Answer:
Part A
[tex]The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}[/tex]
Plugging in the given values we get;
[tex]The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12[/tex]
R = 12 inches
The radius of the circumscribing circle is 12 inches
Part B
The length of each side of the hexagon, 's', is;
[tex]s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)[/tex]
Therefore;
[tex]s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12[/tex]
s = 12 inches
The perimeter, P = n × s = 6 × 12 = 72 inches
The perimeter of the hexagon is 72 inches
Step-by-step explanation:
The given parameters of the regular hexagon are;
The length of the apothem of the regular hexagon, a = 6·√3 inches
The relationship between the apothem, 'a', and the circumradius, 'R', is given as follows;
[tex]a = R \cdot cos \left(\dfrac{\pi}{n} \right)[/tex]
Where;
n = The number of sides of the regular polygon = 6 for a hexagon
'a = 6·√3 inches', and 'R' are the apothem and the circumradius respectively;
Part A
Therefore, we have;
[tex]The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}[/tex]
Plugging in the values gives;
[tex]The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12[/tex]
The circumradius, R = 12 inches
Part B
The length of each side of the hexagon, 's', is given as follows;
[tex]s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)[/tex]
Therefore, we get;
[tex]s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12[/tex]
The length of each side of the hexagon, s = 12 inches
The perimeter of the hexagon, P = n × s = 6 × 12 = 72 inches
The perimeter of the hexagon = 72 inches
Answer: radius = 12, perimeter = 72
Step-by-step explanation:
We know that in 30-60-90 right triangles, the hypotenuse is exactly twice the length of the short leg and the long leg is the short leg times √3.
so therefore, if the long leg (apothem) is equal to 6√3, the short leg is equal to 6
long leg = 6√3
long leg = short leg √3
short leg = 6
hypotenuse (radius) = 2(short leg)
hypotenuse (radius) = 2(6)
hypotenuse (radius) = 12
The radius of hexagon ABCDEF = 12 inches
Perimeter = r (sides)
Perimeter = r (6)
Perimeter = 12 (6)
Perimeter = 72
The perimeter of hexagon ABCDEF = 72 inches
Divide the polynomial in the numerator by the monomial in the denominator. Simplify your answer. 20x^5 – 6x^4 + 12x^3 + 12x^2 10x^2
Step-by-step explanation:
do u have a picture? its mixed up
Answer:
2x • (2x2 + 1) • (5x - 3)
Step-by-step explanation:
5.4 Find roots (zeroes) of : F(x) = 2x2 + 1
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 2 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1,2
of the Trailing Constant : 1
Final result :
2x • (2x2 + 1) • (5x - 3)
someone please help me answer this question
Answer:
10. $33.5, c=3.50r+9
11. $51
Step-by-step explanation:
Bella surveyed the first 15 students in the lunch line.
Is this sample of the students in the school likely to be representative?
yes
no
Answer:
No
Step-by-step explanation:
Only people in the lunch line got surveyed, that on it's own is biased.
Only 15 people out of the entire school.
Only the first people got surveyed.
I did my best to fit it all lol, can someone please help? <3
Answer:
8a. 0 8b. -1/3
Step-by-step explanation:
slope formula: [tex]\frac{y_{2} - y_{1}}{x_{2} - x{1}}[/tex]
8a. => (8 + 12)/(17 - 17) = 20/0 = 0
8b. (1 + 2)/(-3 - 6) = 3/-9 = - 1/3
Answer:
8a: 0 8b: -1/3
Step-by-step explanation:
slope is y2-y1/x2-x1
8a: 8+12/0=0
8b: 1+2/-3-6=3/-9=-1/3
11. Oliver had $10. On his birthday, he received $25. Use the equation below to find how much money Oliver has now. equation: 10 + 25 = m *
Answer: 35
Step-by-step explanation:
helpppp helping my sister
Answer:
i wanna say scalene is the first and thrid triangle. The second one is the 5th triangle and the rest go into the last catigorrie
Step-by-step explanation:
GIVING BRAINLIEST!!!!!
What type of triangle is shown in the image?
Acute triangle
Right triangle
Equilateral triangle
Obtuse triangle
Answer:
Well wheres the image?
Step-by-step explanation:
Answer:
Obtuse triangle
Step-by-step explanation:
Someone said so
What is the volume, in cubic feet, of a rectangular prism with a height of 5 feet, aho
width of 20 feet, and a length of 5 feet?
Answer:
500 cubic feet
Step-by-step explanation:
5 * 20 * 5 = 500 cubic feet
Here is some more
Find the value of x: 3x−7=8x+23
Answer: x=6
Step-by-step explanation:
Answer:
x = -6
Step-by-step explanation:
Subtract 3x from both sides to get -7=5x+23.
Subtract 23 from both sides to get -30=5x.
Divide 5 from both sides.
x = -6.
A rectangle has a length of 2x+3 and a width of 10x-4. Find the perimeter and area of the figure
Step-by-step explanation:
perimeter is 4x+6 +20x-8=20x-2
area is 20x^2+22x-12
What is
7.5% tax on
a $18
sweater?
19.35 or 1.35
Answer:
$1.35 will be your answer
Step-by-step explanation:
18 x 0.075 = 1.35
Answer:
[tex]1.35[/tex]
Step-by-step explanation:
7.5% of 18$ is 1.35.
It would make no sense if the tax cost more than the actual item.
how many boys are in the choir
9514 1404 393
Answer:
D. 210
Step-by-step explanation:
If b is the number of boys in the choir, the ratio of boys to girls is ...
b/150 = 7/5
b = 150(7/5) = 30(7) = 210
There are 210 boys in the choir.
Pls help I have this homework !! bye I will mark you the best or brainliest!!
Answer:
90-54w
Step-by-step explanation:
18(5−3w)=
18*5=90 , 18*3w= 54w =
so simplified it would be = (90-54w)
Please mark me as brainliest :D
2/5 meters= blank cm
Answer:
⅖ m = 40 cm
Step-by-step explanation:
1 meter = 100 cm
1 : 100 = 2/5 : y
1 × y = 100 × 2/5
y = 40
PLEASE HELP ME
A student bought 24 pencils for every 16 markers. The number of pencils bought is directly proportional to the number of markers.
What is the constant of proportionality that relates the number of pencils to the number of markers?
5/3
2/3
3/2
3/5
0.73 recurring can be writeen as 11/15
Answer:
yes , see explanation
Step-by-step explanation:
We require 2 equations with the recurring 3 placed after the decimal point.
let x = 0.7333.. ( multiply both sides by 10 and 100 )
10x = 7.333... → (1)
100x = 73.333.... → (2)
Subtract (1) from (2) , eliminating the recurring 3
90x = 66 ( divide both sides by 90 )
x = [tex]\frac{66}{90}[/tex] = [tex]\frac{11}{15}[/tex]
determine equation for line that is perpendicular to x=-2 and passes through the point (6,1)
Answer:
y = 1
Step-by-step explanation:
On an island there are 7 cities each 2 of them connected by a direct road they are building a 8th city they also want it to connect with the other 7 existing cities how many roads will there be after they build the 8th city
Answer:
After the 8th city is built there will be 28 roads between the cities
Step-by-step explanation:
The given parameters are;
The number of cities initially on the island = 7 cities
The number of roads between each 2 cities = 1 road
Therefore, we have the number of roads between the 7 cities are;
7 cities taking 2 at a time = ₇C₂
[tex]_7C_2 = \dfrac{7!}{(7 - 2)!\cdot 2!} = 21[/tex]
The initial number of roads between the 7 cities = 21 roads
The number of roads, 'n' there will be after the 8th city is built is therefore;
[tex]n = _8C_2 = \dfrac{8!}{(8 - 2)!\cdot 2!} = 28[/tex]
The number of roads there will be after the 8th city is built, n = 28 roads.
Please help i'm not doing good in math i will give you the crown
Answer:
B
Step-by-step explanation:
The format for quadrant 2 would be (-,+) and answer choice be fits that because it is(-3,2)
Please help ill give brainlest
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Please help me with the answer to these. The second picture goes along with the first
7x + 2y - 3 = 0 in slope intercept form.
Answer:
y=(-7/2)x+3
Step-by-step explanation:
7x+2y-3=0
7x+2y=3
2y=-7x+3
y=(-7/2)x+3
Answer:
y = - [tex]\frac{7}{2}[/tex] x + [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c
Given
7x + 2y - 3 = 0 ( subtract 7x - 3 from both sides )
2y = - 7x + 3 ( divide each term by 2 )
y = - [tex]\frac{7}{2}[/tex] x + [tex]\frac{3}{2}[/tex] ← in slope- intercept form
Topografía. La superficie de una montaña se modela mediante la ecuación ℎ(, ) = 5000 − 0.001 2 − 0.004 2 . Un montañista se encuentra en el punto (500, 300, 4390). ¿En qué dirección debe moverse para ascender con la mayor rapidez?
Respuesta:
(-1, - 2,4)
Explicación paso a paso:
Dada la función:
ℎ (x, y) = 5000 - 0,001x2 - 0,004y2
Tomando la derivada parcial con respecto a ambas direcciones (xey) se obtiene la dirección del vector de gradiente, donde es posible el movimiento más rápido
H '(x, y) = (dh / dx, dh / dy)
dh / dx = 2 (-0.001x) = - 0.002x
dh / dy = 2 (-0.004y) = - 0.008y
H '(500, 300) = (- 0,002 (500); - 0,008 (300))
H '(500, 300) = (- 1; - 2,4)
Por lo tanto, el montañista ascenderá con la mayor velocidad en el punto (-1, - 2.4)
write the following quotient in scientific notation:
Answer:
0.7
Step-by-step explanation:
what is the product of the polynomials? (3x-2)(12x+7)
Answer:
36x²-3x-14
Step-by-step explanation:
(3x-2)(12x+7)
36x²+21x-24x-14
36x²-3x-14
The worlds heaviest lobster weighted 44 pounds 6 ounces. What is the lobsters weight in ounces. Explain your thinking
Answer:710
Step-by-step explanation:
If the buses run on schedule, when is the next time a red line and a blue line bus will leave together? Show your work.
Answer:
So the next time they will leave together is 4:24 pm
Step-by-step explanation:
Since both the buses left at 4 pm and red line bus leaves every 6minutes and blue line bus leaves every 8 minutes they next time they leave together can be found by taking the L.C. M of 6 and 8.
The L.C. M is found by multiplying all the factors and chosing one which common in both numbers.
Factors of 6 = 2*3
Factors of 8= 2*2*2
In these numbers 2 is common in both.The rest of the numbers( 2*2*3 )are multiplied with the the common 2 to get the L.C.M
L.C.M= 2*2*2*3= 24 minutes
So the next time they will leave together is 4:24 pm
can someone please help me?
Answer:
A
Step-by-step explanation:
Answer:
A) 18.75
Step-by-step explanation:
As I said in the comments,
The question is asking for volume, so -
50 x 1.5 x 0.25 = 18.75
Hope this helped :)
pls help me!! will give brainliest
Answer: (0,0)
If AB is translated right 5 units and down two then both points are translated by that amount.
A currently is (-5, 2)
x=-5 and y=2
Since youre going right by five your x value will increase by 5 so the point will instead be at x=0
Since youre going down by two your y value will decrease by 2 so the point will instead be at y=0
x=0 and y=0
(0,0)
Answer: its 0,0
Step-by-step explanation:
The first four terms of an arithmetic sequence are shown below.
1, 5, 9, 13,......
(a) Write down the nth term of the sequence (general formula).
(b) Calculate the 100th term of the sequence.
(c) Find the sum of the first 100 terms of the sequence.
Answer:
a) n = 4(n-1)+1
b) 397
c) 19900
Step-by-step explanation:
