Rounded to three decimal places, the value of the irrational number e is .A.3.142B.3.615C.2.718D.2.947
Answers
REQUIRED:
Round to 3 decimal placed the value of the irrational number e.
Step-by-step solution/explanation;
The letter e in mathematics is also known as the Eular's number and is a mathematical constant used in many calculations especially natural logarithms of numbers.
The value of the Eular's number is approximately;
[tex]e\approx2.71828182846...[/tex]It can continue till infinity, however approximations of this number is always used to avoid unnecessary complications.
Therefore, rounded to 3 decimal places, the value of e is now;
ANSWER:
[tex]e\approx2.718[/tex]Note that we take 3 digits aftre the decimal and then if the fourth digit after the decimal is 5 or greater than 5, we make it 1 and add that 1 to the third digit after the decimal. Otherwise we simply make it zero and cancel it along with all other digits after it.
The digit that follows 8 (third digit) is less than 5, therefore, we write it off along with all other digits after it, and we are left with the decimal point and then ...718.
Option C is the correct answer.
Related Questions
A store is having a sale on jelly beans and trail mix today. The table below shows the amount of each type of food (in pounds) and the total cost (in dollars) of two purchases today.
Let x be the cost (in dollars) for each pound of jelly beans.
Let y be the cost (in dollars) for each pound of trail mix.
please refer to the image
Answers
The required equation of the given data is 6x + 5y = 28 and 2x + 3y = 14. And the cost of each pound of jelly beans and trail mix is $1.75 and $3.5 respectively.
What is the equation?the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Let x be the cost (in dollars) for each pound of jelly beans.
Let y be the cost (in dollars) for each pound of trail mix.
According to the question,
6x + 5y = 28 - - - - (1)
2x + 3y = 14 - - - - (2)
Solving equations 1 and 2 by substitution method we get,
x = 7/4 = and y = 7/2
Thus, the required equation of the given data is 6x + 5y = 28 and 2x + 3y = 14. And the cost of each pound of jelly beans and trail mix is $1.75 and $3.5 respectively.
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Camera has Alyssa price of $768.95 before tax the sales tax rate is 8.25% final total find the total cost of the camera with sales tax included round your answer to the nearest cent as necessary
Answers
We know that the listed price of the camera is $768.95 and the tax rate is 8.25%.
To find the total cost we must use the next formula
[tex]\text{Total cost }=\text{listed price before tax+(listed price before tax }\cdot\text{rate tax)}[/tex]Now, we must replace the values in the formula using that 8.25% = 0.0825
[tex]\text{Total cost}=768.95+(768.95\cdot0.0825)[/tex]Simplifying,
[tex]\text{Total cost}=832.39[/tex]ANSWER:
$O32
The longest at an airport has the shape of a rectangle and an area of 2,181,600 this runaway is 180 feet wide how long is the runaway
Answers
The longest at an airport has the shape of a rectangle and an area of 2,181,600 this runaway is 180 feet wide how long is the runaway
Remember that
The area ofa rectangle is equal to
A=L*W
in this problem we have
A=2,181,600 ft2
W=180 ft
substitute given values
2,181,600=L*180
Solve for L
L=2,181,600/180
L=12,120 ftRewrite the equation in Ax+By=C form.Use integers for A, B, and C.y-4=-5(x+1)
Answers
The given equation is
[tex]y-4=5(x+1)[/tex]To write the equation in standard form, first, we have to use the distributive property.
[tex]y-4=5x+5[/tex]Now, we subtract 5x and 5 on both sides.
[tex]\begin{gathered} y-4-5x-5=5x+5-5x-5 \\ -5x+y-9=0 \end{gathered}[/tex]Now, we add 9 on each side
[tex]\begin{gathered} -5x+y-9+9=0+9 \\ -5x+y=9 \end{gathered}[/tex]Therefore, the standard form of the given equation is[tex]-5x+y=9[/tex]Where A = -5, B = 1, and C = 9.In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11. What is the probability that the mixture will test positive?
Answers
From the information available, the mixture will test negative if all 6 samples are negative.
The probability of each is independent of the other for all 6 samples.
The probability of a sample testing positive is 0.11. That means the probability of a sample testing negative would be
[tex]\begin{gathered} P\lbrack neg\rbrack=1-P\lbrack pos\rbrack \\ P\lbrack\text{neg\rbrack}=1-0.11 \\ P\lbrack\text{neg\rbrack}=0.89 \end{gathered}[/tex]However, for all 6 samples, the probability of having a negative result would be a product of probabilities, that is;
[tex]\begin{gathered} P\lbrack tests\text{ negative}\rbrack=0.89\times0.89\times0.89\times0.89\times0.89\times0.89 \\ P\lbrack\text{tests negative}\rbrack=0.89^6 \\ P\lbrack\text{tests negative\rbrack}=0.4969 \end{gathered}[/tex]Therefore if we have the probability of the mixture testing negative as
[tex]P_{\text{neg}}=0.4969[/tex]The probability of the mixture testing positive would be;
[tex]\begin{gathered} P_{\text{pos}}=1-P_{\text{neg}} \\ P_{\text{pos}}=1-0.4969 \\ P_{\text{pos}}=0.5031 \end{gathered}[/tex]ANSWER:
The probability that the mixture will test positive is 0.5031
Rounded to 2 decimal places,
[tex]P_{\text{pos}}=0.50[/tex]If the expression 1/ square root of x was placed in form x^a, then which of the following would be the value of a?
Answers
4) -1/2
1) Rewriting the expression:
[tex]\frac{1}{\sqrt[]{x}}[/tex]2) As a power we can write this way, considering that we can rewrite any radical as a power and that when we have a radical on the denominator we can rewrite it as a negative rational exponent. So we can write it out:
[tex]\frac{1}{\sqrt[]{x}}=\frac{1}{x^{\frac{1}{2}}}=x^{-\frac{1}{2}}[/tex]3) Hence, the answer is 4) -1/2
The Wong family and the Nguyen family each used their sprinklers last summer. The water output rate for the Wong familys sprinkler was 35 L per hour. The water output for the Nguyen familys sprinkler was 20 L per hour. The families used their spirit for a combined total of 75 hours, resulting in a total water output of 2100 L. How long was each sprinkler used?
Answers
Let W be the time of the wong family and N the time of the Nguyen family. We are told that the output rate of the Wong family is 35 L/h and the output for the Nguyen family is 20 L/h, if the total water output is 2100 L, then we can write this mathematically as:
[tex]35W+20N=2100,(1)[/tex]Where "35W" is the total water output of the wong family and "20N" is the total water output of the Nguyen family. The two outputs combined must be 2100. We are also told that the total time is 75 hours, therefore we have:
[tex]W+N=75,(2)[/tex]We get a system of two equations and two variables. We can solve for "W" in equation (2), by subtracting "N" from both sides:
[tex]W=75-N[/tex]Now we can replace this value in equation (1):
[tex]35(75-N)+20N=2100[/tex]Now we apply the distributive property:
[tex]2625-35N+20N=2100[/tex]Now we add like terms;
[tex]2625-15N=2100[/tex]Now we subtract 2625 from both sides:
[tex]\begin{gathered} -15N=2100-2625 \\ -15N=-525 \end{gathered}[/tex]Now we divide both sides by 15:
[tex]N=-\frac{525}{-15}=35[/tex]Now we replace this value in equation (2) where we already solved for W:
[tex]\begin{gathered} W=75-35 \\ W=40 \end{gathered}[/tex]Therefore, the time for the Wong family is 40 hours and the Nguyen family is 35 hours.
The diameter of a circle is 6 ft. Find its circumference in terms of \piπ.
Answers
The circumference of circle with diameter 6 feet will be 6π feet.
According to the question,
We have the following information:
Diameter of the circle = 6 feet
Now, we will find the radius of the circle. We know that the radius of the circle is half that of its diameter.
Radius of the circle = Diameter/2
Radius of the circle = 6/2 feet
Radius of the circle = 3 feet
We know that the following formula is used to find the circumference of the circle:
Circumference of the circle = 2πr
Circumference of the circle = 2π*3
Circumference of the circle = 6π feet
Hence, the circumference of the circle is 6π feet.
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a motorboat travels 456 km in 8 hours going upstream and 783 km in 9 hours going downstream. what is the rate of the boat in still water and what is the rate of current?
Answers
A middle school football game has four 12-minute quarters. Jason plays 8 minutes in each quarter.Which ratio represents Jason's playing time compared to the total number of minutes of playing time possible?1 to 3 2 to 33 to 24 to 1I’m
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The total minutes in the game is 48. The total playing game for Jason is 32. The ratio is
[tex]\frac{32}{48}[/tex]Simplifying it, we have
[tex]\frac{32}{48}=\frac{16}{24}=\frac{8}{12}=\frac{4}{6}=\frac{2}{3}[/tex]So, the playing ratio is 2 to 3 for Jason.
Write an equation of the line that passes through (4, 3) and is parallel to the line defined by 5x-2y-3. Write the answer in slope-intercept form (if possible)
and in standard form (Ax+By-C) with smallest integer coefficients. Use the "Cannot be written" button, if applicable.
Answers
The final answer to the question is highlighted in the box
shirts are 15% off. The original price of one shirt is $20. What is the total cost, in dollars, of a shirt, at the sales price, including a 10% sales tax?
Answers
The original price of the shirt is , 20 dollar.
It is given that the shirts are 15% off.
Therefore, the price of the shirt is ,
[tex]20-20\times\frac{15}{100}=17.[/tex]The price of the shirt is, 17 dollar after 15% off.
It is also given that there are 10% sales tax.
The total cost of the shirt is determined by including the sales tax in the price of the shirt after 15% off.
[tex]17+(17\times\frac{10}{100})=18.7[/tex]Thus, The total cost of shirt is calculated as, 18.7 dollar.
Assume the normal distribution of data has a mean of 14 and a standard Deviation of 3. use the 65-95-99.7 rule to find the percentage of values that lie below 8
Answers
By the 65-95-99.7 rule,
[tex]\begin{gathered} 65\text{ \% of the distribution lies below }\bar{x}+\sigma\text{ and above }\bar{x}-\sigma \\ 95\text{ \% of the distribution lies below }\bar{x}+2\sigma\text{ and above }\bar{x}-2\sigma \\ 99.7\text{ \% of the distribution lies below }\bar{x}+3\sigma\text{ and above }\bar{x}-3\sigma \end{gathered}[/tex]By symmetry,
[tex]\begin{gathered} 47.5\text{ \% of the distribution lies above }\bar{x}-\sigma\text{ and below }\bar{x} \\ \text{ Hence,} \\ 2.5\text{ \% of the values lies below }\bar{x}-\sigma \end{gathered}[/tex]In our case,
[tex]\bar{x}=14,\sigma=3[/tex]Therefore,
[tex]\begin{gathered} 8=14-6=14-2(3) \\ \text{Hence,'} \\ 8=\bar{x}-2\sigma \end{gathered}[/tex]Hence, 2.5 % of the values lie below 8
What is the diameter of a circle with radius 15
Answers
Given Data:
The radius of the circle is r=15.
The diameter of the circle can be determined as,
[tex]\begin{gathered} d=2r \\ =2\times15 \\ =30 \end{gathered}[/tex]Thus, the required diameter of a circle is 30.
Solve pls. I neeeeeeeeed your help.
Answers
Answer:
70 over 39
Step-by-step explanation:
here's the solution first multiple the numbers with the fraction then calculate after that simply the fractions and the answer is
[tex] \frac{70}{39} [/tex]
Determine the value of x Round results to an appropriate number of significant digits
Answers
Given
Find
The value of x.
Explanation
length of AB = 22 - 3 = 19
using the trignometric ratios , we have
[tex]\begin{gathered} \sin13\degree=\frac{BD}{AB} \\ \sin13\degree=\frac{\frac{x}{2}}{19} \\ \sin13\degree\times38=x \\ 8.548=x \end{gathered}[/tex]Final Answer
Therefore , the length of x is 8.548
solve the equation by completing the square. Show all solutions8x^2 + 16x = 42
Answers
8x² + 16x = 42
x² + 16/8x = 42/8 dividing by 8 at both sides
x² + 2x = 5.25
x² + 2x - 5.25 = 0
If we compute (x + 1)², we get:
(x + 1)² = x² + 2*x*1 + 1² = x² + 2x + 1
Then,
x² + 2x - 5.25 + 1 - 1 = 0
(x² + 2x + 1) + (-5.25 - 1) = 0
(x + 1)² - 6.25 = 0
(x + 1)² = 6.25
x + 1 = √6.25
This has 2 solutions,
x + 1 = 2.5 or x + 1 = -2.5
x = 2.5 - 1 x = -2.5 - 1
x = 1.5 x = -3.5
what is the area if one of the triangular side of the figure?
Answers
Compound Shape
The shape of the figure attached consists on four triangles and one square.
The base of each triangle is B=12 cm and the height is H=10 cm, thus the area is:
[tex]A_t=\frac{BH}{2}[/tex]Calculating:
[tex]A_t=\frac{12\cdot10}{2}=60[/tex]The area of each triangle is 60 square cm.
Now for the square of a side length of L=12.
The area of a square of side length a, is:
[tex]A_s=a^2[/tex]Calculate the area of the square:
[tex]A_s=12^2=144[/tex]The total surface area is:
A = 60*4 + 144
A= 240 + 144
A = 384 square cm
Find the quantities indicated in the picture (Type an integer or decimal rounded to the nearest TENTH as needed.)
Answers
Remember that 3, 4 and 5 is a Pythagorean triple, since:
[tex]3^2+4^2=5^2[/tex]Since one side of the given right triangle has a length of 3 and the hypotenuse has a length of 5, then, the remaining leg b must have a length of 4.
Therefore:
[tex]b=4[/tex]The angles A and B can be found using trigonometric identities.
Remember that the sine of an angle equals the quotient of the lengths of the side opposite to it and the hypotenuse of the right triangle.
The side opposite to A has a length of 3 and the length of the side opposite to B is 4. Then:
[tex]\begin{gathered} \sin (A)=\frac{3}{5} \\ \sin (B)=\frac{4}{5} \end{gathered}[/tex]Use the inverse sine function to find A and B:
[tex]\begin{gathered} \Rightarrow A=\sin ^{-1}(\frac{3}{5})=36.86989765\ldotsº \\ \Rightarrow B=\sin ^{-1}(\frac{4}{5})=53.13010235\ldotsº \end{gathered}[/tex]Then, to the nearest tenth:
[tex]\begin{gathered} A=36.9º \\ B=53.1º \end{gathered}[/tex]Therefore, the answers are:
[tex]undefined[/tex]If RT = 36, RS = 2x + 3 and ST = 7x + 6, find RSand ST.
Answers
We know that RT=36 and that RS=2x+3 and ST=7x+6. We notice that
[tex]RT=RS+ST[/tex]Then, plugging the corresponding values and expressions we have
[tex]36=(2x+3)+(7x+6)[/tex]Solving this equation for x,
[tex]\begin{gathered} 36=(2x+3)+(7x+6) \\ 36=2x+3+7x+6 \\ 36=9x+9 \\ 36-9=9x \\ 27=9x \\ x=\frac{27}{9} \\ x=3 \end{gathered}[/tex]Then te value of x is 3.
Once we have the value of x we are able to find the value of RS and ST, we just have to substitute said value in the expressions. Then
[tex]\begin{gathered} RS=2(3)+3=6+3=9 \\ ST=7(3)+6=21+6=27 \end{gathered}[/tex]Therefore RS=9 and ST=27.
i inserted a picture of the questions 19 and 20 that i need help with.
Answers
WE are given that 9 tickets have a total cost of $94.50. To determine the price for each ticket we must find the quotient between the total amount spent and the number of tickets, like this:
[tex]\frac{94.50}{9}[/tex]Solving the operations we get:
[tex]\frac{94.50}{9}=10.5[/tex]Therefore, each ticket has a price of $10.50
Find the restricted values of x for the following rational expression. If there are no restricted values of x, Indicate "No Restrictions".
−5r – 8/x² + 4
Answers
The restricted values of x for the following rational expression.
x = 0
x = -3/4
What are restriction value?Restricted values are those values in a rational expression that bring the denominator to zero. When referring to "Market Value," the term "restricted value" denotes the property's value under the assumption that it is subject to a temporary governmental or private limit on rentals and tenant income levels. The denominator's real numbers that have a value of 0 are not included in the domain. The word "restrictions" refers to these values. Similar to how fractions are simplified, rational expressions can be too. Cancel the common factors after factoring the numerator and denominator. Place a zero as the denominator. Put the equation to rest. The restricted values are the answer or answers.
Rational expressions should first be multiplied, and then the numerator and denominator should be factored. Next, common factors should be cancelled. Notify yourself of the domain's limitations.
−5x– 8/x² + 4 = 0
- 5x - 8/[tex]x^{2}[/tex] = -4
x = 0
x = -3/4
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Eight less than a number n is at least 10
Answers
Answer:
n - 8 ≥ 10
n ≥ 18
Step-by-step explanation:
Hello!
8 less than the number n can be represented as n - 8.
To be atleast 10, we can have values greater than 10 and equal to 10, but cannot be less than 10 . We can use the ≥ symbol to represent this.
The inequality would be n - 8 ≥ 10
Solving for n:n - 8 ≥ 10n ≥ 18n has to be greater than or equal to 18
after a translation 8 units left
Answers
The given transformation is 8 units left.
The pre-image vertices are A(1,-4), B(1,-6), C(5,-6), and D(5,-4).
Using the transformation, we have:
[tex]\begin{gathered} A^{\prime}(1-8,-4)=A^{\prime}(-7,-4) \\ B^{\prime}(1-8,-6)=B^{\prime}(-7,-6) \\ C^{\prime}(5-8,-6)=C^{\prime}(-3,-6) \\ D^{\prime}(5-8,-4)=D^{\prime}(-3,-4) \end{gathered}[/tex]The image below shows the graph of the image
Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of g and f.
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EXPLANATION
Since we have the function:
[tex]f(x)=(\frac{1}{3})^x[/tex]Graphing this an the transformation into a graph calculator we have:
We can see that the transformated function is translated 2 units to the right, and that It is also translated 4 units down.
Thus, the transformations are the following:
g(x) is the graph of f(x) translated 2 units to the right and 4 units down.
Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P,P, in terms of x,x, representing Madeline's total pay on a day on which she sells xx computers.
I need equation
Answers
The equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x.
Given, At an electronics store, Madeline sells computers as a salesperson. She receives a $80-per-day base salary in addition to a $20 commission for each computer she sells.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We can model the equation for Madeline's total pay as follows -
P = base pay + (number of sold computer) × (cost of 1 computer)
P = 80 + 20x
Therefore, the equation for 'P', representing Madeline's total pay on a day on which she sells 'x' computers is → P = 80 + 20x
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You are making a kite and need to figure out how much binding to buy. You need the binding for the perimeter of the kite. The binding comes
in packages of two yards. How many packages should you buy?
12 in.
15 in.
12 in.
20 in.
You should buy packages.
Answers
With the help of the Pythagorean theorem, we know that we should buy 3 packages.
What is the Pythagorean theorem?The Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.So, Pythagorean formula: c² = a² + b²
Each package contains 2 yards of binding.In the kite, there are right triangles, so use the Pythagorean theorem.(Refer to the image of the kite attached below)
△1:
a² + b² = c²15² + 12² = x₁²x₁ = √15² + 12²x₁ = 19.2 in△2:
x₂ = x₁ = 19.2 in
△3:
a² + b² = c²12² + 20² = x₃²x₃ = √12² + 20²x₁ = 23.3 in△4:
x₄ = x₃ = 23.3 inTotal: 19.2(2) + 15 + 2(12) + 20 + 2(23.3) = 144 in
Total (actual) > 144 inNow,
1 package = 2 yards = 6ft = 72 in2 yards × 3ft/1yrd × 12in/1ft = 72 in2 packages: 2(72) = 144 in3 packages: 3(72) > 144So, we should buy 3 packages.
Therefore, with the help of the Pythagorean theorem, we know that we should buy 3 packages.
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“John is buying carpet for his house. He pays $1.30 per square foot for the first 1000 square feet. He pays $1.00 peradditional square foot after 1000 square feet.Part A: Write an equation for the total price when John buys less than 1000 square feet of carpet. Let c representthe amount of carpet needed in square feet, and p represent the total price in dollars.Enter vour equation in the first response boxPart B: John calculates that the total price will be $1500. How many square feet of carpet will he buy?Place your answer in the second response box”
Answers
EXPLANATION:
Given:
We are told that John pays $1.30 per square foot for the first 1000 square feet of carpet he buys. Then he pays $1.00 per additional square foot after the first 1000 square feet.
Required:
We are required to write an equation to represent the total price when he buys less than 1000 square feet.
Step-by-step solution;
Take note that he pays $1.30 per square foot for the first 1000 square feet. The amount spent, that is the price would be represented by p while, c would represent the amount of carpet to be bought.
Hence, for buying less than 1000 square feet;
[tex]p=1.30c[/tex]Next we note that John calculates that the total price would be $1500.
If John pays the amount of $1.30 for the first 1000 square feet, then he would have paid;
[tex]p=1.30(1000)[/tex][tex]p=1300[/tex]However, we are told that John calculates a total of $1500. This simply means that he will buy more than 1000 square feet of carpet.
He is going to spend an extra $200 (that is 1500 minus 1300). The cost of any extra foot after the first 1000 is $1.00. That means;
[tex]Extra\text{ }carpet=\frac{200}{1.00}[/tex][tex]Extra\text{ }carpet=200ft^2[/tex]That means John would be paying the sum of $1500 to buy 1,200 square feet of carpet.
ANSWER:
[tex]\begin{gathered} Part\text{ }A: \\ p=1.30c \end{gathered}[/tex][tex]\begin{gathered} Part\text{ }B: \\ 1200ft^2 \end{gathered}[/tex]Find the measurement of each side indicated and round to the nearest tenth for both triangles
Answers
a) We have a right triangle.
We have to find the value of x, which is the hypotenuse.
We can relate the angle B, the side AC and x with a trigonometric ratio as:
[tex]\begin{gathered} \sin (B)=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{AC}{AB} \\ \sin (57\degree)=\frac{10.8}{x} \\ x=\frac{10.8}{\sin (57\degree)} \\ x\approx\frac{10.8}{0.83867} \\ x\approx12.9 \end{gathered}[/tex]b) In this case, x is the adyacent side to angle A.
We can relate the sides and the angle as:
[tex]\begin{gathered} \cos (A)=\frac{\text{Adyacent}}{\text{Hypotenuse}}=\frac{AC}{AB} \\ \cos (47\degree)=\frac{x}{3} \\ x=3\cdot\cos (47\degree) \\ x\approx3\cdot0.682 \\ x\approx2.0 \end{gathered}[/tex]Answer:
a) x = 12.9
b) x = 2.0
Find the equations (in terms of x) of the line through the points (-2,-3) and (3,-5)
Answers
The general equation of a line passing through two points (xb₁,y₁)Pxb₂,y₂) is expressed as
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{where} \\ m\Rightarrow slope\text{ of the line, expr}essed\text{ as }m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)\Rightarrow coordinate_{}\text{ of point P} \\ (x_2,y_2)\Rightarrow coordinate_{}\text{ of point Q} \end{gathered}[/tex]Given that the coordinates of the two points are (-2, -3) and (3, -5), we have
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(-2,\text{ -3)} \\ (x_2,y_2)\Rightarrow(3,\text{ -5)} \end{gathered}[/tex]Step 1:
Evaluate the slope o the line.
The slope is thus evaluated as
[tex]\begin{gathered} m\text{ = = }\frac{y_2-y_1}{x_2-x_1} \\ \text{ = }\frac{\text{-5-(-3)}}{3-(-2)} \\ =\frac{-5+3}{3+2} \\ \Rightarrow m\text{ = -}\frac{2}{5} \end{gathered}[/tex]Step 2:
Substitute the values of x₁,
Thus, we have
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ x_1=-2 \\ y_1=-3 \\ m\text{ =- }\frac{2}{5} \\ \text{thus,} \\ y-(-3)\text{ = -}\frac{2}{5}(x-(-2)) \\ y+3\text{ =- }\frac{2}{5}(x+2) \end{gathered}[/tex]Step 3:
Make .
[tex]\begin{gathered} y+3\text{ =- }\frac{2}{5}(x+2) \\ \text{Multiply both sides of the equation by 5 } \\ 5(y+3)\text{ = -2(x+2)} \\ \text{open brackets} \\ 5y\text{ + 15 =- 2x - 4} \\ \Rightarrow5y\text{ =- 2x - 4 -15} \\ 5y\text{ = -2x-1}9 \\ \text{divide both sides of the equation by the coefficient of y, which is 5.} \\ \text{thus,} \\ \frac{5y}{5}=\frac{-\text{2x-1}9}{5} \\ \Rightarrow y\text{ =- }\frac{2}{5}x\text{ - }\frac{19}{5} \end{gathered}[/tex]Hence, the equation of the line is
[tex]y\text{ = -}\frac{2}{5}x\text{ - }\frac{19}{5}[/tex]y₁ and m into the general equation of the line.
