The sum of the angles in a hexagon is 720°.
a. Write an equation that can be used to determine the value of x.
b. Solve your equation algebraically
c. Determine the measure of angle c.
Answers
Given:
The sum of the angles in a hexagon is 720°.
[tex]m\angle A=90^\circ,m\angle B=126.87^\circ,m\angle C=(3x)^\circ,m\angle D=90^\circ, m\angle E=143.13^\circ, m\angle F=143.13^\circ.[/tex]
To find:
(a) Equation to solve the value of x.
(b) The value of x.
(c) The measure of angle C.
Solution:
(a)
We have,
[tex]m\angle A=90^\circ,m\angle B=126.87^\circ,m\angle C=(3x)^\circ,m\angle D=90^\circ, m\angle E=143.13^\circ, m\angle F=143.13^\circ.[/tex]
The sum of the angles in a hexagon is 720°.
[tex]m\angle A+m\angle B+m\angle C+m\angle D+m\angle E+m\angle F =270^\circ[/tex]
[tex]90^\circ+126.87^\circ+(3x)^\circ+90^\circ+143.13^\circ+143.13^\circ =270^\circ[/tex]
[tex]90+126.87+(3x)+90+143.13+143.13 =720[/tex]
Therefore, the required equation is [tex]90+126.87+(3x)+90+143.13+143.13 =720[/tex].
(b)
On solving the above equation, we get
[tex]593.13+3x =720[/tex]
[tex]3x =720-593.13[/tex]
[tex]3x =126.87[/tex]
Divide both sides by 3.
[tex]x =\dfrac{126.87}{3}[/tex]
[tex]x =42.29[/tex]
Therefore, the value of x is 42.29.
(c)
We need to find the measure of angle C.
[tex]m\angle C=(3x)^\circ[/tex]
[tex]m\angle C=(3\times 42.29)^\circ[/tex]
[tex]m\angle C=126.87^\circ[/tex]
Therefore, the measure of angle C is 126.87 degrees.
Related Questions
Laura used 12 1/2 square feet of cloth to make 3 dresses. How many square feet of cloth are required to make 12 similar dresses?
Answers
Answer:
50 sq ft
Step-by-step explanation:
12.5 sq ft is used to make 3 dresses. Laura will repeat this 4 times since she is making 12 dresses (3x4=12). So, 12.5 x 4 = 50
Therefore, the answer is 50 sq ft.
Hope it help! Don't forget to give me Brainliest!!
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what is 6/10 in simplist form
Answers
Answer:
3/5
Step-by-step explanation:
both 6 and 10 divide by 2. divide each number by 2 and you get 3/5
Answer:
3/5
Step-by-step explanation:
To find the simplest form of 6/10, you must reduce the fraction.
I did this by dividing both the numerator and denominator by 2, therefore making it 3/5, (because it cannot be reduced evenly anymore).
Hope this helps :)
What is the value of
NICO
?
81
16
16
81
16
81
81
16
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Sasha is filling a rectangular box with ribbon and wants to know the amount of space in the box. A prism has a length of 12 inches, height of 3 inches, and width of 4 inches. Which statement is true about the amount of space inside the box? The space inside the box is the surface area, which is 192 in.2. The space inside the box is the surface area, which is 144 in.2. The space inside the box is the volume, which is 192 in.3. The space inside the box is the volume, which is 144 in.3.
Answers
Answer:
82
Step-by-step explanation:
Answer:
The answer is D) The space inside the box is the volume, which is 144 in.3.
Step-by-step explanation:
plot the numbers -1.5,3/2,-3/2,-4/3 on the number line. label each point with its numeric value.
Answers
Answer:
so 3%5+=67K and 9+=-8 is -1
Step-by-step explanation:
solve the equation (2y-6)(y+3)=0
Answers
Answers :
y = 3
Step-by-step explanation:
Mary invests $1.200 in an account that earns 6% annual interest, compounded continuously. What is the value of the account after 7 years? Round your answer to the nearest dollar
Answers
Answer:
$1,826
Step-by-step explanation:
Given that
The amount invested is $1,200
The annual rate of interest is 6%
And, the time period is 7
We need to find the value of the account after 7 years in the case of compounded continuously
We know that for compounded continuously, the following formula should be used
= Amount invested ×e^(rate, time)
= $1,200 × e^(0.06 ×7)
= $1,200 × e^0.42
= $1,826
Iliana was part of a group that was working on changing 0.ModifyingAbove 4 with bar to a fraction. Each member of the group had a different answer. Which answer is correct?
Answers
Answer:
4 /9
Step-by-step explanation:
All we have to do is evaluate the options in other to compare the result :
4 / 10 = 0.4
4 / 9 = 0.4444444...
9/ 4 = 2.25
I need someone to do a whole semesters worth of work for 7 classes
Answers
Answer:
same
Step-by-step explanation:
we are screwed
ahhh
PLEASE HELP IT'S DUE TODAY-
The Toblerone company packages chocolate candy in a container that is a triangular prism. The base is an equilateral triangle and each side of the triangle is 60 mm. The height of the triangular prism is 405 mm.
1) What is the total surface area of this triangular prism? Show all work and give answers to 2 decimal places
2) What is the volume of this triangular prism? Show all work and give answers to 2 decimal places
3) If the chocolate inside the package is 335954.96 mm3, how much empty volume/space is inside the container? Show all work and give answers to 2 decimal places
Bonus Question: What percentage of the container is empty space? Show all work and give answers to 2 decimal places.
Answers
Answer:
1. 76017.69 mm^2 or 76.02 m^2
2. 631332.52 mm^3 or 631.33 m^3
Step-by-step explanation:
1. The equation for the surface area of an equilateral trianglula prism is
2 * ( ( sqrt(3) / 4 ) * s^2) + 3( h * s )
2 * ( ( sqrt(3) / 4 ) * 60^2) + 3( 405 * 60 )
76017.69 mm^2 or 76.02 m^2
2. The equation for the volume of an equilateral trianglula prism is
( sqrt(3) / 4 ) * s^2 * h
( sqrt(3) / 4 ) * 60^2 *405
631332.52 mm^3 or 631.33 m^3
20 POINTS! The managers of an automotive insurance company investigated whether the customers in region A have a higher proportion of speeding tickets than the customers in region B. The managers selected 154
customers from region A at random and found that 79 have had a speeding ticket. The managers also selected 148 customers from region B and found that 67
have had a speeding ticket.
To test whether the results could be explained by random chance, the managers simulated 1,000 rerandomizations of the data and then subtracted the sample proportion of region B from the sample proportion of region A in each of the simulations. The table shows the results of the differences.
SEE PICTURES BEFORE ANSWERING
Answers
Answer:
Every year, a pet food company sells its food to stores across the nation. ... In the first month of the new year, the Midwest region secured sales orders from ... Suppose the strategy of the pet food company is to increase the proportion of ... Do you think additional field training is necessary for all of the sales representatives?
Step-by-step explanation:
(b) Beth multiplies a number by 3 and divides the answer by 10.
By what fraction has the number been reduced?
(b)
[2]
Answers
Answer:
3/10
Step-by-step explanation:
Multiplies:
x*3
divides
x*3
10
The number is reduced by a fraction 3/10
FractionsFractions are expressed in the form a/b where a and b are integers;
Let the unknown number be "x"
If Beth multiplies a number by 3, the resulting expression will be 3xIf the result is divided by 10, the final expression will be 3x/10From the final expression, you can see that the coefficient of the unknown variable x is 3/10. Hence the number is reduced by a fraction 3/10
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I need help with the answer
Answers
Answer:
30
Step-by-step explanation:
A=b*h*1/2
b=10
h=6
10*6*1/2=30
4+4x+x^2 = y Given x = 3
Answers
Answer:
y=25
Step-by-step explanation:
y=4+4x+x^2
x=3
y=4+4(3)+(3)^2
y=4+12+(3)^2
y=4+12+(3x3)
y=4+12+(9)
y=16+9
y=25
If this helps please mark as brainliest
Please do all four, thanks :)
I'm feeling generous today *40 points*
Answers
Step-by-step explanation:
A. x^2-9x+18
B. x^2-8x+16
C. 2x^2-5x-12
D. 12x^2-31x+7
A tower has a cone-shaped attic. The diameter of the attic is 10 ft and its height is 6 ft.
The volume of the space in the attic is approximately___ cubic feet.
Use 3.14 for pi.
Answers
Answer:
Step-by-step explanation:
radius r=10/2=5 ft
h=6 ft.
volume of cone=1/3 πr²h=1/3×3.14×5²×6=157 cubic ft.
How long will it take $10,000 to grow to $200,000 if it is invested at 7.5% compounded continuously?
Answers
Answer:
40 Years he will have $200,793.48
Step-by-step explanation:
What is the simplified form of StartRoot 10,000 x Superscript 64 Baseline EndRoot ?
5000x Superscript 32
5000x Superscript 8
100x Superscript 8
100x Superscript 32
Answers
Answer:
5000x^8
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Determine the rational roots of 2x 5 - 11x 4 + 14x 3 - 2x 2 + 12x + 9 = 0.
1/2
1
3/2
3
9/2
9
-1/2
-1
-3/2
-3
-9/2
-9
Answers
Answer:
i would show you how i got it but unfortunately it's too much work. but the answers are
x = -1/2, 3, ±i
Step-by-step explanation:
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The diameter of this circular cutting board is 16 inches.
What is the area of the cutting board in terms of pi?
A. 32 square inches
B. 64 square inches
C. 256 square inches
D. 16 square inches
Answers
Answer:
B. 64 square inches
Step-by-step explanation:
you just add
Answer:
Step-by-step explanation:
4
When AB=3x+8 and GJ=2x+24 what is AB?
Answers
Answer:
AB= GJ ➗2
2x+24➗2= x+12
i'm not sure
Imagine the bike shop sells bike rentals for a local bike tour. The tour costs $50 for equipment plus $7.50 per hour. Explain how you could find the total cost of a 5-hour bike tour.
Answers
Answer:87.5
Step-by-step explanation: I can find the total cost of a 5 hire bike tour because I'm given the unit rate and the amount of time to multiply it by.
The total cost of the five hours bike tour is $87.50
Cost of equipment = $50
Cost per hour = $7.50 per hour
The total cost of the equipment for five hours will be the addition of the fixed cost and the variable cost. This will be:
= $50 + $7.50h
where, h = number of hours = 5 hours
Total cost = $50 + $7.50(h)
= $50 + $7.50(5)
= $50 + $37.50
= $87.50
The total cost of the five hours bike tour is $87.50
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A chess club with 80 members is electing a new president. Ryan received 12 votes. What percentage of the club members voted for Ryan
Answers
Answer:
15%
Step-by-step explanation:
A chess club with 80 members is electing a new president. Ryan received 12 votes.
12 votes = 12 Members
The percentage of the club members that voted for Ryan is calculated as:
12 members/ 80 members × 100
= 15%
Therefore, 15% of the club members voted for Ryan
Help please!! If right I will mark the brainliest!!!!
Answers
Answer:
[tex] \frac{1}{3} h = a \\ a = 10cm[/tex]
What is the mean amount raised by the students?
Answers
Step-by-step explanation:
[tex]mean = \frac{(25.25 + 17.50 + 4.75 + 45.00 + 33.50 + 11.70 + 23.80 + 38.00 + 17.75 + 14.25)}{10} \\ = 23.15[/tex]
what is 9+m=1.5
i need the answer for m
Answers
Answer:
m = - 7.5
Step-by-step explanation:
Given
9 + m = 1.5 ( subtract 9 from both sides )
m = - 7.5
hey! please help i’ll give brainliest
Answers
Answer:
-ing
Step-by-step explanation:
The only example I can give is: trying to be. -ing "to be" makes the statement a continuous present tense.
Hope this helps :)
Each of these equations represents the same function written in different forms.
Standard Form: f(x)=x2−2x−8
Factored Form: f(x)=(x+2)(x−4)
Vertex Form: f(x)=(x−1)2−9
The zeros of a function are the values of x for which the function is equal to zero. Which form of the equation makes it easiest to see the zeros of the function?
Answers
Answer: f(x)=(x+2)(x−4) because you can see when each factor is equal to zero.
Step-by-step explanation:
The form of the equation that makes it easiest to see the zeros of the function is (b) Factored Form: f(x)=(x+2)(x−4)
How to determine the true statement?When an equation has been factored, the zeros of the equation can be determined by equation the function to 0.
This means that we simply equate the factored form of the equation to 0.
Hence, the form of the equation that makes it easiest to see the zeros of the function is (b) Factored Form
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PLEASE HELP DUE IN A FEW MINUTES TOO(FOR THE PERSON THIS IS MEANT FOR INSTEAD OF 66 YOU WILL GET 67)
Evaluate these two following angle
Answers
Answer:
..
Step-by-step explanation:
for the first one is 40 and d and f are 140
for the second one g is 155 and h is 180
Answer:
Hello!
1st problem: e = 40 d = 140 f = 140
Each of these will add up to 360 degrees so what I did was find the measurements that would accurately add up and thats how i got my answers
2nd problem: g = 155 h = 180
What is the value of i^20+1?
a. 1
b. -1
c. -i
d. i
Answers
Answer:
i
Step-by-step explanation:
The powers of i repeat in cycle of 4. For example, here are the first 4:
1: i
2: -1
3: -i
4: 1
If a number is divisible by 4, i to the power of that number would be 1. So, i^20 is 1, but we are multiplying it by i again, so the answer would be 1 * i = i
Answer: I
Step-by-step explanation: