The value of 994 to the power 1/3 is 9.97.
The binomial theorem involves the method of expanding an expression which is raised to a finite power. A binomial theorem has its application in probability, algebra, etc.
A binomial expression is said to have two dissimilar terms.
The total number of terms in (x + y)ⁿ are n+1.
The expansion of (1 + x)ⁿ can be written as,
(1 + x)ⁿ = 1 + nx + [n*(n-1)]/2! x² + [n*(n-1)*(n-2)]/3! x³ + ....
Let us find the value of 994 to the power 1/3,
⇒ (993 + 1)¹/³
⇒ 1 + 993/3 + 993* 993* [1/3* (-2/3)]/2! + 993* 993* 993* [1/3* (-2/3)* (-5/3)]/3! + ...
⇒ 1 + 331 - 54780.5 + 60441151.67 - ...
⇒ 9.97
Thus, the required value is 9.97.
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please help me im struggling in math
Corresponding angles theorem states that parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
To prove m∠ = m∠2.
Then,
m∠3 + m∠2 = 180m∠1 + m∠3 = 180m∠1 = m∠2How to prove corresponding angles?The corresponding angles theorem states that If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
Corresponding angles are formed when a transversal passes through two lines.
As we know that line segment m is parallel to the line segment n.
m || n .
Hence,
m∠3 + m∠2 = 180 (same interior angles)
Same side interior angles are two angles that are on the same side of the transversal and on the interior of (between) the two lines.
Same side interior angles are supplementary.
m∠1 + m∠3 = 180(sum of angles on a straight line)
Angles on a straight line is supplementary.
So, by transitive property of equality, we get:
m∠ = m∠2
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(Laws of Exponents with Integer Exponents LC)
Create an equivalent expression for 17−7 • 175.
one over seventeen raised to the second power
one over seventeen raised to the power of negative two
172
−172
One over seventeen raised to the second power is (1/17)².One over seventeen raised to the power of negative two is (1/17)⁻².
Define power and exponents.In mathematics, a base number raised to an exponent is referred to as a power. The base number is the factor that is multiplied by itself, and the exponent indicates how many times the base number has been multiplied. Let's learn more about power and exponent. A power is a phrase that depicts the same component being multiplied repeatedly. For instance, in the number 52, the base is the number 5, and the exponent is the number 2. The base is multiplied by the exponent, which is 2, to get the total number of factors.
Given,
one over seventeen raised to the second power
(1/17)²
one over seventeen raised to the power of negative two
(1/17)⁻²
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60% of all the students passed an exam. if a random sample of 10 students is selected, what is the mean and standard deviation ? write every rule you are going to use.
If a random sample of 10 students is selected from 60% passed students,with mean 6 and standard deviation 1.5492.
The mean and standard deviation of a random sample of 10 students can be calculated in order to determine the probability that a given student has passed an exam. This requires knowledge of some basic principles of statistics and probability.
Probability , p = 0.6 (60%=60/100)
Number of trial,n = 10(selected)
Mean = number of trial ✕ probability
= 10 ✕ 0.6
= 6.0
Mean is 6.0
Standard deviation :
σ = np(1-p)
= 10 ✕ 0.6 ✕(1- 0.6 )
= 2.4
Standard deviation = 1.5492
If a random sample of 10 students is selected from 60% passed students,with mean 6 and standard deviation 1.5492.
Rules of Probability : The first rule of probability used in this essay is the definition of a random sample. A random sample is a set of data taken from a larger population that is chosen by a method that gives each element of the population an equal chance.
The mean and standard deviation of a random sample of 10 students can be calculated in order to determine the probability that a given student has passed an exam. This requires knowledge of some basic principles of statistics and probability.
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What do you mean by 3 more than 7?
The statement 3 more than 7 means, a number is 3 more than a given number. Since here the number is 7 so the required number will be 7+3= 10
In numerical more than simply refers to adding and less than refers to subtracting. If it is given that a number let's say Z is Y more than X then the value will be Z= X+Y
If a given number let's say Z is Y less than X then the value of Z will be
Z=X-Y
More than means add which gives us a bigger value. Less than means subtract which gives us a smaller value
So, 3 more than 7 means 7+3 = 10
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Drag each tile to the correct box.
Arrange the rooms in increasing order of their areas.
bedroom
hallway
drawing
room
kitchen
TV room
The arrangement of the rooms in increasing order of their areas:
Drawing Room = 72m²
Balcony = 87.5 m²
T.V Room = 156m²
Hallway = 216m²
Bedroom = 225m²
Kitchen = 250m²
What is the area of a shape called?
The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area. Draw a square on a piece of paper with a pencil. It is a two-dimensional figure. The area of the shape on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.
We have,
kitchen:
40 feet × 10 feet
bedroom
15 feet × 15 feet
hallway
15 feet
TV room
12 feet × 13 feet
balcony:
5 feet × 12 feet × 12 feet
drawing room:
8 feet × 13 feet
Areas of the various spaces in the house:
Drawing Room = 72m²
Balcony = 87.5 m²
T.V Room = 156m²
Hallway = 216m²
Bedroom = 225m²
Kitchen = 250m²
Hence, the arrangement of the rooms in increasing order of their areas:
Drawing Room = 72m²
Balcony = 87.5 m²
T.V Room = 156m²
Hallway = 216m²
Bedroom = 225m²
Kitchen = 250m²
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the names of 5 students from section a, 6 students from section b and 7 students from section c were selected. the age of all the 18 students was different. again, one name was selected from them and it was found that it was of section b. what was the probability that it was the youngest student of the section b?
The probability that the selected student was the youngest student from Section B is 2/6.
The total number of students is 18 which include
Section A: 5 students
Section B: 6 students
Section C: 7 students
Given that the selected student was from Section B
Calculate the probability of selecting a student from Section B
P(Section B) = 6/18 = 1/3
Calculate the probability of selecting the youngest student from Section B
Since there are 6 students in Section B, the probability of selecting the youngest student is 1/6.
Calculate the probability of selecting the youngest student from Section B given that the selected student was from Section B
P(Youngest student from Section B|Section B) = P(Youngest student from Section B ∩ Section B) / P(Section B)
= (1/6) / (1/3)
= 2/6
Therefore, the probability that the selected student was the youngest student from Section B is 2/6.
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What is the SAS theorem?
The side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.
What is the congruence of triangles?If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.
Slide, twist, flip, and turn these triangles to create an identical appearance.
They are in alignment with one another when moved.
The first such theorem is the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are equivalent to two sides and an included angle of another triangle.
Therefore, the side-angle-side (SAS) theorem, which states that two sides and an included angle of one triangle are congruent if they are comparable to two sides and an included angle of another triangle, is the first of these theorems.
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Pregunta 2
La recta L3 pasa por la intersección de las rectas L₁ : 2x + 3y - 8 = 0 y L2: 2x 9y+4= 0 y por el
punto (1; 2). Determinar la ecuación de L3.
-
The linear function for Line L3 is given as follows:
y = -2/3x + 8/3.
How to define the linear function?The lines L1 and L2 are given as follows:
L1: y = -2/3x + 8/3.L2: y = -2/9x - 4/9.The x-coordinate of intersection is obtained as follows:
-2/3x + 8/3 = -2/9x - 4/9.
Multiplying everything by 9, the expression is given as follows:
-6x + 24 = -2x - 4.
4x = 28
x = 7.
The y-coordinate is given as follows:
y = -2/3(7) + 8/3 = -2.
Then the points on line L3 are given as follows:
(7,-2) and (1,2).
Given two points, the slope is calculated by the division of the change in y by the change in x, hence:
m = (-2 - 2)/(7 - 1)
m = -2/3.
Then:
y = -2/3x + b
When x = 1, y = 2, then the intercept b is calculated as follows:
2 = -2/3 + b
b = 2 + 2/3
b = 8/3.
Thus:
y = -2/3x + 8/3.
What is the translation?The problem asks for the definition of the line L3, which passes through the intersection of the linear L1 and L2 and through point (1,2).
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Mikaela is completing in a race in which she both runs and rides a bicycle. She runs 5 kilometers in 0.5 hour and rides her bicycle 20 kilometers in 0. 8 hour.
At the rate given, how many kilometers can Mikaela run in 1hour?
At the rate given, how many kilometers can Mikaela bike in 1 hour?
If Mikaela runs for 1 hour and bikes for 1 hour at the rates given, how far will she travel
Answer:
Mikaela run 10 km in 1hour
Mikaela bikes 25km in 1hour
35km If Mikaela runs for 1 hour and bikes for 1 hour at the rates given
Step-by-step explanation:
Let's solve how many km Mikaela runs in 1 hour.
0.5 hour = 30 minutes
5km = 30 minutes
10km = 60 minute
Let's solve how many km Mikaela bikes in 1 hour.
0.8 hour = 48 minutes
20km = 48 minutes
To get from 48 minutes to 60 minutes, we times 1.25. So, we take 20 times 1.25 = 25km
So, Mikaela bikes 25km in 1 hour.
Let's solve how far she traveled If Mikaela runs for 1 hour and bikes for 1 hour at the rates given
10km+ 25km = 35km
Gavin has a deck that measures 6 feet by
3 feet. He wants to increase each
dimension by equal lengths so that its
area is tripled. By how much should he
increase each dimension?
Answer:
feet
Each dimension should be increased by four times so that the area is tripled and each dimension is equal in length.
What is a quadratic equation?
Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
In mathematics, a dimension is the length or width of an area, region, or space in one direction.
area = length × width
a = l × w
But, we want to triple than area;
3A = 3 (l × w)
3A = (k × l) (k × w)
k² = 3
k = √3
The new dimensions will be: 6√3 and 3√3
Increased Dimension: 6√3 - 6 and 3√3 - 3
let x is the amount of increase in each side:
(x + 6) (x + 3) = 3(18)
x² + 3x + 6x + 18 = 54
x² + 9x + 18 = 54
x² + 9x - 36 = 0
∵ x = 4
Hence, each dimension should be increased by four times so that the area is tripled and each dimension is equal in length.
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Answer:3
Step-by-step explanation:
Which coordinates BEST represent the y-intercept of the line graphed below? (0, 2) (6, 0) (2, 0) (0, 6)
Solve for x.
5(x - 2) = -x + 2
/3
x = [?]
Answer:
x = 2
Step-by-step explanation:
[tex]\frac{5(x-2)}{3} = -x + 2[/tex]
expand left side:
[tex]\frac{5(x-2)}{3} = -x + 2\\\\\frac{5x-10}{3} = -x + 2[/tex]
multiply both sides by 3:
[tex]3(\frac{5x-10}{3}) = 3(-x + 2)\\\\ =5x - 10 = -3x + 6[/tex]
Add 3x to both sides:
5x - 10 + 3x = -3x + 6 + 3x
8x - 10 = 6
add 10 to both sides:
8x - 10 + 10 = 6 + 10
8x = 16
divide both sides by 8:
8x/8 = 16/8
x = 2
need your help please
Answer:
Hi ! the answer is .38!
Step-by-step explanation:
What are the 3 types of numbers in the real number system?
Three types of numbers fall under the heading of "real numbers," which we will discuss in a moment. Real numbers include all types of numbers, including whole, rational, and irrational numbers.
What is Real number?A real number is a quantity that may be represented mathematically by an endless decimal expansion. In contrast to the counting-derived natural numbers 1, 2, 3,..., real numbers are used to quantify constantly altering quantities such as size and time. Rational and irrational numbers are both included in real numbers. Real numbers include both irrational and rational numbers such as 3, 22/7, and integers such as (-2, 0, 1), fractions such as (1/2), and decimal numbers such as (1/2).
whole = 0,1,2,3,4,5,6,7,8,9,10,11........….
rational = 12/23,3,3/4,5/6,...…
irrational = [tex]\sqrt{8}[/tex], [tex]\sqrt{-56}[/tex]etc
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question 8 true/false: outliers should always be removed from the data set prior to final analysis. 1 point false; we only remove outliers if we have very good justification that suggests that removing the outlier is appropriate. true; outliers distort model fit and must be removed to assure reliable results. false; we only remove outliers after checking to make sure doing so drastically improves model fit.
False; we only remove outliers if we have a very good justification that suggests that removing the outlier is appropriate.
You should discard the outlier if it is clear that it resulted from inaccurately measured or recorded data. You may discard the outlier if it has no effect on the results but has an impact on the assumptions. Outliers might occasionally point to a data-gathering error. However, there are situations when they might have an impact on data collection, making them crucial to keep in mind in order to fully comprehend the information. Eliminating outliers gives some of my variables a normal distribution and improves the effectiveness of modifications for the other variables. As a result, it would appear that eliminating outliers before transformation is the best course of action.
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How do you find the inverses?
To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.
Inverse function
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f^-1 or F^-1.
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8. Solve the Right Triangle.
The length of the perpendicular of the right-angle triangle will be 20.4 meters.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The hypotenuse is 30 m and the base is 22 m. Then the length of the perpendicular is given as,
30² = P² + 22²
900 = P² + 484
P² = 900 - 484
P² = 416
P = 20.4 m
The length of the perpendicular of the right-angle triangle will be 20.4 meters.
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How did slavery benefit the industrial revolution?
The provision of a necessary raw material for industrial production by industrial revolution benefitted for slavery.
what is industrial revolution?Agrarian and handicraft economies were replaced by industrial and machine production during the Industrial Revolution in modern history. These technical developments brought about new methods of working and living that dramatically altered civilization.
the provision of a necessary raw material for industrial production by industrial revolution benefitted for slavery.
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what correlation is obtained when the pearson correlation is computed for data that have been converted to ranks? group of answer choices the phi coefficient the spearman correlation it is still called a pearson correlation the point-biserial correlation
When data are transformed to ranks and the Pearson correlation is performed, the Spearman correlation is what is obtained as a correlation.
What is meant by correlation?A statistical measure known as correlation expresses how linearly connected two variables are (meaning they change together at a constant rate). It is a typical strategy for describing straightforward relationships without explicitly stating cause and effect. The degree of a linear link between two quantitative variables is measured by the term "correlation." The degree to which two or more variables change in relation to one another is indicated by the statistical concept of correlation. A statistical metric known as correlation, which is given as a number, describes the strength and direction of a relationship between two or more variables.Therefore, the correct answer is A)the Spearman correlation
The complete question is:
What correlation is obtained when the Pearson correlation is computed for data that have been converted to ranks?
a) the Spearman correlation
b) the point-biserial correlation
c) the phi coefficient
d) it is still called a Pearson correlation
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Discuss the difference between r and p. Choose the correct answers below. r represents the p represents the sample correlation coefficient thing critical value for the correlation coefficient. population correlation coefficient. Click to select your answer(s) 1 - 35 of 35 Type here to search o te Discuss the difference between r and p. Choose the correct answers below. r represents the p represents the critical value for the correlation coefficient. population correlation coefficient. sample correlation coefficient. Click to select your answers) 1.35 of 35
The difference between r and p. is that r represents the sample correlation coefficient while p represents the p-value
What is the sample correlation coefficient?Generally, r represents the sample correlation coefficient, which is a measure of the strength and direction of the linear relationship between two variables in a sample of data. It ranges from -1 to 1, where -1 represents a perfect negative correlation, 0 represents no correlation, and 1 represents a perfect positive correlation.
p represents the p-value, which is a measure of the statistical significance of the sample correlation coefficient. It represents the probability that the observed correlation occurred by chance, assuming that there is no true correlation in the population.
A p-value of less than 0.05 is often used as a threshold for determining statistical significance, meaning that the observed correlation is unlikely to have occurred by chance and is likely to reflect a true correlation in the population.
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Does someone mind helping me with this problem? Thank you!
Answer:
y = - [tex]\frac{1}{4}[/tex] x - 10
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 4x - 2 ← is in slope- intercept form
with slope m = 4
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{4}[/tex] , then
y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation
to find c substitute (4, - 11 ) into the partial equation
- 11 = - [tex]\frac{1}{4}[/tex] (4) + c = - 1 + c ( add 1 to both sides )
- 10 = c
y = - [tex]\frac{1}{4}[/tex] x + (- 10) , that is
y = - [tex]\frac{1}{4}[/tex] x - 10 ← equation of line
a researcher found that the number of days of school missed per semester by college students was normally distributed with a mean of 4.00 and standard deviation of 1.00. what conclusion can you draw from these data?
With the Application of normal distribution conclusion can be All students missed at least one day of school per semester
what is normal distribution?
The normal distribution is a type of probability function that describes the distribution of a variable's values. Since most of the observations cluster around the middle peak of the curve, it is symmetric. When values of the distribution are far from the mean, the probability for those values narrow off evenly in both directions.
solution:
mean - ( standard deviation ) = 4 - 1 = 3
All students missed at least one day of school per semester
Therefore, conclusion can be All students missed at least one day of school per semester
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what is the value of y if the slope of the line is 3 and two points on the line is (0,y) and (2,4)
The value of y is -2.
What is coordinate of point?
The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph. There are two coordinates in every point or ordered pair.
Given points are (0,y) and (2,4).
The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
The slope of the given line is (4 - y)/(2 - 0) = (4 - y)/2.
Again given that the slope of the line is 3.
Therefore,
(4 - y)/2 = 3
Multiply both sides by 2
4 - y = 6
Subtract 4 from both sides:
-y = 2
Multiply both sides by -1:
y = -2
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Find the volume of the solid below. Round your answer to the nearest tenth if necessary.
Width 13 m
Length 17 m
Hight 2m
What’s the volume
Answer: 442
Step-by-step explanation: volume is length x width x height
so plug it in to get 17 x 13 x 2 = 442
Which of the following lists all the roots of x^4 =x^3 +x^2 + x+2?
F {−1, 2}
H {−2, −1}
G {−1, 2, i, −i}
J {−2, −1, i, −i}
Answer:
G
Step-by-step explanation:
[tex]x^4-x^3-x^2-x-2=0 \\ \\ (x+1)(x^3+x-2x^2-2)=0 \\ \\ (x+1)(x(x^2+1)-2(x^2+1))=0 \\ \\ (x+1)(x-2)(x^2+1)=0 \\ \\ (x+1)(x-2)(x-i)(x+i)=0 \\ \\ x=-1, 2, i, -i[/tex]
How do you sum a column in Excel on a Mac?
To see the steps of sum a column in Excel on a Mac.
Now, According to the question:
1. Click the first empty cell below a column of numbers.
2. Do one of the following: Excel 2016 for Mac: : On the Home tab, click AutoSum. Excel for Mac 2011: On the Standard toolbar, click AutoSum. ...
3. Press RETURN .
How do you sum cells on a Mac?
Once the cells are selected, press the Command key and the = (equal sign) key at the same time. This will automatically sum the selected cells. If you want to sum a specific range of cells, you can do so by selecting the first cell in the range, pressing the Shift key, and then selecting the last cell in the range.
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What are the roots of the quadratic equation 2x² 5x 3?
The roots of the quadratic equation 2x^2 + 5x + 3 are the two values of x that make the equation equal to 0. These two values are x = -3 and x = -1/2.
The roots of a quadratic equation are the two values of x that make the equation equal to 0. To find the roots of the equation 2x^2 + 5x + 3, we need to set the equation equal to 0 and solve for x. We can do this by using the Quadratic Formula, which states that the two roots of a quadratic equation ax^2 + bx + c = 0 are x = [-b +/- sqrt(b^2 - 4ac)] / 2a. In this equation, a = 2, b = 5, and c = 3. We can plug these values into the formula to get x = [-5 +/- sqrt(25 - 24)] / 4. Simplifying this expression gives us x = -3 and x = -1/2, which are the two roots of the equation 2x^2 + 5x + 3.
x = [-5 +/- sqrt(25 - 24)] / 4
x = [-5 +/- sqrt(1)] / 4
x = [-5 +/- 1] / 4
x = -3 and x = -1/2
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What are the 10 expressions?
The 10 expressions in Math are:
1. Sum 2. Difference 3. Product 4. Quotient 5. Exponent 6. Root 7. Absolute Value 8. Factor 9. Power 10. FractionUnderstanding the Basics of Math Through the 10 ExpressionsMath is a subject that can be intimidating to many, but it is a fundamental part of life that is necessary to understand. It is important to have a basic grasp of different expressions in order to be successful in math. This essay will explore the ten expressions of math and provide insight into their importance.
The first expression is the sum. This is the answer you get when adding two or more numbers together. For example, if you have the numbers 5, 7, and 8, the sum would be 20. Sums can also be used to find the total amount of a group of objects.
The second expression is the difference. This is the answer you get when subtracting two or more numbers. For example, if you have the numbers 8 and 5, the difference would be 3. Differences can also be used to find the difference between two amounts.
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What are 3 odd consecutive numbers of 75?
The three consecutive odd numbers of the number 75 are:
77, 79 and 81
What are consecutive numbers?Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.
In our case we have a specific value and this is the number 75, if we want to know the consecutive numbers immediately we add +1, +2 and so on.
But as we only want the odd numbers we will add +2, +4 and +6, having as a result the following numbers:
75 + 2 = 7775 + 4 = 7975 + 6 = 81The consecutive and odd numbers will be 77, 79, 81.
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4x+3y=23 x-5y=0 substitution
The required solution of given equation is x = 5, y = 1.
What is substitution method to equation?The effective use of substitution relies upon two things: first, given a circumstance in which factors happen, a replacement is just a difference in factor; second, it is just successful if the difference in factor improves on the circumstance and, ideally, empowers one to take care of the worked on issue.
According to question:We have,
4x+3y=23---------()1
And
x-5y=0 ⇒ x = 5y
Put the value of x in equation(1)
4(5y) + 3y = 23
20y + 3y = 23
23y = 23
y = 1
Then x = 5y = 5(1) = 5
Thus, solution of equation x = 5, y = 1
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