Mathematics High School

In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?

Enter your answer in the box.

Answers

Answer 1
Yes the answer is

10cm

Because (The 30-60-90 Triangle Theorem)
In a 30-60-90 triangle, the length of the hypotenuse is TWICE the length of the shorter leg.

Thanks Shellbag101 
Answer 2

The length of the hypotenuse is 10cm

SOH CAH TOA identity

Given a  30-60-90 triangle where:

Length of the shorter leg = 5cm (adjacent)

The hypotenuse is what we need.

[tex]cos \theta = \frac{adj}{hyp} \\ [/tex]

Substitute the given parameters

[tex]cos 60 = \frac{5}{h}\\ h =\frac{5}{cos 60}\\ h = \frac{5}{0.5}\\ h = 10cm[/tex]

Hence the length of the hypotenuse is 10cm

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Related Questions

How do I solve this

Answers

Hi there!

Since the complementary angle adds up to 90 degrees, we would add 55° and (3x + 8)° and set it equal to 90°.

55° + (3x + 8)° = 90°

Now, to find x, we simplify.

63 + 3x = 90
3x = 27
x = 9

So, x is 9 degrees.

Hope this helps!

15.5 ft + 1.25 ft + 13.5 ft=

Answers

Adding all these numbers together, you should get 30.25 ft.
30.25ft. First you add the whole numbers then you add the decimals.

Which graph matches this situation

Answers

Well, one way to eliminate the possible options, is to look for the point of the starting mass, which is 8 milligrams. This eliminates graphs A and B, this leaves graphs C and D, knowing the mass is decreasing and not increasing, the correct graph would be D.

We can check this, by taking the mass of the substance and dividing it by 2, the remaining mass of the substance would be 4 mg.










your primary jobs gross income is 3468.73/month deductions are fica (7.65%) federal tax witholding (11.5%) and state tax withholding (7.8%) how much are your ficed expenses if they are 36% of your relized income

Answers

sierah907 Your primary job’s gross income is $3,468.73/month. Deductions are FICA (7.65%), federal tax withholding (11.5%), and state tax withholding (7.8%). How much are your fixed expenses if they are 36% of your realized income?


$1,388.65


$814.92


$912.21


$1,068.57





To get your realized income you: add your deductions which equals to a total of 26.95%. 

Then you subtract that amount  from your gross income. 
(3468.72 - 26.95% = 2533.91) 

 After that you need to find what 36% of your realized income equals to: 

and it equals to, 912.20. 

Therefore, your answer is C.




Answer 2: 

our deductions are 7.65% , 11.5% and 7.8% . Total 26.95% .

So deduct that from your Gross . $3468.73 - 26.95% leaves you with $ 2533.91.
That's your Realized Income . $2533.91 .

So you need to find 36% of that . It's $912.20.

And that is your answer . Your fixed expenses are $ 912.20 .

Answer:

$912.21

Step-by-step explanation:

Your primary jobs gross income = $3468.73

All deductions 7.65% (fica) + 11.5% (federal) + 7.8% (state tax) = 26.95%

Income after deductions = 3468.73 - ( 26.95% × 3468.73 )

                                         = 3468.73 - (0.2695 × 3468.73)

                                         = 3468.73 - 934.82

                                         = $2,533.91

Fixed expenses on your realized income = 36%

Fixed expenses = 36% × 2,533.91

                          = 0.36 × 2,533.91

                          = $912.2076 ≈ $912.21

Fixed expenses are $912.21

The result of rounding the whole number 72,341 to the nearest hundreds place is:
72,300.
72,000.
70,000.
72,340

Answers

Hi there ,
the answer will be 72,300.
Hope it helps
Nearest hundreds.

72, 341:

7 is in the ten thousands place
2 is in the thousands place
3 is in the hundreds place
4 is in the tens place
1 is in the ones place

To find the hundreds place, look at the place value to the right of it (or tens place in this case).

In the tens case is a 4, which is less than 5, so you round down 
( 5 and greater, round up, 4 and less, round down)

So your answer is 72,300

hope this helps

What is the value of x in the diagram below?

Answers

Hi, 
The answer will be [tex] \frac{ 18\sqrt{2} }{ \sqrt{3} } [/tex] .

Now how is that, there is a rule for the right angled triangle which says:

cosθ = [tex] \frac{adjacent side}{hypotenuse} [/tex] so, if we applied this rule on the lower triangle we can say: cos30°= [tex] \frac{9}{hypotenuse} [/tex] and therefore the hypotenuse = [tex] \frac{9}{cos30} [/tex] = [tex] \frac{18}{ \sqrt{3} } [/tex] .

now in the upper triangle we will apply the same rule so,
cos45°=[tex] \frac{adjacent side}{hypotenuse} [/tex]
and the adjacent side in the upper triangle is [tex] \frac{18}{ \sqrt{3} } [/tex] and the hypotenuse is x.
so cos45°=[tex] \frac{( \frac{18}{ \sqrt{3} } )}{x} [/tex] and then we can say 
x=[tex] \frac{ \frac{18}{ \sqrt{3} } }{cos45} [/tex] = [tex] \frac{ 18\sqrt{2} }{ \sqrt{3} } [/tex] .

Answer: B

Step-by-step explanation: EDGE 2022

Use a property of equality to solve this equation: 4.5x = 18 (never mind i figured out the answer.)

Answers

To solve this equality we are going to use the division property of equality, which says that you can divide both sides of the equality by the same number; notice that the number in question cannot be zero since you cannot divide by zero. In our case we are going to divide both sides by 4.5 to get rid of the 4.5 that is multiplying [tex]x[/tex]:
[tex]4.5x=18[/tex]
[tex] \frac{4.5x}{4.5} = \frac{18}{4.5} [/tex]
[tex]x= \frac{18}{4.5} [/tex]
[tex]x=4[/tex]

The solution to the equation 4.5x = 18 is x = 4.

We have,

To solve the equation 4.5x = 18, we can use the property of equality which states that if two quantities are equal, then multiplying or dividing both sides by the same non-zero number will still yield an equal equation.

In this case,

We want to isolate x, so we need to get rid of the coefficient 4.5.

To do this, we can divide both sides of the equation by 4.5:

(4.5x) / 4.5 = 18 / 4.5

Simplifying, we have:

x = 4

Therefore,

The solution to the equation 4.5x = 18 is x = 4.

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Suppose a sheet of 100 stamps is 0.77 millimeters thick. If a stack of sheets contains 100,000 stamps, how many millimeters thick is the stack? Write the answer in scientific notation.
7.7 × 104 mm
0.77 × 103 mm
7.7 × 102 mm
77.0 × 101 mm

Answers

Final answer:

To find the thickness of the stack, multiply the thickness of a single sheet by the number of sheets. So, 0.77 mm times 1,000 equals 770 mm. In scientific notation, this is 7.7 × 10² mm.

Explanation:

To find out how many millimeters thick the stack is, you need to multiply the thickness of a single sheet of stamps by the number of sheets in the stack. In this case, the thickness of a single sheet is 0.77 millimeters, and there are 1,000 sheets in the stack (since 100,000 stamps divided by 100 stamps per sheet is 1,000).

To represent the thickness of the stack in scientific notation, you would multiply the thickness of a single sheet (0.77) by the number of sheets in the stack (1,000). Multiplying 0.77 by 1,000 gives you 770. To represent this in scientific notation, you would break it down into a number between 1 and 10 multiplied by a power of 10. So, the thickness of the stack is 7.7 × 10² mm.

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How do you write an absolute value equation!? Pls help! 20 points.

Answers

The answer is always positive, unless there’s a negative outside |x|
It can be anything like: I3+4I > 5 or I-3I.



1. What is the vertex of the parabola?
A. (-1,0) B. (0, -3) C. (1, -4) D. (3, 0)

2. Which of the following has a graph that is wider than the graph of y=3x^2+2?
A. Y=3X^2+3
B. Y=0.5X^2+1
C. Y=-4X^2-1
D.Y=4X^2+1

3. Which graph represents the unction y=-2x^2-5?

4. What is the order, form narrowest to widest graph, of the quadratic functions f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2

A. f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2
B. f(x)-2x^2, f(x)=-10x^2, f(x)=0.5x^2
C. f(x)=0.5x^2, f(x)=2x^2, f(x)=-10x^2
D. f(x)=0.5X62, f(x)=-10x^2, f(x)=2x^2

Answers

Answer: Without the pictures, the only questions we can answer are #2 and #4.

#2
Choice B is wider than the graph of y = 3x^2 + 2. In a quadratic function like this, the value in front of the x^2 controls the width. Any positive number smaller than 3 would be wider.

#4
Choice A has the correct order. Again, the value in front of the x^2 controls how wide or narrow the graph is. First, take the absolute value of each value. Then, place them in order from greatest to least. The greater the number the narrower the graph.

Answer:

1. what is the vertex of the parabola?

C : ( 1, -4 )

2. Which of the following has a graph that is wider than the graph of y=3x^2+2?

B : Y=0.5X^2+1

3. Which graph represents the unction y=-2x^2-5?

D : choose the graph that has the smaller curve and arrows facing down

4. What is the order, form narrowest to widest graph, of the quadratic functions f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2

A : f(x)=-10x^2, f(x)=2x^2, f(x)=0.5x^2

Step-by-step explanation:

these are the correct answers for 2022

i finished the quick check   UwU

A right angle has an acute angle that measures 42°. what are th measures of the other angles.´?

Answers

Right angle = 90°

Unknown angle = 180 - 90 - 42 = 48°

---------------------------------------------------------------------------------
Answer: The other angle measures 48°
---------------------------------------------------------------------------------

The limit as h approaches 0 of (e^(2+h)-e^2)/h = ?
The answer is e^2; please explain how to get that?

Answers

First, separate the exponents of the first exponential:

[tex] \lim_{h \to 0} \frac{e^{2} e^{h} - e^{2} }{h} [/tex]

Regroup e² on the numerator:
[tex] \lim_{h \to 0} \frac{ e^{2} (e^{h} - 1) }{h} [/tex]

e² is now a constant that can be brought outside the limit:

[tex] e^{2} \lim_{h \to 0} \frac{ e^{h} - 1}{h} [/tex]

This limit is a notable one, and we know it is equal to 1,

therefore:

e² · 1 = e²



What do you consider to be the advantages of the numerical values? What do you consider to be the advantages of the visual representations? Which do you prefer working with, and why?

Answers

For these models there are methods such as the perturbation method which can be used to find an approximate analytical solution within a certain range. The advantage here over a numerical solution is that you end up with an equation (instead of just a long list of numbers) which you can gain some insight from.

x y
2, 65
4, 74
6, 81
8, 96
10, 109
@directrix
Identify the equation of the least squares regression line that most
closely matches the data set.

yˆ = 0.17x − 13.2
yˆ = 5.5x + 52
yˆ = 3.5x − 6921.2
yˆ = −2.2x + 13.8

Answers

The answer is yˆ = 5.5x + 52 
The closest to this is that equation, you can check it to prove that it is closer than the other options.

Let, yˆ = 5.5x + 52  be the equation

X=2,4,6,8,10
y=?

x1=2
y1=5.5(2) + 52
=63

x2=4
y2=5.5(4) + 52
=74

x3=6
y3=5.5(6) + 52
=85

x4=8
y4=5.5(8) + 52
=96

x5=10
y5=5.5(10) + 52
=107

Find the equation of line passing through (-7,-9) and parallel to the 8x-9y+2=0

Answers

Lets get started :)

8x - 9y + 2 = 0
9y = 8x + 2
y = [tex] \frac{8}{9}x + \frac{2}{9} [/tex]

Since the equation of this line is parallel to the one to be found, both have the same slopes: [tex] \frac{8}{9} [/tex]

Coordinates : ( - 7 , - 9 )

y - ( -9 ) = [tex] \frac{8}{9} [/tex] ( x - ( -7 ) )
y + 9 = [tex] \frac{8}{9}x + \frac{56}{9} [/tex]
y = [tex] \frac{8}{9}x + \frac{56}{9} - 9 [/tex]

y = [tex] \frac{8}{9}x - \frac{25}{9} [/tex]

Determine the measures of the angles of triangle DEF if the measures are in the ratio 1:1:16

Answers

the sum of all interior angles in a triangle is 180°, now, if we split that in (1+1+16) even pieces, that'd be 180 ÷ 18.

and then we give the ratio of 1, one of those pieces, the other ratio of 1, the same, and the ratio of 16, sixteen of those pieces.

[tex]\bf 1:1:16\qquad \cfrac{180}{1+1+16}\implies \cfrac{180}{18}\implies 10\quad \qquad \stackrel{1}{10}~:~\stackrel{1}{10}~:~\stackrel{16}{160}[/tex]

Final answer:

The angles of triangle DEF with the ratio 1:1:16 are 10 degrees, 10 degrees, and 160 degrees, using the property that the sum of interior angles in a triangle is 180 degrees.

Explanation:

To determine the measures of the angles of triangle DEF with the ratio 1:1:16, we utilize the property that the sum of the interior angles of any triangle is always 180 degrees. We can represent the measures of the angles as follows: let the first angle be x, the second angle be x, and the third angle be 16x. Since the sum of angles in a triangle is 180 degrees, we can write the equation:

x + x + 16x = 180

Simplifying the left side of the equation, we get:

18x = 180

Dividing both sides by 18 gives us:

x = 10

Therefore, the measures of the angles are 10 degrees, 10 degrees, and 160 degrees.

Corollary: At least two angles of a triangle are acute. In this case, the two angles with the ratio 1:1 are both acute since they measure 10 degrees each, which is less than 90 degrees.

The office of student services at a large western state university maintains information on the study habits of its full-time students. their studies indicate that the mean amount of time undergraduate students study per week is 20 hours. the hours studied follows the normal distribution with a standard deviation of six hours. suppose we select a random sample of 144 current students. what is the probability that the mean of this sample is less than 19.25 hours?

Answers

Answer: 45.03%

To find the answer for this problem, you first need to find the z-score for a value of 19.25.

The z-score is the number of standard deviations from the mean.

Here is the work for our z-score:

19.25 - 20 = -0.75 / 6 = -0.125

Now, you just have to use a standard normal distribution table and look up the probability for a z-score of -0.125. I used the average of the probability for z-scores of -0.12 and -0.13 to get 45.03%.
Final answer:

There is a 22.66% probability that the mean study time of a random sample of 144 students at the large western state university will be less than 19.25 hours.

Explanation:

To solve this problem, we need to use the formula for the z-score, which is (X - μ) / (σ / √n), where X is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

Here, n=144, μ=20, σ=6 and X=19.25. Substituting these values into the formula, we get z = (19.25 - 20) / (6/√144) = -0.75.

The z-score tells us how many standard deviations the value is away from the mean. A negative z-score indicates that the data point is less than the mean.

To find the probability, we need to look up this z-score in the z-table, which gives the area to the left of the z-score on a standard normal distribution. The value associated with z=-0.75 on the table is approximately 0.2266, or 22.66%.

So, there is a 22.66% probability that the mean study time of a random sample of 144 students will be less than 19.25 hours.

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The bar graph shows the z-score results of four employees for two different work weeks.

Which employee had the least earnings for Week 1?



Usan

Percy

Oberto

Michael

Answers

We observe that week 1 is represented by the color blue.
 Therefore, you should check the bars in blue for the four employees.
We observe that the smallest z-cores is -0.5.
 Therefore, Oberto has the lowest earnings for week 1.
 Answer: 
 Oberto had the least earnings for Week 1

BRAINLIESTTT ASAP!! :)

How do you know if a parabola has a maximum or a minimum?

Answers

The the parabola opens upward it has a minimum and if it opens downward then it has a maximum :)
look at the officiant of the terms, is a >0 then the parabola opens up upward and the graph has has a minimum at its vertex.

NEED HELP ASAP!!!

What is the value of x?

/Users/mikaylee/Desktop/8104613-NG_IMC_SemB_09_UT_01.png

Answers

◆ Lines n Angles ◆

Hey !!

Check the attachment.
Hope it helps you :)

The following polynomials can be factored using the techniques of this lesson. x^2-36

Answers

the correct answer to that question would be true

Answer:

true

Step-by-step explanation:

A P E X

PLEASE HELP ME QUICK PLEASE!!!!!!

10 PTS ILL GIVE BRAINLIEST IF U ANSWER CORRECTLY

THX

Answers

Only constraint 2 would be met if 9 vanilla cups and 18 chocolate cups were purchased

Only constraint 1 would be met if 6 vanilla cups and 18 chocolate cups were purchased

The cost of removing x percent of pollutants is expressed by the function , where C is in thousands of dollars. Which conclusion can be derived from this statement?
a)The cost of removing 40 percent of the pollutants is $120,000.
b)The cost of removing 80 percent of the pollutants is $960,000.
c)The vertical asymptote lies at x = 0.
d)The vertical asymptote lies at x = 240.

Answers

the vertical asymptote lies at x=240

Chen has an MP3 player called the Jumble. The Jumble randomly selects a song for the user to listen to. Chen's Jumble has 4 classical songs,3 rock songs,and 2 rap songs on it.Chen is going to listen to 360 songs.What is the best prediction for the number of classical songs that Chen will listen to?

Answers

about 10 songs because if you add up all ten numbers of all the songs then you divide, then you divide again you will get 10 songs

simplest form of the expression
3sqrt750+3sqrt2058-3sqrt48
can someone explain

Answers

First, you have to decompose the numbers under the square root:
750 = 2·3·5²
2058 = 2·3·7³
48 = 2⁴·3

Then, enlight all the exponents multiple of 2 (which is the index of the root):
3·√(2·3·5²) + 3·√(2·3·7²·7) + 3·√(2⁴·3)

At this point, you can take outside the square root everything that has an even number, and doing so you have to halve the exponent; you'll get:
3·5·√(2·3) + 3·7·√(2·3·7) + 3·2²·√3

You can now multiply:
15√6 + 21√42 + 12√3
which is the simplest form of your expression.

I need some help
A student answers all 48 questions on a multiple-choice test by guessing. Each question has four possible answers, only one of which is correct. Find the probability that the student gets exactly 15 correct answers. Use the normal distribution to aproximate the binomial distribution.

I used BinomCdf(48,.25,15) and get 0.0767 but that isn't one of the choices. The choices are
0.7967
0.0606
0.0823
0.8577,

Answers

The probability that the student gets exactly 15 correct answers is  0.0823

How to determine the probability?

The given parameters are:

Sample size, n = 48Correct answers, x = 15Probability of right an answer, p = 0.25 i.e. 1 of 4 options is correct

Start by calculating the mean

[tex]\bar x = np[/tex]

[tex]\bar x = 48 * 0.25[/tex]

[tex]\bar x = 12[/tex]

Calculate the standard deviation

[tex]\sigma = \sqrt{np(1 -p)}[/tex]

[tex]\sigma = \sqrt{12 * (1 -0.25)}[/tex]

[tex]\sigma = 3[/tex]

To get exactly 15,we make use of the range 14.5 to 15.5.

So, we calculate the z scores at these values using:

[tex]z = \frac{x - \bar x}{\sigma}[/tex]

This gives

[tex]z = \frac{14.5 - 12}{3} = 0.83[/tex]

[tex]z = \frac{15.5 - 12}{3} = 1.17[/tex]

The probability is then calculated using

P(14.5 < x < 15.5) = p(0.83 < z < 1.17)

This gives

P(14.5 < x < 15.5) = 0.082269

Approximate

P(14.5 < x < 15.5) = 0.0823

Hence, the probability that the student gets exactly 15 correct answers is  0.0823

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Shawn is typing a paper for class. He can type 1 5/12 pages in 1/3 of an hour. How many pages can Shawn type in one hour?

Answers

the amount of pages typed after 1/3 of an hour is given. Multiply this number by 3 to get the full hour of pages types.

1 5/12 * 3 = 3(1) + 3(5/12)
= 3 5/4
= 4 1/4 pages

Answer:

i think he is right

50 POINTS PLZZZZZ HELP NOW I NEED FULL EXPLANATION AND RIGHT ANSWERS

IF the area of the frame was 64inches², what would be 2 possible sets of dimensions that could be used to make a frame with that area?

Answers

The side lengths could be 4 in. x 16 in. because that equals 64 inches^2. It could also be 8 in. x 8 in. because that also equals 64 inches^2.
Hello!

We know that the area of the frame is 64 inches^2. Let's list the factors of 64. They are:

1, 2, 4, 8, 16, 32, and 64.

There are many possible sets of dimensions.

The dimensions could be 1 in × 64 in, 2 in × 32 in, 4 in × 16 in, or 8 in × 8 in.

If the frame is shaped like a rectangle, then the first three sets of dimensions would be possible.
If it is a square, then the last (8 × 8) are possible.

Last month, the seventh grade and eighth grade math classes at Moore Middle School collected canned goods for the local food shelter. The dot plots below show the number of canned goods collected by the classes.


The mean absolute deviation for each grade level is 1.6. The difference between the mean number of canned goods collected by each grade level is how many times the mean absolute deviation?
A. 5
B. 4
C. 3
D. 6

Answers

To answer this question you will need to find the mean of each class and then subtract them. You will then compare this difference to the MAD of 1.6.

Mean of 7th grade class is:
420/20=21

Mean of 8th grade class:
325/25=13

21-13=8

To find how many times , divide 8 by 1.6.

8/1.6= 5 times

The difference of the means is 5 times the MAD (mean absolute deviation).

The ancient Babylonians developed a method for calculating nonperfect squares by 1700 BCE. Complete the statements to demonstrate how to use this method to find the approximate value of . In order to determine , let G1 = 2, a number whose square is close to 5. 5 ÷ G1 = , which is not equal to G1, so further action is necessary. Average 2 and G1 to find G2 = 2.25. 5 ÷ G2 ≈ (rounded to the nearest thousandth), which is not equal to G2, so further action is necessary. Average 2.25 and G2 to find G3 = 2.236. 5 ÷ G3 ≈ (rounded to the nearest thousandth), which is equal to G3. That means is approximately 2.236.

Answers

... find the approximate value of √5. In order to determine √5, let ...

5 ÷ G1 = 2.5
5 ÷ G2 = 2.222
5 ÷ G3 = 2.236

That means √5 is approximately 2.236.

Using the Babylonian method, [tex]\( \sqrt{5} = 2.236}[/tex]. This method involves iteratively averaging and recalculating until the calculated value stabilizes to the desired accuracy.

To demonstrate the Babylonian method for finding the approximate value of [tex]\( \sqrt{5} \)[/tex]

A. In order to determine [tex]\( \sqrt{5} \)[/tex], let [tex]\( G_1 = 2 \)[/tex], a number whose square is close to [tex]5.[/tex]

B. Calculate [tex]\( \frac{5}{G_1} = \frac{5}{2} = 2.5 \)[/tex], which is not equal to [tex]\( G_1 \)[/tex], so further action is necessary. Average [tex]\( 2 \)[/tex] and [tex]\( G_1 \)[/tex] to find [tex]\( G_2 = \frac{2 + 2}{2} = 2.25 \). \( \frac{5}{G_2} = \frac{5}{2.25} = 2.222 \)[/tex], which is not equal to [tex]\( G_2 \)[/tex], so further action is necessary.

C. Average [tex]\( 2.25 \)[/tex] and [tex]\( G_2 \)[/tex] to find [tex]\( G_3 = \frac{2.25 + 2.222}{2} = 2.236 \). \( \frac{5}{G_3} = \frac{5}{2.236} = 2.237 \)[/tex], which is equal to [tex]\( G_3 \)[/tex]. That means [tex]\( \sqrt{5} \)[/tex] is approximately [tex]\( 2.236 \).[/tex]

The complete Question is

The ancient Babylonians developed a method for calculating nonperfect squares by 1700 BCE. Complete the statements to demonstrate how to use this method to find the approximate value of .

A. In order to determine , let G1 = 2, a number whose square is close to 5.

B. 5 ÷ G1 = , which is not equal to G1, so further action is necessary. Average 2 and G1 to find G2 = 2.25. 5 ÷ G2 ≈ (rounded to the nearest thousandth), which is not equal to G2, so further action is necessary.

C. Average 2.25 and G2 to find G3 = 2.236. 5 ÷ G3 ≈ (rounded to the nearest thousandth), which is equal to G3. That means is approximately 2.236.

Other Questions
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