ABCDE is a regular pentagon. Find each lettered angle measure.

ABCDE Is A Regular Pentagon. Find Each Lettered Angle Measure.

Answers

Answer 1

Answer:

x° = 36°, y° = 36°, z° = 72°

Step-by-step explanation:

Each interior angle of a regular polygon is given by the following formula;

Interior angle = (n - 2)×180°/n

Where;

n = The number of sides on the polygon

For the pentagon, we have;

n = 5, therefore;

Interior angle = (5 - 2)×180°/5 = 108°

ΔDCA is an isosceles triangle, with the segments CD and CA being equal, therefore;

∠ADC = ∠DAC = x°, and ∠ACD = 108°

Therefore

x° = (180° - 108°)/2 = 36°

x° = 36°

∠BAC = 2·x° + y° = 108°

∴ y° = 108° - 2·x° = 108° - 2 × 36° = 36°

y° = 36°

ΔADE is an isosceles triangle, with segments AD and AE equal, therefore, the base angles are z° each

Therefore, in ΔADE, we have;

z° = (180° - 36°)/2 = 72°

z° = 72°


Related Questions

4. If 100.0g of nitrogen gas (N2) is reacted with 100.0g of hydrogen gas (H2) to form NH3. What are the limiting and excess reactants?

Hint: Convert grams to moles for each reactant and then convert to moles of NH3. You need your balanced equation from answer 1 to determine the mole relationship between each reactant and the product NH3. Use the periodic table to determine the molar mass of all chemical formulas. Fill in the “?” blanks below to show your work.

Balanced equation: 1N2 (g) + 3H2(g)  2NH3(g)

Molar mass of H2 = g/mol

100.0"g " "H" _2×(1"mol " "H" _2)/( ? "g " "H" _2 )×(" ? mol N" "H" _3)/(" ? mol " "H" _2 )= ? "mol N" "H" _3

Molar Mass of N2 = g/mol

100.0"g " "N" _2×(1"mol " "N" _2)/(" ? g " "N" _2 )×(" ? mole N" "H" _3)/(" ? mol " "N" _2 )= ? "mol N" "H" _3

A. What is the excess reactant? Hint: it is the reactant above that makes the most amount of product

B. What is the limiting reactant? Hint: it is the reactant above that makes the least amount of product

C. What is the theoretical yield of ammonia of the reaction?
Molar mass of NH3 = g/mol

100.0"g " "N" _2×(1"mol " "N" _2)/( ? "g " "N" _2 )×( ? "mol N" "H" _3)/( ? "mol " "N" _2 )×(" ? g N" "H" _3)/( 1 "mol N" "H" _3 )= ? "g N" "H" _3

Answers

Nitrogen (N) has a molar mass of about 14.007 g/mol, so you have

100.0 g N₂ = (100.0 g) • (1/28.014 mol/g) ≈ 3.570 mol N₂

Hydrogen (H) has a molar mass of about 1.008 g/mol, so

100.0 g H₂ = (100.0 g) • (1/2.016 mol/g) ≈ 49.60 mol H₂

In the balanced reaction, 1 mole of N₂ reacts with 3 moles of H₂ to make 2 moles of NH₃. We have

3.570 • 3 ≈ 10.71

so the reaction would use up all 3.570 mol N₂ and 10.71 mol H₂ to produce about 7.139 mol NH₃.

(A) H₂ is the excess reactant. There is an excess of 49.60 - 10.71 ≈ 38.89 mol H₂.

(B) N₂ is the limiting reactant. All of the N₂ gets consumed in the reaction.

(C) NH₃ has a molar mass of (14.007 + 3 • 1.008) g/mol = 17.031 g/mol. This reaction would theoretically yield about 7.139 mol NH₃, or

7.139 mol NH₃ = (7.139 mol) • (17.031 g/mol) ≈ 121.6 g NH₃

Simplify.
12 + 15 : 3x6 - 4

Answers

Answer:

Step-by-step explanation:

Divide the numbers

12+153⋅6−412+153⋅x6−412+315​⋅x6−412+56−412+5x6−4 12+5x6−4

Samantha invested $670 in an account paying an interest rate of 5.5% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $1,740?

Answers

Answer:

  17 years

Step-by-step explanation:

The formula for the value of an account earning compound interest can be used to find the number of years. That formula is ...

  A = P(1 +r/n)^(nt)

where P is the principal invested at annual rate r compounded n times per year for t years.

__

Solving for t, we find ...

  A/P = (1 +r/n)^(nt) . . . . . . divide by P

  log(A/P) = nt·log(1 +r/n) . . . . take logarithms

  t = log(A/P)/(n·log(1 +r/n)) . . . . . divide by the coefficient of t

For the given values, the time required is ...

  t = log(1740/670)/(365·log(1 +0.055/365)) ≈ 17.353

It would take about 17 years for the account value to reach $1740.

_____

Additional comment

The time-value-of-money (TVM) apps of your calculator or spreadsheet can be used to find the time period of interest. Here, setting P/Y = 1 gives N in years.

Lacey is buying a new car. She can get a station wagon, a truck, a hatchback, or a convertible. The outside paint comes in yellow or green. The seats can be covered with white leather or gray fabric. Given these choices, how many different combinations does Lacey have to choose from?

Answers

Step-by-step explanation:

4 different vehicles,

2 different paints,

2 different seats.

Total number of combinations = 4 * 2 * 2 = 16.

Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
\begin{cases} y=-7x+3 \\\\ y=-x-3 \end{cases}









y=−7x+3
y=−x−3

Answers

Answer:

(1,-4)

Step-by-step explanation:

Given:

y = −7x+3

y = −x−3

Computation:

y = −7x+3......eq1

y = −x−3.......eq2

Eq 1 - 2

-6x + 6 = 0

x = 1

So,

y = −7x+3

y = −7(1)+3

y = -4

So,

(1,-4)

Need help geometric sequences see pic for details

Answers

Given:

The recursive formula of a geometric sequence is

[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]

[tex]a_1=-3[/tex]

To find:

The explicit formula of the given geometric sequence.

Solution:

We know that, first term of geometric sequence is [tex]a_1=-3[/tex].

Recursive formula of a geometric sequence is

[tex]a_n=a_{n-1}\times r[/tex]      ...(i)

where, r is common ratio.

We have,

[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]    ...(ii)

On comparing (i) and (ii), we get

[tex]r=\dfrac{1}{8}[/tex]

The explicit formula of a geometric sequence is

[tex]a_n=a_1r^{n-1}[/tex]

Putting [tex]a_1=-3[/tex] and [tex]r=\dfrac{1}{8}[/tex], we get

[tex]a_n=-3\left(\dfrac{1}{8}\right)^{n-1}[/tex]

Therefore, the correct option is D.

A cylindrical soup can has a radius of 8.4 cm and a height of 13.2 cm. What is the volume of the soup can to the nearest tenth of a cubic centimeter?
A= 110.9 cm3

B= 348.3 cm3

C= 673.8 cm3

D= 2926.1 cm3

Answers

Answer:

Option D: 2926.1 cm³

Step-by-step explanation:

Dimensions of the cylidrincal soup can are given as;

Radius; r = 8.4 cm

height; h = 13.2 cm

Formula for area of cylinder is;

A = πr²h

Plugging in the relevant values gives;

A = π × 8.4² × 13.2

A = 2926.05 cm³

Approximating to the nearest tenth gives;

A = 2926.1 cm³

how many men have a waist measurement of more than 85cm

Answers

Answer:

29

Step-by-step explanation:

The answer is 29 hope this helps you! :)

A car is traveling at a rate of 48 miles per hour. If the car continues to travel at this same rate, how many hours will it take the car to travel 612 miles?

Answers

Answer:

12.75

Step-by-step explanation:

If you make a proportion: 48/1=612/x

1(612)= 612

612/48

12.75 hours

At a speed of 48 miles per hour, the car will take approximately 12.75 hours to go 612 miles.

What is the distance?

A mathematical number known as distance measures "how much ground an object has traveled" while moving. Distance is defined as the product of speed and time.

A car is traveling at a rate of 48 miles per hour.

To determine the number of hours it will take the car to travel 612 miles at a rate of 48 miles per hour, you can divide the distance traveled by the rate at which the car is traveling:

⇒ distance ÷ rate

⇒ 612 miles / 48 miles/hour

Apply the division operation, and we get

⇒ 12.75 hours

Therefore, it will take the car about 12.75 hours to travel 612 miles at a rate of 48 miles per hour.

Learn more about the distance here:

brainly.com/question/13269893

#SPJ2

What is the sum of 2x-5y+x+y

Answers

Answer:

3x - 4y

Step-by-step explanation:

2x + -5y + x + y

Group Like terms:

2x + x + -5y + y

2x + x = 3x

-5y + y = -4y

3x - 4y

Count by 5’s starting with 99

Answers

104, 109, 114, 119, 124, 129, 134, 139, 144, 149

hehe

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

How many solutions does this equation have?
-3n = -4n + 7

Answers

Answer:

just one: 7 you isolate the numbers by doing -3n + 4n = 7, and u get n = 7

Answer:

2

Step-by-step explanation:

my soulstinos were Solution 1)

3

n

+

7

=

1

3

n

+

7

7

=

1

7

3

n

+

0

=

8

3

n

=

8

3

n

3

=

8

3

3

n

3

=

8

3

n

=

8

3

Solution 2)

3

n

+

7

=

1

3

n

+

7

7

=

1

7

3

n

+

0

=

6

3

n

=

6

3

n

3

=

6

3

3

n

3

=

2

n

=

2

The solution is:

n

=

8

3

and

n

=

2

(a)
Evaluate each of the following:
(i)
10! X 20!
17! X 9!


Answers

Answer:

[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]

[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]

Step-by-step explanation:

1)

Given the expression

[tex]10!\times \:20![/tex]

[tex]\mathrm{Apply\:factorial\:rule}:\quad \:n!=1\times 2\times 3\times \ldots \times \:n[/tex]

[tex]10!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10[/tex]

[tex]20!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:18\times \:19\times \:20[/tex]

Now, multiplying the result

[tex]10!\times \:20!= 1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:18\times \:19\times \:20[/tex]

so

[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]

Thus, we conclude that:

[tex]10!\:\times \:20!=\:8.82851\:\times\:10^{24}[/tex]

2)

Given the expression

[tex]17!\:\times \:9![/tex]

[tex]\mathrm{Apply\:factorial\:rule}:\quad \:n!=1\times 2\times 3\times \ldots \times \:n[/tex]

[tex]17!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17[/tex]

[tex]9!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9[/tex]

Now, multiplying the result

[tex]17!\:\times \:9!=1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9\times \:10\times \:11\times \:12\times \:13\times \:14\times \:15\times \:16\times \:17\times \:1\times \:2\times \:3\times \:4\times \:5\times \:6\times \:7\times \:8\times \:9[/tex]

so

[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]

Thus, we conclude that:

[tex]17!\:\times \:9!\:=\:1.29072\:\times \:10^{20}[/tex]

Mr. and Mrs. Brown went to two movies. The first one lasted 3 1/2 hours and the second one lasted 1 1/3 hours . How much longer was the first than the second movie?

Answers

Answer:

2 1/6 longer

Step-by-step explanation:

3 1/2-1 1/3

7/2 - 4/3

21/6-8/6

13/6 or 2 1/6

so 2 1/6 longer.

Hope this helps :D

Answer:

2 1/6 hours longer

Step-by-step explanation:

Hope the helps!

BRAINLIST AND MANY OTHERS THINGS

Kyle's home is located at point (0 , 0). Kyle travels up for 5 miles, right for 6 miles, down for 10 miles, left for 6 miles, and finally up again for 5 miles. What is Kyle's new location?

Answers

Answer:

1, 0

Step-by-step explanation:

Just go on a chart graph and do what it asks and you get that.

What is the value of the expression below when x=5?

Answers

Answer:

790

Step-by-step explanation:

You put 5 instead of x and you calculat

6*5^3 +8*5= 750+40=790

The answer should be 790

In ΔDEF, if DE ≅ DF and EF is the hypotenuse, then ΔDEF is
a acute and scalene. c. right and isosceles.
b right and scalene. d. obtuse and isosceles.

Answers

Answer:

C. Right and isosceles

Explanation:

Since two sides of the triangle are equal in length ([tex]DE[/tex] and [tex]DF[/tex]), this means that the triangle is an isosceles triangle. Since [tex]EF[/tex] is the hypotenuse of this triangle, it also means that the triangle is a right-angle triangle (the hypotenuse refers to the longest side of a right triangle). Therefore, we can conclude that ΔDEF is right and isosceles.

Hope this helps :)

Answer:

It is C.

Step-by-step explanation:

Hope this helped have an amazing day!

Which value is equivalent to the expression 4^5

Answers

Answer:

20

Step-by-step explanation:

Solve the following equations | 3x + 3/7 | = 2 1/3

Answers

Answer:

X∈[tex]\frac{5}{63}, -\frac{23}{63}[/tex]

Step-by-step explanation:

HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.

Stats question, I'm really stck please help me!

Answers

Answer:

The 99% confidence interval is   [tex] 165.776  <  \mu <  180.224  [/tex]  

Step-by-step explanation:

From the question we are told that

     The sample size is  n  = 100

     The sample mean is  [tex]\= x = 173 \ days[/tex]

      The population standard deviation is  [tex]\sigma = 28 \ days[/tex]  

From the question we are told the confidence level is  99% , hence the level of significance is    

      [tex]\alpha = (100 - 99 ) \%[/tex]

=>   [tex]\alpha = 0.01[/tex]

Generally from the normal distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] is  

   [tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = Z_{\frac{\alpha }{2} } *  \frac{\sigma }{\sqrt{n} }[/tex]

      [tex]E = 2.58  *  \frac{28 }{\sqrt{100} }[/tex]

=>    [tex]E = 7.224 [/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x -E <  \mu <  \=x  +E[/tex]

=>     [tex] 173 -7.224  <  \mu < 173 + 7.224  [/tex]    

=>     [tex] 165.776  <  \mu < 180.224  [/tex]  

     

Which expressions are equivalent to 6a(5+d) ?

Select each correct answer.


30a+6ad

30ad

30a+(6a⋅d)

(6a⋅5)+(6a⋅d)

11a + d

Answers

Answer: A is correct i think

Step-by-step explanation:  6a x 5 = 30a

                                              6a x d = 6ad

Answer:

A

Step-by-step explanation:

Solve for u .

-24 = u ÷ 6

u =

Answers

Answer:

[tex]u = - 144[/tex]

Step-by-step explanation:

[tex] - 24 = u \div 6[/tex]

[tex] - 24 \times 6 = u[/tex]

[tex] - 144 = u[/tex]

to be sure

[tex] - 24 { = }^{?} - 144÷6[/tex]

[tex] - 24 = - 24[/tex]

Answer:

u = -144

Step-by-step explanation:

-24 = u ÷ 6

Multiply both side by 6.

-24 × 6 = u ÷ 6 × 6

-144 = u

Verification:-

-24 = -144 ÷ 6

-24 = -24

LHS = RHS

what is the final position of (-7) + (-2) on a number line ?

Answers

Answer:

answer is A, source: a calculator

Step-by-step explanation:

if you are adding two negitives, take the signs away and add normal, then add the sign back at the end, ONLY WORKS WITH TWO NEGITIVES AND HAS TO BE ADDITION

Answer:

Step-by-step explanation:

It’s 9 because you make 7 and 2 a positive number

Y’all know this anything about this?

Answers

We are given:

Parallelogram CDEF∠C = 13x - 10∠D = 5x + 10

To Find: ∠E

Concept Used:

Adjacent angles of a Parallelogram are Supplementary

Finding the value of 'x':

Since adjacent angles of a parallelogram are Supplementary:

∠D + ∠C = 180

5x + 10 + 13x - 10 = 180              [replacing the values of angle C and D]

18x = 180

x = 10                                          [dividing both sides by 18]

__________________________________________________________

Finding Measure of Angle D:

We are given that:

∠D = 5x + 10

∠D = 5(10) + 10                    [since x = 10]

∠D = 60°

__________________________________________________________

Finding the measure of ∠E:

∠D and ∠E are Adjacent angles

Since Adjacent angles are Supplementary:

∠D + ∠E = 180

60 + ∠E = 180

∠E = 120°                                  [subtracting 60 from both sides]

Hence, the measure of ∠E = 120°

Evaluate -5-15+4+15−5−15+4+15minus, 5, minus, 15, plus, 4, plus, 15.

Answers

Answer:

-2

Step-by-step explanation:

ur welcome

-1

Step-By step Explanation:

Please please please hellllllppp meeeeee !!!!!!!!!

Answers

ANSWER: 77
Explanation: Making 88 in 8 minutes means that the machine is making 11 per minute thus being said if the machine worked for 7 minutes it would make 77 pens.
88/8=11
11*7=77

good monke good monke dog

Answers

Answer:

very inspirational thanks

Step-by-step explanation:

Answer:

monke

Step-by-step explanation:

Write the data from greatest to least: 0.8, 0.79, 0.08, 0.81, 0.09, 0.9, 0.89

Answers

Answer:

0.9, 0.89, 0.81, 0.8, 0.79, 0.09, 0.08

Step-by-step explanation:

Answer: 0.09 , 0.89 , 0.81, 0.08, 0.79 , 0.9, 0.8

Step-by-step explanation:

First find the greatest

0.09, 0.89,0.81, 0.08, 0,79

Then the least

0.9 .0.8

Now put it all together  

0.09, 0.89. 0.81 , 0.08, 0.79 , 0.9, and lastly 0.8

Ellen already knew 50 appetizer recipes before starting culinary school, and she will learn 4 new appetizer recipes during each week of school. After 73 weeks of culinary school, how many total appetizer recipes will Ellen know? Write and solve an equation to find the answer.

Answers

Answer:

342

Step-by-step explanation:

50+4x=y

x=73

Which point on the number line could represent-25? А вс D 54 -3 -2 -1 0 1 2 3 4 5 А OB ОС OD. I will mark 1 answer brainlist ​

Answers

Answer:

B

Step-by-step explanation:

The number, -2¼, if it is to be represented on a directed line, would be about -2¼ places below point zero.

Therefore, the point that would represent -2¼ on a number line is B, as shown in the diagram.

Other Questions
James calculated the height of a cylinder that has a volume of 324 pi cubic inches and a radius of 12 inches. His work is shown below. V = B h Step 1: 324 pi = pi 12 squared h Step 2: 324 pi = 24 pi h Step 3: StartFraction 324 pi over 24 pi EndFraction = StartFraction 24 pi over 24 pi EndFraction h Step 4: h = 13.5 pi inches What is the first error that James made when calculating the height of the cylinder? In step 1, he substituted into the volume formula incorrectly. In step 2, he calculated 12 squared incorrectly. It should be 144 rather than 24. In step 4, the Pi should have canceled, making the correct answer 13.5 cm. James calculated the height of the cylinder correctly. QUICK HELP!!!____ living cells can be the trigger for cancers.What is the missing word in this sentence? What is the value of the expression below when x=5? Who made the better argument Lincoln or Douglas ? Explain why Please help me with this What is the sum of 2x-5y+x+y What else is produced when sodium carbonate decomposes?Na2Co3 - Na2O+ One codon has the instructions to make Which of these are an atom's valence electrons? Mr. and Mrs. Brown went to two movies. The first one lasted 3 1/2 hours and the second one lasted 1 1/3 hours . How much longer was the first than the second movie? One of the main problems with the reservation system was that government agents How much is 2% of 3.50 Solve the following equations | 3x + 3/7 | = 2 1/3 The amount of force that muscles can aply to move a heavy object is known as: A. Explosive strength B. Dynamic strength C. power D. static strength WHOEVER ANSWERS IT CORRECT ILL GIVE 100 POINTS TO What is Migration?D. The Lifecycle of a Butterfly E. Another name for Butterfly LarvaeF. The Seasonal Movement from one region to Another*I want Nice people that can Answer this question, not People that are rude* Which best describes a connection between these two text? A both looks ways that manufacturing could be improved in the south. B none of these presents a connection that could be made between these particular techs. See both speak of the need for the south to improve its condition by including all people. Need both look at ways of improving race relationships in the south in the wake of the Civil War Expand the expression 2(y + 5x) What is the current structure of Local Government in Ghana? Okay, Daily Question!My friend is telling her crush she likes him and she wanted me to come up with a ship-name? I made some suggestions but she didn't like any of them and she gave me a deadline of 3:00 to give her a 'good' one. Here are the names:Nate/Nathan + Addy/AddisonHave any ideas? Express 0.495 in standard form