what is the measure of angle x

What Is The Measure Of Angle X

Answers

Answer 1

Answer:

147

Step-by-step explanation:

Angles in a triangle add up to 180:

x + 23 + 10 = 180

x = 147


Related Questions

math!! please helpp!!!

What is the y intercept of the line below?

( i attached an image)

a) -3

b) 1/3

c) 4

d) (-1.5,0)

e) -1.5

f) (4,0)

g) 3

Answers

Answer:

f (4,0)

Step-by-step explanation:

Hope it helps!!!

y=4

x=0

_______________________________________________________

Answer:

4

Step-by-step explanation:

[tex]\large\displaystyle\begin{gathered} \sf{The \ y-intercept \ is \ the \ point \ where \ the \ graph \ intercepts \ the \ y \ axis. \\ \sf{Thus, \ assuming \ that \ each \ little \ square \ represents \ one \ unit, \ the \ y-intercept} \\ \sf{is \ 4} \end{gathered}[/tex]

done !!

⊱_______________________________________________________⊰

Cαlligɾαρhγ

PLEASE HELP!!!!!!!!!!!!!!

Answers

Answer:

The first answer is correct:

[tex]\{\frac{1}{3},-3.45,\sqrt{9}\}[/tex]

Step-by-step explanation:

Since [tex]\frac{1}{3}, -3.45, \sqrt{9}=3[/tex] are all rational numbers, the set that contains those numbers is the set of rational numbers.

In the second set, number [tex]\sqrt{37}[/tex] is irrational number since it can not be written as quotient.

Also in the third and fourth set, numbers [tex]\sqrt{44}[/tex] and [tex]\sqrt{2}[/tex] are irrational numbers.

Therefore, the first answer is correct.

Minerva starts a savings account with $50. The interest on the account balance is compounded annually. The graph below shows the account balance in terms of x ,the number of years since the account was opened.



After 12 years, Minerva's account balance should be about $100, assuming that she does not add or withdraw any money from the account.

Cannot be determined from the information given.
False
True

Answers

Minerva's account balance will be about $100 ,  it is True and Option A is the correct answer.

What is meaning of Compounded annually ?

Compounded Annually means when the interest is given even on the interest accrued from the principal amount . This is done once a year.

It is given that

Principal Amount = $50

From the graph attached in the answer which was missing in the question ,

It can be confirmed that after 12 years

Minerva's account balance should be about $100.

Therefore it is True and Option A is the correct answer.

The graph missing is attached

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Write an equation in slope intercept form for the line with slope -1/2 and y-intercept -5

Answers

Answer: -1/2x - 5 = Y

Step-by-step explanation:

- slope intercept form is mx + b = Y

- m is the slope

- b is the y intercept

- leave x and y as variables

- since your y intercept is negative the + will be a -

- so the equation becomes -1/2x - 5 = Y

hope this helps :)

Suppose that $x$ is a multiple of 6 (not necessarily positive). If the square of $x$ is less than 200, how many possible values of $x$ are there

Answers

All multiple of 6 under 14 are: -12, -6, 0, 6, 12

How do we get 14 here:

√200= 14.142 (Round to thousandth place)

This is how many x we have found.

A multiple in math is the number you get when you multiply a certain number by using an integer. for example, multiples of 5 are: 10, 15, 20, 25, 30…, and so forth. Multiples of 7 are 14, 21, 28, 35, 42, 49…and many others.

In math, the meaning of a multiple is the product result of one number multiplied by another number. Here, 56 is a multiple of the integer 7. Here is an example of multiples: Fun facts. 0 is a multiple of every number as the product of 0 multiplied by any number is 0.

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A trapezoid has bases measuring 5cm and 9cm, and an area of 42cm. Find the height

Answers

The height of the trapezoid is 6 cm

How to find the height?

The given parameters are:

Bases = 5cm and 9cm

Area = 42 square cm

The height is calculated using

Area = 0.5 * (Sum of bases) * Height

So, we have:

42 = 0.5 * (5 + 9)* Height

This gives

42 = 7* Height

Divide through by 7

Height= 6

Hence, the height of the trapezoid is 6 cm

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A farmer has 45 horses and 20 cows.
(i) Write this as a ratio horses : cows.
Give your answer in its simplest form.

Answers

Answer: 9 : 4

Step-by-step explanation:

45 : 20

simplify

9 : 4

If 3x + 7 =22, what is the value of x

Answers

Answer:

x=5

Step-by-step explanation:

solution,

3x+7=22

or,3x=22-7

or,3x=15

or,x=15/3

:×=5

The value of x in the equation 3x + 7 = 22 is x = 5.

To find the value of x in the equation 3x + 7 = 22, we can solve for x as follows:

Subtract 7 from both sides of the equation:

3x + 7 - 7 = 22 - 7

3x = 15

Divide both sides of the equation by 3 to isolate x:

(3x)/3 = 15/3

x = 5

Therefore, the value of x in the equation 3x + 7 = 22 is x = 5.

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In the diagram, JKLM∼EFGH. Find the perimeter of each polygon.

Answers

The perimeter of polygon JKLM = 85 units

The perimeter of polygon EFGH = 34 units.

What is the Perimeter of a Polygon?

The perimeter of polygon JKLM = JK + KL + LM + JM

The perimeter of polygon EFGH = EF + FG + GH + EH

Find the missing lengths using the similarity theorem:

JK/EF = KL/FG = LM/GH = JM/EH

Plug in the values

20/8 = KL/11 = LM/3 = 30/EH

20/8 = KL/11

KL = (20 × 11)/8 = 27.5

20/8 = LM/3

LM = (20 × 3)/8

LM = 7.5

20/8 = 30/EH

EH = (30 × 8)/20

EH = 12

The perimeter of polygon JKLM = 20 + 27.5 + 7.5 + 30 = 85 units

The perimeter of polygon EFGH = 8 + 11 + 3 + 12 = 34 units.

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Find the number, d, if the sum of five times d and five times five is a
hundred.

Answers

The value of d from the given expression is 15

Word problem leading to equation

From the given statement the sum of five times d and five times five is a

hundred is interpreted as;

5d + 5(5) = 100

5d + 25 = 100

Subtract 25 from both sides

5d = 100 - 25

5d = 75

d =15

Hence the value of d from the given expression is 15

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4. Point P is not on line . Describe the shortest distance from the point to the line
P
8

Answers

Answer:

a line that is perpendicular to the line l

A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 20 child bikes and 6 adult bikes in the week. (2 points)

No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100

Answers

Considering the definition of an inequality and system of inequalities, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."

Definition of inequality

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

System of inequalities

A system of inequalities is made up of two or more inequalities.

The solution will be formed by the intersection of the half-planes of each of the inequalities, that is, it will be the enclosure that all the inequalities have in common. That is, the solution of the system is given by the region of the common plane of the half-planes that define each one of the inequalities.

System of inequality in this case

In this case:

c represents child bikes.a represents adult bikes.Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. The company is able to have up to 120 hours of building time and 100 hours of testing time for a week.

Then, the system of inequality is:

[tex]\left \{ {{4c+6a\leq 120} \atop {4c+4a\leq 100}} \right.[/tex]

On the other hand, the company can build 20 child bikes and 6 adult bikes in the week. So, checking the equations, for given c=20 and a=6:

4×20 + 6×6= 116 < 120

4×20 + 4×6= 104 >100

Finally, the correct option is: "No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100."

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The area and one side of a rectangle are given. Determine the missing dimension

Answers

The missing dimension is x + 4

How to determine the missing dimension?

The given parameters are:

Area = 4x^2 + 13x - 12

Length = 4x - 3

The width is calculated using:

Width = Area/Length

This gives

Width = (4x^2 + 13x - 12)/(4x - 3)

Expand

Width = (4x^2 + 16x - 3x - 12)/(4x - 3)

Factorize

Width = (4x(x + 4) - 3(x + 4)/(4x - 3)

Factor out x + 4

Width = (4x - 3)(x + 4)/(4x - 3)

Cancel out the common factor

Width = x + 4

Hence, the missing dimension is x + 4

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An article marked to give 120% profit originally cost $60. what is the marked price?

Answers

Answer is $72.00
Reason
We know cost is $60
We know profit percent is 120%
So 60x 120% = $72 marked price

If x is inversely proportional to y, then as x decreases, y decreases.​

Answers

Answer:

Yes

Step-by-step explanation:

Let's assume that x=1/y.

For y=1, x=1

For y=2, x=0.5

For y=4, x=0.25

And so on

For the following exercises, find the x- and y-intercepts of the graphs of each function.
28. f(x) = −2| x +1 | + 6

Answers

The x- and y-intercepts of the graphs of the function described are; (2,0) and (4,0) respectively.

What are the x- and y-intercepts of the graph of the function?

It follows from the task content that the function given is; f(x) = −2| x +1 | + 6.

Since the x- and y-intercepts corresponds to x and y values for which y and x are zero respectively, it follows that;

x -intercept is;

0 = -2(x+1) + 6

2x = -2 +6

2x = 4

x = 4/2 = 2

y-intercept is;

y = -2(0+1) +6

y = 4.

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Which of the following completes the two-column proof below?

Given: ∠1≅∠2, p⊥r
Prove: q⊥r
Proof:

1. ∠1≅∠2 (Given)

2. p∥q (?)

3. p⊥r (?)

4. q⊥r (?)

The figure shows lines p and q and transversal r. The intersection of line p and transversal r forms four angles, the top right angle is labeled as a right angle, the top left angle is labeled as 1. The intersection of line q and transversal r forms four angles, the bottom right angle is labeled as 2.

Answers

2. Converse of corresponding angles theorem.

3. Given

4. Perpendicular transverse theorem

What is the Converse of Corresponding Angles Theorem?

According to the converse of corresponding angles theorem, if two corresponding angles are congruent, then the lines cut by the transversal that both angles line on are parallel to each other.

Thus, given that ∠1 ≅ ∠2, lines p and q will be parallel based on the converse of corresponding angles theorem.

We are given that lines p and r are perpendicular to each other, therefore, we can conclude that, based on the perpendicular transverse theorem, q⊥r.

The missing reasons in the proof are:

2. Converse of corresponding angles theorem.

3. Given

4. Perpendicular transverse theorem

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He length of the hypotenuse of a right triangle is 24 inches. if the length of one leg is 8 inches, what is the approximate length of the other leg? 16.0 inches 18.4 inches 22.6 inches 25.3 inches

Answers

Answer:

22.6

Step-by-step explanation:

a^2 + b^2 = c^2  We know one of the legs and the hypotenuse.  The hypotenuse must be c.  The leg that we do know can be a or b.  It is our choice.  I am going to let it be a

8^2 + b^2 = 24^2  Plug in the numbers that I know

64 + b^2 = 576   Square the numbers that I know

b^2 = 512   Subtract 64 from both sides

b = 22.6  Put this in your calculator to find the square root and round.

Select the correct answer.
The product of two numbers is 21. If the first number is-3, which equation represents this situation and what is the second number?
OA The equation that represents this situation is x-3=21. The second number is 24.
OB. The equation that represents this situation is 3x=21. The second number is 7.
OC. The equation that represents this situation is-3x=21. The second number is-7.
OD. The equation that represents this situation is -3+x=21. The second number is 18.

Answers

Option B is correct

Why

3x=21

3(7) =21

21=21

Step-by-step explanation:

Answer:

[tex]-3x=21 , -7[/tex]

Step-by-step explanation:

[tex]-3x=21\\x=\frac{21}{-3} =-7[/tex]

What is the circumference of the given circle in terms of л

Answers

Answer:

30π in

Step-by-step explanation:

Circumference of a circle = 2πr

Where r is the radius

In the given diagram, the radius is 15 in

2×π×15 in = 30π in


Using the quadratic formula, solve for "t" in
the function: 0= -16t2 + 5t + 104. Keep in
mind that time CANNOT be "negative'!!!
t = 1.1 s
t = 1.9 s
t=2.71 s
t=2.2 s

Answers

Here is the answer. Rechecking with your teacher if it is correct or not.

4^x + 3 = 7 using the change of base formula log y =
log y/log b

Answers

Answer:

x=1

Step-by-step explanation:

It's pretty obvious to see that x equals 1 after you subtract 3 from both sides, but this question specifies using change base, so:

log(b)a means log base b with a as the contents
1.
4^x+3-3=7-3


4^x=4


log(4)4^x=log(4)4    (both logs are base 4 in this case to free the x)


x=log(4)4

x=log(10)4/log(10)4   (both logs are base 10 in this case)

x=1

Change base is definitely unnecessary in this problem

If the zeros of a quadratic equation are 7 and - 4 , what would be the factors?

Answers

Answer:

(x - 7) , (x + 4)

Step-by-step explanation:

given the zeros of a quadratic equation x = a and x = b , then

the corresponding factors are (x - a) and (x - b)

here the zeros are x = 7 and x = - 4 then factors are

(x - 7) and (x - (- 4) ) , that is

(x - 7) and (x + 4)

A survey of 150 people at a local high school about playing video games was conducted, and the results are posted in the table.


Play Video Games Do Not Play Video Games
Juniors 48 12
Seniors 45 25
Teachers 6 14


What is the probability of choosing a person at random who is a teacher and plays video games? Are these independent events?
The P(teacher and video games) = 4%; the two events are not independent.
The P(teacher and video games) = 4%; the two events are independent.
The P(teacher and video games) = 9%; the two events are not independent.
The P(teacher and video games) = 9%; the two events are independent.

Answers

The P(teacher and video games) = 4%; the two events are not independent.

What is the probability?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

P(teacher and video games) = number of teachers who play video game / total number of respondents

6/150 = 0.04 = 4%

Independents events are events whose occurrence do not depend on each other. They are random events.

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Answer:

The P(junior and video games) = 32%; the two events are not independent.

Step-by-step explanation:

i got it right aswell

Casey was at the surface of a swimming pool and recorded the following two measurements, in feet, on a number line:

−8, which represents the depth of water in the swimming pool
+7, which represents the height of the slide at the pool

Part A: What does 0 represent in this situation? (3 points)

Part B: Describe the height of the slide in relation to 0 in the situation. (3 points)

Part C: Casey held a pole in the swimming pool. The bottom of the pole was at a depth of 2 feet. How should Casey mark the level of the bottom of the pole on the number line? Explain how you determined this. (4 points)

Answers

The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that −8 represents the depth of water in the swimming pool. Hence:

The point 0 represents the surface of the water. The height of the slide is 7 feet above the surface of the water. The bottom of the pole can be represented by -2 on the number line.

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Evaluate 3 × 5². A. 30 B. 75 C. 150 D. 225

Answers

Answer:

B: 75

Step-by-step explanation:

5^2 is 5 times itself twice, so 5 times 5 = 25

3 times 25 is 75

Answer:

Hello! The answer to your question is B. 75.

Step-by-step explanation:

To solve this question, you have to first convert the exponents:

[tex]5^2 = 25[/tex]

Now that you have converted the exponents, you can multiply:

3 × 25 = 75

Two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. What is the probability that after they are painted, the cubes can be rotated to be identical in appearance

Answers

Answer:

Step-by-step explanation:

Define two ways of painting to be in the same class  if one can be rotated to form the other.We can count the number of ways of painting for each specific class .

Case 1: Black-white color distribution is 0-6 (out of 6 total faces)

Trivially [tex]1^{2}[/tex]=1 way to paint the cubes.

Case 2: Black-white color distribution is 1-5

Trivially all [tex]\frac{6}{5}[/tex] =6 ways belong to the same class , so [tex]6^{2}[/tex] ways to paint the cubes.

Case 3: Black-white color distribution is 2-4

There are two classes for this case: the class  where the two red faces are touching and the other class where the two red faces are on opposite faces. There are 3 members of the latter class  since there are  3 unordered pairs of  2 opposite faces of a cube. Thus, there are [tex]\frac{6}{4}[/tex]-3=12  members of the former class . Thus, [tex]12^{2} + 3^{2}[/tex] ways to paint the cubes for this case.

Case 4: Black-white color distribution is 3-3

By simple intuition, there are also two classes  for this case, the  class where the three red faces meet at a single vertex, and the other class where the three red faces are in a "straight line" along the edges of the cube. Note that since there are 8 vertices in a cube, there are 8  members of the former class and [tex]\frac{6}{3} -8=12[/tex] members of the latter class. Thus, [tex]12^{2} - 8^{2}[/tex]  ways to paint the cubes for this case.

Note that by symmetry (since we are only switching the colors), the number of ways to paint the cubes for black-white color distributions 4-2, 5-1, and 6-0 is 2-4, 1-5, and 0-6 (respectively).

Thus, our total answer is[tex]\frac{2*(6^{2} + 1^{2}+ 12^{2}+ 3^{2})+12^{2}+8^{2}}{2^{12} } =\frac{588}{4096} = \frac{147}{1024}[/tex]

Type the correct answer in the box. Use numerals instead of words.
The graphs of functions f and g are shown.

Graph shows 2 functions. First curve f begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 2), (8, 3) in quadrant 1. Second curve g begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 4), and (8, 6) in quadrant 1.

Function g is defined as . What is the value of k?

The value of k is
.

Answers

Step-by-step explanation:

Type the correct answer in the box. Use numerals instead of words.

The graphs of functions f and g are shown.

Graph shows 2 functions. First curve f begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 2), (8, 3) in quadrant 1. Second curve g begins close to Y-axis in quadrant 3 and rises through (1, 0), (4, 4), and (8, 6) in quadrant 1.

Function g is defined as . What is the value of k?

The value of k is

(1,0)

Find the polar equation of the conic with focus at the pole, directrix y=3, and eccentricity of 2. a. r= 6/1+2 sin theta b. r= 6/1-2 sin theta c. r= 3/ 1- 2 cos theta d. r= 1/3+2 cos theta

Answers

The required polar equation of a conic is given be: [tex]r = \frac{6}{1-2sin\Theta }[/tex]. option b is correct.

For a conic we have directrix = 3 and eccentricity = 2

What is polar equation?

Polar equation can be identified as of the form of x= a+b.sinФ.
Which contain simple variable along with trigonometric operators.

Here,

Standard polar equation for the conic is given as,

    [tex]r=\frac{ep}{1-esin\theta}[/tex]  
By putting given values
[tex]r = \frac{6}{1-2sin\Theta }[/tex].
Thus, the required polar equation for the conic is  [tex]r = \frac{6}{1-2sin\Theta }[/tex].

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Riddle-if you solve it i will delete your answer and you have to post the riddle. Riddle-you enter a room. 2 dogs, 4 horses, 1 giraffe and a duck are lying on the bed. 3 chickens are flying over a chair. How many legs are on the ground?.

Answers

Answer:

10

Step-by-step explanation:

2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.

The answer will be either 8 or 4 or 0.

What is a riddle?

A riddle is an intentionally framed ambiguous question or statement that requires ingenuity and critical thinking to solve or understand.

In the given riddle, all the two dogs, four horses, one giraffe and a duck are lying on the bed. Three chickens are flying over a chair.

Assumptions:

1) Bed is placed on the ground.

2) Bed and chair considered are of standard type.

case1:

If we consider the legs of only living organisms, the number of legs on the ground at the given instant will be 0.

case2:

If that's not the case, then a typical chair will have four legs, and a standard bed will also have four legs. So a total of 8 legs will be on the ground or floor of the room.

case3:

And if we consider the possibility of the chair being placed on the bed, then the legs of the chair will not touch the ground. So a total of 4 legs will be on the ground or floor of the room.

∴ From different perspectives, the number of legs on the ground will be either 8 or 4 or 0.

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Which expression is equivalent to (3x + 4x-7)(x-2)?OA. (3x2 + 4x-7)(x) + (3x + 4x-7)(-2)OB. 2x(3x + 4x-7)OC. x(3x + 4x-7) - 2OD. x(3x + 4x-7)+2(3x + 4x-7) Describe the steps you used to solve the equation andfind the amount of Carrie's allowance.Linear equation:a+a+8=22 please help me I don't understand this After a mass extinction event, the organisms that survive face unique circumstances in which there are fewer predators and more resources available. This leads to unique opportunities for the surviving organisms to colonize new habitats and diversify. This is termed _______. How long does it take for the brain to become dependent on a prescription depressant?. Use the function below to find F(4). Which of the following segments is a radius of OK?MKOA. KMB. MRC. RTD. MTSUB Identify the center and the radius of acircle that has a diameter with endpoints at (2, 7)and (8, 9). If you rolled two dice, what is the probabilityGivethat you would roll a sum of 5?your answer as a simplified fraction. Enterthenumber that belongs in the green box.secondfirst1 23 4561 1,1 1,2 1,3 1,4 1,5 1,62 2,1 2,2 2,3 2,4 2,5 2,63 3,1 3,2 3,3 3,4 3,5 3,64 4,1 4,2 4,3 4,4 4,5 4,65 5,1 5,2 5,3 5,4 5,5 5,66 6,1 6,2 6,36,4 6,5 6,6 In the diagram of AABC shown below, DE || BC.BA3) 34) 15EIf AB= 10, AD = 8, and AE = 12, what is thelength of EC?1) 62) 2Cdd or createk as donenmentsAsto Susan Guha the economy is doing well, but inflation is a concern. How should the Federal Reserve respond to help slow down the economy? Explain Plss someone help PLEASE HELPPPPPPP1.The most important constitutional right that Americans have is...2. Why do you think so? List at least three reasons why that right is central to the daily life of an American.It might be best to write only three to five different ideas here so that your paragraph isn't too long.3. The ideas you just wrote down for question 2 are the body of your paragraph. Restate them as evidence that supports your topic sentence.Write one paragraph that explains why the constitutional right you chose is most important. You can use the topic sentence just the way it is, or you can change it a little. Remember to give your paragraph a conclusion. Geometry help ??!!??!&& Shamrock, Inc. recorded a loss of $9800 when it sold a van that originally cost $71000 for $14600. Accumulated depreciation on the van must have been $61200. $66200. $24400. $46600. Use the function below to find F(3). Select the correct answer. The graph of function f is shown. An exponential function with vertex at (1, 3) and passes through (minus 2, 10), (8, 2) also intercepts the y-axis at 4 units. Function g is represented by the equation. Which statement correctly compares the two functions? Arrange the events in chronological order PLEASE HELP ME ANSWER THESE QUESTIONS!1.) Calculate the number of moles (n) in 14.0 g of sodium hydroxide (NaOH)2.) Calculate the number of moles (n) in 0.05 g of sulfuric acid (H2SO4)3.) What is the mass of 4.75 moles of lead atoms4.) What is the mass 0.04 mol of hydrochloric acid (HCl)5.) How many atoms are there in 5.00 mol of silver6.) How many atoms are there in 3 X 10 - 10 mol of copper Before the invention of the camera, our early ancestors were creating what type of visual art?interpretive dancessongsselfiescave paintings The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height(y), in mm, to which it grows:Y=2+4xWhat does the y- intercept of this function represent?