The figure below shows circle with center O and regular hexagon ABCDEF constructed inscribed in a circle.Which of the following steps will help prove that triangle FBD is equilateral?
Answers
Triangle FBD in the given regular hexagon inscribed in a circle can be proven to be an equilateral triangle based on the equal lengths of radii and the angle of 60 degrees subtended at the center by the side of the hexagon.
Explanation:
To prove that triangle FBD is an equilateral triangle, we first need to understand a few properties of a regular hexagon and a circle. In a regular hexagon inscribed in a circle, every angle at the center of the circle subtended by the sides of the hexagon is 60 degrees because the total degree measure at the center of the circle is 360, and this is divided equally among the six sides of the hexagon.
Triangle FBD is formed by joining the center of the circle, O, and two consecutive vertices of the hexagon, B and F. As the hexagon is regular and inscribed in a circle, both OB and OF are radii of the circle. By definition, all radii of a given circle are equal in length. Therefore, OB = OF.
The angle BFO subtended at the center by the side BF of the hexagon is 60 degrees. Hence, triangle FBD is an equilateral triangle because it has two equal sides and the included angle is 60 degrees, which are the properties of an equilateral triangle.
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To prove that triangle FBD is equilateral, one can show that the central angles corresponding to the three sides of the hexagon (angle AOB, angle BOC, and so on) are all equal. Therefore, demonstrating that angle FOB, angle BOD, and angle DOF are each 120 degrees will establish that triangle FBD is equilateral.
Explanation:In a regular hexagon inscribed in a circle, the central angles formed by connecting the center of the circle (O) to consecutive vertices of the hexagon are all equal. Since each interior angle of a regular hexagon is 120 degrees, the central angles (e.g., angle AOB, angle BOC, etc.) are also 120 degrees. To prove that triangle FBD is equilateral, one needs to focus on the central angles corresponding to its sides.
The central angles associated with triangle FBD are angle FOB, angle BOD, and angle DOF. By demonstrating that each of these angles is 120 degrees, it can be concluded that triangle FBD is equilateral. The regularity of the hexagon ensures that the central angles are equal, making this an effective and straightforward way to prove the equilaterality of triangle FBD.
In conclusion, to establish the equilaterality of triangle FBD, one should emphasize the properties of central angles within the context of a regular hexagon. Specifically, showing that angle FOB, angle BOD, and angle DOF are each 120 degrees serves as a valid proof for the equilateral nature of triangle FBD within the given geometric configuration.
Related Questions
which of the following comparisons is false 4 liters< 1 gallon, 1 foot< 1 meter, 25 grams< 1 ounce, 10 kilometer< 9 miles
Answers
1 Liter = 1.005 Quarts
4 Quarts = 1 Gallon
4 Liters = 1.05 Gallons
How do you use the half angle formula for
sin (5π/12)?
Answers
To determine sin(5π/12) using the half-angle formula, we establish a known cos value for the double of the angle, i.e., cos(5π/6)=-√3/2. Substituting it into the half-angle sin formula: Sin(5π/12)=±√{(1+√3/2)/2}. Simplifying gives Sin(5π/12)=√{3+√3/4}.
Explanation:The half angle formula for sine is given by:
Sin(x/2) = ±√{(1 - cos x) / 2}
To solve for sin(5π/12) using the half angle formula, we would look for an angle whose double is easily recognized in terms of standard angles (multiples of 30° or 45°). Luckily, the double of 5π/12 is 5π/6, a recognizable angle, and we know that cos(5π/6) = -√3/2.
Step 1: Substitute cos x value (-√3/2) into the formula:
Sin(5π/12) = √{(1 - (-√3/2 )) / 2}
Step 2: Simplify the expression inside the square root:
Sin(5π/12) = √{(1 + √3 / 2) / 2}
Step 3: Calculate the square root:
Sin(5π/12) = ± √{3 + √3 / 4}
Usually, we choose the positive root for a result in the first or second quadrant and the negative root for a result in the third or fourth quadrant. Since the angle 5π/12 is in the first quadrant, we choose the positive root:
Sin(5π/12) = √{3 + √3 / 4}
So, sin(5π/12) using the half angle formula is √{3 + √3 / 4}.
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**PLEASE HELP??? ****STUCK ON THIS!!!!
Suppose that f(w) varies inversely with w and f(w) = 0.75 when w= 8.
What is f(w) when w= 2?
A.) 12
B.) 6
C.) 3
D.) 1.5
My answer choice is C.) 3. I'm not very confident in my answer so..... :/
Answers
Answer:
C.3
Step-by-step explanation:
We are given that
f(w) varies inversely with w.
f(w)=0.75 when w=8
We have to find the value of f(w) when w=2
According to question
[tex]f(w)\propto\frac{1}{w}[/tex]
[tex]f(w)=\frac{k}{w}[/tex]
Where k=proportionality constant
Substitute the given values then, we get
[tex]0.75=\frac{k}{8}[/tex]
[tex]k=0.75\times 8[/tex]
[tex]k=6[/tex]
Substitute the value of k then, we get
[tex]f(w)=\frac{6}{w}[/tex]
Substitute the value of w=2
Then, we get
[tex]f(w)=\frac{6}{2}=3[/tex]
[tex]f(w)=3[/tex]
Hence, option C is true.
Identify the factors of x2 + 25y2. ...?
Answers
Answer:
(x-5y)^2 or (x-5y)(x-5y).
Step-by-step explanation:
hope this helps have a nice day! :D
Final answer:
To find the factors of x² + 25y², use the properties of complex numbers like i² = -1. The factors are (x + 5yi)(x - 5yi), representing complex conjugates.
Explanation:
The factors of x² + 25y² are (x + 5yi)(x - 5yi).
To factorize the expression, we use the fact that i² = -1, so we can rewrite 25y² as (5y)²
By factoring this expression, we can see that it represents a sum of two squares in the form of complex conjugates.
solve for x. 27^(2x)=9^(x-3) ...?
Answers
[tex] 27^{2x} = 9^{(x-3)} \\ (3^{3} )^{2x} = (3^{2}) ^{(x-3)} \\ \\ (x^{a} )^{b}= x^{a*b} \\ 3^{3*2x} =3^{2*(x-3)} \\ 3^{6x} =3^{(2x-6)} [/tex]
Now, logarithm both sides of the equation:
[tex]log(3^{6x} )=log(3^{(2x-6)}) \\ \\ log (x^{a}) =a*log(x) \\ 6x*log(3)=(2x-6)*log(3)[/tex]
Divide both sides of the equation by log(3):
[tex]6x=2x-6 \\ 6x-2x = -6 \\ 4x = -3 \\ x = - \frac{4}{3} [/tex]
Choose the words or phrases that best complete the sentences.
A fifth degree polynomial (could or must) have 5 linear factors. The factors (could, but do not have to be, or must) be distinct.
Answers
Answer: A fifth degree polynomial could have 5 linear factors. But the factors do not have to be be distinct.
Step-by-step explanation:
The fundamental theorem of algebra tells that every non-constant single-variable polynomial with complex coefficients has at least one complex root.Corollary to the fundamental theorem tells that every polynomial of m>0 degree has exactly m zeroes.Thus by corollary to fundamental theorem of algebra, a fifth degree polynomial must have 5 zeroes . But A fifth degree polynomial could have 5 linear factors if all zeroes are real numbers.
The factors could be distinct or similar.
Thus , The factors do not have to be distinct .
help with secx/sinx-sinx/cosx
Answers
1/cos(x)sin(x) - sin(x)/cos(x)
(1 - sin²(x))/[sin(x)cos(x)]
cos²(x) / sin(x)cos(x)
cos(x)/sin(x)
cot(x)
When point E (-9, 3) is rotated 180� about the origin, its coordinate becomes (3, 9).
True
False
...?
Answers
The answer should be (9,-3) because when a point is rotated 180 degrees about the origin, its coordinates change signs.
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
At a pet show, the ratio of dogs to cats is 4:3. if the number of cats is 45, find the number of dogs at the show.answer:
Answers
cross multiply because this is a proportion
(3)(d) = (45)(4)
3d = 180
d = 180/3
d = 60
so when there is 45 cats, there is 60 dogs
The number of dogs would be 60 when the ratio of dogs to cats is 4:3.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
Given that the ratio of dogs to cats is 4:3. if the number of cats is 45
We have to determine the number of dogs.
Let the number of dogs would be x
As per the given condition, we can write a proportion as
4 dogs : 3 cats = x : 45 cats
⇒ 4 / 3 = x / 45
Apply the cross-multiplication operation,
⇒ 45 × 4 = x × 3
⇒ x = (45 × 4)/3
⇒ x = 15 × 4
⇒ x = 60
Therefore, the number of dogs would be 60.
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Which is the most accurate name for the polygon shown?
concave pentagon
convex pentagon
concave hexagon
convex hexagon
Answers
How much of the circle is shaded? Write your answer with as a simplified fraction, with an explanation. Thank you.
Answers
Five Twenty-Eighths
or,
5/28
Hope this Helps!
What is the additive inverse of the polynomial 9xy^2 + 6x^2y – 5x^3?
A.9xy2 – 6x2y + 5x3
B. 9xy2 – 6x2y – 5x3
C. 9xy2 + 6x2y + 5x3
D. 9xy2 – 6x2y + 5x3
Answers
Answer:
The answer is B.
Step-by-step explanation:
The additive inverse of the given polynomial is:
-9xy^2 - 6x^2y + 5x^3
How to find the additive inverse of a polynomial?The additive inverse of a polynomial would be another polynomial, such that when we add the two, the outcome is zero.
For a given polynomial the additive inverse is given by multiplying the given polynomial by -1.
Here we have:
p(x) = 9xy^2 + 6x^2y – 5x^3
Then the additive inverse is:
q(x) = -p(x) = -9xy^2 - 6x^2y + 5x^3
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What is the value of the expression when a = 5 and b = 2? a 2b−3
Answers
a 2b-3
5 2(2) - 3
5 4 - 3
20-3
17
So, your answer is 17
Hope it helped.
Integrate (2 ln x)/x ...?
Answers
u = ln x
d u = d x / x
----------------
[tex] \int { \frac{2 lnx}{x} } \, dx = \\ \int {2u} \, du = \\ =2* u^{2}/2 = u^{2}= [/tex]
= ln² x + C
To get to work, matt walks 0.75 miles from his house to the bus stop and rides the bus 3.8 miles to his office. if he walks at a pace of 3.6 miles per hour and the bus drives at an average speed of 15 miles per hour, how long is his commute?
Answers
Witch Decimal is equal to six-tenths?
0.6 0.15 0.2 0.3 0.4
Answers
Hope this helped! :)
~Shadow
FIRST ANSWER IS BRAINIEST QUICKKK FIRST ANSWER IS BRAINIEST QUICKKK FIRST ANSWER IS BRAINIEST QUICKKK
What is the equation in point slope form of the line that passes through the point (1, –2) and has a slope of 3?
y−2=3(x+1)
y+2=3(x−1)
y+1=3(x−2)
y−1=3(x+2)
Answers
where m is the slope and c is the constant
the slope here is given and equal to 3
so, m= 3
y= 3x +c
to get the constant c, substitute with the point in this equation
y= -2 & x = 1
-2 = 3*1 + c
c = -5
then the equation of the line is y = 3x -5
y = 3x -3 -2
y +2 = 3(x-1)
the answer is (B)
The Sky High Ski Club dues are $450 per season. This fee includes transportation to and from the slopes and lift tickets. Skis cost $159.90, boots $78.25, and poles $19. What is the total cost?
Answers
Answer:
The total cost is $707.15.
Step-by-step explanation:
The Sky High Club dues are = $450 per person
and the Skis costs = $159.90
Cost for boots = $78.25
Cost of poles = $19.00
To find the total cost we will add all the amounts.
Total cost = 450 + 159.90 + 78.25 + 19.00
= $707.15
The total cost is $707.15.
Use implicit differentiation to find dy/dx.
ln xy + 5x = 30. Please write out the steps.
Answers
Final answer:
To find dy/dx using implicit differentiation, differentiate both sides of the equation with respect to x. Then apply the chain rule and simplify.
Explanation:
To find dy/dx using implicit differentiation, we first differentiate both sides of the equation with respect to x. Let's go through the steps:
ln(xy) + 5x = 30Differentiate both sides with respect to x:d/dx[ln(xy) + 5x] = d/dx[30]Apply the chain rule to differentiate ln(xy):(1/xy) * (x(dy/dx) + y) + 5 = 0Simplify the equation:x(dy/dx) + y + 5xy(dy/dx) = 0Collect terms with dy/dx:dy/dx = -(y + 5xy)/(x + 5xy)
10. Mr. Falcone's pizza shop offers three sizes of pizza. The small, medium and large pizzas have diameters of 8 inches, 10 inches and 12 inches. Small Medium Large a) What is the circumference of each size of pizza? Small = _________________ Medium = ___________________ b) What is the area of each size of pizza? Small = _________________ Medium = _________________ Large = _______________ Large = _________________ c) Joey is very hungry. He says he wants to eat a 100-square-inch area of pizza. Which size(s) of pizza should he order? Why?
Answers
i)Circumference of small pizza with radius of 8 inches; = 2*3.14*8 = 50.24 in.²
ii)Circumference of medium pizza with radius of 10 inches; = 2*3.14*10 = 62.8 in.²
iii)Circumference of large pizza with radius of 12 inches; = 2*3.14*12 = 75.36 in.²
b) we know, area of a circle = πr²
i)Area of small pizza with radius of 8 inches;= 3.14 * 8²= 200.96 in.²
ii)Area of medium pizza with radius of 10 inches = 3.14 * 10² = 314 in.²²
iii)Area of large pizza with radius of 12 inches; = 3.14*12² = 452.16 in.²
c) Joey should order pizzas of larger size 'cause he is very hungry & it will be most helpful for him 'cause of larger area.
Hope this helps!
Answer:
Step-by-step explanation:The employees must sell 78 pizzas in order to get the bonus.
The percentage decrease is 0.05%
Step-by-step explanation:
Number of pizzas sold yesterday is 65 pizzas.
The owner offers the employees a bonus if the number of pizzas sold increases by 20%
So 20% of 65 pizzas is, pizzas.
Therefore, the employees must sell 65+13=78 pizzas in order to get the bonus.
But the actual number of pizzas sold today was 60. So the number of pizza sold has decreased. Then the percent decrease is,
Therefore, the percentage decrease
Four milliliters of ink A is added to 10 milliliters of ink B, forming a mixture of inks. Ink A contains 10% blue pigment. Ink B contains an unknown percentage of blue pigment. The mixture of the two inks contains 35% blue pigment.
What percentage of blue pigment is in the mixture of the two inks?
45%
49%
60%
75%
Answers
1. Calculate how many ml of blue pigment are in 4ml of ink A if it contains 10% blue pigment:
4 ml is 100%
a ml = 10%
4 ml : 100% = a : 10%
a = 4 ml * 10% : 100% = 0.4 ml
2. Calculate how many ml of blue pigment are in 10ml of ink A if it contains x% blue pigment:
10 ml is 100%
b ml = x%
10 ml : 100% = b : x%
b = 10 ml * x% : 100% = x/10 ml
3. 2. Calculate how many ml of blue pigment are in 14ml (because Four milliliters of ink A is added to 10 milliliters of ink B) of total mixture if it contains 35% blue pigment:
14 ml is 100%
t ml = 35%
14 ml : 100% = t : 35%
t = 14 ml * 35% : 100% = 4.9 ml
4. What percentage of blue pigment is in the mixture of the two inks:
a + b = t
0.4 + x/10 = 4.9
x/10 = 4.9 - 0.4
x/10 = 4.5
x = 4.5 * 10 = 45
Answer:
45%
Step-by-step explanation:
I took the test!
The altitude dropped to the base of an isosceles triangle is a median, an angle-bisector, and a perpendicular bisector?
True
False ...?
Answers
What is 9 x ( 3 x 5 ) = ( 9 x n ) x 5?
Answers
Answer:
n=3
Step-by-step explanation:
HELP ASAP!!!
The markup on candy at the discount store is 45%. A bag of candy has a wholesale cost of $1.15. What will be the retail price for the candy?
A. $1.45
B. $1.60
C. $1.67
D. $1.78
Answers
Answer:
Option C. $1.67
Step-by-step explanation:
The price of a bag of candy at wholesale = $1.15
The markup on candy at the discount store = 45%
The retail price for the candy = 1.15 +(45% × 1.15)
= 1.15 + ([tex]\frac{45}{100}[/tex]×1.15)
= 1.15 + (0.45 × 1.15)
= 1.15 + 0.5175
= 1.6675 ≈ $1.67
The retail price for the candy would be $1.67.
The diagonals of a rhombus divide it into four triangles of equal area.
True
False
Answers
Since a rhombus has 4 equal sides, and its diagonals are equal, then it means that its triangles are also going to be equal.
Answer:
True
Step-by-step explanation:
9/5 times c plus 32 how do solve this
Answers
if it is equal to 0 then
c=-32 ×5/9
c = -160/9
Answer:
9/5×c+32 I.e.
if it is equal to 0 then
c=-32 ×5/9
c = -160/9
Step-by-step explanation:
A painting crew bought 30 gal of paint for a job. The crew members used 3 gal of paint per hour until they used all the paint.
Which sketch represents this situation?
Answers
If the crew members used 3 gal of paint per hour and bought 30 gal of paint for a job, then they will work 30:3=10 hours.
They start at x=0 hours with y=30 gal of paint;They end at x=10 hours with y=0 gal of paint (they worked until they used all the paint).The dependence between x and y is linear.Conclusion: the only possible sketch is A.
Answer: correct choice is A.
The triangle PQR shown on the coordinate grid below is reflected once to map onto triangle P´Q´R´.
If vertex P’ is at (7, -6), what are the coordinates of vertex R’?
A)(5, -3)
B)(3, -5)
C) (3, -2)
D)(5, -2)
Answers
The answer is (5,-2)
To find the coordinates of vertex R' in the reflected triangle, we can use the midpoint formula. Using the given point P' at (7, -6) and the original point P at (x, y), the x-coordinate of vertex R' is 5. Similarly, using the given point P' at (7, -6) and the original point R at (x, y), the y-coordinate of vertex R' is -2.
Explanation:To find the coordinates of vertex R', we need to map the reflection of triangle PQR onto triangle P'Q'R'. Since vertex P' is at (7, -6), we can use the midpoint formula to find the coordinates of the reflected point R'.
The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the two endpoints.
Using the given point P' at (7, -6) and the original point P at (x, y), we can write the equation:
(x + 7) / 2 = 7
Solving for x, we get x = 5.
Similarly, using the given point P' at (7, -6) and the original point R at (x, y), we can write the equation:
(y - 6) / 2 = -2
Solving for y, we get y = -2.
Therefore, the coordinates of vertex R' are (5, -2).
You purchase a home for $125,000. The value of the property increases by 1.9% every year. After ten years, you decide to sell the home. In the meantime, you have made renovations and improvements to the house which increase its sale value by $48,300. How much will you sell the house for, to the nearest hundred dollars?
Answers
We can use the formula:
F = P · ( 1 + i )^n
where: P = $125,000, i = 0.019 ( 1.9 %), n = 10
F = $125,000 · ( 1 + 0.019 )^10
F = $125,000 · 1.019^10
F = $125,000 · 1.207096
F = $150,887
And we have to add $48,3000 ( for renovations and improvements )
$150,887 + $48,300 = $199,187 ≈ $199,200
Answer: You will be sell the house for $199,200.
Answer:
$199,200
Step-by-step explanation:
What is is the answer for g-9=-19?