Please help need postulate for both questions with explanations

Please Help Need Postulate For Both Questions With Explanations

Answers

Answer 1

1. ΔABD ≅ ΔCBD by SAS congruence theorem.

2. ΔABD ≅ ΔCBD by SSS congruence theorem.

What is the SAS and the SSS Congruence Theorem?

The SAS Congruence Theorem and the SSS Congruence Theorem are two postulates used in geometry to determine whether two triangles are congruent. The SAS Congruence Theorem requires that two sides and the included angle of one triangle be congruent to two sides and the included angle of another triangle for them to be congruent.

The SSS Congruence Theorem requires that all three sides of one triangle be congruent to the corresponding sides of another triangle for them to be congruent.

1. With the given information, we can deduce that, both triangles have two pairs of congruent sides which are:

BD ≅ BD (based on reflexive property)

AB ≅ CB (midpoint definition)

<ABD ≅ <CBD (right angles are congruent)

Thus, we can conclude that ΔABD ≅ ΔCBD by SAS congruence theorem.

2. Given the new information, it means that the two triangles have three pairs of congruent sides which are:

AD ≅ CD (given)

BD ≅ BD (based on reflexive property)

AB ≅ CB (midpoint definition)

Therefore, ΔABD ≅ ΔCBD by SSS congruence theorem.

Learn more about the SAS and SSS Congruence Theorem on:

https://brainly.com/question/2102943

#SPJ1


Related Questions

A plastic bag contains 0.80 mol of gas and occupies a volume of 18 L. A leak in the bag allows gas to escape until the volume becomes 16 L. How many moles of gas remain in the bag?
0.31 mol
0.91 mol
0.51 mol
0.71 mol

Answers

To find the moles of gas remaining in the bag, we can use the initial and final volumes and the initial moles of gas. Since the temperature and pressure remain constant, we can use the formula:

Initial moles × Initial volume = Final moles × Final volume
0.80 mol × 18 L = Final moles × 16 L

Solve for the final moles:
(0.80 mol × 18 L) / 16 L = Final moles

14.4 mol / 16 L = Final moles
Final moles = 0.9 mol

So, 0.9 moles of gas remain in the bag after the leak. The closest answer is 0.91 mol, so the correct option is:
0.91 moles of gas remain in the bag.

To know more about moles of gas visit:

https://brainly.com/question/30917880

#SPJ11

a list of numbers is considered increasing if each value after the first is greater than or equal to the preceding value. the following procedure is intended to return true if numberlist is increasing and return false otherwise. assume that numberlist contains at least two elements.

Answers

Option C is the correct option for the given problem; let’s consider all options and identify the different reasons in the number list.

How would we write this code?

From the second element (index 1) through the last element, this procedure iterates through the list of numbers using a for loop. It determines whether the current number is lower than the previous number after each repetition. If it is, the process gives a prompt False response, meaning that the list is not growing.

The procedure returns True, indicating that the list is growing, if the for loop concludes without running into a number that is less than the number it encountered before.

According to the issue definition, this technique implies the list has at least two elements. This guarantees that the for loop will always have a previous number to compare to.

Comments are written in italic to explain the code

Line 1: PROCEDURE Is Increasing(numberList)//start Is Increasing procedure with a list number List

Line 2: {//start procedure

Line 3: count<-2//set count to be 2

Line 4: REPEAT UNTIL (count -> LENGTH(numberList)//repeat from element 2 to last

Line 5: {//start repeat

Line 6: IF(numberList[count] < numberList[count-1]//if previous number is greater

Line 7: {//start if

Line 8: RETURN(true)//return true as next is greater than

Line 9: }//end if

Line 10: count<- count +1//increment to next element

Line 11: }//end repeat

Line 12: RETURN (false)//return false

Line 13: }//end procedure

To learn more about code here:

brainly.com/question/29328443

#SPJ4

Complete question is:

A list of numbers is considered increasing if each value after the first is greater than or equal to the preceding value. The following procedure is intended to return true if numberList is increasing and return false otherwise. Assume that numberList contains at least two elements. PROCEDURE isIncreasing(numberList) Tue 61 Line 1: Line 2: { Line 3: count 2 Line 4: REPEAT UNTIL(count > LENGTH(numberList)) Line 5: } IF(numberList[count] < numberList[count - 1]) Line 6: Line 7: To entd Line 8: RETURN(true) :80 onij { count count + 1 Line 9: Line 10: er onil Line 11: } Line 12: RETURN(false) BELAS(ConuE) Line 13: } Which of the following changes is needed for the program to work as intended? Lines 8 and 12 should be interchanged. c. In line 6, < should be changed to >=. a. b. Lines 10 and 11 should be interchanged. d. In line 3, 2 should be changed to 1. 3.

Sally left the city for vacation. Sandy left six hours later going 82 miles faster to catch up. After 5 hours Sandy caught up. What was Sally's average speed?

Answers

Answer: It took Sandy 11 hours to travel the same distance that Sam took 5 hours. {{{R[s]*11=5*75}}}

{{{R[s]=(5/11)*75}}}

{{{R[s]=34.9}}}{{{mph}}}

Don't ask sometimes i don't make sense...

The final answer is 11 hours... Hope this helps... Stay safe and have a great weekend!!! :D

Answer:

68 1/3

Step-by-step explanation:

Going 82 mph faster for 5 hours, Mary closed a (82 mi/h)×(5 h) = 410 mile gap. That gap was created in 3 hours by Sandy going.

 (410 mi)/(6 h) = 68 1/3 mi/h

please mark me as brainliest. l am bagging you please.

Solve the system using substitution:
y = -6x + 7

3x – 2y = 16

helppp

Answers

Answer:

x=-6 y=-1

Step-by-step explanation:

// Solve equation [2] for the variable  y  

 

 [2]    y = -x - 7

// Plug this in for variable  y  in equation [1]

  [1]    3x - 2•(-x -7) = -16

  [1]    5x = -30

// Solve equation [1] for the variable  x  

  [1]    5x = - 30  

  [1]    x = - 6  

// By now we know this much :

   x = -6

   y = -x-7

// Use the  x  value to solve for  y  

   y = -(-6)-7 = -1  

Solution :

{x,y} = {-6,-1}

Answer: 1 .x=-1/6y+7/6 (2.x=2/3y+16/3

Step-by-step explanation:

I need help with this practice problem solving from the trig section in my ACT prep guide

I need help with this practice problem solving from the trig section in my ACT prep guide

Answers

Step 1

Find the polar coordinates of the rectangular coordinates

\((-\sqrt[]{3},1)\)

To convert from the cartesian coordinates (x,y) to polar coordinates (r,θ), we use the following equation.

\(r^2=x^2+y^2\)\(\theta=arc\tan (\frac{y}{x})\)

Step 2

We have;

\((x,y)=(-\sqrt[]{3},1)\)\(\begin{gathered} r^2=(-\sqrt[]{3})^2+1^2 \\ r^2=3+1 \\ r=\sqrt[]{4} \\ r=2 \\ \end{gathered}\)\(\begin{gathered} \theta=arc\tan (\frac{y}{x}) \\ \theta=arc\tan (\frac{1}{-\sqrt[]{3}}) \\ \theta=\arctan (\frac{1}{-\sqrt[]{3}}\times\frac{\sqrt[]{3}}{\sqrt[]{3}}) \\ \theta=\arctan \frac{\sqrt[]{3}}{-3} \\ \theta=-\frac{\pi}{6}+\pi \\ \theta=\frac{5}{6}\pi \end{gathered}\)

The answer therefore is;

\((2,\frac{5\pi}{6})\)

Another easy question need fast please

Another easy question need fast please

Answers

Answer:

30.25

Step-by-step explanation:

All angles of a line must add up to 180. Since we already know that one angle is 90 degrees, we know that the other angles should add up to 90 degrees in order for all of the angles to add up to 180 degrees:

(3x-7)+(x+8)=90

4x+1=90

4x=89

x=22.25

22.25+8= 30.25

IM GIVING 100PTS & BRAINLIEST! -- ]

You are paid $10 per hour. You work 13 hours each week. Your taxes are federal, 10%; FICA, 7.65%; and state, 3%. You also contribute $30 to your company's retirement plan.
If you are paid weekly, how much is your realized income?

Answers

If i paid weekly, I realized my income is $73.155.

Answer:

Solution given;

1 hour =$10

13 hour = 13*10=$130

Taxes

federal :10%

FICA:7.65%

state: 3%

contribute to company: $30

now

My income each week :

$130-10%of $130-7.65% of $130-3% of $130-$30$130-$30-$13-$9.945-$3.9$73.155

Three objective functions for linear programming problems are 7A+10B,6A+4B, and −4A+7B. Show the graph of each for objective function values equal to 420 .

Answers

Graph of each objective function using linear programming.

Here,

Putting the equation equal to 420 and plotting the graph by finding the value of A and By putting A=0 and finding B then putting B=0 and finging A.

For example putting A=0 in 7A+10B=420 will yield  (0,42) and Putting B=0 will yield (60, 0). plotting theses points on graph and joining them to generated the line.

Repeating thin step for each objective function and plotting the graph.

7A + 10B = 420 is labelled as a.

6A+4B = 420 is labelled as b.

-4A + 7B = 420 is labelled as c .

The graph of each function is attached below.

Know more about linear programming,

https://brainly.com/question/30763902

#SPJ4

Three objective functions for linear programming problems are 7A+10B,6A+4B, and 4A+7B. Show the graph

If an Australian contractor ordered $340,000 U.S. Dollars worth of steel from an American company, what is the cost of the steel in Australian dollars? (Enter a number as an exact integer or decimal.)

Answers

Answer:

466895

Step-by-step explanation:

If you know the conversion, it's easy.

1 US dollar is about 1.37322 Australian.

so, you multiply 340,000 times 1.37322 and get about 466895 Australian dollars

The formula for relating a man's shoe size S and the length of his foot L in inches is
S3L
26. Find the length of a man's foot if he wears a size 12 shoe.

The formula for relating a man's shoe size S and the length of his foot L in inches isS3L26. Find the

Answers

Answer:

  12 5/6 inches

Step-by-step explanation:

You want to find the value of L when S=12 1/2, using the formula S = 3L -26.

Foot length

You can substitute for S in the formula before or after you solve for L. Here, we'll solve for L first:

  S +26 = 3L . . . . add 26 to both sides

  (S +26)/3 = L . . . . divide both sides by 3

Substituting 12 1/2 for S, this becomes ...

  L = (12 1/2 +26)/3 = (38 1/2)/3 = (77/2)/3 = 77/6 = 12 5/6

A man's foot is 12 5/6 inches long if he wears a size 12 1/2 shoe.

Answer:

the length of his foot in inches is 12

Please help me answer this question, it was due yesterday .​

Please help me answer this question, it was due yesterday .

Answers

Answer:

FA=7.29

Step-by-step explanation:

\(FD=\sqrt{10^{2}-8^{2} } \\FD=\sqrt{36} \\FD=6\\\)

∠EDF=53° (properties of retangle)

∠EAD=180-90-53 (∠ sum of Δ)

          =37

\(\frac{AD}{sin90} =\frac{8}{sin37} \\AD=13.29\)

FA=AD-FD

FA=7.29

Evaluate the triple integral of
f(x,y,z)=z(x2+y2+z2)−3/2f(x,y,z)=z(x2+y2+z2)−3/2 over the part of
the ball x2+y2+z2≤81x2+y2+z2≤81 defined by z≥4.5z≥4.5.

Answers

The value of the triple integral is 21π/8.

To evaluate the triple integral, we use spherical coordinates since we are dealing with a ball. The bounds for the radius r are 0 to 9, the bounds for the polar angle θ are 0 to 2π, and the bounds for the polar angle φ are arccos(4.5/9) to π. Substituting these bounds into the integral expression, we integrate the function

\(f(x, y, z) = z(x^2 + y^2 + z^2)^(-3/2)\)

over the given region. After performing the calculations, the value of the triple integral is found to be 21π/8, representing the volume under the function over the specified region of the ball.

learn more about triple integral here:

https://brainly.com/question/31955395

#SPJ11

There are 5 pencils in a pack.
Catalina has 2 packs. How many
pencils in all?
(unit)
Reese has 20 packs. How many
pencils in all?
(unit)

There are 5 pencils in a pack.Catalina has 2 packs. How manypencils in all?(unit)Reese has 20 packs.

Answers

Answer:

Catalina has 10 pencils total. (2 x 5 = 10)

Reese has 100 pencils total. (20 x 5 = 100)

Answer:

1. 10 2. 100

Step-by-step explanation

5 x 2= 10

20x 5= 100

for adults in the town of bridgeport, systolic blood pressure is normally distributed with a mean of 137 mmhg and a standard deviation of 9 mmhg. what percentage of adults in the town have a systolic bloo pressure less than 110 mmhg

Answers

99.85% of adults in the city have a systolic blood pressure of less than 110 mmHg.

Using 68-95-99.7 rule, we know that

99.7% of values lie between the interval (mean - 3 × standard deviation, mean + 3 × standard deviation)

(100 - 99.7) = 0.3% values lie outside the interval (mean - 3 × standard deviation, mean + 3 × standard deviation).

Since the normal distribution is bell-curved and symmetrical,

we can say

0.3/2 = 0.15% values are less than the mean - 3 × standard deviation

and 0.3/2 = 0.15% values are greater than mean + 3 × standard deviation.

Here,

Mean + 3 × standard deviation.

= 110 + 3 × 10 = 140

So, 0.15% of values  are greater than 140

So, (100 - 0.15) = 99.85% values are less than 140.

To learn more about systolic blood pressure

https://brainly.com/question/14507800

#SPJ4

a sphereical balloon is inflating with helium at a rate of 128pi ft^3/min. how fast is the balloon's radius increasing at the instant the radius is 4 ft

Answers

A sphereical balloon is inflating with helium at a rate of \(128\pi ft^3/min\).The balloon's radius is increasing at a rate of 8 ft/min when the radius is 4 ft.

To find the rate at which the balloon's radius is increasing, we can use the relationship between the volume of a sphere and its radius. The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.

We are given that the volume is increasing at a rate of 128π ft³/min. Taking the derivative of the volume formula with respect to time, we have dV/dt = 4πr²(dr/dt), where dV/dt represents the rate of change of volume and dr/dt represents the rate of change of the radius.

At the instant when the radius is 4 ft, we can substitute r = 4 into the equation. Solving for dr/dt, we have 128π = 4π(4)²(dr/dt), which simplifies to dr/dt = 8 ft/min.

Therefore, the balloon's radius is increasing at a rate of 8 ft/min when the radius is 4 ft.

Learn more about volume here:

https://brainly.com/question/21623450

#SPJ11

Khalil has a game board as shown below, which is a square with 20 cm sides. The area of the largest circle is 314
square centimeters
What is the probability of scoring 1, 3, or 5 points with one randomly thrown dart?
O 50%
O 62.5%
O75%
O78.5%

Khalil has a game board as shown below, which is a square with 20 cm sides. The area of the largest circle

Answers

Answer:

78.5

Step-by-step explanation:

The probability of scoring 1 , 3 or 5 points is 78.5% ( optionD)

What is probability?

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 and it's 100% in percentage.

probability is expressed as;

probably = sample space/total outcome

The area of the square is expressed as;

A = l²

= 20 × 20

= 400cm²

The area of the biggest circle is 314 cm²

The probability of scoring 1, 3 or 5

= 314/400 = 0.785

in percentage = 0.785 × 100

= 78.5%

learn more about probability from

https://brainly.com/question/13604758

#SPJ3

Simplify 3x + 5y + 2x – 4y

Answers

Answer:

5x + y

Step-by-step explanation:

3x + 5y + 2x – 4y=> 5x + y

Conclusion:

Therefore:

5x + y

Hoped this helped.

\(GeniusUser\)

The simplified form of the given expression is 7x+y.

The given expression is 3x+5y+2x-4y.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Group the like terms and simplify, we get

(3x+2x)+(5y-4y)

= 7x+y

Therefore, the simplified form of the given expression is 7x+y.

To learn more about an expression visit;

https://brainly.com/question/28170201.

#SPJ4

Under what circumstances is an atomic electron's probability density distribution spherically symmetric? Why?

Answers

An atomic electron's probability density distribution is in a symmetrical three-dimensional electron cloud around the nucleus under certain circumstances.

When the electron is in a spherically symmetric orbital, such as an s orbital (e.g., 1s, 2s, 3s), its probability density distribution is spherically symmetric.

S orbitals have a spherical shape, with the highest probability of finding the electron at the nucleus, gradually decreasing as we move away from the nucleus in all directions.

This spherically symmetric distribution occurs because s orbitals have no angular momentum and are characterized by a single quantum number, indicating a spherical symmetry.

In contrast, other atomic orbitals, such as p, d, and f orbitals, have different shapes and are not spherically symmetric due to their angular momentum and additional quantum numbers.

The spherically symmetric probability density distribution of an atomic electron in an s orbital allows for an equal likelihood of finding the electron in any direction from the nucleus, resulting in a symmetrical three-dimensional electron cloud around the nucleus.

To learn more about probability click here:

brainly.com/question/31828911

#SPJ11

Is (–39, 42) a solution to the equation y = x + 81?

Answers

Answer:

Yes

Step-by-step explanation:

Yes because if you insert -39 for x and 42 for y then your equation is:

42 = -39 + 81

If you were to solve this equation it would be true.

please help me with this ixl please

please help me with this ixl please

Answers

Answer:

plot these points on the graph and connect them

Step-by-step explanation:

T(5,-10)

U(9,-10)

V(2,0)

a scatter plot would be useful for question 17 options: showing the trend of sales, over time, of five different brands of blank dvds showing the relationship between the sales of blank cds and blank dvds showing the top selling brands of blank dvds showing the relative number of sales of four different brands of blank dvds

Answers

A scatter plot would be useful for showing the trend of sales, over time, of five different brands of blank DVDs. So, the correct answer is B).

A scatter plot is a type of graph that represents the relationship between two variables. It is particularly useful for showing the trend or pattern in data over time.

In this case, option B is the most appropriate because it involves plotting the sales data of different brands of blank DVDs over time. The scatter plot would allow for visualizing how the sales of each brand vary over different time periods, enabling the identification of any trends or patterns in the sales data.

So, the correct option is B).

To know more about scatter plot:

https://brainly.com/question/29231735

#SPJ4

--The given question is incomplete, the complete question is given below " A scatter plot would be useful for

A. Showing the relative number of sales of four different brands of blank DVDs

B. Showing the trend of sales, over time, of five different brands of blank DVDs

C. Showing the relationship between the sales of blank CDs and blank DVDs

D. Showing the top selling brands of blank DVDs"--

5.4 cm
12.8 cm
x cm
Work out the value of x.
Give your answer correct to 3 significant figure

Answers

Answer:

890w

bro if i know i will tell u but the problem that d

Suppose an odd function f has a local minimum at c. Does f have a local maximum or minimum at - c? If f is odd with a local minimum at c, f has a local at -

Answers

If f is an odd function and it has a local minimum at c, then f has a local maximum at -c. Since f is an odd function, we know that f(-c) = -f(c).

Given that f has a local minimum at c, we know that there exists an interval (c-d, c+d) containing c such that f(x) ≥ f(c) for all x in (c-d, c+d).

For simplicity, let's say that d = 1 (i.e., we have an interval (c-1, c+1) that contains c).

Then we know that f(c-1) ≤ f(c) and f(c+1) ≤ f(c). Using the fact that f is odd, we have:

f(-c-1) = -f(c+1) ≥ -f(c) = f(-c)f(-c+1) = -f(c-1) ≥ -f(c) = f(-c)

We can rewrite these inequalities as -f(-c) ≤ f(-c+1) and -f(-c) ≤ f(-c-1).

Thus, there exists an interval (-c-1, -c+1) containing -c such that f(x) ≤ f(-c) for all x in (-c-1, -c+1).

Therefore, f has a local maximum at -c.

Therefore, if an odd function f has a local minimum at c, then f has a local maximum at -c. This is true for any odd function f with a local minimum at any point c in its domain.

Thus, if an odd function f has a local minimum at c, it has a local maximum at -c. The proof uses the definition of an odd function, which is a function that satisfies f(-x) = -f(x) for all x in the domain of f.

To know more about  local maximum visit:

brainly.com/question/29404086

#SPJ11

Fractions 7/8+ 1/5
Evaluate the expression shown below and write your answer as a fraction in simplest form

Answers

The simplest form of fraction of the given terms is 43/40.

According to the statement

we have to find that the simplest form of the fraction by evaluating.

So, For this purpose, we know that the

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.

The given expression is

7/8+ 1/5

Now, to solve it take a LCM of it then

35+8/40

Now solve the term then the equation become

43/40.

Now, The simple form of the fraction become the 43/40.

So, The simplest form of fraction of the given terms is 43/40.

Learn more about fraction here

https://brainly.com/question/1622425

#SPJ9

Your sock drawer has two white socks, four brown socks, and two black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot. Find the probability of this occuring.

Answers

Answer:

The probability of this occurring is 1/7

Step-by-step explanation:

Okay, here is a probability question.

From the question, we can identify the following;

Total number of socks = 2 + 4 + 2 = 8 socks

Since we are not given the order in which the socks was worn, we can assume any order.

Let’s say the right leg socks was worn first.

From the question, the socks on the right leg is a brown one.

So now let’s calculate the probability of selecting a brown socks out of the mix

That would be ;

number of brown socks/ total number of socks = 4/8 = 1/2

Now, for the left foot, we are having white sock here.

Kindly recall that since we already have a sock on the right foot, we have 7 socks left to pick from.

Now we need the probability of picking a white sock from the total 7. That would be ; 2/7

So the probability of both action occurring is simply the product of both probabilities and that is ;

1/2 * 2/7 = 1/7

George's dog ran out of its crate. It ran 22 meters, turned and ran 11 meters, and then turned 120° to face its crate. How far away from its crate is George's dog? Round to the nearest hundredth.

Answers

George's dog is approximately 32.41 meters away from its crate, if it ran 22 meters, turned and ran 11 meters, and then turned 120° to face its crate.

To determine the distance from George's dog to its crate after the described movements, we can use the concept of a triangle and trigonometry.

The dog initially runs 22 meters, then turns and runs 11 meters, forming the two sides of a triangle. The third side of the triangle represents the distance from the dog's final position to the crate.

To find this distance, we can use the Law of Cosines, which states that in a triangle with sides a, b, and c and angle C opposite side c, the equation is c² = a² + b² - 2abcos(C).

In this case, a = 22 meters, b = 11 meters, and C = 120°. Plugging these values into the equation, we have

c² = 22² + 11² - 2(22)(11)cos(120°).

Evaluating the expression, we get

c ≈ 32.41 meters.

To learn more about distance click on,

https://brainly.com/question/31954234

#SPJ4

what is 20% of 24cm?

Answers

Answer:

20% of 24cm=20/100×24=4.8cm

Answer:

4.8cm

Step-by-step explanation:

24x20%=20×0.20=4.8cm

14. Find the reciprocal of 20.95 to4 decimal places using the tables of reciprocals (1mk)​

Answers

The reciprocal of 20.95 to 4 decimal places using the table of reciprocals is 0.0478.

Reciprocal of a number

To find the reciprocal of 20.95, we can look up the reciprocal of 20.9 or 21 in the table and then interpolate to get a more accurate value for 20.95.

reciprocal of 20.9 = 0.04784reciprocal of 21 = 0.04762

To interpolate, we can calculate the difference between 20.95 and 20.9, which is 0.05, and the difference between the reciprocals of 20.95 and 20.9, which is 0.00009.

Then we can use the formula:

reciprocal of 20.95 = reciprocal of 20.9 + (difference / interval) x (reciprocal of 21 - reciprocal of 20.9)

where interval is the difference between the numbers in the table (which is 0.1 in this case).

Thus:

reciprocal of 20.95 = 0.04784 + (0.05 / 0.1) x (0.04762 - 0.04784)

= 0.04784 + 0.025 x (-0.00022)

= 0.04784 - 0.0000055

= 0.0478345

In other words, the reciprocal of 20.95 to 4 decimal places using the tables of reciprocals is 0.0478.

More on the reciprocal of numbers can be found here: https://brainly.com/question/15590281

#SPJ1

A man in a lighthouse tower that is 30 ft. He spots a ship at sea at an angle of depression of 10°. How far is the ship from the base of the lighthouse?

Answers

Answer:

170.16 ft

Step-by-step explanation:

tan10° = 30/x

x = 30x/ tan 10° = 30/0.1763

=170.16 ft

The distance from the vertex to the centroid of the equilateral triangle is 12√3 cm. Calculate the volume.​

Answers

2,304 cubic centimetres is the required volume of the regular tetrahedron.

The distance from the vertex to the centroid of the equilateral triangle.

Let's denote the side length of the equilateral triangle as "s". We know that the distance from the vertex (pointing downwards) to the centroid (the center of mass) is 12√3 cm.

Since the centroid divides each median in a 2:1 ratio, we know that the distance from the centroid to the midpoint of a side is 1/3 of the total distance from the centroid to the vertex. Therefore, the distance from the centroid to each side is:

(1/3) * 12√3 = 4√3 cm

Let's draw an altitude from the centroid to one of the sides of the triangle, creating a right triangle. The length of the altitude is:

h = 4√3 cm

The length of the base of the right triangle (half of one side of the equilateral triangle) is:

b = s/2

The length of the hypotenuse of the right triangle (the distance from the centroid to the vertex) is:

c = 12√3 cm

Using the Pythagorean theorem, we can write:

c^2 = b^2 + h^2

Solving for s, we get:

s = 2b = 2√(c^2 - h^2)

s = 2√((12√3)^2 - (4√3)^2)

s = 2√(1443 - 163)

s = 2√(128*3) = 32√3

Now we can calculate the area of the equilateral triangle:

A = √(3)/4)s^2 = √((3)/4)(32√3)^2 = 192√3 cm^2

Finally, we can use the formula for the volume of a regular tetrahedron:

V = (1/3)Ah

where A is the area of the equilateral triangle and h is the height of the tetrahedron, which is the distance from the vertex to the centroid.

Plugging in the values we have found, we get:

V = (1/3)192√312√3 = 2,304 cm^3

Therefore, the volume of the regular tetrahedron with the given properties is 2,304 cubic centimeters.

Learn more vertex and centroid of equilateral triangle here: https://brainly.com/question/30095629

#SPJ1

Other Questions
find the midpoint of the line segment with end coordinates of (2,1) and (4,5) Opposition to Roe v.Wade rulingDecreased role of federalgovernmentWhich organization would best fit in the blank above?OOB. Anti-Defamation LeagueOC. The Moral MajorityA. ACT UP?D. The Weather UndergroundIncreased militaryspending Please someone tell the answers I give up! which of the following types of fitness-related businesses is defined as for-profit facilities that offer fitness services as well as raquet sports, pools, and gymnasiums? Which equation results from taking the square root of both sides of (x 9)2 = 81? last month, hildebrand corporation generated sales of $800,000 and incurred selling and administrative expenses of $320,000, of which half were variable. this month, the company estimates that it will generate sales of $900,000. management does not anticipate any changes in unit variable costs. however, it does expect fixed selling and administrative costs to increase by $4,000. volcanoes that have submerged beneath the surface of the sea are termed ________. group of answer choices seamounts mid-ocean ridges guyots fracture zones If y= cos x, then d^75y/dx^75? (A) -sin x (B) sin x (C) -cos x (D) cos X Someone please help me! 12. One endpoint of a segment is (-3,5). Themidpoint of this segment is (4, -1). What isthe coordinate of the other endpoint? On a far-away (hypothetical) planet, a student is conducting an experiment to study vertical motion. The student fires a cannon directly upward, and then records the position of the cannonball every second until it falls back to the ground. Their data is shown in the table below. Based on their data below, answer the following two questions:1) What is the acceleration due to gravity on this planet? Clearly show how you calculated this.2) Is there significant air resistance affecting the experiment? Write an evidence-based argument to justify your claim.- One of the pieces of evidence that you use must be a graph based on the given data. The quantities on the graph are up to you; they can be position and time themselves, or different quantities that you calculate from the given position and time data. - If you'd like, you can also include outside evidence from your own lab or research. This is not required; only include it if it makes your argument stronger.Answer both questions on one document. The document can be digital, hand-written, or a mix of both (copy and paste images of your handwritten work into a doc). Time (s)Position (m)00195217032254260527562707245820091351050 What do you prefer: online classes pe face to face? Why?Urgent!! Dau coroana!!! Why is a protein compared to a paragraph and not just single letters had no stock transactions in 2021, so the change in stockholders' equity for 2021 was due to net income and dividends. if dividends were $45,000, how much was murphy's net income for 2021? use the accounting equation and the statement of retained earnings. replication is most likely used to: a. reduce portfolio risk. b. increase leverage. c. exploit pricing differentials. What is the value of the expression 2 + (8.5) (9 14)? Express the answer as a decimal. why can't x+4x+1 be factored You have CDN$800 to spend during abeach vacation in Florida. How much in US dollars will you have tospend if the exchange rate is US$1.00 = CDN$1.30? what is the authors primary argument for the frozen tissue lab aaaaaaaaaaaaaaaaaa pls help