Step-by-step explanation:
The covariance of two variables X and Y is a measure of the relationship between their changes. It is calculated as:
cov(X, Y) = (1/n) * sum((x_i - mean(X)) * (y_i - mean(Y)))
where n is the number of observations, x_i and y_i are the values of X and Y respectively for the i-th observation, mean(X) and mean(Y) are the means of X and Y respectively.
In Python, you can use the numpy library to calculate the covariance as follows:
import numpy as np
X = [x_1, x_2, ..., x_n]
Y = [y_1, y_2, ..., y_n]
cov = np.cov(X, Y)[0][1]
A measurement of the intensity and direction of the linear relationship between two random variables, X and Y, is called covariance. A definition of covariance is:
Cov(X, Y) is equal to E[(X - E(X))(Y - E(Y))].
where E[...] is the anticipated value operator and E(X) and E(Y) is the expected values of X and Y, respectively.
If Cov(X, Y) is positive, X and Y have the propensity to rise or fall together. Cov(X, Y) is a measure of the tendency for two variables to move in opposite directions. When Cov(X, Y) equals 0, X and Y are said to be uncorrelated.
You must be aware of the expected values as well as the joint probability distribution of X and Y in order to compute the covariance of X and Y.
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The ratio of red to yellow counters is 1:4. What fraction of the counters are red
Answer:
[tex]\frac{1}{5}[/tex] are red
Step-by-step explanation:
ratio of red : yellow = 1 : 4
total of ratio parts = 1 + 4 = 5 parts
then fraction of red counters is
[tex]\frac{1}{5}[/tex]
fraction of yellow counters is [tex]\frac{4}{5}[/tex]
solve for a side in right triangle
AB=
Answer:
3.125 cm
Step-by-step explanation:
cos50 ≈ 0.64 = b/h
b = 2
∴ h = 2/0.64 = 3.125 cm
If lim fx) 5, must f be defined at x 1? If it is, must f1) 5? Can anything be concluded about the values of fat x 1? Explain. X-1 Must f be defined at x- 1? YesNo
No conclusion can be drawn with the given information regarding function.
No conclusion can be drawn about whether f is defined at x=1 or whether f(1)=5 based solely on the statement "lim f(x) = 5." The limit of a function only describes the behavior of the function near a particular value, not necessarily the value of the function at that point.
It is possible for a function to have a limit at a point without being defined at that point, or for a function to be defined at a point but have a different value there than its limit.
Hence, no conclusion.
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Find all real zeros of the function y=3x+1 a. 1/3 b.-1/3 c. 3, 1 d. 3
Answer:
The zeroes of the function are: [tex]\frac{-1}{3}[/tex].
Option b would be the correct answer.
Step-by-step explanation:
The zeros of a function are defined as the point at which the value of the function is zero. We can say the zeros are the x values where the graph intersects the x-axis. We obtain these algebraically by setting the function equal to zero then solving.
Given
[tex]y=3x+1[/tex]
Lets find all real zeros of the function.
Replace [tex]y[/tex] with 0.
[tex]0=3x+1[/tex]
Subtract 1 from both sides of the equation
[tex]-1=3x[/tex]
Divide both sides of the equation by 3.
[tex]\frac{-1}{3} =\frac{3x}{3}[/tex]
Simplify the right side by cancelling the common factor of 3.
[tex]\frac{-1}{3} =x[/tex]
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are –6x + 15 < 10 – 5x and an open circle is at 5 and a bold line that starts at 5 and is pointing to the right which is denoted as option C and D.
What is Inequality?This is referred to as a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
Workings:
-3(2x-5)<5(2-x)
-3(2x-5)<5(2-x)
-6x+15<10-5x --- C
Subtract 15 from both the sides of the inequality
-6x + 15 -15 < 10 -5x -15
-6x < -5 -5x
-6x +5x < -5
-x < -5
Multiply both sides by (-1) ,
x > 5 .
x> 5 on the number line depicts an open circle is at 5 and a bold line starts at 5 and is pointing to the right .
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The full question is:
Which are correct representations of the inequality -3(2x - 5) < 5(2 - x)? Select two options.
(a) x < 5
(b) –6x – 5 < 10 – x
(c) –6x + 15 < 10 – 5x
(d) A number line from negative 3 to 7 in increments of 1 , An open circle is at 5 and a bold line that starts at 5 and is pointing to the right.
(e) A number line from negative 7 to 3 in increments of 1, An open circle is at negative 5 and a bold line that starts at negative 5 and is pointing to the left.
in the figure two parallel lines AB and CD are intersected by transversal EF at G and H if AGH is x and EGB is y and GHD is 60 find the value of x and y.
∠AGH = ∠GHD = 60° (alternating angles)
∠EGB = ∠AGH = 60° (Vertically Opposite Angles)
What are Parallel Line ?Coplanar infinite straight lines that are parallel have no points of intersection. In the same three-dimensional space, parallel planes are any planes that never cross. Curves that are parallel to one another and maintain a predetermined minimum distance do not touch or intersect.
Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. Angles that are vertically opposed to one another are equal.
According to the alternative angle theorem, when a transversal cuts two parallel lines, the resulting alternate interior angles or alternate exterior angles are congruent. To demonstrate: If a transversal cuts two parallel lines, then the opposing interior angles are equal.
It is given that AB and CD are parallel to each other
EF is the transversal
∠GHD = 60°
∠AGH = ∠GHD = 60°(alternating angles)
∠EGB = ∠AGH = 60° (Vertically Opposite Angles)
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Katya measured the growth of a plant seedling. The seedling grew 1/3 inch by the end of the end of the first week and another 5/6 inch by the second week. About how much did the seedling grow in the first 2 weeks
Answer:
1 and 1/6
Step-by-step explanation:
You have to add together the growth of the 2 weeks. So, 1/3 + 5/6 but to add these you need to find the common denominator. I would change 1/3 to have a denominator of 6. To turn 3 into 6 you have to multiply by 2 and whatever you do to the bottom you do to the top so 1 x 2. Now that your fraction of 1/3 is 2/6, you can add the 2 weeks together. 2/6 + 5/6 = 7/6, which can also be written as 1 and 1/6.
The apothem of a regular hexagon is 8. The area is 144. What is the length of a side of the regular hexagon?
Answer:
The answer is 18.
Step-by-step explanation:
You need to divide 144 by 8 to end up with 18.
five-sixths of a kilofram of mixed nuts costs 60 cents. how much does half a kilogram of mixednuts cost
Half a kilogram of mixed nuts costs 36 cents.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Five-sixths of a kilogram costs 60 cents.
That means,
1 kilogram of mixed nuts costs = 60 x 6/5 = 72 cents.
So,
half a kilogram of mixed nuts costs = 72/2 = 36 cents.
Therefore, the required cost is 36 cents.
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Harp seals spend much of their time swimming and diving in the icy waters of the Arctic ocean. if 86 seals dove for a combined total depth of 10,578 meters, how many meters each seal dive
pls help ASAP its literally 12:00 where i live
Answer: 122.81
Step-by-step explanation:
If 86 seals dove for a combined total depth of 10,578 meters, each seal would have dove an average of 122.81 meters (10,578 meters / 86 seals)
[tex]10578 \div 86 = 122.81[/tex]
3ft= how many inches
Answer:
36 inches.
There are 12 inches in 1 foot, and snce there are 3, then you will multiply:
12 * 3 = 36
Step-by-step explanation:
Hope it helps! =D
a rectangle has side lengths s and 2s. its area is represented by the expressions 2s^2. The area of the rectangle is a function of its side lengths. does the situation represent a linear or nonlinear function
The situation represent a non-linear function
What is a function?A function can be described as an expression, law or rule that explains the relationship between two variables.
These variables are;
The dependent variableThe independent variableThe different types of functions are;
The linear functionsThe non-linear functionsPower functionsQuadratic functions, ectWhat is a non-linear function?A nonlinear function is defined as a function having a graph that is not a straight line.
This means that the equation of the graph does not that the mathematical form, ax +b
From the information given, we have that;
Area = 2s²
Hence, it is a non-linear function.
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Last month, Carmen paid a gas and electric utility bill of $55. The part of the bill was $30. Write the ratio of the payment for to the payment for electricity. i need the answer quick
Step-by-step explanation:
To find the ratio of the payment for gas to the payment for electricity, we can use the following formula:
(Payment for gas) : (Payment for electricity) = (Gas payment) : (Electricity payment)
We know that the total bill was $55 and the payment for electricity was $30.
So, the payment for gas would be: $55 - $30 = $25
Therefore, the ratio of the payment for gas to the payment for electricity is:
($25) : ($30) = 25 : 30
You can simplify this ratio to 5:6 or you can write it as 25:30
a soccer ball is kicked at an angle of 61° to the horizontal with an initial speed of 25 m/s. assume for the moment that we can neglect air resistance. (a) for how much time is the ball in the air?
A soccer ball in the air for time 4.929 seconds.
Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory
The vertical position of a projectile launched from the ground with velocity v and angle θ is:
y(t)=−4.9t^2+(vsinθ)t
We can factor this as:
y(t)=t(−4.9t+vsinθ)
Now we know that t=0 is one root, when you first kick it, so we only need to solve for the other root
−4.9t+vsinθ=0
t=vsinθ/4.9
Plugging in what we have:
t=25sin61/4.9
t = 25 *0.96611777 /4.9
t≈4.929 sec
So about 4.929 seconds.
A soccer ball in the air for time 4.929 seconds.
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What is the answer?!!!!!!!
Answer:
Mistake: From line 4 to 5
Correct Solution:
7x - 5 = 5x + 9
2x = 14
x = 7
Step-by-step explanation:
On line 4 to 5, Ms.Shreve should've subtracted 5 to 7, and add 5 to 9, not vice versa.
sluar
IT
7. Shiloh and Mario went to the movies. At the theater a small box of popcorn costs $2.50 each and each
drink costs $1.25 each. Shiloh and Mario only have $9 to spend. Write an inequality to describe the
number of small boxes of popcorn (p) and drinks (d) they can buy.
(SIS-)
The linear inequality will be 2.5x+1.5y<=9, where x=boxes of popcorn and y=no. of drinks.
What are linear inequalities?
Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Maths. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Maths are polynomial inequality, rational inequality, absolute value inequality.
The symbols ‘<‘ and ‘>’ express the strict inequalities and the symbols ‘≤’ and ‘≥’ denote slack inequalities. A linear inequality seems exactly like a linear equation but there is a change in the symbol that relates two expressions.
e.g. y>x+2
Now,
Given that Shiloh and Mario went to the movies. At the theater a small box of popcorn costs $2.50 each and each drink costs $1.25 each.
Shiloh and Mario only have $9 to spend.
So, let x=boxes of popcorn and y=no. of drinks
Therefore, given statements can be satisfied by linear inequality given
as 2.5x+1.5y<=9.
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Given right triangle XYZ, with altitude
WZ, find each length.
a. If XW = 3 and WY= 12, determine
WZ.
b. If WZ=4 and XW= 2, determine
WY.
c. If XY = 22 and XW = 9, determine
WZ.
d. If XZ = 10 and XW = 4, determine XY.
e. If WZ 18 and XW = 9, determine XZ.
=
f. If WZ = 4, XW = x, and XY = 10, determine ZY.
Answer:
c.
the length of WZ is
[tex] \sqrt[3]{13} [/tex]
24 x 1 and one sixth
Answer:
24×1 equal 24 and multiply it by 1/6 is 24/6 and simplifying it would make 4.
answer=4
not sure if this is what u want
Step-by-step explanation:
hope it helps
The um of Lia' age and myra age i 40. In 10 year lia will be three time a older than myra. How old i each peron
The present age of Lia is 35 and the present age of Myra is 5.
The sum of Lia's age and Myra's age is 40.
Let the present age of Myra is x and the present age of Lia is y.
So the equation should be
x + y = 40..................(1)
After 10 year the age of Myra is x + 10 and age of Lia is y + 10.
In 10 year Lia will be three time a older than Myra.
y + 10 = 3(x + 10)
Simplify
y + 10 = 3x + 30
Subtract 10 on both side, we get
y = 3x + 20
Now putting the value of y in the equation 1.
x + 3x + 20 = 40
4x + 20 = 40
Subtract 20 on both side, we get
4x = 20
Divide by 4 on both side, we get
x = 5
The present age of Myra is 5.
Now putting the value of x in equation 1
x + y = 40
5 + y = 40
Subtract 5 on both side, we get
y = 35
The present age of Lia is 35.
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The complete question is:
The sum of Lia's age and Myra's age is 40. In 10 year Lia will be three time a older than Myra. How old is each person?
Use the graph to find the center of dilation.
The center of dilation of the triangle is (7, 5)
How to determine the center of dilation.From the question, we have the following parameters that can be used in our computation:
Two triangles
The center of dilation of the triangles is the center of both triangles
From the figure, we can see that the center is located at (7, 5)
Hence, the center is (7, 5)
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Which expressions are factors of this polynomial?
2x^4 + x^3 - 29x^2 - 34x + 24
The factors of given polynomial are (2x-1) ( x+2 ) (x-4) (x+2 ) .
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given expression,
2x^4 + x^3 - 29x^2 - 34x + 24 = 0
By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term 24 and q divides the leading coefficient 2. One such root is 4. Factor the polynomial by dividing it by x-4.
(x-4)(2x^3 + 9x^2 + 7x-6)
Consider 2x³+9x²+7x-6. By Rational Root Theorem, all rational roots of a polynomial are in the form p/q, where p divides the constant term -6 and q divides the leading coefficient 2. One such root is -3. Factor the polynomial by dividing it by x+3.
(x+3) ( 2x^2+3x-2)
Consider 2x²+3x-2. Factor the expression by grouping. First, the expression needs to be rewritten as 2x²+ax+bx-2. To find a and b, set up a system to be solved.
a+b = 3
ab = 2(-2) = -4
As ab is negative, a and b have the opposite signs. As a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -4.
(-1,4)
(-2,2)
Calculate the sum for each pair.
-1+ 4 = 3
-2+2 = 0
The solution is the pair that gives sum 3.
a = -1
b = 4
Rewrite ( 2x^2+3x-2) as ( 2x^2-x ) + (4x - 2 )
( 2x^2-x ) + (4x - 2 )
Exclude x in the first group and 2 in the second group.
x (2x-1 ) + 2 (2x-1)
Factor out common term 2x-1 by using distributive property.
(2x-1 ) ( x +2 )
Rewrite the complete factored expression
(2x-1) ( x+2 ) (x-4) (x+2 ) .
Hence, The factors of given polynomial are (2x-1) ( x+2 ) (x-4) (x+2 ) .
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Two week ago i bought 10 cupcake lat week i bought 7 today id like to follow thi pattern how many cupcake do i want
Two week ago I bought 10 cupcake last week I bought 7 today id like to follow this pattern so 4 cupcakes are needed.
A pattern is a specific arrangement of numbers or any term which will follow a specific code or hint.
Another example is 2,4,16,256 in this pattern each term is the square of the previous term and this will become its specific pattern.
As per the given,
Number of cupcakes in two weeks ago = 10
Number of cupcakes in last weeks ago = 7
Decrement of cupcakes = 10 - 7 = 3
Thus,
Number of cupcakes in today = 7 - 3 = 4
Hence "The number of cupcakes is 10 - 7 = 3 thus with follow this pattern the number of cupcakes today will be 7 - 3 = 4 cupcakes".
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help me with this topic pls, thanks
The numbers are classified as rational or irrational as follows:
98.73: rational.-35.93(periodic 93): rational.-2 x square root of 6: irrational.-16π: irrational.- square root of 1: rational.What are rational and irrational numbers?Rational numbers are the whole numbers plus decimals that can be represented by fractions, involving both positive and negative numbers.
The set of irrational numbers is composed by numbers that cannot be represented by fractions, such as non-exact roots, which are non-terminating and non-repeating decimal numbers.
Hence the numbers are classified as follows:
98.73: rational -> exact decimal.-35.93(periodic 93): rational -> periodic = repeating decimal.-2 x square root of 6: irrational. -> square root of 6 is non - exact.-16π: irrational. -> π is a non-terminating decimal, multiplication of a rational with an irrational is always irrational.- square root of 1: rational -> negative of exact square root.More can be learned about rational numbers at brainly.com/question/12088221
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determine the amount of fence needed to enclose a rectangular garden with length 14 feet and width 31 feet.
The amount of fence needed to enclose a rectangular garden is 90 feet.
To determine the amount of fence needed to enclose a rectangular garden with length 14 feet and width 31 feet, you need to calculate the perimeter of the rectangle. The perimeter is the total length of all four sides of the rectangle.
The formula for the perimeter of a rectangle is given by
2 * (length + width)
In this case, the length is 14 feet and the width is 31 feet, so the perimeter is
2 * (14 + 31) = 2 * 45 = 90 feet
This means that 90 feet of fence is needed to enclose the rectangular garden.
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let f(x)=−x4−9x3 4x−6 . find the open intervals on which f is concave up (down). then determine the x -coordinates of all inflection points of f .
The x-coordinates of the inflection points of this function are −1 and −1/3.
In this case, we are looking for the open intervals on which the function f(x) = −x⁴ − 9x³ + 4x − 6 is concave up (down) and the x-coordinates of the inflection points of the function.
To find the open intervals on which f is concave up, we must first calculate the second derivative of the function.
The second derivative of the function f(x) is
=> f''(x) = −12x³ − 27x² + 4.
This means that the function f is concave up when f''(x) > 0 and concave down when f''(x) < 0. Solving the equation f''(x) > 0 will give us the intervals on which the function is concave up.
These are the intervals (−∞, −1), (−1, −1/3), and (−1/3, ∞).
Similarly, solving the equation f''(x) < 0 will give us the intervals on which the function is concave down. These intervals are (−1, −1/3) and (−1/3, 0).
We can now determine the x-coordinates of all inflection points of the function f by finding the x-values at which the second derivative is equal to zero.
Solving the equation f''(x) = 0 will give us the x-coordinates of the inflection points, in this case −1 and −1/3.
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Find the area of rectangle WXYZ. Round your answer to the nearest tenth if necessary.
W
X
Y
Z
10.8 in
16.2 in
10
PLS HELP FAST
Answer:
The area of rectangle WXYZ is 175.36 square inches. To find the area, you multiply the length (10.8 inches) by the width (16.2 inches). 10.8 x 16.2 = 175.36.
Kareem borrowed a total of 6000 from two tudent loan. One loan charged 4% imple interet and the other charged 3. 5% imple interet, both payable after graduation. If the interet he owed after 5 year wa $1062. 50 , determine the amount of principal for each loan
The amount borrowed with 4% interest was 1100, and the amount borrowed with 3.5% interest was 6000 - 1100 = 4900.
Let x be the amount of the loan with 4% interest and y be the amount of the loan with 3.5% interest. Then, x + y = 6000, because the total amount borrowed is 6000.
The interest owed on the 4% loan after 5 years is 4% of x per year, so the total interest owed after 5 years is 5 * 0.04x = 0.20x.
Similarly,
The interest owed on the 3.5% loan after 5 years is 3.5% of y per year, so the total interest owed after 5 years is 5 * 0.035y = 0.175y.
The total interest owed after 5 years is $1062.50, so 0.20x + 0.175y = 1062.50.
Now we have two equations, so we can solve for x and y.
First, substitute x + y = 6000 into the second equation, and we get,
0.20x + 0.175(6000 - x) = 1062.50
Expanding the second term, we get,
0.20x + 1035 - 0.175x = 1062.50
0.025x = 27.50
Dividing both sides by 0.025,
x = 1100
So the amount borrowed with 4% interest was 1100, and the amount borrowed with 3.5% interest was 6000 - 1100 = 4900.
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the numerator of a fraction is 1 less than the denominator. if the numerator and the denominator are both increased by 4, the new fraction will be 1/8 more than the original fraction. find the original fraction.
Using fractions subtraction, we know that the original fraction in the given situation is -7/8.
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
Proper fractions, improper fractions, mixed fractions, like fractions, unit fractions, equivalent fractions, and same numerator fractions are the seven different types of fractions.
So, we have the fraction:
1/8
Now, the original fraction would be:
1/8 - 4/4
1-8/8
-7/8
Therefore, using fractions subtraction, we know that the original fraction in the given situation is -7/8.
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What is the greatest common monomial factor of this polynomial? 14x^3y^5z^2 - 98x^2y^4x^2 + 28x^2y^3
The greatest common monomial factor of this polynomial will be 14x²y³.
What is the greatest common factor?Simply said, it is the biggest common element. The highest consistent element in the above example is 15, making 15 the greatest common factor amongst 15, 30, and 105. The biggest chunk of the common factors is called the "Greatest Common Factor" (of two or more numbers).
The polynomial is given below.
⇒ 14x³y⁵z² - 98x²y⁴x² + 28x²y³
⇒ 14x²y³(xy²z² - 7x²y + 2)
The greatest common monomial factor of this polynomial will be 14x²y³.
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a rectangle has perimeter 74 inches, and its area is 322 square-inches. find the dimensions of this rectangle.
the dimensions of rectangle is l = 23 and w = 14
Rectangle
Given,
A rectangle has perimeter 74 inches, and its area is 322 square-inches
To find the dimensions of this rectangle.
Steps:
With this question it is known that the perimeter of the rectangle is 74 inches and the area is 322 inches. the question is what is the length and width of the rectangle.
The formula for the perimeter of a square is P = l + l + w + w or P= 2(l + w) and the formula for the area of a rectangle is A = l x w.
the formula for the perimeter of a rectangle is P= 2(l + w) that means w=l(p/2-l) and the formula for the area of a rectangle is A = l x w, usually l is longer than w
insert the w equation with the perimeter formula into the area formula A = l (p/2-l) to
solve this equation: [tex]l\\^{2}[/tex] - ([tex]\frac{P}{2}[/tex]) x l + A=0 to get l
[tex]l\\^{2}[/tex] - (74/2) l +322=0
[tex]l\\^{2}[/tex] - 37l + 322=0
(l-23)(l-14)=0 so
l =23 and l=14,
it can be concluded that l = 23 and w = 14
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