Using the diagram of a regular hexagon, fill in the blanks for the steps to solve for the area of a hexagon with sides equal to 16 cm.
(1) How many equilateral triangles are there? _____
(2) What is the measure of each of the three angles in the equilateral triangle? _____
(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____
(4) What is the vocabulary word for the segment a? _____
(5) What is the length of the short side of one of the 30-60-90 triangles? _____
(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____
(8) What is the height of one of the the equilateral triangles? _____
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____
Answers
Answer:
(1) How many equilateral triangles are there? ___6__
(2) What is the measure of each of the three angles in the equilateral triangle? __60°_
(3) If we cut an equilateral triangle down the middle (green line), what special right triangle do you create? _30-60-90_
(4) What is the vocabulary word for the green line? _Perpendicular bisector_
(5) What is the length of the short side of one 30-60-90 triangle? __4_cm_
(6) What is the length of the hypotenuse of one 30-60-90 triangle? __8 cm
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg. _4√3_cm
(8) What is the height of the equilateral triangle? _4√3_cm
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. ½(8)(4√3) = 16√3 cm²
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _8(16√3) = 128√3 cm²_
Step-by-step explanation:
In geometry, a hexagon can be defined as a polygon with six sides. The two-dimensional shape has 6 sides, 6 vertices and 6 angles
What is Hexagone?In geometry, a hexagon can be defined as a polygon with six sides. The two-dimensional shape has 6 sides, 6 vertices and 6 angles
The answers of all the fill in the blanks are given below:
(1) How many equilateral triangles are there ___6__
(2) What is the measure of each of the three angles in the equilateral triangle __60°_
(3) If we cut an equilateral triangle down the middle (green line), what special right triangle do you create? _30-60-90_
(4) What is the vocabulary word for the green line? _Perpendicular bisector_
(5) What is the length of the short side of one 30-60-90 triangle? __4_cm_
(6) What is the length of the hypotenuse of one 30-60-90 triangle? __8 cm
(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg. _4√3_cm
(8) What is the height of the equilateral triangle? _4√3_cm
(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. ½(8)(4√3) = 16√3 cm²
(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _8(16√3) = 128√3 cm²
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Related Questions
if tan2
x = 3 then value of
x is
Answers
Answer:
If tan2 x = 3 then the value of x is 3. So three is your answer!
Step-by-step explanation:
What are the coordinates of point P' if point P(3, -4) is reflected over the line y = x? *
Answers
Answer:
(4,3)
Step-by-step explanation:
please mark as brainliest if correct
thank you
19NBoli
n-(m+n): use m= 2,and n=-3
Answers
Answer:
the answer is in the photo below
ends of diameter: (9, 15) and (15, 7)
Answers
(
x
−
12
)
2
+
(
y
−
11
)
2
=
25
What are the steps for solving and graphing 2x - 3y = 9?
please help!
Answers
Answer:
Step-by-step explanation:
Which statement about the slope of a line is true?
A line with a negative slope increases as it is viewed from left to right.
A line with a positive slope increases as it is viewed from left to right.
A line with a positive slope decreases as it is viewed from left to right.
Answers
Answer:
B) A line with a positive slope increases as it is viewed from left to right.
Step-by-step explanation:
A line with a positive slope increases as it is viewed from left to right.
A positive slope means that as a line on the line graph moves from left to right, the line rises.
Hope this helps :)
A weight-loss clinic advertised that last month its patients, on average,8lb lost . Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements is true, mark the appropriate box. Last month all of their patients lost at8lb least . Last month more than half of their patients lost at least 8lb. Last month some of their patients lost more than4lb . Last month at least one of their patients lost exactly 8lb. Two months ago some of their patients lost at least 8bl. None of the above statements are true.
Answers
Answer:
Given:
A weight-loss clinic advertised that last month its patients, on average, lost 8 lbs
Average refers to mean
a. Last month all of their patients lost at least 8 lbs.
Answer: Mean or average is a measure of central tendency or in other terms refers to the central value of the dataset. If the value of mean/average is 8lb, it signifies that there are some patients who have lost weights more than 8 lbs. So, this statement is False
b. Last month at least one of their patients lost exactly 8 lbs.
Answer: It is a possibility that all the patients have lost their weights greater than or less than 8 lbs. Since the mean is computed by summing up all the values (weight loss in this case) by the total number of observations, it is possible that there can be no patient who has lost exactly 8lbs. So, this statement is False.
c. Two months ago some of their patients lost at least 8 lbs.
Answer: It is clearly mentioned that last month its patients, on average, lost 8 lbs. No information is given about the weight loss of patients before the last month. So, there is not sufficient data to check whether this statement is correct or not.
d. Last month at least one of their patients lost less than 3 lbs.
Answer: It is a possibility that all the patients have lost their weights greater than 3 lbs. Since the mean is computed by summing up all the values (weight loss in this case) by the total number of observations, it is possible that there can be no patient who has lost less than 3lbs. So, this statement is False.
e. Last month, the number of their clients who lost less than 8 lbs was equal to the number of their clients who lost more than 8 lbs.
Answer: Mean is a measure of central tendency which is computed by the diving sum of all observations with the number of all observations (the sum of observations lesser than the mean is compensated by the sum of observations greater than the mean) and for the mean equal to 8lbs, there should be an equal number of people who lost less than 8 lbs and the number of people who lost more than 8 lbs. Hence, this statement is True.
Answer e.Last month, the number of their clients who lost less than 8 lbs was equal to the number of their clients who lost more than 8 lbs is True
the statements that must be true based on the information are:
- Last month all of their patients lost at least 8 lb.
- Last month more than half of their patients lost at least 8 lb.
- Last month some of their patients lost more than 4 lb.
- Last month at least one of their patients lost exactly 8 lb.
Based on the information provided, we can make the following conclusions:
1. Last month, all of their patients lost at least 8 lb. (This statement is true since the average refers to the mean, and the average weight loss was 8 lb. Therefore, all patients must have lost at least 8 lb.)
2. Last month, more than half of their patients lost at least 8 lb. (This statement is true since the average weight loss was 8 lb, which means that at least half of the patients must have lost 8 lb or more. As the average is pulled up by higher values, more than half should have achieved at least 8 lb weight loss.)
3. Last month, some of their patients lost more than 4 lb. (This statement is true since the average weight loss was 8 lb. If the average is 8 lb, then there must be patients who lost more than that, and losing more than 4 lb is definitely possible.)
4. Last month, at least one of their patients lost exactly 8 lb. (This statement is true since the average weight loss was 8 lb. For the average to be exactly 8 lb, at least one patient must have lost exactly 8 lb.)
5. Two months ago, some of their patients lost at least 8 lb. (There is no information provided in the given data to make any claims about weight loss two months ago, so we cannot conclude this statement based on the information given.)
So, the statements that must be true based on the information are:
- Last month all of their patients lost at least 8 lb.
- Last month more than half of their patients lost at least 8 lb.
- Last month some of their patients lost more than 4 lb.
- Last month at least one of their patients lost exactly 8 lb.
The statement "Two months ago some of their patients lost at least 8 lb" cannot be determined from the given information, so it is not necessarily true or false based on the data provided.
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Helen counted six dollars and four cents in her purse. She recorded this amount in decimal form as $6.40. Did she record it correctly? If she made a mistake, what is the correct way
to record this amount of money as a decimal?
Pls answer will give brainiest
Answers
Answer:
6 dollars and 4 cents
Step-by-step explanation:
which number line represents the solution of 1 - 2x ≥ 3
Answers
Answer:
Number line D
Step-by-step explanation:
1 - 2x ≥ 3
Subtraact 1 from both sides
-2x ≥ 2
Multiply both sides by -1
When multiplying by a negative the inequality is reversed
2x ≤ -2
Divide both sides by 2
x ≤ -1
Number line D
Solve the compound inequality.
3x + 1 <4 or 9x > 31
Answers
Answer:
Step-by-step explanation:
3x < 4 - 1 or x > 31/9
3x < 3 or x > 31/9
x < 1 or x > 31/9
What is 2x=6 pls answer fasttt
Answers
Answer:
×=6/2=3
Step-by-step explanation:
Please take a look at the picture
Answers
Write a linear function f give f(0)=2 f(3)=-1
Answers
Answer:
f(x) = ax + b,
Step-by-step explanation:
Am Not Really Sure About The Answer, So Pls Try And Cross Check It
What is the perimeter of the shape below?
3 cm
4 cm
8 cm
4 cm
Answers
Answer:
:D
Step-by-step explanation:
it is 19 cm
A driver driving a business trip of 240 miles would have reached his destination if he'd been able to drive 12 mph faster than he made the trip. Find the average speed of his trip.
Answers
The average speed of his trip is = 12 mile/ hour
The total distance covered by the driver = 240 miles
The rate at which he traveled = 12 miles per hour
Therefore, the time he used to cover his distance
= 240/12
= 20 hrs
But average speed = distance/ time
= 240/ 20
= 12 miles/ hour
Therefore, the average speed of his trip is = 12 mile/ hour
Learn more here:
https://brainly.com/question/11753352
3. Sarah has a goal to save $81.84 for a new gan
If she has 12 weeks to save the money, how much does she need
to save each week?
Answers
Answer:
93.84
Step-by-step explanation:
I think I'm not sure
pleasee help meeeeeee
Answers
Step-by-step explanation:
we mulyiply 3*1 =x-7
3=x-7
-x= -7-3
-x= -11 so when we divide -11 by -x it becomes 11
Help please!! I will mark brainilist and give a lot of points.
This is Pythagorean theorem.
Formula: a^2+b^2=c^2
When I say ^2 I mean to the power of 2.
The question is asking me to solve for a.
Then give me b and c which is b = 17 1/3 and c = 16.
How do I solve for a when b is greater than c? Won’t that give me a negative a? You can’t have a negative a right?
Unless I’m wrong.
Please help my solve this!!!!! :D
Answers
Hello there,
I just looked into the question and you are absolutely right whatever you inferred.I think the question might be wrong.The value of c should be greater than b.I guess it will like this:[tex]b = 16 \: \: \: c = 17 \frac{1}{3} [/tex]The values should be like this.I am solving the equation by this:[tex] {a}^{2} = {c}^{2} - {b}^{2} \\ = > {a}^{2} = {(17 \frac{1}{3}) }^{2} - {(16)}^{2} \\ = > {a}^{2} = {( \frac{52}{3} )}^{2} - {(16)}^{2} \\ = > {a}^{2} = ( \frac{52}{3} - 16)( \frac{52}{3} + 16) \\ = > {a}^{2} = ( \frac{52 - 48}{3} )( \frac{52 + 48}{3} ) \\ = > {a}^{2} = \frac{4}{3} \times \frac{100}{3} \\ = > {a}^{2} = \frac{400}{9} \\ = > a = \sqrt{ \frac{400}{9} } \\ = > a = \frac{20}{3} \\ = > a = 6 \frac{2}{3} [/tex]So, the value of a is[tex]a = 6 \frac{2}{3} [/tex]
Hope you could get an idea from it.
Doubt clarification - use comment section.
Pleas someone help me with this it's my last question
Answers
Answer:
we need to find out if the following get x = 2 as a final product
-2(x-4) = 4
-2x + 8 = 4
-2x = -4
x = 2
so it is a solution
26/x = 13
26 = 13x
x = 26/13
x = 2
so it’s a solution
-3.8x = -7.4
x = 7.4/3.8 ≠ 2
you get ≈ 1.95
so it’s not a solution
4(x-1) - 3(x-2) = -8
4x - 4 - 3x + 6 = -8
x + 2 = -8
x = -10
so it’s not a solution
Answer:
x= 2 is the solution of first two equations.
Step-by-step explanation:
what is the value of the digit 4 in 0.342
Answers
Answer:
0.04 = four hundredths
Step-by-step explanation:
To find the value of a digit in a number, set all the other digits to zero.
The value of the 4 is ...
0.040
The 4 is in the hundredths place, so its value is four hundredths.
Bradley is 27 years older than Madison. Seven years ago, the sum of their age was 59. How old are they now?
Answers
Answer:
bradley is 50 and madison is 23
Step-by-step explanation:
m + 27 = b
(b - 7) + (m - 7) = 59
[(m + 27) - 7] + (m - 7) = 59
m + 20 + m -7 = 59
2m + 13 = 59
2m = 46
m = 23, b = 23 + 27 = 50
A certain length measurement is performed 500 times. The mean value is 5.0m, and the standard deviation is 2cms. Assuming a normal distribution for the error in the measurement, how many readings fall within 5.15cm of the mean value
Answers
Using the normal distribution, it is found that 495 readings fall within 5.15cm of the mean value.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
Mean of 5m, hence [tex]\mu = 5[/tex].Standard deviation of 2 cm, hence [tex]\sigma = 0.02[/tex]To find the proportion of readings that fall within 5.15cm of the mean value, first we need to find the following z-score:
[tex]z = \frac{0.0515}{0.02}[/tex]
[tex]z = 2.575[/tex]
The proportion is P(|z| < 2.575), which is the p-value of z = 2.575 subtracted by the p-value of z = -2.575.
Looking at the z-table, z = -2.575 has a p-value of 0.005, and z = 2.575 has a p-value of 0.995.
0.995 - 0.05 = 0.99
Out of 500 measurements:
(0.99)500 = 495
495 readings fall within 5.15cm of the mean value.
A similar problem is given at https://brainly.com/question/24663213
Mrs. sanders is bringing colored marshmallows to school so her students can do a graphing experiment. she has 25 students. if she gives each student 1/2 cup of marshmallows , how many cups of marshmallows will she need to bring to class?
Answers
Answer:
25 x 1/2 = 12.5
12 1/2 cups
A rectangle has a length of 72 cm and a width of 56 cm. A second rectangle has the same area as this one, but its width is 21 cm. What is the length of the second rectangle?
Answers
Answer:
192
Step-by-step explanation:
Well if the first rectangle is 72 and 56, then we can find the area of that by multiplying length times width which would be 4032, so that would be the area of the second one. then we divide 4032 by 21, which is 192.
P.S, This is my first question answered, so if im wrong please let me know, thank you!
Answer: 192
Step-by-step explanation:
As given, the other rectangle has the same area as this one, but its width is 21 cm. Hence, the length is 192 cm.
The low temperatures in December at each of three locations are shown.
Location 1: 18°F
Location 2: –5°F
Location 3: –22°F
Choose each statement that is both true and correctly justified based on this information.
(A) Because 18 < –22, it was colder, on average, at Location 3 than at Location 1.
(B) Because 18 < –22, it was warmer, on average, at Location 3 than at Location 1.
(C) Because –22 < 18, it was colder, on average, at Location 3 than at Location 1.
(D) Because –22 < 18, it was warmer, on average, at Location 3 than at Location 1.
(E) Because –22 < –5, it was warmer, on average, at Location 2 than at Location 3.
Answers
Answer:
According to me answer is option C and E
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Guys what's 1 9/15+ 1 5/15
Answers
Answer:
2 14/15. answer need to be 20
Answer the following questions,
0
(a) What number is 95% of 80
0
(b) 85% of what is 51?
Answers
Answer:
95% of 80 is 76 and 85% of 60 is 51.
Step-by-step explanation:
Answer:
a. 76, b. 60.
Step-by-step explanation:
a) 80 * 0.95 = 76.
b) 0.85 x = 51
x = 51/0.85 = 60.
The diameter of the smallest visible particle is 0.0002 in. Express this number in scientific notation.
Answers
Answer:
Diameter = 2 × [tex]10^{-4}[/tex] inches
Step-by-step explanation:
Given the diameter of the smallest visible particle, 0.0002 inches, we can express this into the following scientific notation: 2 × [tex]10^{-4}[/tex] inches.
In expressing decimal forms into scientific notation, the goal is to move the decimal point towards the right, until there is only one non-zero digit remaining towards the left-side of the decimal point. In this case, it will take 4 units towards the right of the sole non-zero digit, which is 2. Moving the decimal point towards the right means that 10 will have a negative exponent.
Therefore, the scientific notation of 0.0002 inches is 2 × [tex]10^{-4}[/tex] inches.
Answer:
2·[tex]10^{-4}[/tex]
Step-by-step explanation:
A bag contains 8 white marbles, 4 green marbles and 3 blue marbles. 2 marbles are selected at random without replacement, find the probability both green
Answers
A triangle has side lengths of (9d+ 4) centimeters, (9d + 2) centimeters, and (3f - 2) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answers
Perimeter is the sum of the 3 sides.
Add the 3 sides together by combining like terms.
9d +4 + 9d+2 + 3f -2
9d+9d = 18d
4 + 2-2 = 4
Combining like terms you get:
18d +3f +4