i need help bru dis is mh last try
What is the inverse of ƒ (x) = (2x + 1)² for x ≥ −½1⁄?

I Need Help Bru Dis Is Mh Last TryWhat Is The Inverse Of (x) = (2x + 1) For X 1?

Answers

Answer 1

The inverse of the given function is (f^-1)(x) = (1/2)×(√x  - 1) for x ≥ 0.

We are given a function f(x). The function f(x) is defined as (2x + 1)². The domain of the given function f(x) is x ≥ -1/2. We need to find the inverse of the function f(x).

Let us suppose that the function f(x) is represented by the variable "y".

y = f(x)

y = (2x + 1)²

Now we will take the square root on both sides of the equation.

√y = √[(2x + 1)²]

When we cancel out the even powers, we need to take the absolute value using modulus.

√y = |2x + 1|

We already know that x ≥ -1/2, so, modulus will open with a positive sign.

√y = +(2x + 1)

√y = 2x + 1

√y  - 1 = 2x

x = (1/2)×(√y  - 1)

At last, we replace the variables y and x by x and (f^-1)(x).

(f^-1)(x) = (1/2)×(√x  - 1) for x ≥ 0

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Related Questions

wilma can mow a lawn in 120 minutes. vanessa can mow the same lawn in 80 minutes. how long does it take for both wilma and vanessa to mow the lawn if they are working together?

Answers

Working together, they can mow the yard in 48 minutes.

Given data;

A lawn can be mowed by Wilma in 120 minutes. In 80 minutes, Vanessa can cut the same lawn. When working together, how long does it take Wilma and Vanessa to mow the lawn?

Let 't' is their time in minutes working together.

Add their rates of working to get their rate working together,

Wilma's rate: [ 1 lawn ] / [ 120 min ]

Vanessa's rate: [ 1 lawn ] / [ 80 min ]

Rate working together: [ 1 lawn ] / [ t min ]

1/120 + 1/80 = 1/t

Multiply both sides by 240t;

2t + 3t = 240

5t = 240

t = 48

It takes them 48 min to mow the lawn working together.

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The scatterplot shows the relationship between the length of a pendulum and the time it takes to complete one full swing.

Which transformations would linearize these data using a power model? Check all that apply.

ln(Length), ln(Time)
ln(Length), Time
log(Length), log(Time)
Length, log(Time)
Length, Time2

Answers

Answer:

a) ln(Length), ln(Time)

c)log(Length), log(Time)

e)Length, Time²

Step-by-step explanation:

Answer:

the person above me is correct!

Step-by-step explanation:

Please help me Find the slope of the line

Answers

Answer:

Step-by-step explanation:

d- down four then right three

what is (2 x 10 to the power of 5) divided by (4 x 10 to the power of 2)

Answers

Answer:

500

Explanation:

PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE

Answers

Answer:

7, 7/1

Step-by-step explanation:

The ratio 7:49 can be simplified to 1:7.

necesito saber como se resuelve

Answers

La ecuación exponencial 9ˣ⁺¹ + 3 = 28.3ˣ tiene una solución en x ≈ 1.922.

¿Cómo resolver un ecuación exponencial?

Aquí tenemos una ecuación exponencial en forma implícita, esto es, que la variable x no está en términos implícitos de las constantes de la ecuación.

Esta forma se puede resolver mediante métodos gráficos, a partir de la graficación del siguiente sistema de ecuaciones:

f(x) = 9ˣ⁺¹ - 28.3ˣ - 3

g(x) = 0

La solución es todo punto tal que f(x) = g(x).

A continuación, se grafica cada ecuación en un plano cartesiano mediante una herramienta gráfica. De acuerdo con la imagen, la solución de la ecuación es x ≈ 1.922.

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A line passes through the point
(8, 7) and has a slope of 4

Write an equation in slope-intercept form for this line.

Answers

[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{ 4}(x-\stackrel{x_1}{8}) \\\\\\ y-7=4x-32\implies {\Large \begin{array}{llll} y=4x-25 \end{array}}[/tex]

Answer:

y = 4x -25

Step-by-step explanation:

y = 4x + b

we must find the y intercept

plug in the point

7 = 4(8) + b

7 = 32 + b

subtract 32 from both sides

-25 = b

the y intercept is -25

plug in -25 for b

y = 4x - 25

If you roll a die three times, how many different sequences are possible? a. 6 cubed = 216 b. 3 superscript 6 baseline = 216 c. 3 superscript 6 baseline = 729 d. 6 cubed = 729

Answers

Total number of outcomes in rolling a die 3 times = [tex]6^3[/tex]  =216

What is outcome of an event?

Suppose an event is happening. The result of the event is called outcome of the event.

For example : let the event be throwing of a die. One of the outcome of the event is getting a 4 on the die

Number of outcomes of rolling a die first time = 6

Number of outcomes of rolling the die second time = 6

Number of outcomes in rolling a die third time = 6

Total number of outcomes in rolling a die 3 times = [tex]6 \times 6 \times 6[/tex]

                                                                                   = [tex]6^3[/tex]

                                                                                   = 216

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Please help pleaseee

Answers

According to the Pythagoras theorem, the value of x is 13.76

Pythagoras theorem:

“In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“ is known as Pythagoras theorem.

Given,

Here we have the triangle with the side values.

Now, we have to find the value of x through this given values.

In order to calculate the value of x,

First, we need the value of the side KM.

Let us consider the value of KM is y.

Then according to the concept of Pythagoras theorem,

The value of y is calculated as,

=> (12.3)² = y² + (5.4)²

=> 151.29 = y² + 29.16

=>  y² = 122.13

=> y = 11.05

Therefore, the value of the hypotenuse  x is calculated as,

=> x² = (11.05)² + (8.2)²

=> x² = 122.13 + 67.24

=> x² = 189.37

=> x = 13.76

Therefore, the value of x is 13.76.

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pls give answer pls pls

Answers

Answer:

k = 13

Hope this helps : )

Step-by-step explanation:

To solve the equation, we need to first isolate the variable by doing the inverse operation which in this case is dividing since 7 is being multiplied with the variable k.

1. Divide 7 on both sides of the equal sign.

7k = 91

7 7

2. Answer.

The 7 cancels out so we are left with k = 13 since

91 ÷ 7 = 13

k = 13

3. Check.

Plug in the variable "k."

7(13) = 91

91 = 91 ✓

order the sides DEF from shortest to longest

Answers

From the given triangle, the order of the sides DEF from shortest to longest is DE, DF, and EF.

Triangle:

The polygon with three edges known as sides and three vertices are known as triangle.

Given,

Here we have the triangle with their corresponding angle.

Now, we have to order the sides from shortest to longest.

Here in the given triangle we know the angles of m∠D = 61, m∠E = 60, and m∠F = 59.

By knowing this measures we can order the sides from shortest to longest, because angles are the opening between to sides, which means if the angle is wide, its opposite side that is in front of the angle is wide too, if the angle is narrow, its opposite side will be narrow.

In this case, the opposite side of ∠D will be the longest, because it is the largest angle. And the opposite side of m∠E will be the second longest, and finally the opposite side of ∠F will be the smallest.

From values, the shortest to longest the order is written as DE, DF and EF.

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Evaluate the expression for the given value of the variable. 52+1/5(-1/2)

Answers

The simplified form of the expression 52 + 1/5(-1/2)  is [tex]\frac{519}{10}[/tex]

What is a fraction?

A fraction is a ratio of two integers.

The integers are always in two parts separated by a division line. the part above the division line is called the numerator and the part below the division line is called the denominator.

52 + 1/5(-1/2)

Multiply out the fraction

we have

52 + (-1/10)

52 - 1/10

to make 52 have the same denominator as 1/10 we multiply 52 by 10/10 so that it becomes

520/10 - 1/10

simplifying the numerator we have,

[tex]\frac{520 - 1}{10}[/tex] =  [tex]\frac{519}{10}[/tex]

In conclusion the solution to 52+1/5(-1/2) is  [tex]\frac{519}{10}[/tex]

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the population of a city increases by 4,000 people each year. in 2005 the population is projected to be 450,000 people. what is an equation that gives the city's population p (in thousands of people) x years after 2010

Answers

Equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.

Total population in 2010 is equal to 470,000 people.

As given in the question,

Let 'p' represent the population in thousands of people.

Let x represents the number of years.

Population projected in 2005 = 450,000 people

                                                 = 450 ( in thousand people)

Population increases by 4000 people each year that is equal to 4 (in thousand of people)

Required equation to represent the population in x years ( in thousand of people ) is given by:

p = 4x + 450

Population in 2010 is equal to :

p = 4 ( 2010 - 2005) + 450

 = 4(5) + 450

= 20 + 450

= 470 ( in thousand of people)

= 470,000 people

Therefore, equation represents the population of the city 'p' in thousand of people in x years when in 2005 projected population is 450,000 and increases by 4,000 people each year is given by p = 4x + 450.

Total population in 2010 is equal to 470,000 people.

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Solve the equation or formula for the variable indicated.
X-2y=1

Answers

Answer:

Step-by-step explanation:

-2y = -x -1
2y = x+1
y = 1/2x+1/2

Type the missing number to complete the proportion.

18 orders in 2 days = 9 orders in
days

Answers

Answer:

18 orders in 2 days 9 orders in 1 day

Answer:

Step-by-step explanation:

9x2=18 which is 2 days so 9x1= 9 which is one day

In the following figure, AD is the bisector of ZBAC. GE is perpendicular to AB, GF is perpendicular to AC.
Andrea says that AAEG = AAFG by the AAS congruence postulate. Do you agree or disagree? Explain.

Answers

I agree with Andrea that Δ AEG ≅ Δ AFG by the AAS congruence postulate

What is congruency of triangle?

Triangles are said to be congruent when the sides and angles equal in accordance to to the triangle congruency rules

Some of the rules include

Side -  Side - Side = SSSSide - Angle - Side = SASAngle - Side - Angle = ASA Angle - Angle - Side = AAS Hypotenuse and one leg = HL

The problem requires the prove by Angle - angle - Side = AAS to ensure that the the triangles are congruent

The AAS have it that the two triangles being compared should have their two angles and the side not included being equal

The Angle - Angle - Side = AAS, here include

< FA,G - < AFG - AG

< EAG - < AEG - AG

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Pls help me thank you

Answers

The value of y is  x/2 + c/5  

Given,

In the question:

5x - 7y = 3y - 2c

To find the value of y.

Now, According to the question:

The equation is given as:

5x - 7y = 3y - 2c

Combine the like terms:

-7y - 3y = -5x - 2c

Calculate the sum or difference:

-10y = -5x - 2c

y = -5x/-10 - 2c/-10

Calculate the product or quotient :

y = x/2 + c/5

Hence, The value of y is  x/2 + c/5

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A square with a perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.

If ( x , y ) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?

Answers

If (x, y) represents the location of any point on the original square, the ordered pair which represents the coordinates of the corresponding point on the resulting square is: (0.4x, 0.4y).

What is dilation?

In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object and the location of its points based on the scale factor, but not its shape.

What is scale factor?

In Geometry, a scale factor can be defined as the ratio of two corresponding side lengths or diameter in two similar geometric objects (shapes) such as equilateral triangles, square, quadrilaterals, polygons, etc., which can be used to either enlarge or reduce their size.

Generally speaking, the transformation rule for the dilation of a geometric object (square) based on a specific scale factor is given by this mathematical expression:

(x, y)      →    (SFx, SFy)  = (0.4x, 0.4y)

Where:

x and y represents the data points.SF represents the scale factor.

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Complete Question:

A square with the perimeter of 20 units is graphed on a coordinate grid. The square is dilated by a scale factor of 0.4 with the origin as the center of dilation.

If (x, y) represents the location of any point on the original square, which ordered pair represents the coordinates of the corresponding point on the resulting square?

answer choices

(0.4x, 0.4y)

(x + 20, y + 20)

(x + 0.4, y + 0.4)

(20x, 20y)

a coin is flipped eight times. each result is either a heads or a tails. how many possible outcomes contain at least 33 tails ?

Answers

The possible outcomes must contain at least three tails, not 33 because a coin is flipped eight times. Then, the possible outcomes that contain at least three tails are 219.

The possible outcome is the possible result of an event. The possible outcomes that contain at least three tails mean the possible outcomes with exactly three tails and more than three. So, the calculation is:

[tex]\frac{8!}{3!5!} + \frac{8!}{4!4!} + \frac{8!}{5!3!} + \frac{8!}{6!2!} + \frac{8!}{7!1!} + \frac{8!}{8!0!}[/tex]56 + 70 + 56 + 28 + 8 + 1= 219

Hence, the possible outcomes that contain at least three tails are 219.

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Which description matches the graph of the inequality y <|x-2| + 1

Answers

A shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.

What is inequality?

Inequality is a relationship between two expressions or values that is not equal to each other.

This inequality may be written in two ways:

(a) y < x - 2 + 1

   or

   y < x - 1

(b) y < -x +2 + 1

   or

    y < -x + 3

A graph of the inequality is shown below. The shaded region satisfies the inequality.

Hence, a shaded region above a solid boundary line matches the graph of the inequality y <|x-2| + 1.

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Match each number with its estimated power of 10

Answers

The matching numbers are:

1) 0.0000225 = 2 x 10⁻⁵

2) 219,000 = 2 x 10⁵

3) 3,40,000 = 3 x 10⁶

4) 297,000 = 3 x 10⁵

5) 0.0000034 = 3 x 10⁻⁶

What are Exponents?

The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

We have to match the following terms :

1) 0.0000225 = 2 x 10⁻⁵
we can write 0.0000225 as
2.25 / 100000
or, 2.25 / 10⁵
then, 2.25 x 10⁻⁵

2) 219,000 =  2 x 10⁵
as the numbers after 2 are 5
therefore we write 10⁵

3) 3,40,000 = 3 x 10⁶
as the numbers after 3 are 6
therefore we write 10⁶

4) 297,000 = 3 x 10⁵
we round off 297 as 300
as the numbers after 3 are 5
therefore we write 10⁵

5) 0.0000034 = 3 x 10⁻⁶
we can write 0.0000034 as
3.4/ 1000000
or, 3.4 / 10⁶
then, 3.4x 10⁻⁶

Hence, the matching numbers are:
1) 0.0000225 = 2 x 10⁻⁵
2) 219,000 = 2 x 10⁵
3) 3,40,000 = 3 x 10⁶
4) 297,000 = 3 x 10⁵
5) 0.0000034 = 3 x 10⁻⁶

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PLEASE HELP ME AND TELL ME HOW YOU DID IT AND THANKS 25 POINTS HELP

Answers

Answer should be A!
50-36 is 14 and just plug 14 into the blanks to see which one fits.

Choose the equation that represents the graph shown

Answers

Answer:

[tex]y=|x|-4[/tex]

Step-by-step explanation:

The vertex of the graph is at (4, 0).

This eliminates all of the options except for [tex]y=|x|-4[/tex].

There are 100 items in a garage sale. 30% of the items are sold during the first hour of the sale. If 10 items are sold during the second hour, what percent of the items have not been sold?

Answers

The percentage of items that have not been sold is: 60%

In mathematics, the percentage is calculated by dividing the given value by the total which is then multiplied by 100.

Percent in itself stands for out of 100.

Let the total number of items= i

Let the percentage be represented as= p

Then,

         i=100 (Given in the question)

Let the number of items sold in the first hour be= a

Let the number of items sold in the second-hour be= b

Since,

         p= Given Value/Total value x100

thus,

        a/100x100=30%

        The hundreds cancel out.

Thus, a=30 -(i)

The number of items sold in the second hour= b

b=10 (provided in the question) -(ii)

Let the total number of items sold be=T

The total number of items sold= a+b

From (i) and (ii)

Total number of items sold=30+10

Thus,

        Total number of items sold=40 -(iii)

Number of items that have not been sold(n)=100-(a+b)

                                                                        =100-T

                                                                        = 100-40

                                                       From (iii)

                                                                     n = 60 -(iv)

Then,

          Percentage of items that have not been sold = n/100x100

                                                                From -(iv)              

                                                                                      = 60/100x100

          Canceling hundred by hundred                      

                                                                                      = 60%

Thus,

          Answer: The percentage of items that have not been sold is: 60%

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A rectangle is 25 cm on one side and 6 cm on another side. What is the perimeter?

Answers

Answer:

31

Step-by-step explanation:

there is a line whose slope is 1 and whose y-intercept is -9, what is its equation in slope-intercept form?

Answers

slope intercept form is y=mx+b. so therefore, y=m1-9

Each month, kaisorn deposits $50. 00 onto her public transportation card. It costs her $2. 50 per trip to ride the subway. Thom deposits $40. 00 on his public transportation card. It costs him $2. 00 per trip to ride the subway. If x represents the number of trips and y represents the amount remaining in each account, which system of equations represents their transportation costs? 50 − 2. 5x = y 40 − 2x = y 50 + 2. 5x = y 40 + 2x = y 50 − 2. 5y = x 40 − 2y = x 50 + 2. 5y = x 40 + 2y = x.

Answers

The system of equations represents their transportation costs is:

50 − 2. 5x = y

40 − 2x = y

The correct option is  (A)

Given,

In the question:

Kaisorn deposits $50. 00 onto her public transportation card.

It costs her $2. 50 per trip to ride the subway.

Thom deposits $40. 00 on his public transportation card.

It costs him $2. 00 per trip to ride the subway.

Now, According to the question:

x → represents  the number of trips

y → represents the amount remaining in each account

According to the given condition:

The system of equations represents their transportation costs is :

50 − 2. 5x = y

40 − 2x = y

Hence, The system of equations represents their transportation costs is:

50 − 2. 5x = y

40 − 2x = y

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Math help needed (grade 9)

Answers

Step-by-step explanation:

volume = base area × height

= (1/2×12×16)×10

=960cm3

surface area:

1. triangle area = 1/2×12×16=96cm2

2.bottom area = 12×10=120cm2

3.side area = 16×10=160cm2

4.slope area = 10×20=200cm2

5.add everything and remember you have two triangle

surface area= 96×2+120+160+200 =672cm2

about 310 000 t of atlantic cod were caught in 1991. in 2001 the mass of the cod caught was 87% less. HOw much cod was caught in 2001

Answers

Number of Atlantic cods caught in the year 2001 is; 40300 t

How to solve percentage word problems?

Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100. This is expressed as;

Percentage = (value / total value) * 100%

Now, we are told that;

Number of Atlantic cods caught in 1991 = 310000 t

We are told that in the year 2001, there were 87% less caught. Thus;

Number by which it was reduced = 310000 * 87% = 269700

Thus;

Number of Atlantic cods caught in the year 2001 = 310000 - 269700

Number of Atlantic cods caught in the year 2001 = 40300 t

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Select the type of cross section formed when a triangular pyramid is cut parallel to its
base.

Answers

The resulting cross section is a rectangle.
Other Questions
suppose an airline took the independent action of reducing fares on its flights. other competing airlines quickly matched the fare cuts. the competitors' actions might be interpreted as: The root system ___ A. Respires B. absorbs water and minerals C. photosynthesizes D. includes the stem E. is the only part of the plant system light from an argon laser strikes a diffraction grating that has 5,735 lines per cm. the first-order principal maxima are separated by 0.5 m on a wall 1.76 m from the grating. what is the wavelength of the laser light in nm? enter an integer. Which sentence BEST describes how the author develops ideas in A Bird of Bad Moral Character? new balance offers a variety of types of shoes to its customers at various price points, typically in 3 basic tiers, based on the quality of the material and components of the shoe. this is an example of managing the product line offering and is known as: 7. The local police department just bought a Reflected Ultraviolet Imaging System (RUVIS) device. What is MOST likely the purpose of this purchase?to test DNA from blood in their labto individualize hair samplesto determine if blood is human or animalto find and process more fingerprints a client has presented in the early phase of labor, experiencing abdominal pain and signs of growing anxiety about the pain. which pain management technique should the nurse prioritize at this stage? A basketball has a volume of about 452.1 cubic inches. Fine the radius of the basketball in inches Which decimal is equivalent to \{31}{9} 931 start fraction, 31, divided by, 9, end fraction? Which of the following roles does a population comparison or ecological study primarily play in establishing contributory cause?Group associationIndividual associationCause precedes the effectAltering the cause alters the effect If sodium (na) has 4 neutrons, 3 protons, and 2 electrons, which would be the correct ion symbol?. Solve the equation without using a calculator[tex]\displaystyle\\3^\frac{x+2}{3x-4}-2\cdot3^\frac{5x-10}{3x-4}=7[/tex] What is the Qurans stance on the topics:learning and business? the ___ oversees all operations of the restaurant. Arab and berber traders helped facilitate the gold-salt trade in africa. What part of africa had an abundant supply of salt that was traded for gold?. select all characteristics that are true of a chaperone protein. check all that apply it is encoded by a structural gene. it is encoded by a structural gene. it acts as an enzyme in an amino acid synthesis pathway. it acts as an enzyme in an amino acid synthesis pathway. it has primary, secondary, and tertiary structure. it has primary, secondary, and tertiary structure. it has an amino-terminal and a carboxyl-terminal end. it has an amino-terminal and a carboxyl-terminal end. it assists other polypeptides with folding into the correct secondary structure. it assists other polypeptides with folding into the correct secondary structure. it assists the ribosome with translation. Physical fitness is an important part of overall health. It makes a person feel great and lowers his or her risk of developing chronic diseases. One aspect of maintaining a physically active lifestyle is to create a safety plan to prevent injury. In the first paragraph, write a personal physical activity plan using current safety guidelines. Your plan should include an approach for assessing your own physical activity level. Include supporting details in the form of facts, statistics, or examples.In the second paragraph, list any personal barriers, and internal and external influences that may prevent you from executing this plan as well as the short- and long-term goals that would ensure your plan is successful. Also, explain one method you could use to monitor how well you progress toward meeting these goals and combating barriers and influences. Include supporting details in the form of facts, statistics, or examples. In the Calculations section you were asked to calculate the percent error in your Hess's Law determination. Discuss at least two possible sources of error that could contribute to your percent error. What approach did you find to help you identify sketches that are not fully constrained in the future? How will you approach adding constraints to achieve full constraint? why is the underlined heading a good choice for this section