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Draw any two convex pentagons. For each of them measure the sum of its interior angles using a protractor. Explain the result of the measuring.
In a convex polygon, all interior angles are less than or equal to 180. So pentagons are polygons of five sides. We need to draw two different pentagons with the previous characteristics and measures of the internal angles. Therefore, we will choose to type of pentagons.
Every pentagon can be divided up into three triangles, either a regular or irregular one and each triangle adds up to 180 degrees. Therefore, the angles in every pentagon must add up to 540 degrees.
1. Drawing of the first convex pentagon (Regular Pentagon).
A polygon is regular when all angles are equal and all sides are equal. The regular pentagon is a 5-sided polygon. This is shown in Figure 1. Note that all angles are equal to 108°.
1.1. Sum of the interior angles of the first convex pentagon.
According to Figure 1, the sum of its interior angles is as follows:
[tex]\alpha=5 \times 108^{\circ}=540^{\circ}[/tex]
As we said, the angles in every pentagon must add up to 540 degrees. If the pentagon is regular each internal angle measures 108°. In fact, in a Regular Polygon with N sides, each angle is:
[tex]\frac{(N-2)180{^\circ}}{N} \\ \\ Since \ N=5 \\ \\ \\ \frac{(5-2)180{^\circ}}{5}= 108^{\circ}[/tex]
2. Drawing of the second convex pentagon (Irregular Pentagon)
This is a type of polygon that does not have all sides equal and all angles equal. In Figure 2 is shown this pentagon. Note that there are five sides and all angles are not equal.
2.1 Sum of the interior angles of the second convex pentagon.
According to Figure 2, the sum of its interior angles is given by:
[tex]\beta=81^{\circ}+139^{\circ}+139^{\circ}+94^{\circ}+87^{\circ}=540^{\circ}[/tex]
As we said, no matter if the pentagon is irregular, the angles in every pentagon must add up to 540 degrees.
Answer with explanation:
A Polygon is said to be convex, if all the diagonals of the polygon lies in the interior of the polygon.
→Sum of interior angle of polygon =(n-2)×180°, where n is the number of sides of the polygon.-----(1)
→A pentagon is said to be convex, if it has 5 sides and all the Diagonals of pentagon lies in the interior.
Sum of interior Angles of Triangle =(3-2)×180°=180°
Sum of interior angles of Quadrilateral = (4-2)×180°=2×180°=360°
Sum of Interior angles of Polygon =(5-2)×180°=3×180°=540°
Used the formula (1) in all the three cases.
Given:
1 = 4
B = D
Prove:
AD = CB
Which of the following triangle congruence theorems would be used in this proof?
SAS
ASA
AAS
Answer: ASA
hope that helps have a nice day
A store has a 25% off sale on coats.With this discount,the price of one coat is $34.50.What is the original price of the coat?
If the sum of interior angles is 180 then what is the sum?
Answer:
Sum = (n -2) * 180
Step-by-step explanation:
Step 1 : The formula for calculating the sum of the interior angles = (n - 2) × 180, where "n" is the number of sides of a regular polygon.
Step 2: Here we are given the sum of the interior angles is 180 degrees. Therefore, the given figure must be triangle.
Which equation is in point-slope form and is depicted by the line in this graph?
a) (y - 3 ) = 3/5 ( x - 2 )
b) (y - 3 ) = - 3/5 ( x + 2 )
c) (y - 3 ) + 5/3 ( x - 2 )
d) (y + 3 ) - 5/3 ( x + 2)
Find the value of x. Round the length to the nearest tenth. Diagram is not drawn to scale.
A.7.2ft
B.6.9ft
C.13.9ft
D.9.7ft
Answer:
(A) [tex]x=7.2 ft[/tex]
Step-by-step explanation:
Given: A triangle whose base angle is 44° and hypotenuse is 10ft.
To find: The value of x.
solution: Using the trigonometry, we have
[tex]\frac{x}{10}=cos44^{{\circ}}[/tex]
⇒[tex]x=10{\times}cos44^{{\circ}}[/tex]
⇒[tex]x=10{\times}0.72[/tex]
⇒[tex]x=7.2 ft[/tex]
Thus,the value of [tex]x=7.2 ft[/tex]
Answer: A. 7.2 ft
Step-by-step explanation:
Given: A right triangle with hypotenuse 10 ft and base angle [tex]44^{\circ}[/tex]
By using Trigonometry, we have
[tex]\cos (44^{\circ})=\frac{\text{side adjacent to }44^{\circ}}{\text{hypotenuse}}\\\\\Rightarrow \cos (44^{\circ})=\frac{x}{10}\\\\\Rightarrow0.71933980033=\frac{x}{10}\\\\\Rightarrow\ x=10\times0.71933980033=7.1933980033\approx7.2\ ft.[/tex]
Hence, the value of x = 7.2 ft.
PLEASE HELP ASAP!!!!! LOTS OF POINTS
Answer:
Your answer is D :)
Step-by-step explanation:
No explanation :) <3
Help Needed
Let f(x)=x2+12x+32. What are the zeros of the function? Enter your answers in the boxes.
Answer:
Step-by-step explanation:
The given equation is:
[tex]f(x)=x^2+12x+32[/tex]
Simplifying the above expression, we have
[tex]f(x)=x^2+4x+8x+32[/tex]
[tex]f(x)=x(x+4)+8(x+4)[/tex]
[tex]f(x)=(x+4)(x+8)[/tex]
Thus, zeroes of the given function will be:
[tex]f(x)=0[/tex]
[tex](x+4)(x+8)=0[/tex]
[tex]x=-4 and x=-8[/tex]
Therefore the zeroes of the given function are [tex]x=-4 and x=-8[/tex].
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Use the triangle pictured to calculate the following measurements.
Perimeter: p = ___ units Semiperimeter: s = ___units Area: A ≈ ___square
Perimeter is 30 units
Semi-perimeter is 15 units
The Area is 39.7 square units
Factor completely: x2 + 6x + 8
* (x + 8)(x + 1)
* (x + 2)(x + 4)
* (x2 + 8)(x + 1)
* Prime
Answer:
(x+2)(x+4)
Step-by-step explanation:
what is 56.4789 rounded to nearest thousandth
what is straight continues in both direction and does not stop
Figure A is reflected over the y-axis and then lowered 6 units. Which sequence describes these transformations.
Marukh can wash the car in 10 minutes. steven can wash the car in 60 minutes. if marukh and steven work together, how long will it take them to wash the car? round your answer to the nearest minute.
Juanita is making bread.She needs 3 1/2 cups of flour.Juanita only has a 1/4-measuring cup.How many 1/4 cups of flour will Juanita use to prepare he bread?
Convert the following Celsius degrees to Fahrenheit.
a. 35° C
b. 500° C
c. 10° C
d. 55° C
Answer:
We know: 0 Celsius = 32 Fahrenheit.
We can convert the Celsius to Fahrenheit using this formula:
[tex](C\times9/5)+32[/tex]
a. 35° C
= [tex](35\times9/5)+32=95[/tex] degrees Fahrenheit
b. 500° C
= [tex](500\times9/5)+32=932[/tex] degrees Fahrenheit
c. 10° C
= [tex](10\times9/5)+32=50[/tex] degrees Fahrenheit
d. 55° C
= [tex](55\times9/5)+32=131[/tex] degrees Fahrenheit
a. 35°C to Fahrenheit: 95°F
b. 500°C to Fahrenheit: 932°F
c. 10°C to Fahrenheit: 50°F
d. 55°C to Fahrenheit: 131°F
1. Formula:
To convert Celsius to Fahrenheit, you can use the formula:
[tex]\[ F = \frac{9}{5}C + 32 \][/tex]
2. Calculations:
a. For 35°C:
[tex]\[ F = \frac{9}{5} \times 35 + 32[/tex]
= 95°F
b. For 500°C:
[tex]\[ F = \frac{9}{5} \times 500 + 32[/tex]
= 932°F
c. For 10°C:
[tex]\[ F = \frac{9}{5} \times 10 + 32[/tex]
= 50°F
d. For 55°C:
[tex]\[ F = \frac{9}{5} \times 55 + 32[/tex]
= 131°F
Triangle GHI is similar to triangle JKL. If JP = 26, MH = 36 and PK = 16 then GM =
A.
44.3
B.
58.5
C.
86
D.
117
Please help me with this math problem.
what is the exponent of 9x9x9x9x7x7
i need help with adding and subtracting fractions
WHAT IS 3/8-3/9 ? I NEED TO SHOW MY WORK
Celina says that each of the following expressions is actually a binomial in disguise:(Expressions in picture) For example, she sees that the expression in (i) it is algebraically equivalent to − , which is indeed a binomial. (She is happy to write this as + (−), if you prefer.) Is she right about the remaining four expressions?
All the given expressions are binomials except the expression in (i) which is a trinomial.
What are binomials in expressions?
Binomials can be defined as the expression that contains two variables that are different in terms.
ii.) 5x³* 2x²- 10x⁴+3x⁵+ 3x * (-2)x⁴
= 10x⁵-10x⁴+3x⁵-6x⁵
= 7x⁵+10x⁴ (this is an example of a binominal)
iii.) (t+2)²- 4t = t²+ 4t+4-4t = t²+4(binomial)
iv.) 5(a-1)-10(a-1)+100(a-1)
= 5a-5-10a+10+100a-100
= 95a - 95 (binomials)
v.) (2πr-πr²)r-(2πr-πr²)2r
= 2πr²-πr³-4πr²+2πr³
= -2πr²+πr³(binomials)
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Tyler has $1000 that he wants to put in a savings account. He wants to save the money for 6 years. After 6 years he plans to take the money out and spend it on college. He looks at two different banks, and they offer him different interest options.
Bank A offers Tyler 4% simple interest. How much would Tyler’s investment be worth after 6 years in this account? Show your calculations below.
Bank B offers Tyler 3% interest compounded annually. How much would Tyler’s investment be worth after 6 years in this account? Show your calculations below.
In which bank should Tyler place the $1000 he is saving for college
Answer:
He should place it in Bank A
For bank A Total amount = $1240
For bank bA= $1196.68
Step-by-step explanation:
For bank A with simple interest rate of 4%
Interest = PRT/100
Interest =( 1000*4*6)/100
Interest=$240
Total amount = principal + interest
Total amount = $1000+$240
Total amount = $1240
For Bank B with compound interest rate of 3%
A = p(1+r/n)^(nt)
A = 1000(1+(0.03/6))^(6*6)
A = 1000*1.19668
A= $1196.68
Find the circumference
Given: MQ = NQ; Q is the midpoint of LP; LM ≅ PN Which congruence theorem can be used to prove △MLQ ≅ △NPQ?
The congruence theorem that can be used to prove △MLQ ≅ △NPQ is the SAS (Side-Angle-Side) congruence theorem.
Explanation:To prove that triangles MLQ and NPQ are congruent, we can use the SAS (Side-Angle-Side) congruence theorem. The given information MQ = NQ indicates that the sides MQ and NQ are congruent. Since Q is the midpoint of LP, we can conclude that the side LQ is congruent to side PQ. Lastly, the fact that LM ≅ PN means that the side LM is congruent to side PN. Therefore, we have congruent corresponding sides and an included congruent angle, allowing us to use the SAS congruence theorem. So, △MLQ ≅ △NPQ.
Learn more about Congruent Triangles here:https://brainly.com/question/22062407
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THE SUM OF A NUMBER X AND 4 ALL DIVIDED BY 3
The sum of a number X and 4 divided by three is (X+4)/3
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol can also be used to indicate the logical syntax's order of operations and other features.
Given that sum of a number X and 4 divided by 3
That makes the expression as;
Sum = x + 4
Then
(X+4) over 3
Therefore, the expression would be (X+4)/3
To know more about an expression follow;
brainly.com/question/19876186
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True or false. This transformation is a dilation
true transformation is a dilation
Yes it is true!! Dilation is a transformation because each point of the object is moved- like tracing- a perfectly strait line! The strait line is drawn from a point called the center of dilation!
Have a great day! :)
Oscar and Kim have $22.00 each to spend at a book fair, where all students receive a 30% discount. They both want to purchase a copy of the same book, which normally sells for $28.50 plus 10% sales tax. To check if he has enough to purchase the book, Oscar takes 30% of $28.50 and subtracts that amount from the normal price. He takes 10% of the discounted selling price and adds it back to find the purchase amount. Kim takes 70% of the normal purchase price and then computes 110% of the reduced price. Is Oscar correct? Is Kim correct? Do they have enough money to purchase the book? Explain your answer using complete sentences, and show your work.
using complete senteces
Both Oscar and Kim are correct and do have enough money to purchase the book.
Using Oscars way:
Multiply the original price by the discount 28.50 x 0.30 = 8.55
Take that amount and subtract it from the price 28.50 - 8.55 = 19.95
Then multiply the discounted price by the sales tax rate 19.95 x 0.10 = 1.995 = 2.00
Add the sales tax amount to get the final cost 19.95 + 2.00 = 21.95 total cost
Kim's way:
Subtracting the discount percent from 100 percent ypu get 70 percent, so multiplying the price by 70 percent will get you the sale price 28.50 x 0.70 = 19.95
Multiplying the sale price by 110 percent calculates the tax amount plus the price together to get the final cost 19.95 x 1.10 = 21945 = 21.95 total cost
Both Oscar and Kim are correct and do have enough money to purchase the book.
For which intervals is the function increasing?
Select each correct answer.
(0, 1)
(2, ∞)
(1, 2)
(−∞, 0)
Note: Multiple choice question
Answer:
The intervals where the function is increasing are [tex](-\infty,0)[/tex] and [tex](1,2)[/tex]
Step-by-step explanation:
We are required to find the intervals in which the function is increasing.
From the figure, we see that,
The graph is going up towards the origin to reach the point (0,0).
Then, it is going down in the interval (0,1).
Then, it is again going up to reach the point (2,0).
Finally, it is going downwards towards infinity.
Thus, we see that,
The intervals where the function is increasing are [tex](-\infty,0)[/tex] and [tex](1,2)[/tex]
Answer:(−∞, 0) and(1,2)
Step-by-step explanation:
A line passes through the point , 8−1 and has a slope of −3/4 . Write an equation in slope-intercept form for this line.
The point of intersection of the lines has an e-coordinate of?