Find the length of side xx in simplest radical form with a rational denominator. 3

Find The Length Of Side Xx In Simplest Radical Form With A Rational Denominator. 3

Answers

Answer 1

The length of x is 6 in simplest radical form.

What is a right-angled triangle?

'A triangle in which one of the interior angles is 90° is called a right-angled triangle. The longest side of the right triangle, which is also the side opposite the right angle, is the hypotenuse and the two arms of the right angle are the perpendicular and the base.'

According to the given ,

Perpendicular = 3

Hypotenuse = x

We know,

sin∅ = 3/x

∅ = 30°

⇒ sin30 = 3/x

⇒ 1/2 = 3/x  [ sin30 = /2  ]

⇒ x = 3 * 2

⇒ x= 6

Hypotenuse = 6

Applying Pythagoras theorem:

Hypotenuse² = Perpendicular² + Base²

6² = 3² + Base²

6² - 3² = Base²

Base² = 25

Base = √25

Base = 5

We can conclude the value of x to be 6.

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Related Questions

5x35 65x76 what the the total

Answers

The solution to the above math arithmetic is 5115.

Addition and subtraction are what?

Finding the sum and difference of two integers are the two main addition and subtraction arithmetic procedures. They are both the other's polar opposite. An ordered group of integers with a shared difference between each word is known as an arithmetic sequence. The common difference, for instance, between the mathematical series 3, 9, 15, 21, and 27 is 6.

What exactly is an algebraic question?

This grouping contains percent difficulties, decimal recognition, addition, subtraction, multiplication, and division as well as fraction and percent equivalences and estimate issues.

For instance, 5 + 6 = 11 and 11 - 6 = 5.

5x35 + 65x76=5115

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What is the image of the point (-7,-8) after a rotation of 180∘ counterclockwise about the origin?

Answers

It should be (7,8). The formula for 180 degree rotations is (x,y)->(-x,-y)

Twelve out of Sixty students are trying out for the spring musical. What is the percentage of students trying out for the musical?​

Answers

If Twelve out of Sixty students are trying out for the spring musical, the percentage of students trying out for the musical is , 20%.

What are percentages?

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Why are percentage representations important?

The usage of percentages is widespread and diverse. For instance, numerous data in the media, bank interest rates, retail discounts, and inflation rates are all reported as percentages. For comprehending the financial elements of daily life, percentages are crucial.

In above question, if Twelve out of Sixty students are trying out for the spring musical, we have,

Number of students trying out for the musical = 12

Total number of students = 60

Percentage of students trying out for the musical is , [tex]\frac{12}{60} *100[/tex] = 20%

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let f(x)= 2x-9. Find the inverse and evaluate f^1 (-2).

Answers

Answer:

f(x)= 2x-9

f(-2)= 2(-2)-9

f(-2)= -4-9

=-13

witch equation is made true by the opposite angles theorem ​

Answers

The option D is correct.Because this equation holds the vertically opposite angle theorem.

What is vertically opposite angle theorem?

Vertically Opposite Angles are holds when two lines intersect each other then the opposite angles formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.

How do you find opposite angles?

Vertical opposite angles that are opposite each other when two lines cross are also known as vertical angles because the two angles share the same corner. Opposite angles are also congruent angles.The equation of a vertical line is given by x = a or x = -a

Now we find

According to vertical opposite angle

x-8=40-2x

x+2x=40+8

3x=48

x=16

We can find value of x by usng vertical opposite angle.

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Solve for x.
A: 14
B: 8
C: 11
D: 9

Answers

An acute triangle is made up of three acute angles. An obtuse triangle is formed by one acute angle and two obtuse angles and x = 9.7692307692

what is triangle?

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. In Euclidean geometry, any three points identify a distinct triangle and, concurrently, a distinct plane if they are not collinear.

13x + 3 + 40 + 10 = 180

13x = 127

x = 9.7692307692

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I’m trying to solve this problem I need to convert it to base 5

Answers

Answer: The answer is 29,446,941,856

Step-by-step explanation:

Find the equation of the exponential function represented by the table below

Answers

The equation of the exponential function represented by the table will be y = 4(3)ˣ.

What is an exponent?

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

Take two points from the table, then the points are (0, 4) and (1, 12).

The equation passes through (0, 4), then we have

4 = a(b)⁰

a = 4

The equation passes through (1, 12), then we have

12 = 4(b)¹

b = 3

Then the equation of the exponential function represented by the table will be y = 4(3)ˣ.

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In triangle ABC, angle A is 37° and angle B is 24*. Select all triangles which are similar to triangle ABC.

D triangle DEF where angle Dis 37° and angle E is 24
• triangle GHI where angle G is 37" and angle I is 34°
O triangle JKL where angle J is 35" and angle L is 125*
• triangle MNO where angle Nis 24* and angle E is 119
O triangle POR where angle O is 24° and angle R is 30

Answers

Answer:

Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.

Step-by-step explanation:

Triangles DEF and JKL are similar to triangle ABC because they have corresponding angles with the same measure.

•The Triangle GHI is not similar to triangle ABC because the measure of angle G does not match the measure of angle A.

•The Triangle MNO is not similar to triangle ABC because the measure of angle N does not match the measure of angle B.

• The Triangle POR is not similar to triangle ABC because the measure of angle R does not match the measure of angle A or B.

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An international company has 22400 employees in one country. If this represents 18.3 of the company's employees, how many employees does it have in total? Round your answer to the nearest whole number.

Answers

The total number of employees that this company would be said to have is given as 122424

How to solve for the number of employees

How to solve for the number of employees in the company

We know that the number of employees in one country is 22400, and that this represents 18.3% of the company's employees in total.

We can use this information to set up a proportion to find the total number of employees in the company.

Employees in one country / Total employees = 18.3 / 100

22400 / X = 18.3/100

To find the total number of employees, we can cross-multiply and divide:

X = (22400 * 100) / 18.3

X = 122424

So the company has a total of 122424 employees.

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DUE SOON! PLEASE HELP!
SHOW ME HOW TO GET IT FOR NEXT TIME! SO CONFUSED AND BEEN STUCK FOREVER PLEASE HELP!
QUESTION DOWN BELOW!

Answers

The value of m in the given equation 4x² -mx +9 will be 13.

What is polynomia?

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics. Polynomials come in various varieties. Monomial, binomial, and trinomial, respectively.

given an equation 4x² -mx + 9 = 0 and the question states that it has a root that is equal to 1

Since 1 is the root of this quadratic equation it will satisfy the equation

Substituting the values in the equation

4 - m + 9 = 0

m = 13

Therefore, In the given equation 4x² -mx +9 the value of m will be 13.

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Dana's survey showed that 3 out of 8 students preferred pepperoni pizza and
1 out of 8 preferred cheese pizza. How many more of the 72 students surveyed by
Dana preferred pepperoni pizza than preferred cheese pizza?

Answers

Answer:

18 more students preferred pepperoni pizza over cheese pizza in the survey.

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] x [tex]\frac{72}{1}[/tex] Can be rewritten

[tex]\frac{3}{1}[/tex] x [tex]\frac{9}{1}[/tex] = [tex]\frac{27}{1}[/tex] = 27   I cross canceled the 8 and 72.  They have a common factor of 8.  8 goes into 8 once and 8 goes into 72 9 times.

27 students preferred pepperoni pizza.

[tex]\frac{1}{8}[/tex] x [tex]\frac{72}{1}[/tex] = [tex]\frac{1}{1}[/tex] x [tex]\frac{9}{1}[/tex] = 9

9 students preferred cheese pizza.

27 - 9 = 18

A boat is purchased for $51,000 and has a resale value of $42,000 after a useful life of 6 years. Using a book value depreciation chart, calculate the number of years until the book value of the boat is $48,000.

Answers

The number of years until the book value of the boat is $ 48, 000, can be found to be 2 years

How to find the number of years ?

To find the number of years till the book value of the boat is $ 48, 000, you first need to find the depreciation rate per year by the formula :

= ( Purchase price of boat - Resale value ) / Useful life

= ( 51, 000 - 42, 000 ) / 6

= 9, 000 / 6 years

= $ 1, 500 per year

In the first year, the value of the boat would depreciate to:

= 51, 000 - 1, 500

= $ 49, 500

In the second year, the value would depreciate to:

= 49, 500 - 1, 500

= $ 48, 000

It therefore takes 2 years for the book value to be $ 48, 000.

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A system of equations is graphed on the coordinate plane.

y=−x+5
y=2x−1

What is the solution to the system of equations? Enter the coordinates of the solution

Answers

The solution to the system of equation shown in the graph is (2, 3)

What is an equation?

An equation shows how two or more numbers and variables are related to each other.

The standard linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Given the equation:

y=−x+5   (1)

y=2x−1   (2)

Solving by elimination method. Subtract equation 2 from 1:

0 = -3x + 6

x = 2

Put x = 2 in eqn 1:

y = -(2) + 5 = 3

The solution is (2, 3)

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BC is the diameter of the semicircle. The area of rectangle ABCD is 20 and the length of line AB is 5.What is the area of the semicircle?

Answers

Answer:

2[tex]\pi[/tex] [tex]units^{2}[/tex]

Step-by-step explanation:

BC is equal to 4 because 5*4=20.

The radius is 2. The equation for the area of a circle is [tex]\pi r^2[/tex].

Therefore, if we plug in 2 we will get [tex]4\pi[/tex].

But then we divide by 2 to get 2[tex]\pi[/tex] [tex]units^{2}[/tex] as our answer.

Hope this helped! :)

What are terms and common rations ? Can someone explain to me how to solve

Answers

For the arithmetic sequence 4 - 2(n - 1), we have that:

The first term is 4.The second term is 2.The third term is zero.The fourth term is -2.The fifth term is -4.The common difference is -2.

For the geometric sequence 6 x 3^(n - 1), we have that:

The first term is 6.The second term is 18.The third term is 54.The fourth term is 162.The fifth term is 486.The common ratio is 3.

How to model the arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which there is a common difference of the numbers, that is, the subtraction between consecutive terms of the sequence is always constant.

The nth term of an arithmetic sequence is given by the equation presented as follows:

[tex]a_n = a_1 + d(n - 1)[/tex]

In which:

[tex]a_1[/tex] is the first term.d is the common difference.

The sequence in this problem is defined as follows:

4 - 2(n - 1)

Which has first term 4 and common difference -2, hence the terms are:

4, 2, 0, -2, -4, -6 and so on...

What is a geometric sequence?

A geometric sequence is a sequence of numbers in which there is a common ratio of the numbers, that is, the quotient between consecutive terms of the sequence is always constant.

The nth term of a geometric sequence is given by the equation presented as follows:

[tex]a_n = a_1 \times q^{n - 1}[/tex]

In which:

[tex]a_1[/tex] is the first term.q is the common ratio.

The sequence for this problem is given as follows:

6 x 3^(n - 1)

Which has first term of 6 and common ratio of 3, hence the terms are given as follows:

6, 18, 54, and so on...

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You buy 8.25 ounces of almonds and 7.5 ounces of cashews. You combine the nuts and divide them equally into 9 bags. How many ounces are in
each bag?

Options:
1.75 ounces
9.5 ounces
15.5 ounces
17.5 ounces

Answers

No. of many ounces are in each bag will be 1.75 ounces

What is the division of decimals?

Unlike the division of natural numbers, the division of decimals is fairly straightforward. To divide decimal numbers by various sorts of numbers, such as whole numbers, decimal numbers, fractions, the powers of ten, etc., we can employ a variety of techniques. You may find answers to division of decimals quizzes and more practise problems in this article.

Dividing decimals is equivalent to dividing whole numbers, except when doing so, we take into account the decimal point as the final answer. The following are many options for splitting decimals:

Dividing by whole numbers with decimalsA decimal number divided by another decimal numberDecimal division using the powers of 10, specifically 10, 100, and 1000

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Check
Annie is comparing the cost to ship a package. One shipping
pound a package weighs. Another shipping company charges $5 for
company charges $7 for the first pound and $0.20 for each additional
the first pound and $0.30 for each additional pound.
Part A
Which equation could be used to determine p, the number of
when the costs for the two shipping companies are the same?
7+0.20p = 5 +0.30p
7+20p = 5 + 30p
A7+0.30p=5+0.20p
B0.20+7p = 0.30 + 5p
Part B
Show
pounds,
For how many pounds is the cost of the two shipping companies the
same?

Answers

Part A: The equation could be used to determine p is B0.20+7p = 0.30 + 5p Part B: Two shipping companies is the same for 25 pounds. Company 1 = $7 + (25 - 1) x $0.20 = $11.80 Company 2 = $5 + (25 - 1) x $0.30 = $11.80.

How to find pounds is the cost of the two shipping companies?

The cost of shipping through two different companies will depend on a variety of factors.

These factors may include the weight and size of the package, the distance it needs to travel, the speed of delivery, and any additional services requested.

Additionally, the cost of shipping may also depend on the type of shipping service used (e.g. ground, air, or express).

To find out the cost of shipping through two different companies, it is best to contact each company directly. This can usually be done by phone, email, or through their website.

Each company will be able to provide a quote based on the package’s specifications. It is then possible to compare the cost of the two shipping companies and determine whether or not the cost is the same.

It is important to note that companies may offer discounts or other incentives for shipping with them.

Therefore, it is important to pay attention to any additional fees or discounts that may apply in order to get the best deal.  

Comparing the cost of two different shipping companies can help to ensure that the most cost-effective option is chosen.

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If these two shapes are similar, what is the measure of the missing length j?

Answers

Step-by-step explanation:

since the 2 shapes are similar then their sides are proportional

9/18= j/90

then j equals 45

which is a solution to (x-2)(x+10)=13

Answers

Answer:

answers 3

Step-by-step explanation:

took more thinking than it should've tbh (3-2=1) (3+10=13) 1x13=13

Trace is buying notebooks. Each notebook is $2 off the original price. He buys 8 notebooks for $28. What is the original price of a notebook?

Answers

The original price of each notebook is $5.5

How to calculate the original price of each notebook ?

Trace is purchasing some notebooks

Each notebook is $2 off the original price

He buys 8 notebooks for $28

The first step is to calculate the price of one notebook

8= 28

1= x

Cross multiply both sides

8x= 28

x= 28/8

x= 3.5

1 notebook is $3.5

$2 was removed from the initial price. Therefore the original price is

2 + 3.5

= 5.5

Hence the original price of the notebook is $5.5

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If a house has decreased 35% since it was purchased and it currently values 117,000 what was purchase value

Answers

Step-by-step explanation:

that means the current value of $117,000 is 100 - 35 = 65% of the original price.

65% = $117,000

1% = 65%/65 = 117000/65 = $1,800

100% = 1%×100 = 1800×100 = $180,000

the original (100%) purchase value was $180,000.

Bismah is building 5 raised garden beds in a community garden. Each raised
garden bed will need 1 7/8 bags of soil. How many bags of soil will Bismah need for
8
all 5 raised garden beds?

5 5/8bags of soil

9 3/8 bags of soil

9 5/8 bags of soil

8 7/8 bags of soil

5 3/8 bags of soil

Answers

The fraction of soil bags Will needs in total for all 5 raised garden beds is   9 3/8.

What is community?

In mathematics, community is the study of how objects interact and relate to each other. It focuses on analyzing the relationships between elements and understanding how they interact to form each other. Also explore how changes in one element affect other elements. Community in mathematics is also about recognizing patterns, finding solutions, and exploring the impact of change. It is an integral part of mathematics and is used in many areas of study such as algebra, geometry, and calculus. This can be calculated by multiplying the number of raised beds (5) by the amount of soil required per raised bed.

(1 7/8 bag).

5 x 1 7/8

= 9 3/8 bags

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Y=(x-3)^2+3
vertex form to standard form

Answers

Answer:

  y = x² -6x +12

Step-by-step explanation:

You want the quadratic equation Y=(x-3)^2+3 written in standard form.

Standard form

Depending on where you go to school, the given equation may already be in standard form.

Other places, standard form means the equation is simplified and terms are written in order of decreasing degree.

  y = (x -3)² +3 = (x² -6x +9) +3

  y = x² -6x +12

M/5 + 9=11
Solve two step equations

Answers

Answer:

m=10

Step-by-step explanation:

m/5+9=11 subtract 9

m/5 = 2 multiply 5 by both sides

m = 10

If given the following scenario: The half-life of Sodium-24 is 15
hours. If you start with 352 grams of Sodium-24 how much would
be left after 8 days?

0.049 grams

Approximately 0 grams

1.375 grams

95.965 grams

Answers

Sodium has two radioactive cosmogenic isotopes (22Na, half-life = 2.605 years; 24Na, half-life = ~ 15 hours) that have been used as tracers in hydrologic studies.

Sodium-24 how much would be left after 8 days?

Sodium-24, a radioactive isotope having a half life of 15 hours is used medically in blood studies and it decays by beta decay.

Na has received considerable attention in hydrologic research because it is a mobile element that participates in precipitation and dissolution reactions in ground water (clay formation, albitization of plagioclase). Their short half-lives (i.e. high decay rate) make their measurement relatively easy by common radioanalytical techniques.

Substantial concentrations of 22Na and 24Na have been measured in precipitation (Roedel, 1970; Perkins et al., 1970). However, no studies have as yet been published documenting the cosmogenic sodium systematics in ground or surface waters.

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6. Larry earns $840 per pay period, plus a commission of 8% on his sales. During the last pay period, Larry earned
a total of $2,440.00. What were Larry's total sales during the pay period?
A. $784
B. $22,500
C. $30,500
D. $38,500

7. Tom's bill at a local restaurant was $19.47. If he wants to leave a 15% tip, approximately how much should he
leave?
A. $0.15
B. $3
C. $4
D. $15

Answers

6. Larry's total sales during the pay period is $20,000.

7. Tom should leave $3 (approximate)

What is the meaning of total sales?

Total sales revenue usually referred to as gross sales is the sum of the value of the products and services a company provides to its clients over the course of a given reporting period.

Given that Larry earns $840 per pay period, plus a commission of 8% on his sales.

Assume that Larry sale $x during the last pay period.

The total earn is 840 + 8% of x

= 840 + 0.08x

According to the question:

840 + 0.08x = 2,440.00

Subtract 840 from both sides:

0.08x = 2,440 - 840

0.08x = 1600

Divide both sides by 0.08

x = 1600/0.08

x = 20,000

The sales is $20,000.

7. Given that,  Tom's bill at a local restaurant was $19.47. He leaves 15% of the total bill as a tip.

15% of $19.47

= 15/100 × $19.47

= 2.920

≈ 3 (approximate)

Tom should leave $3.

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A triangle has dimensions 9ft by 12ft if you wanted to increase the size of the triangle by a scale factor of 10 over three what would the area of the new triangle be

Answers

The area of the new triangle is  600ft²

How determine the area of the new triangle?

To increase the size of a triangle by a scale factor of 10/3, multiply each dimension of the triangle by 10/3.

The new dimensions of the triangle will be:

10/3 × 9ft = 30ft

10/3 × 12ft = 40ft

The area of a triangle is given by the formula A = 1/2  × b  ×h,

where b is the length of the base and h is the height of the triangle.

Thus, the area of the new triangle will be:

A = 1/2  × 30 × 40 = 600ft²

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Work out the circumference and area of the circular piee of glass needed for the top of a display cabinet which has a diameter of 1.8m. Use #=3.14? Circumference = in m and Area = in m2

Answers

Hello there!

Answer:

Circumference: [tex]l = 2\pi r = 2*3.14*0.9 = 5.652 (m)[/tex]

Area: [tex]S = \pi r^2 = 3.14 * 0.9^2 = 2.5434(m^2)[/tex]

Step-by-step explanation:

We should know 2 important formulas:

Circumference: [tex]l = 2\pi r[/tex]

Area: [tex]S = \pi r^{2}[/tex]

So we need to find the value of r (radius) which equal to a half of diameter:

[tex]r = d/2[/tex]

[tex]r = 1.8/2 = 0.9(m)[/tex]

Circumference: [tex]l = 2\pi r = 2*3.14*0.9 = 5.652 (m)[/tex]

Area: [tex]S = \pi r^2 = 3.14 * 0.9^2 = 2.5434(m^2)[/tex]

Which statement is true based on a graph of the line that passes through the given coordinates? (2, 1), (3,3), (5,7), (6,9) Please help

A. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.

B. The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin.

C. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.

D. The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.

Answers

The correct statement regarding the linear function passing through the coordinates (2, 1), (3,3), (5,7), (6,9) is given as follows:

A. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.

When does a linear function represents a proportional relationship?

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

m is the slope, representing the change in y divided by the change in x.b is the y-intercept, representing the value of y when x = 0.

A linear function represents a proportional relationship if it has an intercept of zero.

For the points in this problem, when x increases by one, y increases by two, hence the slope is given as follows:

m = 2/1 = 2.

Hence:

y = 2x + b.

When x = 2, y = 1, hence the intercept b is given as follows:

1 = 2 + b

b = -1.

As the intercept is different of zero, this is not a proportional relationship, and option A is correct.

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Compare and contrast the title Amanda Gormans poem "THE HILL WE CLIMB" and The title of Maya Angelous poem "On the Pulse of Morning. " proportional or not propotional? What does pointing to mean? When a judge delays a defendant's serving of a sentence after he or she has been convicted or found guilty in order to allow the defendant to perform a period of community supervision, it is referred to as a(n) ________. At 2:15 pm ET, a customer gives his registered representative a market order to buy 100 shares of ABC at the close. What should the registered representative do with the order Which line L has a slope of zero? What is 5x in share market? Please answer question 10 and 11 please If 70% of the members remembered the password but 21 members forgot, then how many members were there in all? Please show work if you canThxs Question 3: Use the graph to fill in the blank with the correct number. f(3) =10A505-5.-10%Your answer cause of supraventricular tachycardia? Those in mission control roles spend about 75 percent of their time actively communicating and controlling active space missions.TrueFalse 45 POINTS -Find the perpendicular line. Dont explain You can include ____ in calculations to indicate which calculation should be done first.a.brackets [ ]b.curly braces { }c.slashes //d.parentheses ( ) Which of the following statements accurately explains why subsequent boundaries are the most common type of boundary? (AP Human Geography Question)a. The process of establishing them happens before people settle in the areab. The process of establishing them does not take cultural differences into accountc. The process of establishing them is lengthy and related to territorialityd. The process of establishing them connects to previously set boundariese. The process of establishing them correlate to the devolution of territoriesPlease explain the answer, and I'll award brainliest =) PLEASE HELP I WILL MARK THE BRAINLIEST AND GIVE 20 POINTSwe should not judge people by their appearance is one of the themes in Frankenstein. how do the events in the story and the characters' behavior convey this? Cite text evidence from the text to support your claims. What led to the rise of fascism after ww1? What is the relationship between the enthalpy (AH) and entropy (AS) of areaction that is never spontaneous?OA. +AH,-ASOB. -AH, +ASOC. -AH-ASOD. +AH, +ASSUBMIT Which is a function of the testes?to initiate ejaculationto produce testosteroneto prevent fertilizationto release semen Which phrase is the best definition for the term collaborate?(1 point) to use technology to use technology to work on a project to work on a project t