15}{x^2}[/tex]Vertical asymptotes:
[tex]For\:rational\:functions,\:the\:vertical\:asymptotes\:are\:the\:undefined\:points,\:also\:known\:as\:the\:zeros\:of\:the\:denominator,\:of\:the\:simplified\:function.[/tex]Taking the denominator and comparing to zero:
[tex]x+5=0[/tex]The following points are undefined:
[tex]x=-5[/tex]Therefore, the vertical asymptote is at x=-5
Horizontal asymptotes:
[tex]\mathrm{If\:denominator's\:degree\:>\:numerator's\:degree,\:the\:horizontal\:asymptote\:is\:the\:x-axis:}\:y=0.[/tex][tex]If\:numerator's\:degree\:=\:1\:+\:denominator's\:degree,\:the\:asymptote\:is\:a\:slant\:asymptote\:of\:the\:form:\:y=mx+b.[/tex][tex]If\:the\:degrees\:are\:equal,\:the\:asymptote\:is:\:y=\frac{numerator's\:leading\:coefficient}{denominator's\:leading\:coefficient}[/tex][tex]\mathrm{If\:numerator's\:degree\:>\:1\:+\:denominator's\:degree,\:there\:is\:no\:horizontal\:asymptote.}[/tex][tex]\mathrm{The\:degree\:of\:the\:numerator}=1.\:\mathrm{The\:degree\:of\:the\:denominator}=1[/tex][tex]\mathrm{The\:degrees\:are\:equal,\:the\:asymptote\:is:}\:y=\frac{\mathrm{numerator's\:leading\:coefficient}}{\mathrm{denominator's\:leading\:coefficient}}[/tex][tex]\mathrm{Numerator's\:leading\:coefficient}=1,\:\mathrm{Denominator's\:leading\:coefficient}=1[/tex][tex]y=\frac{1}{1}[/tex][tex]\mathrm{The\:horizontal\:asymptote\:is:}[/tex][tex]y=1[/tex]In conclusion:
[tex]\mathrm{Vertical}\text{ asymptotes}:\:x=-5,\:\mathrm{Horizontal}\text{ asymptotes}:\:y=1[/tex]Select the correct answer.
Eric traveled to two cities on a single highway. The total distance one way was 200 miles. The distance from his original location to the first city was 40
miles less than the distance from the first city to the second city. Suppose that x represents the distance from the original location to the first city and y
represents the distance from the first city to the second city. The following system of equations represents the given situation
x + y = 200
x = y - 40
Which pair of coordinates represents the solution (in miles) to this system of equations?
O A.
(70, 130)
(80, 120)
(160, 120)
(100, 100)
B.
O c.
D.
E. (140, 60)
Answers
In linear equation, The solution to this system is (80, 120)
What is a linear equation example?
Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5.Finding both intercepts of an equation in this format is rather simple (x and y).The following system of equations represents the given situation
x + y = 200
x = y - 40; substituting x from this equation to the first:
y - 40 + y = 200
2y = 240
y = 120
Corresponding value of x:
x = 120 - 40
x = 80
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-21x + 3 (-x-4) - 8x
Answers
Answer:
Step-by-step explanation:
-21x + 3(-x-4) -8x =
-21x -3x -12 - 8x=
-32x -12=
-32x = 12
X= -3/8
Julia works for a company selling light bulbs. She sells fluorescent light bulbs for $5 a piece and incandescent light bulbs for $2. To meet her quota, she needs to sell over 100 light bulbs and make at least $350.If the solution region is the amount of light bulbs Julia needs to sell to meet her quota, which graph's shaded area represents the solution region?
Answers
Given:
Julia works for a company selling light bulbs. She sells fluorescent light bulbs for $5 a piece and incandescent light bulbs for $2.
Let the number of the fluorescent light bulbs = y
And the number of the incandescent light bulbs = x
To meet her quota, she needs to sell over 100 light bulbs and make at least $350.
So, we can write the following system of inequalities:
[tex]\begin{gathered} x+y>100 \\ 2x+5y\ge350 \end{gathered}[/tex]Now, we will graph the system of the inequalities to find the area of the solution
The graph will be as follows:
So, the answer will be the graph that is on the upper right-side.
Graph x
where can I find L1 and L4 ? for missing alternate angles
Answers
< 1 = 113.1 degrees
< 4 = 66.9 degrees
Explanation:Alternate interior angles are equal
< 1 = < 3 = 113.1 degrees
< 2 = < 4 = 66.9 degrees
I just need to answer I'm trying to verify question
Answers
You have the following system of equations:
x + 3y = 1
y = 2x + 5
in order to solve the previous system, replace the expression y = 2x + 5, into the first equation and solve for x, as follow:
x + 3y = 1
x + 3(2x + 5) = 1 apply distribution property
x + 6x + 15 = 1 simplify lef side
7x + 15 = 1 subtrac 15 both sides
7x = 1 - 15
7x = -14 divide by 2 both sides
x = -14/2
x = -7
replace the previous value of x into the second equation to get y:
y = 2x + 5
y = 2(-7) + 5
y = -14 + 5
y = -9
Hence, the solution to the given system of equations is:
x = -7
y = -9
(-7 , -9)
Don Williams wised his small motorboat to go 5 miles upstream to his favorite fishing spot. Against the current, the trip takes 5/6 hour. With the current the trip takes 1/2 hour. How fast can the boat travel in still water ? What is the speed of the current in still water the boat speed is __ mph. The speed of the current is ___ mph
Answers
let s = speed in still water
let c = rate of the current
then
(s-c) = effective speed up-stream
and
(s+c) = effective speed down-stream
Write a distance equation for each way; dist = time * speed
5/6*(s-c) = 5
1/2 *(s+c) = 5
Now we get rid of the fractions
5(s-c)=30
s + c = 10
5s - 5c = 30
s + c = 10
siplifying:
s - c = 6 (1)
s + c = 10 (2)
adding:
2s = 16, then s = 8
8 mph is the boat speed in still water
According with (2):
8 + c = 10, then c = 2
2 mph is the speed of the current
Factor the trinomial completely.3x2 - 13x - 10
Answers
3x2 - 13x - 10
multiplying the first and third terms we have
-30x2
The factors of -30 that will be added to get - 13 are -15 and 2
so we split the expression further
= 3x2 - 15x + 2x - 10
= 3x (x - 5) + 2 (x - 5)
= (x -5)(3x + 2)
Javier biked 4 miles on Tuesday, 2 miles on Wednesday , and 7 miles on Saturday . if he hopes to bikes a total of 30 miles for the week , how many miles should Javier bike on Sunday
Answers
Answer:
Step-by-step explanation:
4 miles plus 2 miles equals 6 miles, then you add 7 miles to the 6 which equals 13, lastly you minus 13 from 30 then you get your answer, which is 17.
which of the following could be the distant of Allyson's map
Answers
The real distance from Mumbai to Bangalore is 845 km.
The real distance from Mumbai to Dehli is 1160 km.
Allyson has made a map in which distance is in cm and is proportional to the real distance.
Since the real distance and the distance on the map are proportional then their ratio must be equal.
Let us compare the ratio of real distance with the distance in given options.
Option A:
Bangalore to Mumbai = 116.5 cm
Mumbai to Dehli = 174 cm
[tex]\begin{gathered} \frac{845}{1160}=\frac{116.5}{174} \\ 0.728\ne0.669 \end{gathered}[/tex]As you can see, the ratio is not equal so this is wrong.
Option B:
Bangalore to Mumbai = 42.25 cm
Mumbai to Dehli = 58 cm
[tex]\begin{gathered} \frac{845}{1160}=\frac{42.25}{58} \\ 0.728=0.728 \end{gathered}[/tex]As you can see, the ratio is equal so this is correct.
Option C:
Bangalore to Mumbai = 23.4 cm
Mumbai to Dehli = 29 cm
[tex]\begin{gathered} \frac{845}{1160}=\frac{23.4}{29} \\ 0.728\ne0.807 \end{gathered}[/tex]As you can see, the ratio is not equal so this is wrong.
Option D:
Bangalore to Mumbai = 16.9 cm
Mumbai to Dehli = 23.2 cm
[tex]\begin{gathered} \frac{845}{1160}=\frac{16.9}{23.2} \\ 0.728=0.728 \end{gathered}[/tex]As you can see, the ratio is equal so this is correct.
Option E:
Bangalore to Mumbai = 25.35 cm
Mumbai to Dehli = 34.8 cm
[tex]\begin{gathered} \frac{845}{1160}=\frac{25.35}{34.8} \\ 0.728=0.728 \end{gathered}[/tex]As you can see, the ratio is equal so this is correct.
Therefore, the following can be the possible distances on Allyson's map
Option B
Option D
Option E
#11 i
Solve 7w-9=13 - 4w.
W =
Answers
Answer:
w=2
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
7w−9=13−4w
7w+−9=13+−4w
7w−9=−4w+13
Step 2: Add 4w to both sides.
7w−9+4w=−4w+13+4w
11w−9=13
Step 3: Add 9 to both sides.
11w−9+9=13+9
11w=22
Step 4: Divide both sides by 11.
11w/11=22/11
w=2
Salma runs 6 miles in 55 minutes. At the same rate, how many miles would she run in 44 minutes?
Answers
Answer:
The number of miles she would run in 44 minutes is;
[tex]4.8\text{ miles}[/tex]Explanation:
Given that;
Salma runs 6 miles in 55 minutes;
The rate at which she run is;
[tex]\text{rate =}\frac{\text{ distance}}{\text{time}}=\frac{6}{55}miles\text{ per minute}[/tex]At the same rate, the distance it will cover in 44 minutes is;
[tex]\begin{gathered} \text{time}=\frac{\text{distance}}{\text{rate}} \\ \text{distance}=\text{time}\times rate \\ \text{distance}=44\times\frac{6}{55} \\ \text{distance = 4.8 miles} \end{gathered}[/tex]The number of miles she would run in 44 minutes is;
[tex]4.8\text{ miles}[/tex]4. A garden sells flowers in trays. Each tray has 11 flowers on it. If the garden sells 124 trays, how many flowers did the garden sell in all?
Answers
A garden sells flowers in trays
each tray has 11 flowers on it
mathematically,
1 tray = 11 flowers
if the garden now sells 124 trays, then how many flowers do we have
1 tray = 11 flowers
124 trays = x flowers
cross multiplication
x * 1 = 124 x 11
x = 1364 flowers
,the answer is 1364 flowers 11 flowers
if the garden now sells 124 trays, then how many flowe