The residual value of coordinate is 0.24.
what is residual?A residual is the discrepancy between a data point's actual value and the value predicted by a regression or trend line.
Trend lines provide the approximate shape of the data and display the general shape the data takes. The most precise trend lines are those that best suit the data.
Given equation y = 1.18x + 5.4
and coordinates (2, 8)
y at x = 2
y = 1.18x + 5.4
y = 1.18(2) + 5.4
y = 7.76
residual value = actual y axis value - predicted y axis value
residual value = 8 - 7.76 = 0.24
Hence the residual value is 0.24.
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Please help quickly
Nova wants to measure the height of a tree. She asks her brother Caden to stand so that the
tip of his shadow coincides with the tip of the tree’s shadow. She stands at the tip of Caden’s
shadow. Caden, who is 1.2 meters tall, is 4.2 meters from Nova and 6.5 meters from the tree.
The tree is ___ meters high. Round your answer to the nearest tenth and write it as a decimal.
Answer:
The tree is 9.1 meters high.
Step-by-step explanation:
We can use the Pythagorean Theorem to solve this problem. Let T be the height of the tree. We can set up the following equation:
4.2^2 + T^2 = 6.5^2
Solving for T, we get:
T = sqrt(6.5^2 - 4.2^2)
T = sqrt(41.25 - 17.64)
T = sqrt(23.61)
T = 4.878
Since the height of the tree is measured to the nearest tenth, we can round this value to 9.1 meters.
Does 9 12 15 make a right triangle?
The side lengths measuring 9 units , 12 units and 15 units make a Right Triangle because the sides satisfy the condition of the Pythagoras Theorem .
According to the Pythagoras Theorem , which states that square of the lonest side (hypotnuse) is equal to the sum of the square of the other two sides ( perpendicular and Base) ,
The side lengths of right triangle are = 9 units , 12 units and 15 units ,
According to the condition of Pythagoras theorem , [tex]15^{2} = 12^{2} + 9^{2}[/tex]
On simplifying ;
we get ;
[tex]225 = 144 + 81[/tex] ;
[tex]225 = 225 ;[/tex]
the condition is satisfied ,
that means the sides form a right triangle .
Therefore , the side 9 units , 12 units and 15 units make a right triangle .
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Find the Dy/Dx of y=7/x using first principle
By using first principle, the value of Dy/Dx is,
⇒ Dy/Dx = - 7 / x²
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ y = 7 / x
Now, Differentiate the function with respect to x, we get;
⇒ y = 7 / x
⇒ Dy/ Dx = D / Dx (7 / x)
= 7 D/Dx (1/x)
= 7 (- 1 × x⁻¹⁻¹ )
= 7 (- x⁻²)
= - 7 / x²
⇒ Dy/Dx = - 7 / x²
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which algebraic expression represents the following phrase "2.5 less than a number d and 4"
The algebraic expression is represented as 4d - 2.5
What is an algebraic expression?An algebraic expression is simply defined as an expression that is composed of coefficients, factors, constants, terms, and variables.
They are also composed of mathematical operations, such as;
AdditionSubtractionDivisionBracketMuitiplicationParentheses, etcFrom the information given, we have that;
The variable = d
The constant = 2.5
The coefficient = 4
This is represented as;
4d - 2.5
Hence, the expression is 4d - 2.5
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Factor the expression completely.
x^4-17x^2+72
Answer:
It's neither:
x =√ 9.000 = 3.00000 or :
x =√ 9.000 = -3.00000 or :
x =√ 8.000 = 2.82843 or :
x =√ 8.000 = -2.82843
Four solutions
Answer:
x^4 - 17x^2 + 72 = (x^2 - 9)(x^2 - 8)
Step-by-step explanation:
First, we need to find two numbers that multiply to give us 72 and whose sum is -17. We can see that 8 and 9 multiply to give us 72, and their sum is 8 + 9 = 17. Since we want the sum to be negative, we need to change one of the signs. So we write -(8 + 9) = -17.
Next, we write the expression as the product of two binomials. We factor out the common factor x^2 from the first two terms: x^4 - 17x^2 + 72 = x^2(x^2 - 17) + 72
Now, we complete the square in the first binomial. To do this, we need to add and subtract (17/2)^2 = (8.5)^2 = 72.25 inside the bracket:
x^2(x^2 - 17) + 72 = x^2(x^2 - 17 + 72.25 - 72.25) + 72 = x^2(x^2 - 17 + 72.25) - 72.25 + 72
Now we can rewrite the square of a binomial :
x^2(x^2 - 17 + 72.25) = x^2((x-8.5)^2)
Finally, we can combine the two binomials
x^2((x-8.5)^2) + 72 = (x^2(x-8.5)^2) + 8(9)
So the expression x^4 - 17x^2 + 72 factors completely as (x^2 - 9)(x^2 - 8)
Hope this helps!
The data below represents the number of desks on each floor of Texter Corporate.
\qquad54,60,65,66,67,69,70,72,73,75,7654,60,65,66,67,69,70,72,73,75,7654, comma, 60, comma, 65, comma, 66, comma, 67, comma, 69, comma, 70, comma, 72, comma, 73, comma, 75, comma, 76
Which box plot correctly summarizes the data?
A box plot that correctly summarizes the set of data is: box plot C.
What is a box-and-whisker plot?In Mathematics, a box plot sometimes also referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided above, the five-number summary for the given data set include the following:
Minimum = 54First quartile = 65.Median = 69.Third quartile = 73.Maximum = 76.In conclusion, we can logically deduce that the median of the given data set is 69 while the first quartile is 65 and the third quartile is equal to 73.
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2. 15 - |-4a|
It says evaluate the expression.
If a = 2
Answer:
7
Step-by-step explanation:
So first you substitute A in
15-|-4(2)|
Then you multiply first because of GEMDAS or PEMDAS
15-|-8|
And because absolute value means how far away it is from 0, -8 is 8 away from 0 , thus |-8| is 8. So we simplify the equation
15-8
=7
write an expression to describe a rule for the sequence. then find the 100th term in the sequence 5 13 21
The expression is 8n – 3; The 100th term is 797
How to calculate the 100th term in sequence?The nth term of an arithmetic sequence is given by:
an=a1+(100-1)d ....[1]
where
a1 is the first term
d is the common difference of two consecutive terms.
n is the number of terms.
Given the sequence:
5, 13, 21, 29, 37, 45, …
This is an arithmetic sequence with first term = 5 and common difference(d) = 8
Since;
13-5 = 8,
21-13 = 8,
29-21 = 8 and so on....
We have to find the 100th term in the sequence
Substitute in [1] we have;
an=a1+(100-1)d
an=5+(n-1)8=5+8n-8 = 8n-3
Substitute the given values and n=100 we have;
a100= 800 - 3 = 797
Therefore, the 100th term in the sequence is, 797 and an expression to describe a rule for the sequence is, 8n – 3;
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1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9
2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)
3. -2 \leq -2 Subtract 6 from both sides, then 8, and then 2
4. -4 < 8 Divide both sides by -4, then by -2
5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?
In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given few inequalities and some operations are performed on them
For first inequality:
=> 4 < 7
Multiply both sides by 3, then by 2, then by 4, then by 9
=> 4 *3 * 2 * 4 * 9 < 7 *3 * 2 * 4 * 9
=> 864 < 1512
there is no change in the inequality sign and it is still true.
For the second inequality:
=>11 > -2
Add 3 to both sides, then add 3, then add (-4)
=> 11 +3 + 3 + (-4) > -2 + 3+3 + (-4)
=> 13 > 0
there is no change in the inequality sign and it is still true.
For the third inequality:
=> -2 ≤ -2
Subtract 6 from both sides, then 8, and then 2
=> -2 -6 -8 -2 ≤ -2 -6 -8 -2
=> -18 ≤ -18
there is no change in the inequality sign and it is still true.
For the fourth inequality:
=> -4 < 8
Divide both sides by -4
=> -4 / -4 < 8 / -4
Since, after dividing or multiplying on both sides by a negative sign, inequality changes its sign
=> 1 > -2
Divide both sides by -2
=> -1/2 < 1
there are two times a change in the inequality sign and it is still true.
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His coordinate grid shows where Alberto's school is located. Each unit represents one block. Alberto's house is at (3, 4). The library is located at the reflection of (3, 4) across the y-axis. Use absolute value to find the distances from Alberto's house to the school and from Alberto's house to the library
The distance from Alberto's house to the school is 4 units and from Alberto's house to the library is 6 units
Consider the following diagram.
From given coordinate grid we can observe that Alberto's school is located at point (-1, 4)
Alberto's house is at (3, 4).
And the library is located at the reflection of (3, 4) across the y-axis.
This means, the libarary is located at point (-3, 4)
We know that the absolute value is nothing but the distance between a number and zero on a number line.
The distance from Alberto's house to the school would be,
= distance between points (3, 4) and (-1, 4)
= |3 - (-1)|
= |3 + 1|
= |4|
= 4 units
And the distance between Alberto's house to the library would be,
= distance between points (3, 4) and (-3, 4)
= |3 - (-3)|
= |3 + 3|
= |6|
= 6 units
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The complete question is:
This coordinate grid shows where Alberto’s school is located. Each unit represents one block. Alberto's house is at (3, 4). The library is located at the reflection of (3, 4) across the y-axis. What are the coordinates of the library?
5 multiply by c 24-47-48 divide 24
Answer:
70
Step-by-step explanation:
nk
Find the inverse of y = √x + 8, y ≥ 8
To find the inverse of a function, you can follow these steps:
Swap the variables x and y in the original function. For example, if the original function is y = √x + 8, you would swap the variables to get x = √y + 8.
Solve the equation for y. In this case, you would get:
x = √y + 8
y = x - 8
Replace y with f^-1(x) to denote the inverse function. The inverse function is defined as f^-1(x) = y, so you would get:
f^-1(x) = x - 8
This is the inverse function of y = √x + 8.
Note that the inverse function is only defined for values of x such that y ≥ 8. This is because the original function y = √x + 8 is only defined for y ≥ 8.
Maisy and Oliver converted some pounds (£) into euros (€) at two different shops. Maisy converted £40 into €47.20 at shop A. Oliver converted £83 into €96.28 at shop B. Byron converted some pounds at one of these shops and received €68.44. What is the smallest amount that he could have converted?
The smallest amount that Byron could have converted is £73.44.
What is exchange rate?An exchange rate is the rate at which one currency can be exchanged for another currency. It is the value of one country's currency against another country's currency. Exchange rates fluctuate based on supply and demand for a particular currency, as well as economic and political factors.
Exchange rates are typically quoted as the value of one currency in terms of another currency. For example, an exchange rate of 1.2 US dollars (USD) to 1 Euro (EUR) means that 1 EUR can be exchanged for 1.2 USD.
There are two types of exchange rates, Floating and Fixed exchange rate.
According to question :-
To determine the smallest amount that Byron could have converted, we can use the exchange rate from shop A, which is €47.20 for £40.
If we divide the amount of euros he received (€68.44) by the exchange rate (€47.20 for £40), we get:
€68.44 ÷ €47.20/£40 = £73.44
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What are the 3 types of solutions for systems?
The three types of solutions for systems are:
Consistent solutionsInconsistent solutionsDependent solutionsA consistent system is one where the number of equations is equal to the number of unknowns, and a unique solution can be found. An inconsistent system is one where the number of equations is greater than the number of unknowns and there is no solution.
A dependent system is one where the number of equations is less than the number of unknowns and an infinite number of solutions exist. In a consistent and dependent system, the solution can be found by using methods such as elimination or substitution.
In an inconsistent system, the system has no solution. In dependent system, the solution can be found by using methods such as elimination or substitution, but the solution is not unique it has infinite solutions.
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Mary reached chool at 7:30 AM, and left for home at 12:45 PM. How long he tayed in the chool
Anwer with explanation
Answer:
5 hours and 15 minutes.
Step-by-step explanation:
7:30 - 8:00 is 30 minutes
8:00 - 12:00 is 4 hours
12:00 - 12:45 is 45 minutes
30 minutes plus 45 minutes is 1 hours and 15 minutes
4hours + 1 hour and 15 minutes is
5 hours and 15 minutes
or
5 1/4 hours
or
315 minutes.
I am not sure what form you want.
What is 1 mole equal to grams?
Therefore, one mole of any substance is equal to its molar mass in grams.
Define molar mass.Mass per mole is a definition of molar mass. In other terms, molar mass is the total mass of all the atoms in a material that makes up a mole. It is measured in gram-per-mole units.
What are atoms?A chemical element is uniquely defined by its atoms, which are tiny pieces of substance. An atom is made up of a core nucleus and one or more negatively charged electrons that orbit it. The positively charged, comparatively hefty protons and neutrons that make up the nucleus may be present.
The molar mass of a substance is the mass of one mole of that substance and is usually expressed in grams per mole (g/mol).
For example, the molar mass of carbon is 12.01 g/mol, so one mole of carbon weighs 12.01 grams.
Therefore, one mole of any substance equals its molar mass in grams.
It is essential to mention that the molar mass is the weight of one mole of a substance and is determined by the atomic or molecular weight of the substance.
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A grocery store has increased its prices over time. The price per pound of apples in 2016 was $0.45. Today, the price per pound of apples is $0.85.
What is the equation of the line that would represent the price increase per pound of apples over time?
Answer:
C = 0.06x + 0.45
Step-by-step explanation:
Today is 2023
So, from 2016 to 2023, it has been 7 years.
0.85 - 0.45 = $0.40
So, $0.40 is the increase in 7 years
0.40 / 7 = $0.06
So, $0.06 is the change per year
Let C represent the total cost and x represent the number of years and we have
C= 0.06x + 0.45
The equation of line p is y= 1 4 x–8. Line q, which is parallel to line p, includes the point (6, – 3). What is the equation of line q?
Answer:
The equation of line q in slope-intercept form is
y= 1/4 x– 9/2
.
Step-by-step explanation:
Is 10 12 15 a Pythagorean triple?
No, 10 12 15 is not a Pythagorean triple. A Pythagorean triple is a set of three positive integers a, b, and c such that a^2 + b^2 = c^2.
To determine whether 10 12 15 is a Pythagorean triple, we need to calculate a^2 + b^2.
In this case, 10^2 + 12^2 = 100 + 144 = 244. Since 244 ≠ 15^2, 10 12 15 is not a Pythagorean triple. We can also confirm this by plugging 10, 12, and 15 into the Pythagorean Theorem, a^2 + b^2 = c^2.
10^2 + 12^2 = 100 + 144 = 244
244 ≠ 15^2
Therefore, 10 12 15 is not a Pythagorean triple.
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Work out the equation of the straight line
shown below.
Give your answer in the form y = mx + C,
where m and c are integers or fractions in
their simplest forms.
Y
6
5
4
3
2-
1
-6 -5 -4 -3 -2 -1 0
-14
-2-
-3+
-4-
-5-
-6-
1 2 3 4 5 6
X
Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.
What is a straight line?A straight line is made up of many points connected at each end. Any straight line's slope, m, is determined by the formula. The slope-intercept formulation of a linear equation is y = mx + b. The equation's variables are X and Y. The slope of the line (m) and the value of y when x is 0 are represented by the values m and b, respectively.
[tex]m = \frac{y2-y1}{x2 - x1}[/tex]
given
the graph is,(0,8) and (9,2)
The slope of the line is,
m = 1/2
Because it crosses the y-axis at the point where the intercept C is equal to 8,
The equation of the line will be :
⇒ y = mx + c
⇒ y = (1/2)x + (8)
⇒ y = x/2 + 8
Where m and c are integers or fractions, the equation of a straight line in the form of y = mx + c becomes y = x/2 + 8.
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Which segment is the shortest?
the smallest angle will yield the shortest opposite side, likewise the largest angle will yield the largest side, Check the picture below.
Write the equation of the line, that passes through the points (- 6, 1) and (10, 0)
Equation:
Now, write an equation of a line that is parallel to the above line and passes through point (-7, 2) in all three forms below.
Point-Slope Form
Slope-Intercept Form
Standard Form
The equation of the line, that passes through the points (- 6, 1) and (10, 0) is y = - (1/16)x + (5/8) and the equation of a line that is parallel to the above line and passes through point (-7, 2) is y = - (1/16)x + (25/16).
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is that the line passes through the points (- 6, 1) and (10, 0).
The slope of the line will be -
{m} = (0 - 1)/(10 + 6) = -1/16
{m} = -1/16
We can write the equation as -
y = - (1/16)x + c
For the point (10, 0), we can write -
0 = - (1/16) x 10 + c
0 = - (10/16) + c
c = 10/16
c = 5/8
So, we can write the equation as -
y = - (1/16)x + (5/8)
The equation of a line that is parallel to the above line and passes through point (-7, 2) is as follows -
y = - (1/16)x + c
2 = - (1/16) x - 7 + c
c = 2 - 7/16
c = 25/16
y = - (1/16)x + (25/16)
Therefore, the equation of the line, that passes through the points (- 6, 1) and (10, 0) is y = - (1/16)x + (5/8) and the equation of a line that is parallel to the above line and passes through point (-7, 2) is y = - (1/16)x + (25/16).
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1. Substitution is the second strategy for: *
a. solving a system of equations
b. finding the x-intercept and y-intercept
c. graphing an equation
The solution is Option A.
Substitution is the second strategy for solving a system of equations
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first equation be represented as A
Now , the value of A is
ax + by = c be equation (1)
Let the second equation be represented as B
dx + ey = f be equation (2)
On adding or subtracting both the equations , we can eliminate one of the variables from the system of equations
And , to calculate the other variable , substitute the value of the variable in either of the equations to solve the system of equations
So , we will get the value of the variable x and y
Hence , the system of equations can be solved by substitution
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PLS SOMEONE HELPP I NEED THIS ASAP
The rate of change for the graph, when x=0 and x=1 is 2 units.
What is average rate of change?
This expression represents the average rate of change of the function f(x) over the range a<=x<=b, is less than or equal to x, and is less than or equal to b -
[f(b)-f(a)]/b-a
The rate of change of graph is determined by the formula -
[f(b)-f(a)]/b-a
[f(1)-f(0)]/1-0
Here, in the graph it can be clearly seen that f(0)=-1 and f(1)=1.
Plugging in the values -
[1-(-1)]/1
(1+1)/1
2
Therefore, the rate of change is 2 units.
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Out of 32 student, 18 voted for Christian as president of the students council. If there are 224 students how many students voted for Christian
Answer:
126
Step-by-step explanation
PLEASE HELP ASAP, I WILL MARK YOU BRAINBLIEST <3 TYSM
The answers to each part is mentioned below.
What is the general equation of a straight line?The general equation of a straight line is -
y = mx + c
{m} - slope.
{c} - intercept along the y - axis.
Given is a straight line problem as shown in the question.
( 1 ) -(a) -
Now, 12 oz of honey will cost $5.4. So, we can write that -
1 ounce of honey will cost - (5.4/12)
Cost of 1 oz honey will be - $(0.45)
(b) -
Now, 12 oz of honey will cost $5.4. So, we can write that -
For $1, you can buy - (12/5.4) oz of honey.
Amount of honey bought in 1 dollar - 2.22 ounces
(c) -
We can write the equation as -
c = 0.45h
(d) -
The graph for this function is attached with the answer.
Therefore, the answers to each part is mentioned above.
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In a math question, Magda correctly answered a question that asked for a typical measure of orange juice in a full family-size jug. Which was her answer
Magda said the typical measure of orange juice in a full family-size jug is 1 gal in value.
What is meant by mathematical expression?A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression. Operations include addition, subtraction, multiplication, and division.
The collection of mathematical symbols that emerges from the right arrangement of numbers is known as a mathematical expression and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.
The three different types of algebraic expressions are monomial, binomial, and polynomial.
The complete question is : In a math question, Magda correctly answered a question that asked for a typical measure of orange juice in a full family-size jug. Which was her answer?
a. 2 cups
b. 1 gal
c. 10 gal
d. 10 fl oz
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Tell whether 30 is divisible by 2
Answer: Yes
Step-by-step explanation
Since the number being divided has a 0, it can be divided by 2
Sunnyvale School is having their
annual lobster race. A team
consists of five lobsters. The
team score is the average of the five finishing place positions. His sister sally’s team has consistently finished behind his team, however, an unusual pattern has been noticed. For example, Sally’s first lobster finished right behind Peter’s first lobster. Her second lobster finished 2 places behind peter’s second lobster. Her third lobster finished 3 places behind peter’s third, her fourth was 4 places behind his fourth and her fifth was 5 places behind his fifth.
What is Sally's team score?
Sally's team score is 6.
We can determine Sally's team score by calculating the average of her team's finishing place positions.
From the information given, we know that:
Sally's first lobster finished one place behind Peter's first lobster.Sally's second lobster finished 2 places behind Peter's second lobster.Sally's third lobster finished 3 places behind Peter's third lobster.Sally's fourth lobster finished 4 places behind Peter's fourth lobster.Sally's fifth lobster finished 5 places behind Peter's fifth lobster.If we assume that Peter's team finished in 1st, 2nd, 3rd, 4th and 5th places, then we can calculate Sally's team score as follows:
Sally's first lobster finished in 2nd placeSally's second lobster finished in 4th placeSally's third lobster finished in 6th placeSally's fourth lobster finished in 8th placeSally's fifth lobster finished in 10th placeTo find the average of the five finishing place positions, we add up all the places and divide by 5:
(2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6
So, Sally's team score is 6.
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What is the formula of perimeter Class 6?
The perimeter of a closed shape is the overall length of the boundary. As a result, the perimeter of that shape is determined by adding up all of its sides. Therefore, Perimeter(P) = Sum of All Sides is the perimeter formula.
The formula is:
Perimeter = (the distance all the way around the outside of the figure).
How to calculate the distance all the way around the outside of the figure
is different for every shape.
A few of them are:
The perimeter of a Square, (P) = 4 × Side units.
The perimeter of a Rectangle, (P) = 2(l + b) units.
The perimeter of a Triangle is = Sum of all three sides.
The perimeter of a Circle = 2 π r = π d.
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