A regular hexagon is shown.
What is the length of the apothem, rounded to the nearest inch? Recall that in a regular hexagon, the length of the radius is equal to the length of each side of the hexagon.
4 in.
5 in.
9 in.
11 in.
Answers
In a 30-60-90 triangle, the sides are is the ratio of:
[tex]x \: \\ x \sqrt{3} \\ and \: 2x[/tex]
where x is opposite the 30° and 2x is opposite the 90°
Since the base is 10 and the hypotenuse is 10, 1/2 that is 5 (the x), and so:
[tex]x \sqrt{3} = 5 \sqrt{3} = 8.66[/tex]
So rounded up, you apothem then is closest to D) 9 in.
The length of the apothem of a regular polygon that has a radius of 10 inches would be 9 inches .
What is the apothem of a regular polygon?The apothem of a regular polygon is defined as a line segment from the center to the midpoint of one of its sides.
It is Given that the hexagon has a radius of 10 inches and the length of the radius is equal to the length of each side of the hexagon.
The apothem AB divides the side of the hexagon into two equal parts of 5 Inches.
Using Pythagoras Theorem
[tex]10^2 = 5^2 + AB^2\\AB^2 = 10^2 -5^2\\AB^2 = 100 - 25\\AB^2 = 75\\AB = \sqrt{75}[/tex]
AB = 8.66
So, rounded up, we get the apothem closest to D that is 9 in.
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Related Questions
One day a store sold 20 sweatshirts. White ones cost $ 10.95 and yellow ones cost $ 13.50. In all, $262.35 worth of sweatshirts were sold. How many of each color were sold?
Answers
How did I get this?
First, we need to figure out what we know.
20 sweatshirts sold
White sweatshirts $10.95
Yellow sweatshirts $13.50
Total spent $262.35
$10.95W + $13.50Y = $262.35
W + Y = 20 sweatshirts
In both equations, the variables represent the amount of sweatshirts sold, which is unknown, but when we know the amount it will add up to $262.35.
Y = 20 - W so lets substitute that into the first equation
10.95w + 13.50(20 - W) = 262.35
Distribute the 13.50 into the parenthesis.
10.95w + 270 - 13.50w = 262.35
Combine like terms.
-2.55w + 270 = 262.35
Subtract both sides by 270, the left side will cancel out.
-2.55w = -7.65
Divide -2.55 by both sides to isolate the variable.
W = -7.65/-2.55
(W)hite = 3 sweatshirts
Put 3 sweatshirts into our second equations.
Y = 20 - 3
(Y)ellow = 17 sweatshirts
So, 17 yellow sweatshirts were sold and 3 white sweatshirts were sold.
Now, lets check our math by substituting the # of sweatshirts into our first equation.
$10.95(3) + $13.50(17) = $262.35
$32.85 + $229.50 = $262.35
$262.35 = $262.35 (correct!)
True or false in a two column proof the right column states your reasons
Answers
In two column proof the right column states your reasons is true statement.
In a two-column proof, the right column typically contains the statements of reasons or justifications for each step taken in the left column.
The left column contains a sequence of statements that represent the logical progression of the proof, while the right column provides the reasoning or logical basis for each step to show that it follows from the previous statements.
This format is commonly used in geometry to provide a clear and organized presentation of the proof's logical structure.
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What might a model for 3 x 3/5 look like? How many fifths would be shaded in all?
Answers
3 times 3/5 comes out to 9/5, which is equivalent to 1 4/5.
You'd need to draw not one but two circles and divide each circle into 5 equal "slices." Then you'd shade one circle completely and shade 4 of the 5 slices of the other circle. 9 fifths (9 slices) would be shaded in all.
What is the least angle measure by which this figure can be rotated so that it maps onto itself? 45° 90° 180° 360° Left right double headed arrow.
Answers
In mathematics, specifically geometry, the least angle measure by which a regular, symmetric figure can be rotated to map onto itself is usually 90°. This concept falls under the umbrella of rotational symmetry.
Explanation:The question is about rotation of objects in geometry. To identify the least angle measure for a figure to map onto itself, we need to know the shape of the figure. However, assuming the figure is regular and symmetric (a square or a rectangle for example), the least angle measure by which it can be rotated to map onto itself is 90°.
It's important to remember the concept of rotational symmetry. A figure has rotational symmetry if it can be rotated less than 360° around a central point and still appear the same. For instance, a regular rectangle or square has a rotational symmetry of 90°, since we can rotate it 90 degrees and it appears the same.
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Please help! Explain how to solve!
Answers
This is what you do.
2/3 - 1/9
= (2*9) - (1*3) / 3*9
= 18 - 3 / 27
= 15/ 27
Simplify.
5/9 + y = 7/9
Now since you need to isolate the variable you have to subtract 5/9 from both sides. Since the denominator is the same you can just subtract the numerator.
So y = 2/9
I hope this helps love! :)
Find the ratio of 1 feet. 4 inches. to 1 yard
Answers
1 yard = (1 yard) * [(3 feet)/(1 yard)] * [(12 inches)/(1 foot)] = 36 inches
The ratio is: (16 inches)/(36 inches) = 16/36 = 4/9
(Note: the ratio has no units; it is expressed here as a fraction)
The ratio of 1 foot 4 inches to 1 yard is 16:36 or 4:9.
To find the ratio of 1 foot 4 inches to 1 yard, we first need to convert both measurements to the same unit. Since there are 3 feet in a yard and 12 inches in a foot, we can express both measurements in inches.
1 foot is equivalent to 12 inches.
Therefore, 1 foot 4 inches is:
1 [tex]\times[/tex] 12 + 4 = 12 + 4 = 16 inches
Now, since there are 3 feet in a yard, and each foot has 12 inches, 1 yard is equivalent to:
3 [tex]\times[/tex] 12 = 36 inches
Now we have both measurements in inches, and we can set up the ratio:
16 inches: 36 inches
Therefore, the simplified ratio is:
16:36.
We can further simplify this ratio by dividing both numbers by 4:
(16/4):(36/4) = 4:9.
At a canning company the daily production cost, y, is given by the quadratic equation y = 650 – 15x + 0.45x2, where x is the number of canned items. What is the MINIMUM daily production cost?
A) $1,025.00 B) $1,186.25 C) $525.00 D) $536.25
Answers
(-b/2a, y)
x = 15/0.9 = 16.67 canned itemz
y = 524.95 $
So it's C.
Answer:
Option C) is correct
Step-by-step explanation:
Given : y is the daily production cost at a canning company such that [tex]y=650-15x+0.45x^2[/tex] wherex is the number of canned items .
To find : Minimum daily production cost
Solution :
[tex]y=650-15x+0.45x^2[/tex]
On differentiating both sides with respect to x, we get
[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=-15+0.9x[/tex]
On putting [tex]\frac{\mathrm{d} y}{\mathrm{d} x}=0[/tex] , we get [tex]-15+0.9x=0\Rightarrow 15=0.9x\Rightarrow x=\frac{15}{0.9}=\frac{150}{9}=\frac{50}{3}[/tex]
We get intervals as \left ( -\infty , \frac{50}{3}\right )\,,\,\left ( \frac{50}{3},\infty \right )[tex]\left ( -\infty , \frac{50}{3}\right )\,,\,\left ( \frac{50}{3},\infty \right )[/tex]
For [tex]x=0\epsilon \left ( -\infty ,\frac{50}{3} \right )[/tex] , [tex]f'(0)=-15< 0[/tex]
For [tex]x=16\epsilon \left ( \frac{50}{3},\infty \right )[/tex] , [tex]f'(18)=-15+0.9(18)=-15+16.2=1.2> 0[/tex]
Therefore, [tex]y=\frac{50}{3}[/tex] is a point of minima.
So, minimum cost is equal to [tex]y\left ( \frac{50}{3} \right )[/tex]
[tex]y\left ( \frac{50}{3} \right )=650-15\left ( \frac{50}{3} \right )+0.45\left ( \frac{50}{3} \right )^2=650-250+125=\$ 525[/tex]
So, option C) is correct .
x = {(2, 4), (3, 4), (4, 4), (5, 4)} Is x a function and why?
Answers
Translate the following statement to an inequality.
A number is at most seven.
x > 7
x < 7
x ≥ 7
x ≤ 7
Answers
Answer:
x ≤ 7
Yuuupeeee
What is the slope of the line passing through the points (−3, 4) and (4, −1)?
35
−1
−57
3
Answers
The slope of a straight line passing through the points (x₁, y₁) and (x₂, y₂) is
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
The two given points are (-3,4) and (4,-1). Therefore the slope is
[tex]m= \frac{-1-4}{4-(-3)} = \frac{-5}{7} [/tex]
Answer: [tex]- \frac{5}{7} [/tex]
Answer:
the answer is C. -5/7
Solve for x.
5x2−34x=−24
Answers
10 - 34x =-24
-10 -10
-34x=-34
/-34 /-34
x= 1
To solve for x in 5x² - 34x = -24, set the equation to equal 0, factor the equation, and find the possible values for x. In this case, the solutions are x = 6/5 and x = 4.
Explanation:This is a problem in algebra, more specifically quadratic equations. To solve for x in the equation 5x² - 34x = -24, you first need to set the equation to equal zero: 5x² – 34x + 24 = 0.
Next you can factor the equation to find the possible values for x. In this case, the factored form is 5x² - 20x - 14x + 24 = 0 which further simplifies to 5x(x - 4) - 6(x - 4) = 0, and then (5x - 6)(x - 4) = 0.
When you set each factor equal to zero, you find the possible solutions for x. From 5x - 6 = 0, x = 6/5; and from x - 4 = 0, x = 4. Therefore the solutions are x = 6/5 and x = 4.
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Jane has $1000 that she would like to put in a savings account. The table below shows the balance over time in her account at a local bank.
Based on this model, how much would Jane have in her account after 12 years? Round to the nearest dollar if necessary.
time (years) balance in account
0 1000
1 1080
2 1166.40
3 1259.71
4 1360.49
answers
A.2518
B.2520
C.3000
D.2500
Answers
A television network counted 1,771,548 viewers watching the golf tournament on its channel.There where 5,861,014 viewers watching a football game on another channel. Round eack number to the nearest thousand about how many viewers were watching the two events on telveision? A. 7,500,000 B. 7,600,000 C.7,700,000 D. 8,000,000
Answers
Hope I helped! ☺♥
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If a class has 10 men and 14 women what is the ratio of men to the class
Answers
The ratio of men to class is 0.41.
We have a class of 10 men and 14 women.
We have to find out what is the ratio of men to the class.
Is a : b same as [tex]\frac{a}{b}[/tex] ?Yes, a : b is same as [tex]\frac{a}{b}[/tex]. Here, ' a ' is called Antecedent and ' b ' is called Consequent.
In the question given -
Total number of men in the class , n(m) = 10
Total number of students in class, n(c) = 24
Ratio of men to class = [tex]\frac{n(m)}{n(c)}[/tex] = [tex]\frac{10}{24}[/tex] = 0.41
Hence, the ratio of men to class is 0.41.
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Final answer:
The ratio of men to the entire class of 10 men and 14 women is 5:12, simplified by dividing the numbers of men and total students by the greatest common divisor.
Explanation:
The question asks to find the ratio of men to the entire class. The class has a total of 10 men and 14 women, which means the class size is 10 (men) + 14 (women) = 24 students.
To calculate the ratio of men to the entire class, divide the number of men by the total number of students: Ratio = 10 (men) / 24 (students). This can be simplified by dividing both numbers by the greatest common divisor, which is 2, giving us a simplified ratio of 5 (men) to 12 (students).
The ratio of men to the class is therefore 5:12.
A population of bacteria doubles every 12 hours initially the population of bacteria is 80 what is the population of bacteria after 30 hours, rounded to the nearest whole number?
Answers
Answer:
not 480, answer is 453 according to K12.
Step-by-step explanation:
took the k12 test, the answer is in fact, 453.
The population of the bacteria after 30 hours will be 400.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the population of bacteria doubles every 12 hours initially the population of bacteria is 80 what is the population of bacteria after 30 hours?
The population will be calculated as,
12 hours = 2 times of 80
1 hour = 2 / 12 times of 80
30 hours = ( 30 x 2 x 80 ) / 12
30 hours = 400 bacterias
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Which set of ordered pairs could be generated by an exponential function?
Answers
The correct answer is option C.
EXPLANATION
In order to determine which ordered pairs are generated by an exponential function, we examine the y-coordinates to see which one has a constant ratio.
As for the first ordered pairs,
[tex] \frac{0}{ \frac{1}{2} } \ne \frac{ \frac{1}{2} }{0} [/tex]
These ordered pairs cannot be generated by an exponential function.
For the second option also,
[tex] \frac{0}{ - 1} \ne \frac{ 1}{0} [/tex]
These ordered pairs too cannot be generated by an exponential function.
For the the third option,
[tex] \frac{1}{ \frac{1}{2} } = \frac{2}{1} = \frac{4}{2} = 2[/tex]
Therefore these ordered pairs were generated by an exponential function.
The fourth option too,
[tex] \frac{0}{1} \ne \: \frac{1}{0} [/tex]
The ordered pairs could not be generated by an exponential function.
Hanna shops for socks that cost $2.99 for each pair and blouses that cost $12.99 each. Let x represent the number of pairs of socks purchased, and let y represent the number of blouses purchased. Which equation models the purchases she made with $43.92?
Answers
and let y represent the number of blouses purchased.
socks that cost $2.99 for each pair
and blouses that cost $12.99 each
equation
2.99x + 12.99y = 43.92
Answer:
[tex]2.99x+12.99y=43.92[/tex]
Step-by-step explanation:
Hanna shops for socks that cost $2.99 for each pair.
And blouses that cost $12.99 each.
Let x represent the number of pairs of socks purchased.
Let y represent the number of blouses purchased.
So, the cost for x socks will be [tex]2.99x[/tex]
And cost of y blouses will be [tex]12.99y[/tex]
Total amount spent by Hanna = $43.92
So, the equation that will model this situation will be:
[tex]2.99x+12.99y=43.92[/tex]
The length and the width of a rectangle are both doubled. What is the ratio of the area of the larger rectangle to the area of the smaller rectangle?
I think it is 2:1. Am I right? If not, what is the ratio?
Answers
Small
A = lw
Large
A = (2l)(2w)
A = 4(lw)
Ratio is 4:1
A=(21)*(2w)=4*L*W
you are comparing 4lw to 1lw
the ratio is 4 to 1 or 4:1 or 4/1
A personal trainer makes $25,000 per year and has just begun contributing 6% of his salary to his 401k plan if his employer matches 9% of his contributions how much will have been contributed to the 401k plan after 4 years
Answers
Write the following inequality in slope-intercept form. −6x + 2y ≤ 42
Answers
y <= 6x + 42
Note: if it were a -2y, you’d have to flip the inequality sign when dividing by that negative 2.
:)
Answer: The required slope-intercept form is [tex]y\leq 3x+21.[/tex].
Step-by-step explanation: We are given to write the following inequality in slope-intercept form :
[tex]-6x+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the slope-intercept form of an inequality of the given form is as follows :
[tex]y\leq mx+c,[/tex] where m is the slope and c is the y-intercept.
From inequality (i), we have
[tex]-6x+2y\leq 42\\\\\Rightarrow 2y\leq6x+42\\\\\Rightarrow y\leq\dfrac{6}{2}x+\dfrac{42}{2}\\\\\Rightarrow y\leq 3x+21.[/tex]
Thus, the required slope-intercept form is [tex]y\leq 3x+21.[/tex].
You need five liters of yoda soda for every 12 guests if you have 36 guests how many liters do you need
Answers
Help me please! |-.-| The struggle is real...
2x^2-13x+4=0
solve using the quadratic formula
Answers
A simple index of three stocks opens the day with these values: The index rises 3.4% over the course of the day. What is the value of the index at the end of the day? Round your answer to the nearest hundred.
Answers
Answer:
The value of the index at the end of the day is $45392.6.
Step-by-step explanation:
Given : A simple index of three stocks opens the day with these values:
[name] [number of shares] [price per share]
stock x 5000 shares $4.10
stock Y 2000 shares $4.50
stock z 4000 shares $3.60
The index rises 3.4% over the course of the day.
To find : What is the value of the index at the end of the day? Round your answer to the nearest hundred ?
Solution :
Stock values of x,y and z is given by,
Stock x,
[tex]5000\times 4.10=\$20500[/tex]
Stock y,
[tex]2000\times 4.50=\$9000[/tex]
Stock z,
[tex]4000\times 3.60=\$14400[/tex]
The total amount will be
[tex]A=20500+9000+14400[/tex]
[tex]A=\$43900[/tex]
The index rises 3.4% over the course of the day.
The value of the index at the end of the day is
[tex]V=43900 \times (1+3.4\%)\\V=43900 \times (1+0.034)\\V=43900 \times 1.034\\V= 45392.6[/tex]
Therefore, the value of the index at the end of the day is $45392.6.
The product of three numbers is -216 but their sum is -18. What are these three numbers?
Answers
Find m∠abc
Geometry>Proving Angles Congruent
Answers
2x + 5x + 5 = 180
first, add 2x and 5x, then subtract 5 from each side
7x = 175
then divide both side by 7
x = 25
plug this value into the equation 5x + 5
5(25) + 5
and your answer will be 130
the measure of angle ABC (m∠ABC) is 130 degrees. it's essential to recognize that the sum of the angles along a straight line is always 180 degrees.
In this case, we have two angles, 2x and 5x+5, forming a straight line with an unknown angle (m∠ABC). So, we set up the equation:
2x + 5x + 5 = 180
Next, combine the like terms on the left side:
7x + 5 = 180
7x = 180 - 5
7x = 175
x = 175/7
x = 25
Therefore, the measure of angle ABC = 5x + 5
= 5(25) + 5
=130 degree
So, the measure of angle ABC (m∠ABC) is 130 degrees.
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I really really need help with this question! PLEASE!
Answers
A nervous kicker usually makes 70% of his first field goal attempts. if he makes his first attempt, his success rate rises to 90%. what is the probability that he makes his first two kicks?
Answers
The probability that the kicker makes his first two kicks is 0.63, or 63%.
Let's denote the events:
A: The kicker makes his first kick
B: The kicker makes his second kick
Given:
P(A) = 0.7 (probability that the kicker makes his first kick)
P(B|A) = 0.9 (probability that the kicker makes his second kick given that he made his first kick)
To find the probability of both events A and B occurring (the kicker making his first two kicks), we can use the multiplication rule of probability:
P(A and B) = P(A) * P(B|A)
Substituting the given probabilities, we have:
P(A and B) = 0.7 * 0.9 = 0.63
Therefore, the probability that the kicker makes his first two kicks is 0.63, or 63%.
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The probability that the kicker makes his first two kicks is 0.63, or 63%.
Explanation:To find the probability that the kicker makes his first two kicks, we need to multiply the probabilities of each individual kick.
The kicker has a 70% chance of making his first kick, which means he has a 30% chance of missing it.
If the first kick is made, his success rate rises to 90%. So, the probability of making the second kick, given that he made the first kick, is 90%.
To find the probability of both kicks being made, we multiply the probability of making the first kick (0.7) with the probability of making the second kick given that the first kick was made (0.9).
0.7 * 0.9 = 0.63
Therefore, the probability that the kicker makes his first two kicks is 0.63, or 63%.
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Which of the following is the range thanks
Answers
Let f(x)=−3x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.
What is the equation for g(x) ?
Enter your answer in the box.
g(x)= ___________
The graph of the function f(x)=|3x| is translated 4 units up.
What is the equation of the transformed function?
Enter your answer in the box.
g(x)= ___________
Answers
Ques 1)
[tex]g(x)=-12x+48[/tex]
Ques 2)
[tex]g(x)=|3x|+4[/tex]
Step-by-step explanation:Ques 1)
We know that if a graph is stretched by a factor of a then the transformation if given by:
f(x) → a f(x)
Also, we know that the translation of a function k units to the right or to the left is given by:
f(x) → f(x+k)
where if k>0 then the shift is k units to the left
and if k<0 then the shift is k units to the right.
Here the graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units right.
This means that the function g(x) is given by:
[tex]g(x)=4f(x-4)\\\\i.e.\\\\g(x)=4(-3(x-4))\\\\i.e.\\\\g(x)=-12(x-4)\\\\i.e.\\\\g(x)=-12x+48[/tex]
Ques 2)
We know that the transformation of the type:
f(x) → f(x)+k
is a shift or translation of the function k units up or down depending on k.
If k>0 then the shift is k units up.
and if k<0 then the shift is k units down.
Here, The graph of the function f(x)=|3x| is translated 4 units up.
This means that the transformed function g(x) is given by:
[tex]g(x)=|3x|+4[/tex]
Answer:
-12(x-4)
Step-by-step explanation:
I just took the test this is the answer!! Basically you take -3 and 4 and times it which would be -12. You then have x and another 4 left over. Since you are translating to the right you will be negative therefore giving us the answer -12(x-4).
The 6 members of the homecoming decorating committee want to make 525 paper flowers for the homecoming dance. Each flower takes about 412 minutes to make. About how long will each member of the committee have to spend making flowers?
Answers
Answer:
About 7 hours per person
Step-by-step explanation:
412 divided by 60 because there are 60 minutes in an hour.
6.8667 which is about 7 hours.
The each member will take 7 hours.
What is Unitary method?The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value
Given:
total member = 6 member
Each flower take = 412 minutes
we know
1 hour= 60 minutes
So, each member will have
=412/60
=6.866
=7 hours
Hence, each member will work for 7 hours
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