The perimeter of this Hexagon is 162 cm. Each longer side measures 1 cm more than twice a shorter side. Find the length of the labled x.
Answers
The length of the shorter side [tex]\( x \)[/tex] is 20 cm.
The length of each shorter side labelled [tex]\( x \)[/tex] in the hexagon is 20 cm. Here's the step-wise calculation:
1. Let [tex]\( x \)[/tex] represent the length of the shorter side.
2. The length of each longer side is given as [tex]\( 1 \)[/tex] cm more than twice a shorter side, so it is [tex]\( 2x + 1 \)[/tex] cm.
3. The perimeter of the hexagon is the sum of the lengths of all its sides, which is given as [tex]\( 162 \)[/tex] cm.
4. Since the hexagon has four shorter sides and two longer sides, the perimeter [tex]\( P \)[/tex] can be expressed as:
[tex]\[ P = 4x + 2(2x + 1) \][/tex]
5. Plugging in the given perimeter value and simplifying the equation:
[tex]\[ 162 = 4x + 4x + 2 \][/tex]
[tex]\[ 162 = 8x + 2 \][/tex]
6. Solving for [tex]\( x \)[/tex] gives:
[tex]\[ 160 = 8x \][/tex]
[tex]\[ x = \frac{160}{8} \][/tex]
[tex]\[ x = 20 \][/tex]
Therefore, the length of the shorter side [tex]\( x \)[/tex] is 20 cm.
Related Questions
What is the quadrant/axis for (7,-12
Answers
Answer:
[tex]\boxed{Quadrant4}[/tex]
The answer should be found in quadrant four it is.
Step-by-step explanation:
x-axis- is a horizontal axis.
y-axis- is a vertical axis.
x-coordinate- is a horizontal position.
y-coordinate- is a vertical position.
quadrant- is a quarter of the coordinate plane.
origin- is a point of intersection of the two axes.
First you had to find quadrant of (7,-12).
Go to the right at it said seven and then go down to the negative twelve and its should be found in quadrant four.
(7,-12) it should be found in quadrant four.
(-7,-12) it should be found in quadrant three.
(-7, 12) it should be found in quadrant two.
(7, 12) it should be found in quadrant one.
Hope this helps!
And thank you for posting your question at here on brainly, and have a great day.
-Charlie
How many 2/3 -cup servings are in four cups of pistachios?
Answers
Answer:
4 Of them
Step-by-step explanation:
So an easy way to do this is by adding 2/3 for a while till we hit max. Like this:
2/3+2/3=1 1/3+2/3= 2+2/3=2 2/3+ 2/3= 3 1/3+2/3= 4. so 6 of them
Hope this helps!
Final answer:
To find out how many 2/3-cup servings are in four cups of pistachios, you divide 4 cups by 2/3 cup, which equals 6 servings.
Explanation:
To determine how many 2/3-cup servings are in four cups of pistachios, you would divide the total number of cups by the size of one serving:
Total servings = Total volume \/ Size of one serving = 4 cups / (2/3 cup)
To divide by a fraction, multiply by its reciprocal:
Total servings = 4 / (2/3) = 4 * (3/2) = 4 * 1.5 = 6
So, there are six 2/3-cup servings in four cups of pistachios.
Create a real-life representation of the following multiplication problem. Explain what the result represents in the problem. 15(2/5)=6
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What is 0.561 rounded to the nearest tenth
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y and x have a proportional relationship, and y = 12 when x = 5. What is the value of y when x = 8?
Answers
12=5k
12/5=2.4
y=2.4*8
y=19.2
Last year there were 52 Starbucks Coffee shops in Orlando. This year they are planning on increasing their numbers by 25%. How many Starbucks Coffee shops with there be now?
Answers
100x = 25•52
100x = 1300
x = 1300 ÷ 100
x = 13
since it is a markup problem:
52+13= 65
So there are 65 Starbucks Coffee Shops.
OR U COULD JUST MULTIPLY .25 BY 52 BC 25% IS 0.25. AND U GET 13. 52 PLUS 13 ISSSS
62
Nata spent $28 on 2 DVDs. at this rate, how much would 5 DVDs cost? at what rate did she spend her money
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2/28= 5/x and x would equal the amount of money she has to spend for 5 DVDs.
cross multiply then you'll get:
140=2x
x=70
She would have to pay $70 for 5 dvds.
Which ratios form a proportion?
A. 4/9, 2/3
B. 6/15, 9/12
C. 12/16, 15/20
D. 18/20, 24/30
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____________________________________________________
describe and correct the error in identifying the like terms in the expression
3x - 5 + 2x*2 + 9x = 3x +2x*2 + 9x - 5
like terms:3x,2x*2, and 9x
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the product of two consecutive even integers is 48 find the integers
Answers
Once you simplify, you should get an equation that looks like a quadratic:
x^2+2x=48. Now, to find the values of x, you have to solve for the roots or zeroes, which means you will have to set the equation to 0. To do this, subtract 48 from both sides and you get: x^2+2x-48=0.
Then, factor the equation and you get: (x+8)(x-6)=0
Now, to solve for x, set each factor to 0, which would look like this:
x+8=0
x-6=0
Now, solve each one for x and you get x=-8 and x=6
Then, to find the pairs for each integer, add 2 to each x and you get that the two sets of integers that equal 48 as their product are -8 and -6; and 6 and 8
The required integers are -8 and -6, or 6 and 8 whose the product of two consecutive even integers is 48
What are Integers?Integers are defined as the collection of Whole Numbers and the negative values of Natural Numbers make up an integer.
Let the two consecutive even integers be 2n and 2(n+1), where n = any integer.
As per the given condition, The product of the two integers is 48
2n × 2(n+1) = 48
Multiply out, and subtract 48 from both sides
4n2+4n-48=0
Divide both sides by 4
n²+n-12=0
Factor the quadratic
(n+4)(n-3)=0
n= -4 and +3
For n= -4, 2n = -8 and 2(n+1) = -6. (-8)(-6) = 48
For n=3, 2n = 6 and 2(n+1) = 8. (8)(6) = 48
Thus, the required integers are -8 and -6, or 6 and 8.
Learn more about Integers here :
brainly.com/question/1768254
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Katy made a card pattern with rows of cards.The table at the left shows the number or cards in each row what is the pattern rule for number of cards
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the output is five times the input
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I need help on 22-27
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Alright, for 22: It doesn't matter how many 0's you add after the main digits (there's an official term for these digits, but I don't exactly recall it at this moment)
BASICALLY, 0's are just being used as placeholders AFTER the main digits, which in this case is 2.6
So, you can say 2.6, 2.60, 2.600, 2.6000, 2.60000000, but those 0's are meaningless really, because they all REALLY have the same value, 2.6. Your choice that they want is 2.06. You can't toss a 0 between the main digits without changing the value.
So, 22=2.06
Using the same methods as I said, notice how the main digits in 23 are 4.07. This is unchanging. Anything that gets tossed in between changes the numbers value. The answer they want is 4.70.
Using the same methods as above, notice how the main digits in 24 are 65.8. The answer they want, the choice that's different, is 65.08
Same thing for 25. The main digits are 37.06, so the choice they are looking for, the only one with a different value, is 37.6
For 26, three decimals that are equivalent:
For example: .5, .50, .500 are all equal.
For 27, rewrite these as fractions. That's easy.
In algebra, there are names for anything after the decimal. The first number that comes after the decimal is known as the "tenth", the second is known as the "hundredth", the third is known as the "thousandth", so on.
Applying that, we can convert these into fractions, using each decimals respective value as the denominator here.
.5 is in the tenth place, so as a fraction it's 5/10
.50 is in the hundredth place total, so as a fraction it's 50/100
.500 is in the thousandths place total (meaning this is where it ends), so it's 500/1000 as a fraction.
But in the end, ALL of these are the same value, 5/10
~Hope this helps!
The domain of a relation is
A. the output (y) values of the relation
B. the input (x) values of the relation
C. a set of points that pair input values with output values
D. x and y values written in the form (x, y)
Answers
explain how the points A(9,-2/5) and B(9,2/5) are related.
Answers
9514 1404 393
Explanation:
Each is a reflection of the other over the x-axis. Their x-coordinates are the same, so they lie on the same vertical line. Their y-coordinates are opposites, so they are equal and opposite distances from the x-axis.
Nora had already read thirty percent of the book before he teacher assigned it to the class she is choosing between two options.option1:read 25%of the remaining pages each night or option2:read 28pages each night
Answers
Nora should choose Option 1 because it will take her 4 nights to finish instead of 25 nights with Option 2.
Let's break down Nora's situation step by step:
1. Calculate the total number of pages in the book:
Since Nora has already read thirty percent of the book, we can find the total number of pages by dividing the portion she read by 30% (or 0.30). Let's denote the total number of pages as ( P ).
[tex]\[ P = \frac{{\text{portion Nora read}}}{{\text{percentage read}}} = \frac{{\text{portion Nora read}}}{{0.30}} \][/tex]
2. Calculate the portion of the book Nora has already read:
If Nora has already read thirty percent of the book, then she has already read [tex]\( 0.30 \times P \)[/tex] pages.
3. Calculate the number of pages Nora has remaining:
Subtract the pages Nora has already read from the total number of pages in the book.
[tex]\[ \text{Pages remaining} = P - (0.30 \times P) = P(1 - 0.30) = 0.70P \][/tex]
4. Option 1: Read 25% of the remaining pages each night:
Nora's plan is to read 25% of the remaining pages each night. Since she has (0.70P) pages remaining, she will read [tex]\( 0.25 \times 0.70P \)[/tex] pages each night.
5. Option 2: Read 28 pages each night:
Nora's other option is to read 28 pages each night.
6. Compare the two options:
To determine which option Nora should choose, we compare the number of nights it will take her to finish each option.
- With Option 1, the number of nights Nora will need to finish the book is [tex]\( \frac{{0.70P}}{{0.25 \times 0.70P}} \).[/tex]
- With Option 2, the number of nights Nora will need to finish the book is [tex]\( \frac{{0.70P}}{{28}} \).[/tex]
7. Choose the more efficient option:
Nora should choose the option that requires fewer nights to finish the book.
Let's summarize the steps:
1. Calculate the total number of pages in the book.
2. Determine the portion of the book Nora has already read.
3. Calculate the number of pages Nora has remaining.
4. Calculate the number of pages Nora will read each night for Option 1.
5. Compare the number of nights needed for each option.
6. Choose the option that requires fewer nights to finish the book.
This process will help Nora decide which option is more efficient for her to finish reading the book.
Let's denote:
- Total number of pages in the book as ( P ).
- Number of pages Nora has already read as ( 0.30P ).
- Number of pages Nora has remaining as ( 0.70P ).
With Option 1, Nora will read [tex]\( 0.25 \times 0.70P = 0.175P \)[/tex] pages each night.
To find the number of nights needed to finish with Option 1:
[tex]\[ \text{Number of nights with Option 1} = \frac{{0.70P}}{{0.175P}} = 4 \][/tex]
With Option 2, Nora will read 28 pages each night.
To find the number of nights needed to finish with Option 2:
[tex]\[ \text{Number of nights with Option 2} = \frac{{0.70P}}{{28}} = 25 \][/tex]
Nora should choose Option 1 because it will take her 4 nights to finish instead of 25 nights with Option 2.
A pickup truck’s gas tank can hold 19.2 gallons and i can go 460.8 miles on a single tank of gas. How many miles per gallon does it get?
Answers
Answer:24 mph
A plumber charges $55 for a service call plus $35 per hour. If the plumber's bill was $160, how many hours was he there?
Answers
Answer:
Plumber worked for 3 hours.
Step-by-step explanation:
A plumber charges $55 for a service call plus $35 per hour.
Let he works for x hours.
Then for x hours of work charges = $35x
Since plumber charges $55 as a fixed charge so the total charges will be = 55 + 35x
This total amount charged by the plumber equals to $160
and the equation representing this situation will be
55 + 35x = 160
35x = 160 - 55
35x = 105
x = [tex]\frac{105}{35}[/tex]
x = 3 hours
Therefore, he worked for 3 hours.
Find the next three numbers in the pattern: 1, 4, 9, 16, 25, 36, ...
Answers
1+3=4
4+5=9
9+7=16
16+9=25
25+11=36
Then the next 3 numbers would be:
36+13= 49
49+15=64
64+17=81
The next three numbers are 49, 64 and 81
The pattern is adding 2 to each number. So 3 is added to 1 to make 4. The next number added to 4 would be 5, so on so forth.
Answer: 49, 64, and 81
Step-by-step explanation: To find the next three terms in this pattern, begin by studying the pattern.
Notice that the difference between 1 and 4 is positive 3, the difference between 4 and 9 is positive 5, the difference between 9 and 16 is positive 7, the difference between 16 and 25 is positive 9, and the difference between 25 and 36 is positive 11.
Since the differences are increasing by 2 each time, we can find the next term in the pattern by adding 36 + 13 to get 49. Next, we will add 49 + 15 to get 64. Then, we will add 64 + 17 to get 81.
Thus, the next three terms in the pattern are 49, 64, and 81.
Ernesto travels for 400km at an average speed of 80km/h how long was his journey
Answers
Ernesto's journey was about 5 hours.
A color called “Passion Purple”is made by mixing 5 oz of red paint and 9 oz of blue paint. What percent of Passion Purple is blue paint? ( Round to the nearest percent.)
Answers
Total paint = 5 + 8 = 14
Then write the blue paint as a fraction of the total.
9/14
And then solve.
Answer is aprox 64%
--- Strep throat is caused by Streptococcus bacteria. The amount of bacteria multiplies at a rate of 10^13 per 10^2 hrs. What is the average growth of bacteria per hour?
Answers
The average growth of the bacteria per hour is [tex]10^{11}[/tex].
To find the average growth of bacteria per hour, we need to determine the rate at which the bacteria multiply per hour.
Given:
The amount of bacteria multiplies at a rate of [tex]\(10^{13}\)[/tex] per [tex]\(10^2\)[/tex] hour.
We want to find the growth rate per hour.
First, let's find out how much the bacteria multiplies per hour:
If the bacteria multiply by [tex]\(10^{13}\)[/tex] in [tex]\(10^2\)[/tex] hours, then the average growth per hour can be found by dividing the total growth in [tex]10^{13[/tex] hours by [tex]10^2[/tex].
So, the growth per hour is:
Growth per hour} = [tex]\frac{10^{13}}{10^2}[/tex]
Growth per hour} = [tex]10^{13 - 2}[/tex]
Growth per hour} = [tex]10^{11}[/tex]
Therefore, the average growth of bacteria per hour is [tex]10^{11}[/tex].
MR.Trek made some trail mix for his backpacking team. He used 2 1/2 cups of granola, 1 3/4 cups of peanuts, 1 1/3 cups of raisins, and 1 cup of chocolate chips. How much trail mix did he make?
Answers
if you want me to explain then just comment back
i need to solve this equation: x= r-h/ y
for h and then for r
Answers
h= xy-r/-1
r= xy+h
Answer:
[tex]h=r-xy[/tex]
[tex]r=xy+h[/tex]
Step-by-step explanation:
[tex]x=\frac{r-h}{y}[/tex]
Solve the equation for h
We need to get 'h' alone
[tex]x=\frac{r-h}{y}[/tex]
multiply y on both sides
[tex]xy=r-h[/tex]
Now add h on both sides
[tex]xy+h=r[/tex]
Subtract xy from both sides
[tex]h=r-xy[/tex]
Now solve the equation for 'r'
[tex]x=\frac{r-h}{y}[/tex]
multiply y on both sides
[tex]xy=r-h[/tex]
Now add h on both sides
[tex]xy+h=r[/tex]
[tex]r=xy+h[/tex]
please chose which gives the lower price (coupon A or coupon B).
please explain and show how you got the answer.
Then tell how what the difference is between the two.
Please and Thank You
Good luck!!
Answers
Plz someone help me do this, i'll award 30 point for who ever gets it right plz someone help ASAP
Graph the following piecewise function: [tex]fx = \left \{ {{x + 4} \atop {2x - 1}} \right. {{if} \atop {if}} \right. {{-4 \ \textless \ x \ \textless \ -3} \atop {3 \ \textless \ x \ \textless \ 6}} \right. [/tex]
Answers
line from (-4,0) to (-3,1)
open circles at points
line from (6,11) to (3,5)
open circles at points
Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 the job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this.
Answers
Answer:
A.) Deepak can only accept jobs that last 4 or more hours.
Step-by-step explanation:
Hope this helps :)
add a thanks...
Deepak must work 4 or fewer hours to earn at least $90 per job.
Explanation:The question is asking about the inequality that Deepak, a landscaper, writes to determine the number of hours he must work during each job in order to earn at least $90 the job. We can break down the equation as follows:
Let x be the number of hours Deepak works.
The equation can be written as: $30 + $15x ≤ $90.
To solve for x, we subtract $30 from both sides: $15x ≤ $60.
Then, we divide both sides by $15: x ≤ 4.
Therefore, Deepak must work 4 or fewer hours to earn at least $90 per job.
A farmer collected eggs from the henhouse. He can put 36 eggs in a carton. A carton will hold 6 eggs in a row How many rows does the egg carton have? what type of problem is it?
A. Array Multiplication
B. Array Division
C. Equal Groups Multiplication
D. Equal Groups division with an Unknown Group Size
E. Equal Groups Division with an Unknown Multiplier
Answers
In an orchestra there are 42 woodwind players to 56 brass players. What is the ratio of woodwinds to brass written as a fraction in simplest form
Answers
42/7= 6 56/7=8 6/2=3 8/2=4
Miss Marcus Bulletin Board is 7 ft long and 4 feet High she has 26 ft of board to use Miss Marcus pool supplies 7 time 4 equals 28 to find the exact amount of the board she needs she concludes that she does not have enough border board for the bulletin board do you agree
Answers
Final answer:
Yes, I agree that Miss Marcus does have enough board for the bulletin board for the given information
Explanation:
The student is trying to determine if Miss Marcus has enough board to use for her bulletin board. The student calculates the area of the bulletin board as 7 ft x 4 ft = 28 ft². However, the student concludes that Miss Marcus does not have enough board because she only has 26 feet of board to use. This is incorrect, as 26 ft is greater than 28 ft². Therefore, Miss Marcus does have enough board for the bulletin board.