An equilateral triangle has a side length of 1.4x + 2 inches. A regular hexagon has a side length of 0.5x + 2 inches. The perimeters are equal. What is the side length of the triangle? What is the side length of the hexagon? Show your work.

Answers

Answer 1

Answer:

9 inches; 4.5 inches.

Step-by-step explanation:

Given the following data;

Length of sides of the equilateral triangle = 1.4x + 2 inches.

Length of sides of the hexagon = 0.5x + 2 inches.

We know that the perimeter of a hexagon is given by the formula;

P = 6 * length of sides

Substituting into the equation, we have;

P = 6*(0.5x + 2)

P = 3x + 12

Perimeter of an equilateral triangle is given by the formula;

P = 3 * length of sides

Substituting into the equation, we have;

P = 3(1.4x + 2)

P = 4.2x + 6

Since perimeter of hexagon = perimeter of equilateral triangle. Therefore;

3x + 12 = 4.2x + 6

Rearranging the equation, we have;

12 - 6 = 4.2x - 3x

6 = 1.2x

x = 6/1.2

x = 5

I. To find the length of each sides of the equilateral triangle;

Length of a side = 1.4x + 2

Substituting the value of "x" into the equation, we have;

Length of sides = 1.4*(5) + 2

Length of sides = 7 + 2

Length of sides = 9 inches.

II. To find the length of each sides of the hexagon;

Length of sides = 0.5x + 2

Substituting the value of "x" into the equation, we have;

Length of sides = 0.5*(5) + 2

Length of sides = 2.5 + 2

Length of sides = 4.5 inches.

Answer 2

The side length of the equilateral triangle 9 inches.

The side length of the hexagon 4.5 inches.

The side length of the equilateral triangle = 1.4x + 2

So, the perimeter = 3(1.4x + 2) = 4.2x + 6.

The side length of the hexagon = 0.5x + 2

So, the perimeter = 6(0.5x + 2) = 3x + 12.

Given tha the perimeters are equal.

So,

[tex]4.2x+6=3x+12\\4.2x-3x=12-6\\1.2x=6\\x=5[/tex]

Hence,

The side length of the equilateral triangle = 1.4x + 2 = 1.4(5) + 2 = 9

The side length of the hexagon = 0.5x + 2 = 0.5(5) + 2 = 4.5

Learn more: https://brainly.com/question/13532036


Related Questions

What’s the common factor for 72 and 84

Answers

Answer:

Step-by-step explanation:

This is the general method for doing this problem. First factor these numbers into primes.

72: 2 * 2 * 2 * 3 * 3

84: 2*2 * 3 * 7

Now each number has at least two 2s

Each number has at least one          3

The highest common factor is 2 * 2 * 3 = 12

solve the following inequality showing all steps -3n+7<4

Answers

[tex]\textsf{Hey there!}[/tex]

[tex]\mathsf{-3n + 7 < 4}\\\\\textsf{SUBTRACT by 7 on your sides}\\\mathsf{-3n+7-7<4-7}\\\mathsf{Cancel\ out: 7-7\ because\ that\ gives\ you\ 0}\\\mathsf{Keep: 4-7\ because\ it\ helps\ us\ solve\ for\ our\ n \ value}\\\bf{{\mathsf{4-7= -3}}}\\\\\mathsf{New\ question: -3n<-3}\\\\\mathsf{DIVIDE\ both\ sides\ by\ -3}\\\mathsf{\dfrac{-3n}{-3}=\dfrac{-3}{-3}}\\\mathsf{Cancel\ out: \dfrac{-3}{-3} \ because\ gives\ us\ 1}\\\mathsf{Keep: \dfrac{-3}{-3}\ because\ it\ gives\ us\ our\ n\ value}[/tex]

[tex]\mathsf{New\ equation: n < \dfrac{-3}{-3}}\\\mathsf{\dfrac{-3}{-3} = -3\div-3 \rightarrow 1}\\\\\huge\textsf{Answer}\huge\downarrow\\\\\boxed{\boxed{\mathsf{Answer: n < 1}}}\checkmark\\\\\\\\\textsf{Good luck on your assignment and enjoy your day!}\\\\\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]

Suppose that P (A)=0.4 AND P (B)=0.2, If events A & B ARE Mutually EXCLUSIVE :
- What is the probability of either A or B occurring
- What is the probability of neither A nor B will happen

Answers

Part (a) Finding the probability of either A or B

We are told that events A and B are mutually exclusive. This means they cannot happen at the same time. We can say P(A and B) = 0

Furthermore,

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.4 + 0.2 - 0

P(A or B) = 0.6

Answer:  0.6

=======================================================

Part (b) Finding the probability of neither A nor B

P(A or B) + P(neither A nor B) = 1

P(neither A nor B) = 1 - P(A or B)

P(neither A nor B) = 1 - 0.6

P(neither A nor B) = 0.4

The reason why this works is to imagine throwing a dart at the Venn diagram. You'll either...

you land in A or B (pick one but not both), OR,you'll land outside both regions A and B.

One or the other must happen. Both events cannot happen simultaneously.

Answer: 0.4

PLEASE SOMEONE HELP ME I NEED THIS ASAP PLEASE HELP ME I BEG YOU .....

Answers

Answer:

9.57

Step-by-step explanation:

Pleaseee Helppppp
Find the minimum value of the function f(x) = x2 + 12x + 31.5 to the
nearest hundredth.

Answers

Answer:

The answer is pie

Step-by-step explanation:

I know best

Answer:

x = -6.00 (rounded to nearest hundredth)

Step-by-step explanation:

for a quadratic equation, [tex]h(x)=ax^2+bx+c[/tex]  we have [tex]f(x)=x^2+12x+31.5[/tex] a = 1 b = 12 to find minimum use equation [tex]x=\frac{-b}{2a}[/tex] [tex]x=\frac{-b}{2a}\\x=\frac{-(12)}{2(1)}\\x=\frac{-12}{2}=-6[/tex]

I need help on this question

Answers

I think it’s B but I’m not 100%

Henry bought 8 DVDs for $19.99 each. How much does Henry spend on the DVDs?
Please Help :))

Answers

Answer:

$159.92

Step-by-step explanation:

8x19.99=$159.92

Could I get help with this one?

Answers

Answer:

x3

Step-by-step explanation:

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?
A. -4
B.-2
C.-1
D. 1

Answers

Answer:

n = -4

Step-by-step explanation:

You must write and solve a symbolic equation.

n - 6 = 5(n + 2), or

n - 6 = 5n + 10

Combining like terms, we get:

-16 = 4n,

and so n = -4

Answer:

A. -4

Step-by-step explanation:


Summer used of her ground beef to make burgers. If she used pounds of beef, how much beef did she have at first?
Do not include units (pounds) in your answer.

Answers

are there any numbers or can you take a picture of the problem

Sam earns $54 275 in a year.
He pays no income tax on the first $8200.
He pays 18% income tax on everything he earns over $8200.
a Work out how much income tax he pays.
b Work out what percentage of his income he pays in tax.
If the income tax rate is increased to 21%, how much more tax will Sam pay?​

Answers

Answer:

he would pay $8,293.5 in income tax.

b:

Step-by-step explanation: he pays  15.280515891294% of his pay in tax. if the income rate was increased to 21% then he would pay 9,675.75‬ in taxes.  Which is 1,382.25 more than 18% tax.

The temperature in Minsk was recorded over a period of four hours. The
equation
y = -5x + 54
describes the temperature over this time, where y is the temperature in
degrees Fahrenheit (°F) and x is the number of hours since measurements
started. Which of the following statements correctly describes the
temperature?
A. It was -5°F after four hours, and it is rising by 54 degrees per
hour.
B. It was 54°F when the temperature was first measured, and it is
dropping by 5 degrees per hour.
c. It was -5°F when the temperature was first measured, and it is
rising by 54 degrees per hour.
O D. It was 54°F after four hours, and it is dropping by 5 degrees per
hour

Answers

Answer:

D.) it was 54 degrees Fahrenheit when the temperature was first measured, and it is dropping by 5 degrees per hour

Step-by-step explanation:

I took the quiz

Answer:

D

Step-by-step explanation:

I took the test

Sam currently has $48 in savings. He had been saving S6 each week. Yesterday he spent $90 of the savings. For how many weeks had he been
saving?
(a) Write an equation that could be used to answer the question
above. First, choose the appropriate form. Then, fill in the blanks
with the numbers 48, 6, and 90. Let w represent the number of
weeks.

(b) Solve the equation in part (a) to find the number of weeks.
w = ?

Answers

Step-by-step explanation:

90 + 48 = 6w

138 = 6w

23 = w

.....

-15= x/-0.5 8= what does x equal

Answers

8*0.5*x=-15
x = -15/4

The two figures shown are congruent. Which statement is true?

Answers

Answer:reflection image of the other

Source:trust me bro

The last choice because it’s like you drawing it on a peace of paper and then folding the paper in half and then rubbing it on the other said of the paper

Complete each of the diamond problems below

Answers

A . left miss diamond -6x1 = -6
Bottom missing diamond -6+1=-5

B. Right missing diamond -5+3= -2
Top missing diamond 3x-2= -6

C. Right missing diamond 11.2-1.2= 10
Top missing diamond 1.2x10= 12

D left missing diamond 6
Right missing diamond 4

Describe the transformation that takes f (x) = x + 1 To g (x) = -x + 4. [ Please No Plagiarism and Will mark brainliest . .​

Answers

Answer:

fliped over y axis and moved up 3

Step-by-step explanation:

fliped over y axis (changed x to -x) and moved up 3 (changed +1 to +4)

Answer:

why did you delete my answer HUH?

Step-by-step explanation:

In 2012, Indonesia experienced an intense earthquake with a magnitude of 8.6 on the Richter scale. In 1952, Uganda experienced an earthquake that measured 6.5 on the Richter scale. Compare the intensities of the two earthquakes. Use a logarithmic model to solve. Round to the nearest whole number.

Answers

Answer:

The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.

Step-by-step explanation:

To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.

Convert the magnitudes to intensities and convert to exponential form.

R=logI

2012 earthquake:

8.6I=logI=108.6

1952 earthquake:

6.5I=logI=106.5

Form a ratio of the intensities.

intensity for 2012intensity for 1952

Substitute in the values and divide by subtracting the exponents to find

108.6106.5102.1≈126.

The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.

Your answer:

The intensity of the 1952 earthquake was about 110 times the intensity of the 2012 earthquake.

Answer:

The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.

Step-by-step explanation:

To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.

Convert the magnitudes to intensities and convert to exponential form.

R=logI

2012 earthquake:

8.6I=logI=108.6

1952 earthquake:

6.5I=logI=106.5

Form a ratio of the intensities.

intensity for 2012intensity for 1952

Substitute in the values and divide by subtracting the exponents to find

108.6106.5102.1≈126.

The intensity of the 2012 earthquake was about 126 times the intensity of the 1952 earthquake.

Identify the slope from the table

NEED HELP PLEASE thank you sb

Answers

The slope is -4 or c on the table

Answer:

-4

Step-by-step explanation:

‘X’ adds by one while ‘y’ adds by -4

9x - y power two - 20 ≥ 0 i need every passage​

Answers

Answer: photo

Step-by-step explanation:

I am not sure but hope it helps

Evaluate the expression.
20² + 6(9 + 3) =

Answers

20 x 20 + 6 x 12 = 400 + 72 = 472

What is the equation of the line that passes through the point (2,0) and has a slope of 5/2

Answers

Answer :

y = 5/2x - 5

Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 5/2 , thus
y = 5/2x + c ← is the partial equation
To find c substitute (2, 0) into the partial equation
0 = 5 + c ⇒ c = 0 - 5
y = 5/2x - 5 ← equation of line

A farmer takes 1 week to fill 5 bins of squash. At this​ rate, how long will it take to fill 350 bin​s?

Answers

Answer:

490 days or 70 weeks

Step-by-step explanation:

Time needed for the farmer to fill 1 bin of squash:

7 days (1 week) divided by 5 = 7/5 days

Time needed to fill 350 bins:

350 x 7/5 days = 490 days or 70 weeks

A bakery offers a sale price of $2.85 for 6 muffins. What is the price per dozen?

Answers

Answer:

2.85 x 2 is equal to 5.7 so that should be the answer

Step-by-step explanation:

Did it on calculator sorry if wrong lol

Answer:

$5.70

Step-by-step explanation:

6 muffins is half a dozen, so double $2.85 and you get $5.70.

Help asap i will do brainlist and everything

Answers

Answer:

the picture isnt showing

Which of the following is a better buy?
7 tickets for $22.75
10 tickets for $31.50

Answers

Answer:

10 tickets for $31.50

Step-by-step explanation:

So If we divide 22.75 by 7 it gives you 3 dollars and 25 cents per ticket

If you divide 31.50 by 10 it gives you 3 dollars and 15 cents.

So In conclusion 10 tickets for $31.50 dollars is the better buy

Answer:

10 Tickets Is The Better Deal

Step-by-step explanation:

So What You Do Is You Will Divide 22.75 By 7

You Will Get 3.25! That Means Its 3.25 Each For 7 Tickets

For The Next One You Do The Same Thing

You Want To Divide 31.50 By 10

You Will Get 3.15! That Means Its 3.15 Each For 10 Tickets

So 3.15 Is 10 Cheaper Than 3.25 So Getting 10 Tickets Is A Better Deal

Hope This Help

DOH! My Brain Hurts

All you need is on the photo

Answers

Answer:

[tex]4^{-3}[/tex]

Step-by-step explanation:

[tex]We\ are\ given\ that,\\4^4*4^{-8}*4\\We\ know\ that,\ for\ any\ real\ number\ n, n^a*n^b=n^{(a+b)}\\Hence,\\First,\ lets\ write\ all\ the\ terms\ in\ an\ exponential\ form.\\4^4*4^{-8}*4^1\\=4^{(4+(-8)+1)}\\=4^{(5-8)}\\=4^{-3}[/tex]

If Jack weighs more that Jill, and they run up the same hill, who has done more work?


If Jack and Jill weigh the same, and Jill runs up the hill in half the time as Jack, who had more power??

Answers

Answer:

1. Jack, because he weighs more and has to use move power to move.

2. Jill

Step-by-step explanation:

Answer:

omg lol. Okay well for the first one the answer is jack does more work going up the hill.

For the second one Jill has more power.

-1/4 ÷ -3/8
Please Hurry

Answers

Answer:

2 /3 (decimal form ≅ 0.6666667 )

Step-by-step explanation:

Unary minus: -1 /4

= -1 /4

Unary minus: -3 /8

= -3 /8

Divide: the result of step No. 1 : the result of step No. 2 = -1 /4 : (-3 /8 ) =

-1 /4  x -8 /3  = -1 (-8)  divided by 4(3)  = 8 /12  = 4(2 ) divided by 4(3)  = 2 /3

The number that represent the parts per 100 is called the part

Answers

Answer: Is their a graph or something that goes with this. I dont understand.

Step-by-step explanation:

Answer:

What do you want to find?

Step-by-step explanation:

I don't understand...

Add more details and then I'll answer

Other Questions
Joey goes to an electronics store to buy video games andCD's. He has $140 from his birthday party and he's looking tobuy video games for $35 each and CD's for $15 each. Write aninequality to describe the possible number of video games andCD's that Joey can buy. If Joey buys 4 CD's, what is themaximum number of video games he can buy?video games check if 7 is a solution of the equation 4 ( Z - 3 ) = 16. step by step plz guys. Carbon-14, which is present in all living tissue, radioactively decays via a first-order process. A one-gram sample of wood taken from a living tree gives a rate for carbon-14 decay of 13.6 counts per minute. If the half-life for carbon-14 is 5720 years, how old is a wood sample that gives a rate for carbon-14 decay of 7.9 counts per minute?A. 5.3 x 102 yr.B. 7.6 x 102 yr.C. 1.1 x 103 yr.D. 9.5 x 103 yr. A square root function has a domain of x > 5 and a range of y > 7. What is the range of its inverse? What is the density of a cube that has a volume of 3 cm3 and a mass of 12 g? Please help, 20 points. (right answers only)In 23 complete sentences, thoroughly explain the protagonist's main motivation or goal in Condensed Milk by Varlam Shalamov? What does the protagonist want? PLEASE HELP ASAP! ILL GIVE BRAINLIEST!This is a graphic organizer that could be used to take notes.A graphic organizer shows 6 boxes on 3 levels of hierarchy with lines connecting boxes between the levels.How should this graphic organizer best be used?to note dates in a sequenceto show how ideas connectto record any assignmentsto identify vocabulary terms Please hurry!!!Analyze how two court casesEngel v. Vitale (1962) and West Virginia Board of Education V. Barnette (1943)confirmed the First Amendment right to freedom of religion. Effie is selling candles to raise money for new soccer league equipment. A small candle sells for $8 and a large candle sells for $12. The number of large candles Effie sells must be greater than or equal to 2 times the number of small candles she sells. She has at most 48 candles to sell.The number of small candles sold is represented by x and the number of large candles sold is represented by y.What is the maximum revenue she can make?$448$512$576$588 A tank containing oxygen, carbon dioxide, and nitrogen gases has a total pressure of 6.7atm. If the O2 has a pressure of 3.0 atm and the carbon dioxide has a pressure of 1.2what is the partial pressure of the nitrogen gas? 4) Who were Alice Pauls Silent Sentinels?A) strike-breakersB) White House protestorsC) soldiers in WWID) hunger-strikers plz help me with question ;-; yall help im drowning in work. 19 = 4a 12 which is a cause of desertification?A. farmingb. creating reservoirsc. overgrazingd. driving motor vehicles? Does anyone know or understand how to do this? Part 3 The bones function as levers in coordination with what body system? CirculatoryDigestiveIntegumentaryMuscular What is the equation for this graph Which expression is equivalent to 2cos2(StartFraction x Over 2 EndFraction) minus cosine (x)?011 2cos(x)1 + 2cos(x) Help me fast pleasee In the least-squares regression line, the desired sum of the errors (residuals) should be:_____.a) maximized.b) 1.c) positive.d) negative.e) zero.