X+2y=5 and 4x-12y=-20 solve using elimination and substitution

Answers

Answer 1

Answer:

(1,2)

Step-by-step explanation:

Substitution:

x + 2y = 5  Solve for x

x = -2y + 5  Substitute -2y + 5 in for x in the second equation

4x - 12y = -20

4(-2y + 5) - 12y = -20  Distribute the 4

-8y + 20 - 12 y = -20  Combine the y term

-20y + 20 = -20  Subtract 20 from both sides

-20y = -40  Divide both sides by -20

y = 2

Plug y into either of the 2 original equations to get x.

x + 2y = 5

x + 2(2) = 5

x + 4 = 5

x = 1

The answer is (2,1).

Elimination:

x + 2y = 5      4x - 12y = -20.  We want to eliminate with the x or the y.  I am going to eliminate the x's that means that I have to multiply the first equation all the way through by -4

(-4)(x + 2y) = (5) (-4)  That makes the equivalent expression

-4x - 8y = -20  I will add that to 4x - 12y = -20

4x - 12y = -20

0x -20y = -40

-20y = -40

y = 2.  Plug 2 into either the 2 original equation to find x.  This time I will select the second original equation to find x.

4x -12y = -20

4x - 12(2) = -20

4x - 24 = -20

4x = 4

x = 1


Related Questions

A bookstore carries 48 magazines. 75% of the magazines are women's magazines. How many women's magazines does the bookstore carry?

Answers

Answer:

36

Step-by-step explanation:

75/100

75/100=0.75

0.75*48 =36

What is the value of the last digit in 3,500.45

Answers

Answer:

five-hundredths

Step-by-step explanation:

Ms. Oshiro teaches her 27 students to make folded-paper birds. Each student can make about 2 birds in 1 minute. About how many birds can all the students make in 55 minutes? A 3,000 B 1,500 C 100 D 60​

Answers

Answer:

The answer is 2970

Step-by-step explanation:

Collectively, all the students can make about 54 books rds per minute (27 * 2)

Therefore in 55 minutes there should be 2970

(54*55) :)

which of the following could be the ratio between the lengths of the two legs of a 30-60-90 triangle ​

Answers

Answer:

A, C

Step-by-step explanation:

See attached image.

Which of the following are polynomials?

A. x^2 + x + 1/x^2 + 1

B. 2/x^3 + x + 1/2

C. 2/3x^2 + x + 1

D. x^2/3 + 0x + 1

E. x^3 + 2x + square root of 2

Answers

Answer: C, E

Step-by-step explanation:

These are polynomials by the definition of a polynomial.

What number should come next in the sequence? 0.8, 0.35, -0.1, -0.55, ... FASTTTTT

Answers

Answer:

-1

Step-by-step explanation:

0.35 - 0.8 = -0.45

-0.1 - 0.35 = -0.45

-0.55 - 0.45 = -1

If 5 bags weigh the same as 3 blocks, how many blocks will 9 bags weigh?
OA) 3 blocks
OB) 4.4 blocks
OC) 5.4 blocks
OD) 15 blocks

Answers

Answer: C. 5.4 Blocks

Step-by-step explanation:

Given information

5 bags = 3 blocks

Set variable

Let x be the number of blocks

Constructure proportional equation

[tex]\frac{3}{5} } ~=~\frac{x}{9}[/tex]

Cross multiply the fraction

[tex](3)~*~(9)~=~(5)~*~(x)[/tex]

[tex]27~=~5x[/tex]

Divide 5 on both sides

[tex]27~/~5~=~5x~/~5[/tex]

[tex]\Large\boxed{x=5.4~blocks}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

oc

Step-by-step explanation:

5 times .6 equals 3

9 times .6 equals 5.4

One circle has a circumference of 12x cm. Another circle has a circumference of 32x cm. What is the ratio of the
radius of the smaller circle to the radius of the larger circle?
O 3:8
O 8:3
O 1:3
O 3:1

Answers

Answer:

3 :8

Step-by-step explanation:

12 : 32 = 3:8

I believe that is right.


Solve:
55) A pool is filling at 3 pts per min. How many gallons per hour is that?

Answers

Conversion factors:
2 pints = 1 quart
4 quarts = 1 gallon
60 minutes = 1 hour

15 pints/minute x 60 minutes/hour x 1 quart/2 pints x 1 gallon/4 quarts = 112.5 gallons/hour

Find the mean for the scores 3,820, 5,500, 8,560, 4,400, 5,350

Answers

Answer:

5,526

Step-by-step explanation:

Mean of scores = Total Value of Scores / Number of Values

= [tex]\frac{3820+5500+8560+4400+5350}{5} \\[/tex]

= 5,526

Answer:5526

Step-by-step explanation: Add everything up and divide by 5 because there are 5 numbers

at a particular high school, 42% of the students participate in sports and 25% of the students participate in drama. if 53% of the students participate in either sports or drama, what is the probability that a student participates in both sports and drama?

Answers

P( A Student participates in Both sports and Drama) =0.07

What is the probability?

The probability of an occurrence can be determined using the probability formula by simply dividing the favorable number of possibilities by the entire number of possible outcomes.

To find the probability that a student participates in both sports and drama:

Let

A =Student  participate in Sport

B = Student  participate in Drama

Thus we have:

P(A) = 0.42

P(B) = 0.25

and

P(Ac and B or A and Bc) =0.53

P(Ac and B ) + P( A and Bc) =0.53

P(B) - P(A and B) + P(A) - P(A and B) = 0.53

0.25 - P(A and B )  +  0.42 - P(A and B) = 0.53

0.25+0.42 - 2 * P( A and B) = 0.53

0.67 - 2 * P(A and B) = 0.53

0.67 - 0.53  = 2* P(A and B)

0.14  =  2 * P(A and B)

0.14 / 2  = P( A and B)

0.07 = P( A and B)

that is:

P( A and B) = 0.07

P( A Student  participate in Both sports and Drama) =0.07.

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The probability that a student participates in both sports and drama is [tex]0.14[/tex].

What is the formula for P(AUB), where A and B are any two events?

If [tex]A[/tex] and [tex]B[/tex] are any two events, then the probability of the joint event [tex](A\cup B)[/tex] is given by the following formula: [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Given that 42% of the students participate in sports and 25% of the students participate in drama and 53% of the students participate in either sports or drama.

Suppose [tex]S[/tex] denotes that "a student participates in sports" and [tex]D[/tex] denotes that "a student participates in drama".
So, we have [tex]P(S)=\frac{42}{100}=0.42[/tex], [tex]P(D)=\frac{25}{100}=0.25[/tex], [tex]P(S\cup D)=\frac{53}{100}=0.53[/tex].

We want to find the probability that a student participates in both sports and drama i.e., we want to find [tex]P(S\cap D)[/tex].

By the above formula, we obtain:

[tex]P(S\cup D)=P(S)+P(D)-P(S\cap D)\\\Longrightarrow P(S\cap D)=P(S)+P(D)-P(S\cup D)\\\Longrightarrow P(S\cap D)=0.42+0.25-0.53\\\therefore P(S\cap D)=0.14=\frac{14}{100}[/tex]

Therefore, the probability that a student participates in both sports and drama is [tex]0.14[/tex].

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imageGiven: a = 2, b = 3, and c = 4. What is m measured angle C degree to the nearest tenth?

Answers

Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.

What is the measured angle C?

From the law of cosines;

cosC = ( a² + b² - c² ) / 2ab

Where C is the angle C and a, b, and c are the three sides of the triangle.

Given the data in the question;

Side a = 2Side b = 3Side c = 4Angle C = ?

Using law of cosine;

cosC = ( a² + b² - c² ) / 2ab

We substitute the values into the equation.

cosC = ( 2² + 3² - 4² ) / ( 2 × 2 × 3 )

cosC = ( 4 + 9 - 16 ) / ( 12 )

cosC = -3 / 12

cosC = -0.25

We find the inverse of cosine.

C = cos⁻¹( -0.25 )

C = 104.477°

C = 104.5°

Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.

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(1 point) Find y as a function of x if
y" - 12y" + 32y' = 0,
y(0) = 5, y'(0) = 2, y" (0) = 1.
0
y(x) =

Answers

y’’(x)= 6x + 1
y’(x)= 3x^2 + x + 2
y(x)= x^3 + 1/2x^2 + 2x + 5

b) The diameter of a circular coin is 1.14 cm. How many coins of the same size are required to place in a straight row to cover 2.85 m length (without leaving any gap between each coin)​

Answers

Answer:

250.

Step-by-step explanation:

if one coin covers 1.14 cm, then the required number can be calculated according the equality:

required_number=(given_length/given_diameter);

Then:

[tex]number=\frac{2.85*100}{1.14} =\frac{285}{1.14} =250[coins].[/tex]

P.S. note, the given length is in [meter], the diameter is in [cm].

Write 80.54 as a mixed number.

Answers

Answer:

Step-by-step explanation:

[tex]80.54=80+0.54=80+\frac{54}{100} =80+\frac{27}{50} =80\frac{27}{50}[/tex]

express 350 as a product of prime factors​

Answers

Answer:

2^1 × 5^2 × 7^1 = 350

Step-by-step explanation:

2, 5, 7 are prime

first step is to divide the number 350 with the prime factor 2

continue dividing the number 175 by the next smallest prime factor

stop until you can't divide anymore

https://www.cuemath.com/numbers/factors-of-350/

Any helppppppp??????

Answers

First find volume of both the cylinders:

Cylinder Volume Formula: πr²h

(r => radius, h => height)

*Container A:

r = 8

h = 15

πr²h = π(8)²(15) = 960π³

*Container B:

r = 11

h = 13

πr²h = π(11)²(13) = 1573π³

What % of container B is empty after the pumping is complete?

The water pumped from A to B, and we want to know remaining that is empty: A < B: 1573π³- 960π³ = 613π³. Now to find %:

[tex]\frac{613\pi^{3} }{1573\pi ^{3}} * 100 = 0.39 * 100 =[/tex] 39% or 40% (Nearest Tenth)

Hope it helps!

Neil emptied his change jar and noticed he only had pennies, nickels, and quarters. He had coins for a total of . He had fewer quarters than nickels. How many pennies did Neil have? The solution is

Answers

Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies

What is an equation?

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

In his piggy bank, Neil has three times as many dimes as nickels and he has four more quarters than nickels. The coins total are 4.60. How many of each coin does he have.

Let x represent dimes (0.1), y represent nickels (0.5) and z represent quarter (0.25)

Hence:

0.1x + 0.05y + 0.25z = 4.6   (1)

Also:

x = 3y   (2)

And:

z = y + 4  (3)

From the equations:

x = 18, y = 6, z = 10

Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies

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ill give you brainliest :)

Answers

Following the instructions for the inequalities gives the following results:

1. 4<7, both sides multiplied by 7

= 28<49, both sides multiplied by 6

= 168<294, both sides multiplied by 3

= 504<882, both sides multiplied by 10

= 5,040<8,820

2. 11>2, add 5 to both sides

= 16>3, add 3 to both sides

= 19>9, add -4

= 15>5

3. -4<-2, subtract 6

= -10<-8, subtract 8

= -18<-16, subtract 2

= -20<-18

4. -8<8, divide by -4

= 2>-2, divide by -2

= -1<1

5. The inequalities remain correct at the end because the same mathematical operations are performed on both sides simultaneously.

What are inequalities?

Inequality is a relationship of a non-equal comparison between two numbers or algebraic expressions.

Inequality can be represented as greater than, greater than or equal to, less than, or less than or equal to.

Thus, the rules for inequalities show that if one adds to, subtracts from, multiplies by, or divides by the same number on both sides of an inequality, the inequality remains true.

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URGENT!!!!!!

Use arrow notation to describe the translation of point P(–5, –4) to point P′(–8, –7).

Answers

The rule of the translation of point P(–5, –4) to point P′(–8, –7) is:

(x,y) -> (x - 3, y - 3).

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, from point P to point P', 3 was subtracted from both the x-coordinate and the y-coordinate, hence the rule is given by:

(x,y) -> (x - 3, y - 3).

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4. Simple Interest: An investment earned 4% simple interest for 8 years. At its maturity, it was worth $5000. What amount was invested? (3​

Answers

Answer:

To solve the problem we have to take 4 percent of 5000 and multiply it by 8 years and the final result is 1600 dollars, which would be the final result.

2х+чу=4 and x + 2y = 3

Answers

Since the values on both sides are equal, hence the system of equation given has no solution

Solving simultaneous equations

Simultaneous equations are equations that consists of two or more equation and unknowns.

Given the equation below

2х+4у=4

x + 2y = 3

From equation 2;

x = 3 - 2y

Substitute into equation 1

2(3-2y) + 4y = 4

Expand

6 - 4y + 4y = 4

6 = 4

Since the values on both sides are equal, hence the system of equation given has no solution

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​Can u guys please give me the correct answe​​

Answers

Answer:

90°

(the figure is poorly drawn)

Step-by-step explanation:

the sum of the interior angles in a triangle is 180°120 ° and y are in a straight line, so 120° + y = 180 °

find y

180 - 120 = 60°

find x

180 - 60 - 30 = 90°

ALOT KF POINTS PLEASE HELP The measures of two exterior angles are given in the figure below.
Choose an equation that could be used to represent one of the exterior
angles and a logical conjecture about the exterior angles of a triangle.

Answers

An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

What is a triangle?

The term triangle refers to a figure that has three sides. There are several types of triangles such as the;

Isosceles triangleScalene triangleRight angled triangle

Despite all these types of triangle, the basic geometric properties of triangles can be applied to all types of triangle that we have mentioned above.

Considering the question, an equation that could be used to represent one of the exterior angles and a logical conjecture about the exterior angles of a triangle is that; m<4 = m<1 + m<2. An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

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A data set has a mean of x = 75 and a standard deviation of 11.4. Find the z-score for each of the following.

Answers

Part (a)

[tex]z=\frac{85-75}{11.4} \approx \boxed{0.88}[/tex]

By similar logic, the answers to the other parts are

(b) 1.75

(c) -2.19

(d) 0

According to indical equation solve 3×=1\81

Answers

Answer:

x = - 4

Step-by-step explanation:

using the rule of indices

[tex]\frac{1}{a^{n} }[/tex] = [tex]a^{-n}[/tex] , then

[tex]3^{x}[/tex] = [tex]\frac{1}{81}[/tex] = [tex]\frac{1}{3^{4} }[/tex] = [tex]3^{-4}[/tex] , that is

[tex]3^{x}[/tex] = [tex]3^{-4}[/tex] , thus

x = - 4

The question is attached

Answers

Answer:

We call the denominator rational.

Step-by-step explanation:

For example:

[tex]\frac{1}{\sqrt{2}} = \frac{\sqrt2}{\sqrt2 \cdot \sqrt2} = \frac{\sqrt2}{2}[/tex]

It's clear that the denominator is now a rational number, not an irrational one anymore.

flying against the jet stream, a jet travels 3000 in 3 hours. Flying with the jet-stream, the same jet travels 5360 miles in 4 hours. What is the rate of the jet in still air and what is the rate of the jet stream?

Answers

Based on the time taken by the jet when flying with the wind versus against it, the rate of the jet and jet streams are:

In still air = 1,170 mphRate of wind = 170 mph

What is the speed of the jet?

The speed of the jet flying against the wind is:

= 3,000 / 3

= 1,000 mph

The speed with the jet stream is:

= 5,360 / 4

= 1,340 mph

Assuming the speed of the jet is x and the rate of wind is y, the formulas are:

x - y = 1,000

x + y = 1,340

Solving gives:

2x = 2,340

x = 1,170 mph

The rate of jet stream is:

x - y = 1,000

1,170 - y = 1,000

y = 170 mph

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GEOMETRY
Surface area of a cube or a rectangular prism
There is a rectangular prism with a length of 8 yd, a width of 6 yd, and a height of 5 yd.
Find the surface area of this rectangular prism.
Be sure to include the correct unit in your answer.

Answers

SA = 2(LW + WH + LH)
SA = 2[8(6) + 6(5) + 8(5)]
SA = 2(48 + 30 + 40)
SA = 2(118)
SA = 236 square yards

The function y = x2 + 3 is a transformation of the function y = x2. How is the y-intercept of the function affected by the transformation?

The y-intercept of the graph of y = x2 is shifted down 3 units.
The y-intercept of the graph of y = x2 is shifted to the left 3 units.
The y-intercept of the graph of y = x2 is shifted to the right 3 units.
The y-intercept of the graph of y = x2 is shifted up 3 units.
-----------------------------------------------------------------------------------------------

Answer on Edmentum is:

The y-intercept of the graph of y = x2 is shifted up 3 units.

Explanation:
The graph of a function in the form y = f(x) + k is the graph of f shifted up k units. The graph of y = x2 + 3 is the graph of y = x2 shifted 3 units up, so the y-intercept of the graph of y = x2 is shifted up 3 units.

Answers

The y-intercept of the graph of y = x2 is shifted up 3 units.

Exponential equation

The standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.

Translation of coordinates

Translations is a transformation technique that changes the position of an object from one point on the plane to another.

Given the parent function f(x) = x^2

If the function is shifted 3 units up, the function g(x) is derived by adding 3 to the function f(x). The resulting function is given as;

g(x) = f(x) + 3

g(x) = x^2 + 3

Hence the equation of the new graph g(x) is expressed as g(x) = x^2 + 3

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material that may be provided.PassageStructures in the inner ear called the "labyrinths" regulate posture by sending signals to the brain indicatingour position in space from moment to moment. When the labyrinths are not functioning properly, because ofa virus (viral labyrinthitis) or other infection, or because their blood supply is reduced by arteriosclerosis ofthe arteries feeding them, the result is dizziness or vertigo. Such an attack is often so sudden and severethat the victim may not even be able to raise his or her head off a pillow. The viral variety usually follows acold and clears up in a few days.QuestionThe primary purpose of the passage is toO explain the structure of labyrinthsO present some effects of viruses on the functioning of the arteriesO distinguish between viral infections and arteriosclerosisO describe what happens when labyrinths do not function as they should A man is said to have one personality trait that dominates his personality. allport would identify this personality trait as a ________ trait. The ____________ collect bile produced in the hepatic lobules and deliver it to the hepatic ducts on their way to the ____________ for storage NO LINKS!! Please help me with this problem b)______ is the number of times a particular value occurs in a given data ________ is dissolved in water to make the solution sold commercially as rubbing alcohol. If your body composition is close to the recommended range, you should probably set a(n) ________ goal What view of human nature claims thta all humans have a relational spiritual self thta is distinct rom the material body has a purpose inderus=res over time and exists? When utilizing the capital asset pricing model approach to value equity, the outcome:_________ The maximum allowable spacing between horizontal wireway supports is___________. What is the molarity of a solution in which 55. 49 g of calcium chloride is dissolved in enough water to make 500. ml of solution? (4 + 8 2) 5 1? . Fireside Poet James Russell Lowell wrote a poem titled "The First Snowfall" a year after one of his young daughters died. Click the Read Me button below to read an excerpt from the poem.Discuss the themes that the poem does and does not have in common with most other American Romantic poems, such as "The Chambered Nautilus" and "The Trailing Arbutus. how many lengths of strings measuring 0.8meters long can be cut from a piece of string measuring 0.5kilometers please help asapRead the text and answer the question:The Human Genome ProjectHow much of who we are is determined by our genes? How similar are the genes of people living in different parts of the world? Which diseases are genetic? The findings of the Human Genome Project, begun in 1990, will help answer these questions and many others. To find the answers, scientists collected blood, hair, skin cell, and saliva samples of people from all over the world. They then retrieved the deoxyribonucleic acid (DNA) from these samples, which is found in the body's 46 chromosomes. Scientists involved in the project have already finished mapping, or "sequencing," DNA molecules, showing the location of genes. Now that the sequencing is finished, researchers have begun the long process of analyzing the results to find out how these genes function. To scientists, this analysis is like Europe's discovery of the New World.Scientists' findings so far are both surprising and promising. One of the unexpected findings is that it turns out people have far fewer genes than scientists thought. Before the project, the scientific world had assumed that there were 100,000 genes in the human body responsible for not only physical characteristics like hair and eye color but also certain behaviors and aptitudes. However, there are in fact only 34,000 genes. This means that there is more at work than just genes in determining why one person commits a crime and another is good at music or sports.Another interesting finding is that although groups of people around the world may look different, they are actually very similar genetically. For instance, there is only a very small number of genes accountable for the difference in skin color.Some of the most hopeful research coming out of the project relates to the study of disease. When the project first began, the medical world knew of about 100 human disease genes. Because of the project, scientists have identified more than 1400 disease genes so far for such conditions as diabetes, Alzheimer's, and certain forms of colon and breast cancer. By studying how these genes work, medical researchers can try to improve treatments. This could include developing more effective medicines as well as manipulating the genes themselves to cure or even prevent illness. Since scientists have already mapped the genomes of other organisms, including the mouse, rat, and fruit fly, they can now compare these to the human genome to learn how different organisms evolve, react to disease, and respond to environmental pollutants.This question has two parts. First, answer part A. Then, answer part B.Part A: Select the statement that best describes how the author's point of view develops over the course of the text.1.The author starts out the text by championing the Human Genome Project, but by the end of the text, the author seems confused by the entire idea of the project.2.The author starts out the text with a skeptical view of the Human Genome Project but slowly builds a stronger positive opinion of it as the text progresses.3.The author starts out the text by championing the Human Genome Project and then carefully supports his reasoning for why the project is worthwhile for humans.4.The author starts out the text with a disapproving point of view and maintains it throughout the text as he points out how much controversy the project is raising in the scientific community.Part B: Which detail from the text best supports your answer for part A?1.The findings of the Human Genome Project, begun in 1990, will help answer these questions and many others. To find the answers, scientists collected blood, hair, skin cell, and saliva samples of people from all over the world.2.Now that the sequencing is finished, researchers have begun the long process of analyzing the results to find out how these genes function. To scientists, this analysis is like Europe's discovery of the New World.3.When the project first began, the medical world knew of about 100 human disease genes. Because of the project, scientists have identified more than 1400 disease genes...4.By studying how these genes work, medical researchers can try to improve treatments. This could include developing more effective medicines as well as manipulating the genes themselves to cure or even prevent illness. Neurons in the hypothalamus regulate the activity of secretory cells in the anterior pituitary gland by:________ The Byzantine Empire produced Christian art that was highly abstracted, partially due to what reason? 1. a strong influence from Iberian Peninsula sculpture 2. a rejection of Greek proportions as outlined in the Canon by Polykleitos 3. a growing support of iconoclasm Find dy/dx when r=2 2cos(theta) , then find slope of tengent line at point(4, 2pi) What systematic problem-solving method guarantees a solution, provided that one exists? heuristic method an algorithm mnemonic device cognitive shortcut chunking method A -4.00 nC point charge is at the origin, and a second -6.00 nC point charge is on the x-axis at x = 0.800 m. Find the net electric force that the two charges would exert on an electron placed at point on the x -axis at x = 0.200 m'