A pyramid has all sides that are equilateral triangles. Each triangle has side lengths of 9 centimeters. If the surface area of the pyramid is 140 4 square centimeters, what is the slant height of the pyramid

Answers

Answer 1

Obviously it would be 38

Answer 2

A pyramid has all sides that are equilateral triangles. Each triangle has side lengths of [tex]9[/tex] centimeters. If the surface area of the pyramid is [tex]140.4[/tex]square centimeters, the slant height of the pyramid is [tex]Slant height= 2*(140.4-81\sqrt{3} )/27[/tex]

To find the slant height of the pyramid, we first need to determine the lateral area of one of the triangular faces of the pyramid.

Since all sides of the equilateral triangle have a length of [tex]9[/tex] centimeters, we can use the formula for the area of an equilateral triangle, which is:

[tex]A=\sqrt{3} /4*side length^{2}[/tex]

Substituting the given side length [tex]9[/tex] centimeters into the formula:

[tex]A=\sqrt{3} /4*9^{2} \\A=\sqrt{3} /4*81\\ A=81\sqrt{3}/4[/tex]

Now, since there are four equilateral triangular faces on the pyramid, the total lateral area of the pyramid is [tex]4*81\sqrt{3}/4=81\sqrt{3}[/tex] square centimeters.

Given that the total surface area of the pyramid is [tex]140.4[/tex] square centimeters, we subtract the area of the base (which is also an equilateral triangle) from the total surface area to find the lateral surface area:

[tex]Lateral surface area=Total surface area-Area of base\\Lateral surface area=140.4-81\sqrt{3}[/tex]

Now, the lateral surface area of a pyramid can be calculated using the formula:

[tex]Lateral surface area=12*perimeter of base*slant[/tex]

For an equilateral triangle, the perimeter is [tex]3*side length=3*9= 27[/tex]centimeters.

So, we have:

[tex]140.4-81\sqrt{3} =1/2*27*slant height\\140.4-81\sqrt{3} =27/2*slant height\\Slant height=2*(140.4-81\sqrt{3} )/27[/tex]

Calculating this expression gives us the value of the slant height of the pyramid.

COMPLETE QUESTION:

Related Questions

A right circular cylinder has a volume of 1296 cubic inches. If you divide the radius of the cylinder by 12, what would be the volume of the smaller cylinder?

Answers

I think the answer would be 108 because I divided 1296 and 12 and that what I got ....I'm not sure if that what I was supposed to do but I think that's the answer

I'm so sorry if I'm wrong but I hope I helped you

Another way is you could divide 1296 by 2 and divide that answer by 12 I another way to get an answer to the question you're asking

What is Eleven less than two times a number is equal to 27

Answers

The answer should be in the equation form would be 2x - 11 = 27.

If you want me to solve 2x - 11 = 27 than its below:

2x = 11 + 27
38 = 2x
38/2 = x
19 = x

-Love, live, and watch anime.

11 less implies: -11

two times a number (x) implies: 2x

equal to 27 implies: = 27

Set the equation together.

2x - 11 = 27 is your equation.

Solve for x. Note the equal sign. What you do to one side you do to the other. Add 11 to both sides

2x - 11 (+11) = 27 (+11)

2x = 38

Isolate the x. Divide 2 from both sides.

2x/2 = 38/2

x = 19

hope this helps

How can you estimate to find the percent of a number? Please give a full explanation.

(do not use an example to demonstrate)

Answers

Gee this gonna be hard to do without giving an example, but one way you could estimate the percentage of a number is to round the number to the nearest benchmark number (10 or 5) and estimate the percentage from that new number.
I hope this helped! :-)

Which of the following represents “the sum of the abscissa and the ordinate is negative four”?

A. x + y = -4

B. xy = 4

C. 4x + 4y = 0

Answers

Answer: A

When you are working with coordinate points, the x-value in the point is called the abscissa. The y-value in the point is called the ordinate.

Therefore all you have to do is add the x and y of the coordinates to get our equation. Don't forget that the sum has to be -4 according to the problem.

Find the first term of the arithmetic sequence in which t22=1008 and d= -8

Answers

tn = nth term
t22 = 22nd term
d = common difference
d = -8
n = number of terms
n = 22
.
tn = t1 + (n - 1)d
t22 = t1 + (n - 1)d
1008 = t1 + (22 - 1)-8
1008 = t1 + (21)-8
1008 = t1 + 168
1008 - 168 = t1
840 = t1

you misunderstood lol

A popular brand of running shoes costs a local store $68 for each pair. If the store sells the shoes for $119, what is the percent of increase in the price?

Answers

The percent would be about 59 percent. WE JUST STUDIED PERCENTS IN CLASS

PLEASE HELP ME I BEG YOU PLEASE PLEA PLEASE

Solve 2x + y + z = 5
4x – 2y – z = 0
3x – y + 2z = 6
(1, 1, 2)
(-1, -1, -2)
(5, 0, 6)
(1, 1, -2)

Solve 3x + 6y – 6z = 9
2x – 5y + 4z = 6
-x +16y + 14z = -3
(5, 0, 1)
(9, 6, -3)
(0, 3, 0)
(3, 0, 0)

Solve –x + y + 2z = 2
2x – y + z = 5
-4x – y + 3z = 3
(2, 5, 3)
(0, 4, -1)
(1, -1, 2)
(-1, 1, -2)

Solve –x + 3y + z = 9
2x + 5y = 27
3x + y – 2z = -18
(1, 3, -2)
(21, -3, 39)
(1, 2, -4)
(22, -1, 26)

Solve x – 2y – 3z = 3
3x + y + z = 12
3x – 2y – 4z = 15
(0, 0, -1)
(3, 12, 15)
(3, 9, -6)
(-3, -9, 6)

Solve x + 3y + z = 1
2x – y – z = 6
5x + y + z = 1
(1, 6, 1)
(1, 2, -6)
(2, 1, -4)
(-1, -2, 6)

Answers

The first one is the first one
The second one is the fourth one
The third one is the third one
The fourth one is the second one
The fifth one is the third one
The sixth one is the second one

Answer:

The first one is (1, 1, 2)

The second one is (3, 0, 0)

The third one is (1, -1, 2)

The fourth one is (21, -3, 39)

The fifth one is (3, 9, -6)

The sixth one is (1, 2, -6)

if a + 8 = 11 what is the value of 8a

Answers

a + 8 = 11
isolate the a, subtract 8 from both sides
a + 8 (-8) = 11 (-8)
subtract
a = 11 - 8
answer for "a"
a = 3

8a
plug in 3 for a, and multiply
8(3) = 24

24 is your answer

hope this helps

a plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour.if the plane resultant speed due to the wind is 180 miles/hour,what is the plane's actual speed. rounded to the nearest integer

Answers

The answer is 135 miles/hour.

I hope this helped!

The plane's actual speed is 135 miles/hour if the plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour option (C) 135 miles/hour is correct.

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

The question in incomplete.

The complete question is:

A plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour. If the plane's resultant speed due to the wind is 180 miles/hour, what is the plane's actual speed, rounded to the nearest integer?

120 miles/hour130 miles/hour135 miles/hour140 miles/hour

From the data given in the question:

Using Cosine Law:

c² = a² + b² - 2 ac cos C

180² = 50² + x² - (2×50)x cos 150°

32400 - 2500 - x² = 86.6x

29,900 - x² = 86.6 x

x² + 86.6x - 29900 = 0

After solving the above quadratic equation:

x = 135 miles/hour

Thus, the plane's actual speed is 135 miles/hour if the plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour option (C) 135 miles/hour is correct.

Learn more about the angle here:

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What is the equation in point-slope form of the line passing through (2,2) and (4,8)

Answers

we have that
points A (2,2) and B (4,8)

we know
the equation in point-slope form of the line is
y-y1=m*(x-x1)

step 1
find the slope m
m=(y2-y1)/(x2-x1)=(8-2)/(4-2)=6/2=3

with the point A (2,2) and m=3
y-2=3*(x-2)------------> this is the equation in point-slope form of the line

The arena intends to give a gift box to each company that hires a stand at the event. Select from the options below the nets which will fold up into a cube.

Answers

! works for certain.
4 should as well.
5 should be OK
3 does not
2 does not

PLEASE HELP WILL GIVE 30 POINTS
Add or subtract. Show your work for each problem
a. (x^2-4x+5)+(7x^2+2x-3) b. (7x^2+4x-6)-(2x^2-3x+1)

Answers

To solve this problem you must apply the proccedure shown below:

a) You must sum terms with same exponents, therefore, you have that the sum of these two polynomials is:

[tex] (x^{2}-4x+5)+(7x^{2}+2x-3) [/tex]

[tex] 8x^{2} -2x+2 [/tex]

b) First, you must mulitply the signs of the second polynomial by the negative sign, and them, you apply an algebraic sum. Therefore, the result is:

[tex] (7x^{2}+4x-6-2x^{2}+3x-1) \\ 5x^{2} +7x-7 [/tex]

The answers are: a)[tex] 8x^{2} -2x+2 [/tex]; b) [tex] 5x^{2} +7x-7 [/tex]

x² - 4x + 5 + 7x² + 2x - 3

8x² - 2x + 2

7x² + 4x - 6 - (2x² - 3x + 1)

7x² + 4x - 6 - 2x² + 3x - 1

5x² + 7x - 7

Pedro was simplifying four over seven divided by five over eight. and his work is shown below. Identify where he made his error. Original problem: four over seven divided by five over eight. Step 1: four over seven multiplied by eight over five . Step 2: four times five over seven times eight. Step 3: twenty over fifty-six. Step 4: five over fourteen.

Answers

Answer: it's the 2nd step

Pedro made an error in step 2, he crossed multiplied instead of multiplying.

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

Pedro was simplifying four over seven divided by five over eight.

= (4/7)/(5/8)

= (4/7)x(8/5)

= 32/35

In Step 2 Pedro made mistake, he crossed multiplied instead of multiplying the numerators, and then the denominators.

Thus, Pedro made an error in step 2, he crossed multiplied instead of multiplying.

Learn more about the fraction here:

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When translating a figure using a combination of two translations, is the resulting figure congruent to the original figure?

Answers

it has to be the original figure but it is in a different spot on the graph

Final answer:

When translating a figure using two translations, the end result is a figure that is congruent to the original. This is due to the fact that translations move the shape without altering its size or orientation.

Explanation:

Yes, when translating a figure using a combination of two translations, the resulting figure is congruent to the original figure. When a figure is translated, it is moved without being turned or flipped, the size and shape remains the same, hence making it congruent. For example, consider a parallelogram. If two different vectors A and B are chosen to translate it, following the rules of vector summation, the figure moved, known as the resultant vector retains the dimensions and angles of the original parallelogram, albeit in a different location.

Learn more about Congruence through Translations here:

https://brainly.com/question/29792559

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HEEEEEEEEEEEEEEEEELP

Answers

Answer:
y = -5x + 6

Explanation:
The equation of line in slope-intercept form is:
y = mx + c
where:
m is the slope
c is the y-intercept

We are given that the slope = -5. Therefore, the equation becomes:
y = -5x + c

Now, we need to get the value of c. To do so, we will substitute with the given point (3,-9) in the equation and solve for c as follows:
y = -5x + c
-9 = -5(3) + c
-9 = -15 + c
c = -9 + 15 = 6

Based on the above, equation of line is:
y = -5x + 6

Hope this helps :)

At a concession stand, three hot dogs and two hamburgers cost $7.75;two hot dogs and three hamburgers cost $8.50. Find the cost of one hot dog and the cost of one hamburger

Answers

Hamburger= $0.75
Hot dog= $3.125
A great deal if you ask me
Hope this helped

Tickets are priced as follows:
Adult Tickets -£12
Child Tickets -£6
Cheryl rings the booking office to buy 6 adult tickets and 3 child tickets
She is told that a 10% booking fee will be added to the ticket price
2% will then be added if she is paying by credit card

Work out the total charge that Cheryl will have to pay if she uses her credit card to pay for the tickets

Answers

Answer:

down there

Step-by-step explanation:

£72 + £18 = £90

90 x 12%= £9 + £1.80

£90 + £10.80 = £100.98

The sides of a right triangle have a relationship as depicted below, where x is the length of the longer leg in inches.

The area of this triangle, A, is equal to the perimeter of this triangle.

Create a system of equations to model this situation. Determine if there are any solutions, and, if possible, whether or not they are viable.

How many total possible solutions are there to this system?

Of any possible solutions, how many are viable solutions for this situation?

Answers

The equation to represent the area of the triangle would be:
y = 1/2(x²) - (7/2)x

The equation to represent the perimeter of the triangle would be:
y = 3x - 6

The solutions to the system would be (12, 30) or (1, -3). The only viable solution is (12, 30).

Explanation
The area of a triangle is found using the formula
A = 1/2bh

For our triangle, b = x and h = x-7, so we have:
A = 1/2(x)(x-7)
A = 1/2(x²-7x)
A = 1/2(x²) - (7/2)x

We will replace A with y, so we have:
y = 1/2(x²) - (7/2)x

The perimeter of a triangle is found by adding together all sides, so we have:
P = (x-7) + x + (x+1)

Combining like terms we get:
P = 3x - 6

We will replace P with y, so we have:
y = 3x - 6

Since both equations have y isolated on one side, it will be easy to use substitution to solve the system:

3x - 6 = 1/2(x²) - (7/2)x

It's easier to work with whole numbers, so we will multiply everything by 2:
6x - 12 = x² - 7x

We want all of the variables on one side, so we will subtract 6x:
6x - 12 - 6x = x² - 7x - 6x
-12 = x² - 13x

When solving quadratics, we want the equation equal to 0, so we will add 12:
-12+12 = x² - 13x + 12
0 = x² - 13x + 12

This is easy to factor, as there are factors of 12 that sum to -13; -12(-1) = 12 and -12+-1 = -13:
0 = (x-12)(x-1)

Using the zero product property, we know that either x-12=0 or x-1=0; therefore x=12 or x=1.

Putting these back into our equation for perimeter (the simplest one) we have:
y = 3(12)-6 = 36-6 = 30; (12, 30);
y = 3(1) - 6 = 3 - 6 = -3; (1, -3)

We cannot have a negative perimeter, so the only viable solution is (12, 30).

Answer:

two possible and one viable

Step-by-step explanation:

hope this helps!

Can anyone PLEASE help me with this? Will mark brainliest

Simplify the expression.

2 1/4x+(4 1/3x-7 4/5) divided by 2 3/5

Answers

47x-36/12

hope this helps

--------------------------------------
Question
--------------------------------------
[tex]2 \dfrac{1}{4} + ( 4\dfrac{1}{3} x - 7 \dfrac{4}{5} ) \div 2 \dfrac{3}{5} [/tex]

--------------------------------------
Start with the bracket
--------------------------------------

--------------------------------------
Change to improper fraction
--------------------------------------
[tex]2 \dfrac{1}{4} + ( \dfrac{13}{3} x - \dfrac{39}{5} ) \div 2 \dfrac{3}{5} [/tex]

--------------------------------------
Make into single fraction
--------------------------------------
[tex]2 \dfrac{1}{4} + \dfrac{65x-117}{15}} \div 2 \dfrac{3}{5} [/tex]

--------------------------------------
Now do the divide
--------------------------------------

--------------------------------------
Convert to improper fraction
--------------------------------------
[tex]2 \dfrac{1}{4} + \dfrac{65x-117}{15}} \div \dfrac{13}{5} [/tex]

--------------------------------------
Change to multiplication fraction
--------------------------------------
[tex]2 \dfrac{1}{4} + \dfrac{65x-117}{15}} \times \dfrac{5}{13} [/tex]

--------------------------------------
Multiply the fraction
--------------------------------------
[tex]2 \dfrac{1}{4} + \dfrac{65x-117}{39}} [/tex]

--------------------------------------
Now do the addition
--------------------------------------

--------------------------------------
Change to improper fraction
--------------------------------------
[tex] \dfrac{9}{4} + \dfrac{65x-117}{39}} [/tex]

--------------------------------------
Put into single fraction
--------------------------------------
[tex] \dfrac{351 + 260x -468}{156} [/tex]

--------------------------------------
Combine like terms
--------------------------------------
[tex] \dfrac{260x -117}{156} [/tex]

Tennis balls are sold in tubes that hold 3 tennis balls each. A store stacks 2 rows of tennis ball tubes on its shelf. Each row has 7 tubes in it. How many tennis balls are there in all?

Answers

There are 42 tennis balls in all

There are a total of 42 tennis balls on the shelf.

To determine the total number of tennis balls on the shelf, we first need to find out how many tennis ball tubes are there. Each row has 7 tubes and there are 2 rows:

Number of tubes per row = 7

Number of rows = 2

Total number of tubes = 7 tubes/row × 2 rows = 14 tubes

Since each tube contains 3 tennis balls, we multiply the total number of tubes by the number of tennis balls per tube:

Number of tennis balls per tube = 3

Total number of tennis balls = 14 tubes × 3 tennis balls/tube = 42 tennis balls

Therefore, the store has a total of 42 tennis balls on the shelf.

Use the formula V = s³, where V is the volume and s is the edge length of the cube, to solve this problem. A cube-shaped bin has an edge length of 34 yard. What is the volume of the container? Enter your answer, as a fraction in simplest form, in the box.

Answers

Volume: 39,304 cubic yards

To find the volume, you simply have to use the formula that is given. It is V = s^3. This means you multiply the side by itself 3 times.

S x S x S = V
34 x 34 x 34 = 39304 cubic yards

The probability that an event will occur is fraction 7 over 8. Which of these best describes the likelihood of the event occurring? a.Likely b.Certain c.Unlikely d.Impossible

Answers

A is your answer! 7/8 is very likely, but not certain. There is a 12.5 % chance that it can occur. I hope I helped!

Answer:

Step-by-step explanation:

A is the correct answer because, 7/8 is very likely. It isn't certain though. There is a 12.5 % chance that it can occur.

how many square feet of outdoor carpet will we need for this hole

Answers

Answer: 36 sq

Step-by-step explanation: you add 24 to 12 and get 36

Answer:

[tex]36\text{ inch}^2[/tex]

Step-by-step explanation:

We have been given an image of outdoor carpet needed for a hole. We are asked to find the area of outdoor carpet needed for this hole.

We can see that there are two pieces needed to cover the given hole.

One pieces equal 24 square inches and another pieces equal 12 square inches.

[tex]\text{Area of carpet needed to cover the hole}=24\text{ inch}^2+12\text{ inch}^2[/tex]

[tex]\text{Area of carpet needed to cover the hole}=36\text{ inch}^2[/tex]

Therefore, [tex]36\text{ inch}^2[/tex] of carpet is needed to cover the given hole.

Is a product of a rational and irrational number, rational or irrational? Give an example

Answers

The product of a rational and irrational number is irrational.

29 plus j is equal to the quotient of 77 and j

Write as an equation

Answers

29 + j = 77/j is the equation.

last month you swim the 50m freestyle in 28.38 seconds. Today you swim it in 27.33 seconds what is your percent of change round to the nearest tenth of a percent if necessary

Answers

27.33/28.38 = 0.96300211
Making it a percent and rounding it to the nearest tenth it’ll be 96.3%

which questions are good examples of a statistical question? check all that apply

a. How many pets do you have

b. do you think a pet is a lot of work?

c. do you like having a pet?

d. how many times a day do you feed your pet?

e. do you feed your pet at night?

Answers

Choices A and D are good statistical questions. The reason is because both of these questions will have numerical answers(different numbers will be the answer) that may vary depending on who you ask. The other 3 questions are all yes/no questions.

Answer:

A and d are pretty good questions

HOW DO u do this?? Plz help!!!! Question 2

Answers

figures F and E ate congruent because they're the exact same shape with the same measurements

Ari bought a DVD that originally cost $15 on sale for 20% off. The sales tax is 5%. How much did Ari pay for the DVD, including tax.

Answers

20% off of $15 is 12.00
And 5% of 12.00 is .60
So your answer is $12.60
If this helps mark as brainliest pls

What is 3/4 of a year ? Write in months.

Answers

9 months because 4/4 is 12 months. 1/4 is 3 months and you do 3 x 1/= 3/4 and then doo 3 times 3 = 9

Hi there!

To make this a bit simpler, first, we should convert a year into months:

1 yr = 12 mo

Now, we multiply 12 by 3/4, since we're trying to find 3/4 of a year.

12 * 3/4 = 9

So, our answer would be 9 months.

Hope this helps!

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