The area of the regular hexagon is 169.74 ft2. A regular hexagon has an apothem with length 7 feet and an area of 169.74 feet squared. What is the perimeter, rounded to the nearest tenth? 24.2 ft 28.3 ft 48.5 ft 56.8 ft
Answer: [tex]48.5\ ft[/tex]
Step-by-step explanation:
Given
Area of the regular hexagon is [tex]169.74\ ft^2[/tex]
Length of the apothem is [tex]l=7\ ft[/tex]
Suppose the side of the hexagon is a
Hexagon can be divided into six equal triangles with same area
Area of a single triangle is
[tex]\Rightarrow A_1=\dfrac{1}{2}\times 7\times a\\\\\Rightarrow A_1=3.5a\ ft^2[/tex]
Area of hexagon will be equal to area of 6 equal area triangles
[tex]\Rightarrow 6A_1=169.74\\\Rightarrow 6\times 3.5a=169.74\\\Rightarrow a=8.08\ ft[/tex]
Perimeter of the hexagon is
[tex]\Rightarrow P=6a\\\Rightarrow P=6\times 8.08\\\Rightarrow P=48.49\approx 48.5\ ft[/tex]
Thus, the perimeter of the hexagon is [tex]48.5\ ft[/tex]
Answer:
C
Step-by-step explanation:
edge 2021
[tex]\sqrt{9\\[/tex]
Answer: 3
Step-by-step explanation:
The check mark with the line is a sauare root symbol. It means find the square root of the number next to it. The square root of something is a number times the same number to get the number. For example, the square root of 16 is 4 because 4x4 is 16. 3x3 is 9 so that’s the square root.
Graph both functions to find the solution(s) to the system.
{y=x²−2x+4
y=2x+1
Use the line tool to graph the line.
Use the parabola tool to graph the parabola. Choose maximum or minimum point first and then a point on the parabola.
graphed it with desmos (free as app and website).
the solutions are in the screenshot
(1, 3)
(3, 7)
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is arn interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.)
[infinity]
Σ (-1)n+1(x-8)/n8n
n=1
I'm guessing the power series given is
[tex]\displaystyle \sum_{n=1}^\infty (-1)^{n+1}\frac{(x-8)^n}{8^n}[/tex]
which you can condense somewhat into
[tex]\displaystyle -\sum_{n=1}^\infty \left(\frac{8-x}8\right)^n[/tex]
You should recognize this as a geometric series, which converges for
[tex]\left|\dfrac{8-x}8\right|<1 \implies |8-x|<8 \implies \boxed{0 < x < 16}[/tex]
In circle O, the length of radius OL is 6 cm and the length of arc LM is 6.3 cm. The measure of angle MON is 75°. Circle O is shown. Line segments L O , M O, and N O are radii. The length of L O is 6 centimeters. Angle M O N is 75 degrees. The measure of arc L M is 6.3 centimeters. Rounded to the nearest tenth of a centimeter, what is the length of arc LMN? 7.9 cm 10.2 cm 12.6 cm 14.2 cm
Answer:
[tex]LMN = 14.2[/tex]cm
Step-by-step explanation:
Given
[tex]r = OL = NO = MO = LO =6cm[/tex] -- radius
[tex]LM = 6.3cm[/tex] -- arc
[tex]\angle MON = 75^o[/tex]
(see attachment)
Required
The length of arc LMN
First, we calculate the length of arc MN using:
[tex]MN = \frac{\alpha}{360} * 2\pi r[/tex] --- length of arc
In this case:
[tex]\alpha = \angle MON = 75^o[/tex]
So, we have:
[tex]MN = \frac{75}{360} * 2 * 3.14* 6[/tex]
[tex]MN = \frac{75* 2 * 3.14* 6}{360}[/tex]
[tex]MN = \frac{2826}{360}[/tex]
[tex]MN = 7.85[/tex]
So, the length of arc LMN is:
[tex]LMN = LM + MN[/tex]
[tex]LMN = 6.3 + 7.85[/tex]
[tex]LMN = 14.15[/tex]
Answer:
D
Step-by-step explanation:
14.2
2. Determine the measure of the angles indicated by letters. Justify your answers with the
properties or theorems you used.
Answer:
a = 50°
b = 130°
c = 50°
d = 50°
e = 130°
f = 130°
g = 50°
Answered by GAUTHMATH
PLEASE FAST lenear equations
Answer:
y = 43
Step-by-step explanation:
(y-4)/3 = (y+9)/4
4(y-4) = 3(y+9)
4y-16 = 3y+27
4y-3y = 27+16
y = 43
What is the nineteenth term of an arithmetic sequence with first term 9 and common difference 5?
Answer:
a₁₉ = 99
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 9 and d = 5 , then
a₁₉ = 9 + (18 × 5) = 9 + 90 = 99
The nineteenth term of arithmetic c sequence with first term 9 and common difference 5 is 99.
What is Arithmetic progression?The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has wider use in mathematics for example sum of natural numbers.
Natural number = 1,2,3,4,5,6,7,8...
Now it has the same difference between any two consecutive terms d =2-1 = 3-2
Given an AP series
First term(a) = 9
Common difference (d) = 5
The nth term is given by
⇒ a + (n - 1)d
So,
19th term = 9 + (19-1)5
⇒ 99
Hence "The nineteenth term of arithmetic c sequence with first term 9 and common difference 5 is 99".
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A restaurant is ordering vegetables for the upcoming week. Potatoes are shipped in 30-pound bags and onions are shipped in 5-pound bags. If the restaurant receives 1,800 pounds of potatoes and onions and there are 25 more bags of potatoes than bags of onions, how many pounds of onions are received?
Answer:
525 pound of onions were recieved
Step-by-step explanation:
1 bag of potatoes: 30 pounds
total pounds of potatoes and onions received= 1800
let the total pounds of onions received be x,
25 bags of potatoes = 25 × 30= 750 pounds
now according to the question,
x + x + 750= 1800
2x = 1800 - 750
x= 1050 ÷ 2
x= 525
Note: plz correct me if I am wrong somewhere
The restaurant receives 150 pounds of onions.
How to determine pounds of onions receivedLet's assume the number of bags of onions is "x". According to the problem, there are 25 more bags of potatoes than bags of onions, which means the number of bags of potatoes is "x + 25".
The weight of each bag of potatoes is 30 pounds, so the total weight of potatoes is 30(x + 25) pounds.
The weight of each bag of onions is 5 pounds, so the total weight of onions is 5x pounds.
According to the problem, the restaurant receives 1,800 pounds of potatoes and onions in total. We can set up the following equation based on this information:
30(x + 25) + 5x = 1800
Simplifying the equation:
30x + 750 + 5x = 1800
35x + 750 = 1800
35x = 1800 - 750
35x = 1050
Dividing both sides by 35:
x = 1050 / 35
x = 30
Therefore, the restaurant receives 30 bags of onions.
To find the weight of onions, we can substitute the value of x into the expression for the weight of onions:
Weight of onions = 5x = 5 * 30 = 150 pounds
Therefore, the restaurant receives 150 pounds of onions.
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thực hiện phép tính
√2+√3 - √2-√3
Answer:
Answer = 0
Step-by-step explanation:
√2+√3 - √2-√3
= 0
Hope this answer helps you :)
Have a great day
Mark brainliest
Please help me factorise these brackets and expand them
Answer:
5ba^2 +ab^2 6a^2 + 2b
Step-by-step explanation:
ab(6a+b)-3a^2 (b-2)+2b(a^2 +1)
6ba^2 +ab^2 -3ba^2 +6a^2 + 2ba^2 +2b
6ba^2 -3ba^2 +2ba^2 +ab^2 +6a^2 +2b
5ba^2 +ab^2 6a^2 + 2b
**URGENT PLEASE HELP**
Find g(x), where g(x) is the translation 2 units right and 13 units down of f(x) = -2x + 5.
Answer:
g(x)=x+9
Step-by-step explanation:
When translating a graph, adding the number of units shifts the graph to the left and subtracting the number of units shifts it to the right. Since you need the graph translated 9 units to the left, you will need to add that many units to x
therefore, g(x)=x+9
Answer:
g(x)=x-8
Step-by-step explanation:
-2+2 = 0, so g(x) = x
5-13 = -8
Instructions: Find the missing side of the triangle.
30
х
50
X=
Answer:
x = 40
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + 30² = 50²
x² + 900 = 2500 ( subtract 900 from both sides )
x² = 1600 ( take the square root of both sides )
x = [tex]\sqrt{1600}[/tex] = 40
Which expression is equivalent to
(4x2x3)(3x*y)2?
Answer:
48(3xy)
Step-by-step explanation:
(4 * 2 * 3)(3xy)2
24(3xy)2
48(3xy)
Rewrite the following polynomial in standard form.
1
23
+
04
+8
Answer:
1/2 x^4 +x^3 +8
Step-by-step explanation:
Standard form means highest power of x to lowest power of x
1/2 x^4 +x^3 +8
L is the point (-2,4) and M is the point(3,-1).A variable pointQ(x,y) in such that /QL/²-/QM/²=10
Answer:
y=x
Step-by-step explanation:
so,
((x - -2)² + (y - 4)²) - ((x - 3)² + (y - -1)²) = 10
(x² + 4x + 4 + y² - 8y + 16) - (x² - 6x + 9 + y² + 2y + 1) = 10
x² + 4x + y² - 8y + 20 - x² + 6x - y² - 2y - 10 = 10
10x - 10y = 0
y = x
In the rhombus, m angle 1 equals 106. What are m angles 2 and 3?
Answer:
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+320Find x.
A. √-2
B. 4
C. √2/2
D. √6/2
Answer:
sqrt(2)
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hyp
sin 45 = x/2
2 sin 45 =x
2 (sqrt(2)/2) =x
sqrt(2) =x
Sally spent half of her allowance going to the movies. She washed the family
car and earned 6 dollars. What is her weekly allowance if she ended with
17 dollars ?
does it give the answer choice or is it a blank space?
The value of a two-digit number is 10 more than 3 times the sum of its digits. The units digit is 1 more than twice the tens digit. What is the two-digit number?
Answer:
49
Step-by-step explanation:
the number is "ab" (2 digits).
ab - 10 = 3×(a+b)
a number is actually the sum of multiplying the digits with their associated powers of 10.
a×10 + b - 10 = 3a + 3b
7a - 2b = 10
b-1 = 2×a
b = 2a + 1
7a - 2×(2a+1) = 10
7a - 4a - 2 = 10
3a = 12
a = 4
b = 2×4 + 1 = 9
The student council needs to make a banner for the seventh-grade dance. The dance committee decides that the length of the banner will be 16 feet. What are the possible widths of the banner if the students can use no more than 40 square feet of material? Find the solution set of the inequality 16w ≤ 40 to solve the problem.
A rectangle with a length of 16 feet and width of w.
What are the possible widths of the banner if the students can use no more than 40 square feet of material?
at most 2.5 ft wide
less than 2.5 ft wide
at least 0.4 ft wide
no more than 0.4 ft wide
Answer: Choice A) at most 2.5 ft wide
Work Shown:
16w ≤ 40
w ≤ 40/16
w ≤ 2.5
This says that the banner must be at most 2.5 ft wide (choice A)
In other words, the largest the width can get is w = 2.5; we can think of this as the ceiling value.
Answer: its a
Step-by-step explanation:
brainly stop taking my answer down pls
Find the volume of the cylinder please
ASAP
Answer:
33ft^3
Step-by-step explanation:
radius is half the diameter, half of 2=1 and 1^2=1
3(1)(11)=33
Answer: V = 33 ft³
Step-by-step explanation:
π = 3
r = (1/2)d = (1/2) (2) = 1 ft
h = 11 ft
Given Formula
V = π r² h
Substitute values into the formula
V = (3) (1)² (11)
Simplify exponents
V = (3) (1) (11)
Simplify by multiplication
V = 33 ft³
Hope this helps!! :)
Please let me know if you have any questions
fifty-five percent of the pupils in a class are girls. What is the ratio of the number of boys in the class?
Answer:
45 boys
Step-by-step explanation:
55 + 45 = 100 so if 55% of the class is girls then the rest of the percentage of the class which is 45 should be boys
Answer:
45 boys
Step-by-step explanation:
55 + 45 = 100 so if 55% of the class is girls then the rest of the percentage of the class which is 45 should be boys
What is
4 times the sum of g and p
Answer:
4(g + p).
Step-by-step explanation:
The sum of g and p is g + p.
Next we multiply this sum by 4.
We need to place the g + p in parentheses to do this.
The measurements of a triangle are given. Is there exactly one triangle that can be formed using the given measurements? If so, identify the appropriate triangle congruence postulate.
∆ABC : m ∠A = 90°, AB = 15, AC = 15
A)No, More than one triangle could be made with these measures
B)Yes, SSS congruency
C)Yes, ASA congruency
D)Yes, SAS congruency
no, more than one triangle could be made with these measures
sss
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction if
needed.
Step-by-step explanation:
[tex] \sin(x) = \frac{12}{13} [/tex]
The value of the trigonometric ratio are; [tex]\sin(x) = \dfrac{\text{12}}{\text{13}}[/tex].
On which triangle can we apply trigonometric ratios?Trigonometric ratio can be defined in terms of ratios of perpendicular, bases and hypotenuse.
Trigonometric ratio are defined only in right angled triangles (triangles whose one angle is of 90 degree measure).
Trigonometric ratios for a right angled triangle are from the perspective of a particular non-right angle.
In a right angled triangle, two such angles are there which are not right angled(not of 90 degrees).
From the considered angle, the side opposite to it is called perpendicular, and the remaining side will be called base.
From that angle suppose its measure is θ,
[tex]\sin(\theta) = \dfrac{\text{Length of perpendicular}}{\text{Length of Hypotenuse}}[/tex]
[tex]\sin(x) = \dfrac{\text{12}}{\text{13}}[/tex]
Therefore, The value of the trigonometric ratio are; [tex]\sin(x) = \dfrac{\text{12}}{\text{13}}[/tex].
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Translate into algebraic expression: 22 decreased by y%
Answer:
Step-by-step explanation:
So first we need to find out what y% of 22 would be,
y% * 22
0.001y*22
= 0.22y
0.22y is equaled to y% of 22. Now we have to subtract 22 by the y%.
Therefore,
22-y%*22
which is:
22-0.22y!
Cheers! I hope you understand the problem now.
Can someone please explain this step by step.
Answer:
-5 and 2
-3 and 0
-2 and -1
...gives -3
Step-by-step explanation:
Answer:
Step-by-step explanation:
(-5,2), (-2,-1), (-3,0)
all pairs add up to -3
given: ray FEH bisects
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Concrete is made by mixing screenings cement and sand in the ratio 3:1:15. How much sand would be needed to make 125 tonnes of concrete?
