The diagonals BF and CE divide the hexagon ABCDEF into two equilateral triangles and a square. Find the perimeter of the hexagon if BF = 3 cm. Answer: P = cm
Answers
Because all the sides are the same size
Answer: The perimeter of the hexagon is 18 cm.
Step-by-step explanation: As given in the question, hexagon is shown in the attached figure.
The diagonals g and h divides the hexagon into two two equilateral triangles and one square .
Also, length of diagonal g = 3 cm.
We are to find the perimeter of hexagon.
We know that all the sides of a square are equal, so we have
length of b = length of h = length of e = length of g = 3 cm.
Since the two triangles are equilateral, so all their sides will be equal.
That is, length of a = length of f = length of g =length of c =length of d = length of h = 3 cm.
We know that the perimeter of a polygon is equal to the sum of the lengths of its sides.
Therefore, the perimeter of hexagon is given by
P = a + b + c + d + e + f = 3 + 3 + 3 + 3 + 3 + 3 = 18 cm.
Thus, the perimeter of the hexagon is 18 cm.
Related Questions
Which of the following statements about diversification is correct
Answers
Diversification means wide variety of different investment options available in the portfolio so that it becomes lesser risky towards minimizing losses in down market.
It provides better protection towards common issues like inflation, market instability, war effects, hike in exchange rates, interest rates reduction etc. So, we can conclude that :-
Diversification is the method to make investments less vulnerable to a catastrophic loss.
Hence, option A is best answer from given choices.
which expression is equivalent to ^3 square root 216x^3 y^6 z^12 ?
6xy^2 z^4
18xy^3 z^6
36xy^2 z^4
72xy^3 z^6
Answers
hope it helps
Answer:
Option A.
Step-by-step explanation:
The given expression is
[tex]\sqrt[3]{216x^3y^6z^{12}}[/tex]
We need to find the simplified form of the given expression.
It can be rewritten as
[tex]\sqrt[3]{6^3x^3y^6z^{12}}[/tex]
Using the properties of exponents, we get
[tex](6^3x^3y^6z^{12})^{\frac{1}{3}}[/tex] [tex][\because \sqrt[n]{x}=x^{\frac{1}{n}}][/tex]
[tex](6^3)^{\frac{1}{3}}(x^3)^{\frac{1}{3}}(y^6)^{\frac{1}{3}}(z^{12})^{\frac{1}{3}}[/tex] [tex][\because (ab)^x=a^xb^x][/tex]
[tex]6^{\frac{3}{3}}x^{\frac{3}{3}}y^{\frac{6}{3}}z^{\frac{12}{3}}[/tex] [tex][\because (x^m)^n=x^{mn}][/tex]
[tex]6^{1}x^{1}y^{2}z^{4}[/tex]
[tex]6xy^{2}z^{4}[/tex]
Hence, the correct option is A.
A pharmacist has an 18% alcohol solution. How much of this solution and how much water must be mixed together to make 10 liters of a 12% alcohol solution? Answer:
Answers
We need a table to do this. 3 rows and 3 columns. Across the top the columns are number of liters, % alcohol, and total. We will label the first row stuff with alcohol, the second row stuff with water, and the third row will be the mix of alcohol and water. In the first column we will put an x for alcohol since we don't know how much alcohol we have in the mix. In the second column we will put the decimal equivalent of the percent alcohol, which is .18. In the total column we will put the product of those 2, which is .18x. Now for the second row, water. We will put a y in the first column since we don't know how much water we have in the mix. In the second column we will put a 0, since water doesn't have any alcohol in it. In the third column we will put the product of the 2 which will be 0. In the third row, the mix row, we put a 10 since we want 10 L of this mix. We will put the decimal equivalent of how much alcohol we want in this mix which is .12. In the total column we put the product of those 2 which is 1.2. Since we are adding the alcohol and the water, x and y, to get a total of 10, this is our first equation. x+y=10. In the total column we will add the percent alcohol in the alcohol and the water to get 1.2. .18x + 0 = 1.2, or just .18x = 1.2. Let's divide both sides by .18 to find the amount of alcohol is in this mix. We get 6 2/3 liters of alcohol. If there is a total of 10 L of this mix, 10 - 6 2/3 = water, and the amount of water then is 3 1/3 L.
What is the difference of 54.59 and 26.61?
Answers
The graph of the function f(x) = ax2 + bx +c (where a, b, and c are real and nonzero) has two x-intercepts. Explain how to find the other x-intercept if one x-intercept is at (-b/a2 +3,0)
Answers
The method to find the other x-intercept for the function f(x) = ax² + bx + c is given in the explanation below the answer.
The other x-intercept is; ((-b/2a - 3), 0)
We are given the equation of the function;
f(x) = ax² + bx + c
where a, b and c are real numbers and non - zero
Now, this is a quadratic equation that has 2 roots and it means there will be two x-intercepts.
Also, in quadratic equations, the formula to find the x-coordinate of the line of symmetry of the graph is;
x = -b/2a
The line of symmetry divides the graph curve into 2 equal parts at the vertex. This means the two x - intercepts will be the same distance from the x-coordinate of the vertex or line of symmetry but on opposite sides.
Thus, if one x-intercept is at ((-b/2a + 3), 0), then the other coordinate using the line of symmetry reason above is; ((-b/2a - 3), 0)
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You are paid $13.70/hr. You work 40 hr/wk and your deductions are FICA (7.65%), federal tax withholding (11.55%), and state tax withholding (8.35%). Your housing and fixed expenses are 30% of your realized income per month and you want to save 6 months’ worth in an emergency fund. How much do you need to save?
Answers
To calculate the six-month emergency fund, we first determined the monthly net income after deductions from the gross monthly pay. Then, we found that 30% of the net income goes towards housing and fixed expenses. Multiplying this expense by six gives the total emergency fund needed, which is $2,848.20.
To calculate the amount needed for a six-month emergency fund, we first need to determine the monthly take-home pay after all deductions. The student earns $13.70 per hour and works 40 hours a week. Deductions include FICA (7.65%), federal tax withholding (11.55%), and state tax withholding (8.35%).
First, calculate the gross monthly income: $13.70/hr * 40 hrs/wk * 4 weeks/mo = $2,184/month.
Next, calculate total deductions: FICA (7.65% of $2,184) + Federal Tax (11.55% of $2,184) + State Tax (8.35% of $2,184) = $166.97 + $252.34 + $182.36 = $601.67.
Now calculate the net monthly income: $2,184 - $601.67 = $1,582.33.
The student's housing and fixed expenses are 30% of the net income, which amounts to $474.70/month. Therefore, for a six-month emergency fund, the student would need:
$474.70 * 6 months = $2,848.20 saved.
To save for a six-month emergency fund, you must first calculate your net monthly pay after deductions from your salary, which is determined to be $1,588.12. Then calculate 30% of this for your monthly fixed expenses, and finally, multiply that amount by six to determine the total savings required for the emergency fund, which amounts to $2,858.64.
To calculate how much you need to save for an emergency fund, we first need to determine your monthly take-home pay after deductions. Your gross pay per week is $13.70 per hour multiplied by 40 hours, which equals $548. Your gross pay per month is then $548 times 4 weeks, totaling $2,192. We will then subtract the deductions: FICA (7.65%), federal tax (11.55%), and state tax (8.35%). Let's calculate each:
FICA: $2,192 x 7.65% = $167.68
Federal Tax: $2,192 x 11.55% = $253.17
State Tax: $2,192 x 8.35% = $183.03
Your total deductions are $167.68 + $253.17 + $183.03 = $603.88.
So, your net monthly pay is $2,192 - $603.88 = $1,588.12.
Next, we calculate your fixed expenses which are 30% of your net income: $1,588.12 x 30% = $476.44.
To determine the amount needed for a six-month emergency fund, you multiply your monthly fixed expenses by six:
$476.44 x 6 = $2,858.64.
Therefore, you need to save $2,858.64 for your emergency fund.
If you had an hour a week to spend with a low-achieving 3rd grader, over say, six weeks, what would you focus on with them?
Answers
You can't do much with an hour in a week for six weeks, even with a 3rd grader. That's the bad news. The good news is that if you get him or her to work with you, and give them a second hour, you might be able to do something. What I would focus on depends on what I find out about what they can do. It also depends on how they take in information. Most people (almost all) learn either by hearing or seeing. Most younger children learn better by doing than by being told.
Always try and make some of what you do physical. You didn't mention the subject area, but I'm assuming mathematics because that's where you listed it.
Find out what your jurisdiction expects a third grader to do. Talk to the teacher if you are the parent of such a child. The process of learning is an extremely complex task. Don't take it on if you are flying blind and are unable to talk to the teacher. You need to be the parent or you need to take the parent along. In almost every place, no teacher will talk to someone who is unrelated to the child.
When you know more about the child, post again. I don't know exactly how you can contact me again (perhaps making me a friend), but when you know more, you are perfectly welcome to contact me again.
1.64*10^0/2.0*10^2 in scientific notation
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[tex]1.64 * 10^0 : 2.0 * 10^2= (1.64:2.0) * 10^0:10^2= 0.82 * 10 ^{0-2} = \\ \\ 0.82 * 10 ^{-2} =0.82 * \frac{1}{10^2} =0.82 * \frac{1}{100} =0.0082= \boxed{ 8.2 * 10^{-3} } [/tex]
The student's expression is simplified by dividing 1.64 by 100 then expressing the result in scientific notation as 1.64 imes 10⁻².
The student's question involves simplifying a mathematical expression that uses scientific notation. The expression is 1.64 times 10⁰ divided by 2.0 times 10². Here's a step-by-step breakdown:
Identify the powers of ten: The denominator has 10 to the power of 2, which is 10 squared or simply 100. The numerator has 10 to the power of 0, which equals 1.
Simplify the expression: Divide 1.64 by 100 (2.0 times 10²), which gives a result of 0.0164.
Express in scientific notation: 0.0164 can be written as 1.64 times 10⁻².
The least natural number that is divisible by three different primes is
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1) We start by writting down natural numbers one by one. Then we check for it's divisors that are prime numbers. We continue doing this until we find the solution. This approach could take quite some time to complete but it will eventually give the correct answer.
2) We need to find natural number that is divisible by three primes. And it needs to be smallest possible. This means that the product of these numbers is our solution.
We can not take any three random primes as they will not give us the requested solution. 7* 11 * 31 = 2387
We need to take three lowest primes. Those are 2, 3 and 5. 1 is not considered to be a prime.
2 * 3 * 5 = 30
So our solution is 30. All lower numbers do not have three primes as divisors.
The least natural number that is divisible by three different primes is 30.
The positive whole numbers are termed as natural Numbers.
Numbers that have only two factors are termed as Prime Numbers.
According to the question, the least natural number that is divisible by three different primes is calculated by multiplying three least prime numbers as-
[tex]2\times 3\times 5=30[/tex].
Here, the natural number should be the least so, you need to take lowest three prime numbers only.
Hence, The least natural number that is divisible by three different primes is 30.
Learn more about prime numbers here:
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Convert 210° from degrees to radians. Use the value of π found on a calculator, and round answers to four decimal places, as needed.
Answers
To solve the exercise above and convert 210° from degrees to radians, you have to mutilply it by π and divide it by 180°, as below:
210° to radians:
=(210°xπ)/180°
Therefore, the result is:
=(7/6)π radians
=3.6651 radians
Answer: 3.6651
Step-by-step explanation:
The formula to convert [tex]\theta[/tex] degrees to radians is given by :-
[tex]\dfrac{\pi}{180^{\circ}}\times\theta[/tex]
Given : Angle : [tex]\theta=210^{\circ}[/tex]
Then , the measure of angle in radians is given by :-
[tex]\dfrac{\pi}{180^{\circ}}\times210^{\circ}[/tex]
Using the value of [tex]\pi=3.14159[/tex], we get
[tex]\dfrac{3.14159}{6}\times7\approx3.6651[/tex]
The price of a condominium is $102,000. The bank requires a 5% down payment and one payment and one point at the time of closing. The cost of the condominium is financed with a 30-year fixed-rate mortage at 8.5%? Find the required down payment.
Answers
https://brainly.com/question/8881392
Tara is taller than Jeff. Jeff is 47 inches tall. Write an inequality that compares Tara's height in inches, t, to Jeff's height
Answers
Answer:
t > 47
Step-by-step explanation:
Tara is taller than Jeff. Jeff is 47 inches tall.
We need to write an inequality that compares Tara's height to Jeff's height
Let t be the height of Tara
and j be the height of Jeff
Tara is taller than Jeff, we use greater than symbol for taller
So inequality becomes t > j
Given Jeff is 47 inches tall, so replace 'j' with 47
Answer is t > 47
Final answer:
To compare Tara's height to Jeff's, the inequality used is t > 47, indicating Tara is taller than Jeff.
Explanation:
The question asks you to write an inequality that compares Tara's height, represented by t, to Jeff's height, which is 47 inches. To represent that Tara is taller than Jeff using an inequality, you use the 'greater than' symbol (>). Therefore, the correct inequality to show that Tara is taller than Jeff is t > 47. This inequality means that Tara's height in inches is greater than 47 inches.
What is the area of this figure?
Enter your answer in the box.
Answers
S=S1+S2, where S1 is area of the parallelogram, S2 is area of the triangle.
S=9*5+0.5*8*9=45+32=77 m².
Answer: 77 m.²
if the parent function is square root x. describe the translation of of the fuction square root x-1
Answers
f(x)->f(x-h)+k
when the functions has been translated h units to the right, and k units up.
Compare with
sqrt(x)->sqrt(x-1)+0
we see that h=1, k=0.
Thus it is a horizontal translation of 1 unit to the right. (zero unit up).
Final answer:
The function √(x-1) is a horizontal translation of the function √x by 1 unit to the right along the x-axis.
Explanation:
The function √(x-1) represents a horizontal translation of the parent function √x. The translation is 1 unit to the right along the x-axis.
In function transformation terms, when a function f(x) is altered to become f(x - a), this translates the graph of the function to the right by 'a' units if 'a' is positive and to the left by 'a' units if 'a' is negative.
To illustrate, the graph of f(x) = √x is translated to become g(x) = √(x-1). Compared with the graph of f(x), every point on the graph of g(x) will be 1 unit to the right.
There are no changes vertically, so there is no translation up or down.
how do you find a meadian?
Answers
Final answer:
The median is a number that measures the center of the data. To find the median, arrange the data in ascending order and determine the middle value. If the data has an even number of values, the median is the average of the two middle values.
Explanation:
The median is a number that measures the center of the data. It separates the data into two halves, with half the values being smaller or equal to the median and the other half being larger or equal to it. To find the median, you need to arrange the data in ascending order and then determine the middle value.
If the data has an even number of values, the median is the average of the two middle values.
Lori is running in a marathon which is 26.2 Miles long so far she has run 1/10 of a marathon how far has Lori run
Answers
If she has run 1/10 of the marathon, we can divide 26.2 by 10.
26.2/10= 2.62
She has run 2.62 miles.
I hope this helps!
~kaikers
Give the equivalent numerator if the denominator is x³y².
Answers
Final answer:
To find the equivalent numerator, we can multiply both sides of the equation by the denominator.
Explanation:
The equivalent numerator can be found by multiplying both sides of the equation by the denominator, which is x³y². This will cancel out the denominator on the right side. The result will be the equivalent numerator.
For example, if we have the equation 2x³y² = 6, we can multiply both sides by x³y² to get rid of the denominator:
equation * (x³y²) = 6 * (x³y²)
The x³y² on the left side will cancel out, leaving us with the equivalent numerator:
equivalent numerator = 6 * (x³y²)
So, the equivalent numerator is 6x³y².
Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.
Find the distance AA'
Answers
distance(AA') = √(2^2 + 1^2)
= √5
= 2.24
answer
Distance AA' = √5 or = 2.24
Answer with Step-by-step explanation:
As we can see from the graph:
A=(0,0) and A'=(2,1)
Distance between (x1,y1) and (x2,y2) is given by:
[tex]\sqrt{{(x1-x2)}^2+{(y1-y2)}^2}[/tex]
Here (x1,y1)=(0,0) and (x2,y2)=(2,1)
Hence, distance between A and A' is:
[tex]\sqrt{{(0-2)}^2+{(0-1)}^2}[/tex]
= [tex]\sqrt{4+1}[/tex]
= [tex]\sqrt{5}[/tex]
Hence, distance AA'=√5
Which statement about BQ←→ is correct?
BQ←→ is a tangent line because m∠ABQ=90°.
BQ←→ is a tangent line because △ABQ is not a right triangle.
BQ←→ is not a tangent line because ∠BAQ is an acute angle.
BQ←→ is not a tangent line because ∠BQA is an acute angle.
Answers
We have a circle A and a line segment BQ is passing through the circle A such that it forms a triangle ABQ.
From the diagram, we have some information about the angles of triangle ΔABQ as follows :-
angle QAB = 36 degrees and angle BAQ = 54 degrees.
We know about the Triangle Sum theorem which states "The sum of all interior angles of any triangle is 180 degrees".
We can use this theorem to find the third angle of the triangle ΔABQ.
∠ABQ + ∠BQA + ∠QAB = 180 degrees
∠ABQ + 54° + 36° = 180°
∠ABQ + 90° = 180°
∠ABQ = 180° - 90°
∠ABQ = 90 degrees
If any line makes a right angle with the radius of any circle, then this line must be a tangent to that circle.
So, BQ would be a tangent line because angle ∠ABQ = 90 degrees. Hence, option A is correct.
A rectangular prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches. What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal.
Answers
A rectangular prism has a length of 3 1/2 inches, a width of 5 inches, and a height of 1 1/2 inches. What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal.
we know that
length=3 1/2 in--------> (3*2+1)/2=7/2 in
width= 5 in
height=1 1/2 in--------> (1*2+1)/2=3/2 in
[volume of the prism]=[length]*[width]*[height]
[volume of the prism]=[7/2]*[5]*[3/2]=105/4 in³-------> 26.25=26 1/4 in³
the answer is 26 1/4 in³
Answer:
26 1/4
Step-by-step explanation:
took the test 100% 4.08 Quiz: Finding the Volume of Rectangular Prisms and Problem Solving
is 1.5 miles greater than 2500 yards
Answers
1.5 miles > 2500 yards
1 mile = 5280 feet
1 yard = 3 feet
1.5 miles = 7920 feet
2500 yards = 7500 feet
7920 feet > 7500 feet
Hope I helped!
Let me know if you need anything else!
~ Zoe
According to our customary units of miles, 1 mile is equal to 5,280 feet - and 3 feet is a yard. That means, we have to divide 5,280 by 3 to figure out how many yards are in a mile:
5280/3 = 1760
That means that one mile is 1760 yards. But we're not finished yet. It says 1/5 miles, not one mile. Therefore, we take one half of the total distance in yards of a mile and add it to that 1760, because it's 1.5, or 1-and-a-half. Which, in technical terms means "1-plus-a-half".
We have:
1760 + 1760/2 = 1760 + 880 = 2640
Therefore, 1/5 miles, since it's 2640 yards, is greater than the 2500 yards specified in the question.
Hope this helps!
how many runners ran times of six to seven minutes?
Answers
The perimeter of a is 35.54 inches longer than the perimeter of a square of side 6.75 Find the perimeter of the rectangle to the nearest inches. tenth of an inch
Answers
Perimeter of rectangle: 27 + 35.54 = 62.54 inches
Sarah and Angela have a collection of pennies and nickels in their piggy banks. Which girl has more coins in her bank? Explain how you know using numbers and symbols.Sarah and Angela have a collection of pennies and nickels in their piggy banks. Which girl has more coins in her bank? Explain how you know using numbers and symbols.
Answers
The speed limit is posted in most areas, but, if not, the ___________ speed limit will be in effect.
Answers
When no specific speed limit is posted, the default speed limit applies. These defaults are set by local or state law and can vary. Drivers must adhere to these limits and drive safely for conditions.
Explanation:In most areas, when specific traffic speed limit signs are not posted, what's known as the default speed limit applies. These default speed limits are not posted on signs and instead are set by local or state law. It's important to stay aware of these limits in different areas, as they can vary. For instance, in many cities, the default speed limit is 25 mph unless otherwise posted. However, it should be noted that these default limits may not protect you from being pulled over if the police deem your speed unsafe for the current conditions. Thus, it's recommended to always drive at a speed that is appropriate for the conditions, even if you are technically within the speed limit.
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Janice earns $3,750 per month. If she works all 12 months of the year, what’s her yearly salary?
Answers
Answer: $45000
Answer:
The answer is 45, 000. if you multiply 3,750 times 12 thats what her yearly salary.
Find the sum of the geometric series with a1 = -1, r = -2 And a10 = 512
Answers
[tex]S_n=a_1+a_2+\cdots+a_{n-1}+a_n[/tex]
[tex]S_n=a_1+ra_1+\cdots+r^{n-2}a_1+r^{n-1}a_1[/tex]
[tex]rS_n=ra_1+r^2a_1+\cdots+r^{n-1}a_1+r^na_1[/tex]
[tex]\implies S_n-rS_n=a_1-r^na_1\iff(1-r)S_n=(1-r^n)a_1\implies S_n=\dfrac{1-r^n}{1-r}a_1[/tex]
You're given that [tex]a_1=-1[/tex] and [tex]r=-2[/tex], so
[tex]S_n=\dfrac{1-(-2)^n}{1-(-2)}(-1)=-\dfrac{1-(-2)^n}3[/tex]
The fact that you're given [tex]a_{10}[/tex] makes me think you're supposed to find [tex]S_{10}[/tex], which is just a matter of setting [tex]n=10[/tex] in the formula above.
[tex]S_{10}=-\dfrac{1-(-2)^{10}}3=-\dfrac{1-1024}3=341[/tex]
The data set represents a progression of hourly temperature measurements.Use the regression equation to predict the temperature during the sixth hour. x 0 1 2 3 4 5 y 20 16 10 0 -7 -20
Answers
Answer:
the answer is C: y = -0.875x^2 - 3.956x + 20.179
Step-by-step explanation:
To predict the temperature during the sixth hour, we need to find the regression equation of the line that best fits the given data. Using the slope and y-intercept, we can substitute x = 6 into the equation to find the predicted temperature, which is -3.42.
Explanation:To predict the temperature during the sixth hour using the regression equation, we need to find the equation of the line that best fits the given data. The regression equation is of the form y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we need to calculate the slope (m) and the y-intercept (b) using the given data points. Then, we can substitute x = 6 into the equation to find the predicted temperature.
Using the formula for the slope (m) and the y-intercept (b), we find that m = -5.07 and b = 22.2. Substituting x = 6 into the regression equation, we get y = -5.07(6) + 22.2 = -3.42. Therefore, the predicted temperature during the sixth hour is -3.42.
Julia has to measure an object.she does not have a ruler. Tell what Julia could do to solve her problem.
Answers
How to simplify this expression
Answers
Answer:
[tex]\dfrac{x+2}{x+1}[/tex]
Step-by-step explanation:
Factor the numerator and cancel common factors from numerator and denominator.
[tex]\dfrac{x^2-4}{(x-2)(x+1)}=\dfrac{(x-2)(x+2)}{(x-2)(x+1)}=\dfrac{x+2}{x+1}[/tex]