The star shape is made from a regular hexagon and six congruent equilateral triangles The area of the star shape is 96cm squared Work out the area of the regular hexagon.
Answers
Answer:
48 Square Centimeters
Step-by-step explanation:
The red triangular exterior pieces are all equilateral triangles with some side length.
We don't need to know what that side length is. It doesn't matter.
The area of one red equilateral triangle is some area A.
There are 6 of these red triangles, so the red exterior triangular parts combine to a total area of 6*A.
The hexagon is composed of equilateral triangles as well.
Each of these blue equilateral triangles is congruent to any outer red triangle because the side length is the same.
Therefore, the 6 blue equilateral triangles composing this hexagon combine to get a total area of 6*A
The area of the star overall is 12*A because we have 6 blue triangles combining with the 6 red triangles.
There is a total of 12 triangles.
Related Questions
A student committee is to consist of 2 freshmen, 5 sophomores, 4 juniors, and 3 seniors. If 6 freshmen, 13 sophomores, 8 juniors, and 14 seniors are eligible to be on the committee, in how many ways can the committee be chosen
Answers
Delete the commas if necessary.
============================================================
Explanation:
There are 6 freshmen total and we want to pick 2 of them, where order doesn't matter. The reason it doesn't matter is because each seat on the committee is the same. No member outranks any other. If the positions were labeled "president", "vice president", "secretary", etc, then the order would matter.
Plug n = 6 and r = 2 into the nCr combination formula below
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\6 C 2 = \frac{6!}{2!*(6-2)!}\\\\6 C 2 = \frac{6!}{2!*4!}\\\\6 C 2 = \frac{6*5*4!}{2!*4!}\\\\ 6 C 2 = \frac{6*5}{2!}\\\\ 6 C 2 = \frac{6*5}{2*1}\\\\ 6 C 2 = \frac{30}{2}\\\\ 6 C 2 = 15\\\\[/tex]
This tells us there are 15 ways to pick the 2 freshmen from a pool of 6 total.
Repeat those steps for the other grade levels.
n = 13 sophomores, r = 5 selections leads to nCr = 13C5 = 1287. This is the number of ways to pick the sophomores.
You would follow the same type of steps shown above to get 1287. Let me know if you need to see these steps.
Similarly, 8C4 = 70 is the number of ways to pick the juniors.
Lastly, 14C3 = 364 is the number of ways to pick the seniors.
-----------------------------
To recap, we have...
15 ways to pick the freshmen1287 ways to pick the sophomores70 ways to pick the juniors364 ways to pick the seniorsMultiply out those values to get to the final answer.
15*1287*70*364 = 491,891,400
This massive number is a little under 492 million.
Which points are solutions to the linear inequality y < 0.5x 2? select three options. (–3, –2) (–2, 1) (–1, –2) (–1, 2) (1, –2)
Answers
The points which are solutions to the linear inequality are; (-3, -2), (-1, -2) and (1, -2)
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
For (–3, –2)-2 < 0.5(-3) + 2
-2 < 0.5 (satisfied)
For (–2, 1)1 < 0.5(-2) + 2
1 < 1 (Not satisfied)
For (–1, –2)-2 < 0.5(-1) + 2
-2 < 1.5 (Satisfied)
For (–1, 2)2 < 0.5(-1) + 2
2 < 1.5 (Not satisfied)
For (1, –2)-2 < 0.5(1) + 2
-2 < 1.5 (Satisfied)
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working together, rocco and giulia can paint a room in 3 hours. it would’ve taken rocco 7 hours to do the job alone. which equation can be used to determine r, giulia’s rate of work in parts per hour?
Answers
Answer:
1/7 + r = 1/3
Step-by-step explanation:
Rocco takes 7 hours to do the job.
In 1 hour, Rocco does 1/7 of the job.
Rocco's rate is 1/7 job per hour.
It takes Giulia x hours to do the job.
In 1 hour, Giulia does 1/x of the job.
Let r = 1/x. Giulia's rate is r part of the job per hour.
Together, Rocco and Giulia take 3 hours to do the job.
In 1 hour, Rocco and Giulia do 1/3 of the job.
Together, their rate is 1/3 of the job per hour.
1/7 + r = 1/3
the number of people with one type of flu doubles every day for several days what type of function represents this pattern
Answers
Answer:
The answer will be Exponential growth.
Please mark me as the brainliest.
Answer:
exponential growth
Step-by-step explanation:
Sara wants to find the input value that produces the same output for the functions represented by the tables.
A table headed with f(x) equals negative 0.5 x plus 2, with 2 columns and 8 rows. The first column, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second row, f(x), has the entries 3.5, 3, 2.5, 2, 1.5, 1, 0.5. A table headed with g(x) equals 2 x minus 3, with 2 columns and 8 rows. The first column, x, has the entries, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second row, g(x), has no entries.
What is the input value that produces the same output value in both charts?
–2
–1
1
2
Answers
The input value that produces the same output value in both charts is 2. so the correct answer is option D.
What is a function?
A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
You are given two functions f (x) = -0.5X +2 and g(x) = 2x - 3
x f(x)
-3 3.5
-2 3
-1 2.5
0 2
1 1.5
2 1
3 0.5
The second table is given below:-
x g(x)
-3
-2
-1
0
1
2
3
We will put the points and will find the value of functions:-
g(-3) = 2(-3) - 3 = -6 -3 = -9
g(-2) = 2 -(-2) -3 = -7
g(-1) = 2( -1) -3 = -3
g(0) = 2 - 0 - 3 = -3
g(1) = 2.1 - 3 = -1
g(2) = 2.2 -3 = 1
g(3) = 2.3 -3 = 3
Hence the second table will be
x g(x)
-3 -9
-2 -7
-1 -5
0 -3
1 -1
2 1
3 3
The input value that produces the same output value in both charts is 2.
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The cost of the fruit is given by the function y= 3x+1, where x is the number of fruits and y is the total cost. Find the
range of the function.
Answers
Answer:
The answer is the second option: {4, 7, 10...}
Please help!!!!!!!
picture below
Answers
If the function is vertically stretched by a factor of 3, the resulting function will be g(x) = [tex]3(5^{x-2})[/tex]
Vertical stretch of a functionGiven the parent function f(x) = x, if the function is vertically stretched by k units, the resulting function will be g(x) = kx
Given the parent function
f(x) = [tex]5^{x-2}[/tex]
If the function is vertically stretched by a factor of 3, the resulting function will be g(x) = [tex]3(5^{x-2})[/tex]
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HELPP
Simplify the expression 6^3+ 5(4 − 2).
28
36
226
234
Answers
Answer:
BODMAS
[tex] {6}^{3 } + 5(4 - 2) = 216 + 5(2) \\ = 216 + 10 \\ = 226[/tex]
Answer: Answer is 226
Step-by-step explanation: Do math
Write the rate in lowest terms a printer can print 22 pages in 55 seconds
Answers
Answer:
2/5
Step-by-step explanation:
22/11=2
55/11=5
Graph the inequality -1 < y +5x<11
Answers
Answer:
b
Step-by-step explanation:
Hii guys please answer this question
After how many places will the decimal expansion of 189/750 terminate ? Also write the decimal form
Answers
Answer:
3 decimal places; 189/750 = 0.252
Step-by-step explanation:
Answer:
3 decimal places.
189/750 = 0.252
Step-by-step explanation:
If you are allowed to use a calculator, you divide. 189/750 means 189 ÷ 750.
You will get 0.252, which is three decimal places. If you are not allowed to use a calculator, you must do long division. The 750 goes outside the dividing frame and the 189 goes inside. There is an unwritten decimal point after the 9 in 189. Since 750 does not go into 189, put 0. to begin and put zeros after the 189 to do the long division. See image. Hopefully you can just use a calculator.
factorise x - 2xz - 2xy + 4y². Show all the steps.
Answers
Answer:
1(x - 2xz - 2xy + 4y²)
Step-by-step explanation:
I notice that no term all of them have. which means itbwill be factorised via 1.
1(x - 2xz - 2xy + 4y²)
How can you find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model?
Answers
The given fractions representing the conditional probability is P(A | B) = P(AnB)/P(B)
Conditional ProbabilityThis is the probability that an event has happened given another event. If the two events are A and B, hence;
The conditional probability of A given B is expressed as:
P(A | B) = P(AnB)/P(B)
This given the fractions representing the conditional probability
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Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.
[tex]\sqrt{4x-3}=5[/tex]
Answers
Answer:
x = 7
Step-by-step explanation:
[tex](\sqrt{4x-3} )^{2} =5^{2}[/tex]
[tex]4x-3=25[/tex]
[tex]4x=25+3[/tex]
[tex]x=\frac{28}{4}[/tex]
[tex]x=7[/tex]
Hope this helps
Mathmatical proofs. please help
Answers
They switched the right angles with their opposite
See picture, that’s the best way I could show you without typing the whole thing over
Switch the two Right angles in the sentence
What is the results of
4-³ × (¼)²
Answers
Answer:
4^-3*(1/4)^2
(1/64)*(1/16)
=(1/1024)
Answer:
0.00025
Step-by-step explanation:
hope it'll help I'll ask . if you feel that it's not that correct please comment so that I can ask my sister who I'm sure she'll help although she's far good day.
Which is equivalent to 3√8* ?
O x √8^3
O 8 ^3/x
O 8 ^x/3
O 8^3x
Answers
Answer:
O 8 ^x/3
Step-by-step explanation:
Remember that :
[tex]\sqrt[n]{x} = x^\frac{1}{n}[/tex]
………………………………
Then
[tex]\sqrt[n]{8^x} = (8^{x})^{\frac{1}{3}}[/tex]
[tex]= 8^{x\times\frac{1}{3}[/tex]
[tex]=8^{\frac{x}{3}[/tex]
The two dot plots below compare the forearm lengths of two groups of schoolchildren:
Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group A and the title for the bottom plot is Forearm Length, Group B. Below the line for each dot plot is written Length followed by inches in parentheses. There are markings from 9 to 12 on each line at intervals of one. For the top line there are 3 dots above the second mark, 4 dots above the third mark and 3 dots above the fourth mark. For the bottom line there are 3 dots above the first mark, 5 dots above the second mark, and 2 dots above the third mark.
Based on visual inspection of the dot plots, which group appears to have the longer average forearm length?
Group A, because seven children have a forearm length longer than 10 inches
Group B, because two children have a forearm length longer than 10 inches
Group A, because one child in the group has the least forearm length of 9 inches
Group B, because three children in the group have the least forearm length of 9 inches
Answers
Answer:
Group A, because seven children have a forearm length longer than 10 inches
Step-by-step explanation:
Create the dot plots based on the given information (please see attached images).
Group A = blue dots
Group B = red dots
From inspection of the attached dot plots, we can see that Group A appears to have the longer average forearm length. This is because 7 children have a forearm length of longer than 10 inches.
To calculate the average forearm length, sum all data values and divide by the total number of data values.
[tex]\textsf{Average of Group A}=\dfrac{ 3 \times 10 + 4 \times 11 + 3 \times 12}{10}=11[/tex]
[tex]\textsf{Average of Group B}=\dfrac{ 3 \times 9 + 5\times 10+ 2\times 11}{10}=9.9[/tex]
Thus proving that Group A has the longer average former length.
According to given text data
Average of both groups
A:-
10(3)+11(4)+12(3)/1030+44+36/1066+44/10110/1011B:-
9(3)+5(10)+11(2)/1027+50+22/1049+50/1099/109.9Group A has bigger average
A pound of chocolate costs 6 dollars. John buys p pounds. Write an equation to represent the total cost c that John pays.
0-0 2
Question 29
XS ?
Answers
Answer:
c=6p
Step-by-step explanation:
you multiply
6 dollars per pound by p pounds
pounds cancel out and you are left with dollars
that is the cost
If u get 2 points every 5 minutes, how long will it take to get 3,600 points?
Answers
Answer:
9,000 minutes (150 hours)
Step-by-step explanation:
You have 3,600 points total; you need to divide it by 2 points.
3,600 ÷ 2 = 1,800
So, now you need to multiply the 1,800 points by 5 minutes.
1,800 × 5 = 9,000
Another way:
You can figure out how long it takes to get 1 point. If 2 points takes 5 minutes, divide 5 by 2.
5 ÷ 2 = 2.5
Now you need to figure out how long it would take to get 3,600 points. If each point takes 2.5 minutes, just multiply.
3,600 × 2.5 = 9,000
It would take 9,000 minutes (which is equivalent to 150 hours) to get to 3,600 points.
Write an expression for the area of the trapezium below.
Expand any brackets and fully simplify your answer.
Answers
21/√7-5√7/2 solve it
Answers
Answer:
√72
Decimal Form:
1.32287565…
Step-by-step explanation:
To subtract fractions, find the LCD and then combine.
Barry’s Burger Barn opened 25 franchises in its first year of operation. The second year, they opened 30 additional franchises. They opened 35 more in the third year and 40 more in the fourth year. If this pattern holds for all future years, perform the following: a. Determine how many franchises Barry’s will open each year in year 5, year 14, and year 26. Explain how you did this. b. Determine how many total franchises Barry’s will have in operation in year 10, year 22, and in year 50. Explain how you did this. c. How did you determine your answers? (Relate the relevant information in the story problem above to your calculations.)
Answers
The number of franchises that Barry will open each year in year 5, year 14, and year 26 will be 45, 90, and 150.
How to compute the value?a = 25
d = 5
The fifth year will be:
= a + (n - 1)d
= 25 + (5 - 1)5
= 25 + (4 × 5)
= 45
The 14th year will be:
= a + 13d
= 25 + 13(5)
= 90
The 26th will be:
= a + 25d
= 25 + 25(5)
= 150
The total franchises Barry’s will have in operation in year 10, year 22, and in year 50 will be:
Year 10 = n/2[2a + (n - 1)d]
= 10/2[5(25) + 45]
= 475
Year 22 = 25[50 + 245]
= 1705
Year 50 = 25(50 + 245)
= 7375
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8. If a conditional is true and its hypothesis is true, then its_____ is true.
Answers
If a conditional is true and its hypothesis is true, then its conclusion is true.
Instructions: Simplify the algebraic expression.
−12(32x−10y)
Answers
Answer:
-384x - 120y
Step-by-step explanation:
General Concepts and Formulas:
Brackets
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Steps:
1) Distribute
[tex]-12(32x-10y)[/tex]
We must distribute the expression above by multiplying -12 by the coefficients and then adding the variables.
So first, multiple -12 by 32 and add the variable 'x' when getting the product:
-12(-384x - 10y)
Now that we have one part, let's solve the other part.
We now must multiple -12 by -10, which gets us 120, now we must plug in:
(-384x - 120y)
(Remove parenthesis)
⇒ -384x - 120y
Hello!
im studying for my future SAT test and my school is over can you please show me steps on this i need to understand it thanks!
Answers
Answer:
Therefore, an integer that's divisible by both 6 and 9 has at least one 2 and two 3s in its prime factorization. That means it is divisible by 2 and 3: 2 x 3 6, 3 x 3 9, and 2 x 3 x 3 = 18. It's not necessarily divisible by 12 or 36, each of which includes two 2s in its prime factorization
This should be easy. Answer it please :D
Answers
Answer:
is it 1 ques or 4 different questions?
If 343 superscript x baseline = 49 superscript 4 minus x, what is the value of x?
Answers
The value of x is 8/5 or 1.6 when 343ˣ = 49⁴ ⁻ ˣ, using the laws of exponents.
Exponents are of the form aˣ, read as "a to the power of x", and signify the product of a multiplied by itself x number of times.
In the question, we are given that 343ˣ = 49⁴ ⁻ ˣ, and are asked to find the value of x.
We try to solve the exponential equation, using the laws of exponents in the following way:
343ˣ = 49⁴ ⁻ ˣ,
or, (7³)ˣ = (7²)⁽⁴ - ˣ⁾ {Since, 343 = 7³ and 49 = 7²}.
or, 7³ˣ = 7⁸ ⁻ ²ˣ {Using the law: [tex](x^{a})^{b} = x^{ab}[/tex]},
or, 3x = 8 - 2x {Using the law: [tex]x^a = x^b \Rightarrow a = b[/tex], when x ≠ 0}.
or, 3x + 2x = 8 - 2x + 2x {Adding 2x to both sides of the equation},
or, 5x = 8 {Simplifying}
or, 5x/5 = 8/5 {Dividing both sides by 5},
or, x = 8/5 or 1.6 {Simplifying}
Therefore, the value of x is 8/5 or 1.6 when 343ˣ = 49⁴ ⁻ ˣ, using the laws of exponents.
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Marilyn is having shelves installed to create a corner pantry. the length of one wall is 21 inches and the length of the other wall is 25 inches. the contractor who is making the shelves, which are shaped like right triangles, needs to know the measure of the angle opposite the short side of the pantry, m∠a. what is the measure of that angle? round your answer to the nearest degree.
Answers
Answer:
He says the answer is 40°
Step-by-step explanation:
Answer is on brainly, here is the link to the answer. Hope it helps with your question!
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Hope this helps!
If not, I am sorry.
Help me solve please with in depth explanation
3. The table shows information about the times for 100 people to complete a task.
Answers
Answer:
kuch bhi hai one kutiya kamini sour hii byy