Answers
Answer: See explanation
Step-by-step explanation:
For questions 1 - 4, it's asking you to plug in numbers into the original functions.
1. f(-2): You would plug -2 into f(x) = 2x^2 - 3x, getting
2(-2)^2 - 3(-2)
2(4) - (-6)
8 + 6 = 14
f(-2) = 14
2. f(x) - g(x): You're basically just subtracting the two functions
(2x^2 - 3x) - (2 - 5x)
2x^2 - 3x - 2 + 5x
Combine like terms
2x^2 + 2x - 2
3. You're multiplying them so (2x^2 - 3x)(2 - 5x)
4. f(g(x)): It's like f(-2), but instead of -2, you plug in the function of g(x)
So in 2x^2 - 3x, x would equal 2 - 5x:
2(2 - 5x)^2 - 3(2 - 5x)
And then simplify that.
For questions 5 - 6, it's asking for shifting from the parent function. Parent function is always f(x) or g(x) or whatever variable it is.
5. f(x - 8) + 9: The 9 is the y value shift, meaning the parent function is shifted up 9 units. For -8, think of what x needs to be for (x - 8) to be 0. If that number is positive, function shifts right; if negative, shift left. In this case, x needs to be 8 in order for (x - 8) to be 0. Therefore, f(x) is shifted right 8 units.
6. -3f(x) - 2: From the previous question, we now know that -2 means f(x) is shifted down 2 units. When you have 3f(x), you're multiplying the entire function by 3, so it's called a vertical stretch of 3. The negative means it's reflected over the x-axis since the y value is the opposite of what it used to be.
Related Questions
suppose the time to process a loan application follows a uniform distribution over the range 8 to 17 days. what is the probability that a randomly sel
Answers
Answer:
0.2
Step-by-step explanation:
Marissa buys a rare gem priced at $82.00. The sales tax rate is 7.9%.
What is the tax amount to the nearest cent?
label required
Answers
The tax amount to the nearest cent:$6.478
What is Tax?
Tax is the sum of money that citizens hand up to the government in exchange for goods and services. A taxpayer and a tax collector are both partners in any tax transaction. An entity that pays taxes to the government is referred to as a taxpayer. Any middleman that collects taxes on the government's behalf, including the government, is a tax collector.
Given,
The price of Rare gem = $82.00
The sales tax = 7.9%
Converting percent into decimal
7.9 / 100 = 0.079
The amount of sales tax = 82 x 0.079
= $6.478
The Total amount of the gem before the sales tax:
82 - 6.478 = $75.522
Hence, The tax amount to the nearest cent is $6.478
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the number of cars produced when x x dollars is spent on labor and y y dollars is spent on capital invested by a manufacturer can be modeled by the equation 45 x 1 3 y 2 3
Answers
The formula in terms of x and y for dy/dx is y/ -2x
The value of dy/dx at the point (1,1) is -0.5
The question is incomplete, the full question is given below:
200 cars can produced when x dollars is spent on labor and y dollars is spent on capital. the equation that relates x and y is 45 x^1/3 y^2/3= 200
a. Find a formula in terms of x and y for dy/dx
b. Find the value of dy/dx at the point (1,1). Round your answer to 4 decimal places
Part a
A formula in terms of x and y for dy/dx
We differentiate equation that relates x and y with respect to x by implicit differentiation:
=d/dx(45 x^1/3 y^2/3) =d/dx( 200)
=> 45 *(1/3) x^-2/3 y^2/3 + 45 x^1/3 2/3 y^ -1/3 dy/dx=0
=> x^-2/3y^2/3+ 2 x^1/3 y^-1/3 dy/dx=0
=> y/x= -2dy/dx
=> log y = -2 log x +log c
=> y= x^ -2 +c
putting x=y=1
c=0
then y= 1/x^2
b) y/x= -2dy/dx
put x=y=1 we get
-1/2 = dy/dx
dy/dx =-0.5
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work out the length of x
Answers
Answer:Tes icahd
Step-by-step explanation:
Consider the first 2 terms of the sequence 28, 14, ...
Determine whether the sequence is arithmetic or geometric. Explain your reasoning.
please help me with 1 and 2
Answers
1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.
2. The common difference of the sequence 28, 14 ..... will be;
d = - 14
And, Next three terms of the arithmetic sequence are;
0, -14, -28
What is Geometric sequence?
An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.
Given that;
The first two terms of the sequence,
28, 14 .....
Now,
Let the sequence is in arithmetic sequence, then;
28, 14 ......
The common difference of the sequence is;
d = 14 - 28
d = - 14
And, Let the sequence is in geometric sequence, then;
28, 14 ......
The common difference of the sequence is;
d = 14/28
d = 1/2
Thus, The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.
2. If the given sequence is in arithmetic sequence, then;
28, 14 ......
The common difference of the sequence is;
d = 14 - 28
d = - 14
And, The nth term of the arithmetic sequence is;
⇒ [tex]a_{n} = a + (n - 1)d[/tex]
Where, 'a' is the first term and 'd' is the common difference of the sequence.
So, The 3rd term of the arithmetic sequence is,
⇒ [tex]a_{n} = a + (n - 1)d[/tex]
[tex]a_{3} = 28 + (3-1)(-14)\\ \\a_{3} = 28 - 2 * 14\\\\a_{3} = 28 - 28\\\\a_{3} = 0[/tex]
And, The 4th term of the arithmetic sequence is,
[tex]a_{4} = 28 + (4-1)(-14)\\ \\a_{4} = 28 - 3 * 14\\\\a_{4} = 28 - 42\\\\a_{4} = -14[/tex]
And, The 5th term of the arithmetic sequence is,
[tex]a_{5} = 28 + (5-1)(-14)\\ \\a_{5} = 28 - 4 * 14\\\\a_{4} = 28 - 56\\\\a_{5} = -28[/tex]
Therefore, Next three terms of the arithmetic sequence are;
⇒ 0, -14, -28
Thus,
1. The given sequence 28, 14 ..... will be either arithmetic or geometric sequence.
2. The common difference of the sequence 28, 14 ..... will be;
d = - 14
And, Next three terms of the arithmetic sequence are;
0, -14, -28
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How many units is 523 from 0?
Answers
Using proportions, it is found that the number 523 is 523 units from zero.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of the problem using arithmetic operations such as multiplication and division with the unit rates of the measures.
One example of application is for the digit values of a number, as:
Each unit is worth 1.Each tenth is worth 10.Each hundredth is worth 100.Each thousandth is worth 1000.And so on...
For the number 523 given in this problem, since each unit is worth one, the number of units that it is away from zero is given by:
523/1 = 523 units.
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Maria paid $240 for a table set after a discount of 40%. What was the original price? Use scratch paper to create a model to help solve the problem (e.g., tape diagram, table, double number line diagram, 10×10 grid).
The original price was $
Answers
Answer:
$400
Step-by-step explanation:
We see that the discount price is (100-40) = 60% of the original price
If 60% corresponds to $240, than 10% corresponds to 240/6 = $40
Since the original price is 100% = 10*10%, the original price is 10* $40 = 400.
I can't make something with scratch paper right now, i hope you will be able yourself to put the above information is a table :-)
Good luck with it!
Click on the graph to choose the correct answer to the equation. y ≥ 2 x + 1
Answers
The graph of the linear inequality can be seen in the image at the end.
How to identify the graph of the inequality?
Here we have the linear inequality:
y ≥ 2x + 1
To graph this, we first need to graph the line.
y = 2x + 1
With a solid line, because we have the symbol ≥, which means that the points on the line are solutions.
Once we graphed that line, we look at our inequality:
y ≥ 2x + 1
It says that y is larger than or equal to the values on the line, so once the line is graphed we need to shade all the region above that line.
The shaded region (and the line itself) represent all the solutions of the linear inequality.
And the graph can be seen below.
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May you guys/girls please help me I have to submit this before midnight and I do not fail because my parents will get me , so may y'all please help me out!?
Answers
Answer:
Answer down below!
Step-by-step explanation:
Let's try and find a point that we can easily start on (a point that lands perfectly on the graph)
The point that we will use is (2,2)
So, starting from there we use rise/run to get our answer
We go up 1 and over -2
So, our slope will be (since we cannot simply it...)
-1/2
Hello!
To find the slope:
==> need to pick two points on the line
(x₁, y₁): (0,3)
(x₂,y₂): (4,1)
[tex]Slope = \dfrac{y_2-y_1}{x_2-x_1} =\dfrac{1-3}{4-0} =\dfrac{-2}{4} =-\dfrac{1}{2}[/tex] <== Answer
Hope that helps!
Julie says that the constant of proportionality in the equation below is 0.45. Is Julie correct?
P = 0.45n
Answers
The constant of proportionality in the equation:
P = 0.45*n
Is k = 0.45, so we can conclude that Julie is correct.
What is the constant of proportionality?A proportional relationship between two variables x and y is written as:
y = k*x
Where k is the constant of proportionality.
In this case, we have the variables P and n, and the proportional relationship is:
P = 0.45*n
So we can see that the value of the constant of proportionality is k = 0.45, so yes, Julie is correct.
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JP Computers produces both laptop
and desktop computers. Laptop
computers take up 2 cubic feet of
space and desktop computers take up
5 cubic feet of space. The maximum
capacity on the delivery truck is 800
cubic feet. Due to demand, they need
to load at least 300 laptop computers.
They profit $225 on each laptop and
$280 on each desktop computer. How
many of each should they load on the
truck to maximize profit?
Answers
The load each should get to maximize the profit is $67,500, $78,700 and $90,000
What Is Profit?
In accounting, a profit is an income that is given to the owner throughout a successful market producing process. Profitability, which is the owner's primary interest in the income-formation process of market production, is measured by profit. There are various profit metrics that are frequently used.
Let x represent the total number of laptops and y represent the total number of desktop computers.
A laptop computer occupies 2 cubic feet, hence x laptops each use 2x cubic feet. Desktop computers take up 5 cubic feet of space, hence 5y cubic feet of room is required for 5y desktop computers.
They require 2x + 5y cubic feet in total.
Since the delivery truck's maximum capacity is 800 cubic feet,
2x + 5y <= 800.
They must load at least 300 laptops because of the demand,
hence, x >= 300
They make $225 on each laptop, which translates to $225 times as many computers. They make a profit of $280 on each desktop computer, or $280y on y desktops.
Total profit is:
P=$(225x + 280y)
Draw the inequality system (see attached diagram)
2x + 5y <= 800.
x >= 300
One of the common region's three vertices will have the most profit:
P(300,0) = 225(300) + 280(0) = $67,500
P(300,40) = 225(300) + 280(40) = $78,700
P(400,0) = 225(400) + 280(0) = $90,000
Hence, each should load $67,500, $78,700 and $90,000 on the truck to maximize profit
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Renz wishes to make an open box froma square piece of cardboard with a sidethat measures 15 inches by cuttingequal squares from the four cornersand folding the sides. what will be thevolume of the box if he cuts a squarewith 2 inch sides?
Answers
2.5 inches will be the volume of the box if he cuts a square with 2 inch sides.
What is volume ?
Every three-dimensional item takes up space in some way. The volume of this area is what is being measured. The area contained by an object's limits in three-dimensional space is referred to as its volume. It is sometimes referred to as the object's capacity.Let each side of he square that's cut-off from each corner be represented by x.
This means that the base of the box will be of dimension of the side 15−2x while the height of the box will be x.
Thus;
Volume of box is:
V = (15 − 2x)(15 − 2x)x
V = (15 − 2x)²x
V = (4x² - 60x + 225)x
V = 4x³ - 60x² + 225x
Let's differentiate with respect to x to get;
dV/dx = 12x² - 120x + 225
Maximum value of x is at dV/dx = 0
12x² - 120x + 225 = 0
Using quadratic formula, we arrive at;
x = 2.5 or 7.5
Now, let's find the second derivative of the volume;
d²V/dx² = 24x - 120
Putting x = 2.5 gives;
d²V/dx² = 24(2.5) - 120
d²V/dx² = -60Thus, V is maximum at x = 2.5, since d²V/dx² is negative
At x = 7.5;
d²V/dx² = 24(7.5) - 120
d²V/dx² = 60
Thus, V is minimum at x = 7.5, since d²V/dx² is negative
Thus,we will use x = 2.5
Maximum volume; V = (15 − 2(2.5))(15 − 2(2.5))(2.5)
V = 10 × 10 × 2.5
V = 250 Sq.inches
Dimensions are;
(15 − 2x) = 15 - 2(2.5) = 10 inches
(15 − 2x) = 15 - 2(2.5) = 10 inches
x = 2.5 inches
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Need help please : Given the equation 6x + 18 = 72: Part A: Write a short word problem about a purchase made to illustrate the equation. Part B: Solve the equation showing all work. Part C: Explain what the value of the variable represents.
Answers
A. A short word problem about a purchase made to illustrate the equation is that John bought six pens and bought books for $18. The total amount is $72. Find the cost of each pen.
B. The cost of each pen is $9
C. The variable is x.
How to illustrate the equation?A. The problem is that John bought six pens and bought books for $18. The
B. The equation to illustrate this will be:
6x + 18 = 72
Collect like terms
6x = 72 - 18
6x = 54
Divide
x = 54 / 6.
x = $9
The cost of each pen is $9.
C. The variable is x = 9. This is the cost of the pen.
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help me please can you solve this for meh
Answers
Answer: 6w^3-3+18u^2
Step-by-step explanation:
Boris received a $20.50 gift card for a photo center. He used it to buy prints that cost 6 cents each. The remaining balance, B
(in dollars), on the card after buying x prints is given by the following function.
B(x)=20.50-0.06.x
What is the remaining balance on the card if Boris bought 15 prints?
Answers
Answer:
$19.6
Step-by-step explanation:
B=20.50-0.06.x
B=20.50-0.06*15
B=20.50-0.9
B=19.6
1) [tex]\frac{2x-3}{3} +\frac{x-1}{5}[/tex]
Answers
Answer:
4_62
Step-by-step explanation:
its is just leave me
PLS HELP
Yan is climbing down a ladder. Each time he descends 4 rungs on the ladder, he stops to see how much farther he has to go. If Yan made 8 stops with no extra steps, which expression best shows another way to write the product of the number of ladder rungs that Yan climbed?
4 + 4 + 4 + 4
8 + 8 + 8 + 8
(Negative 1) (4 + 4 + 4 + 4)
(Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)
Answers
The expression shows the product of the number of ladder rungs that Yan climbed is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)
What is an expression?
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We have been given that each time Yan descends 4 rungs on the ladder.
SInce, each time the number of ladder rungs that Yan climbed is negative 4, where negative sign represent descends.
Yan made eight stops with no extra steps.
-4 x 8 = -32
It can also written as; (-4) + (-4)+(-4)+(-4)+(-4)+(-4)+(-4)+(-4)
The correct answer is D. (Negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4) + (negative 4)
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Karyn proofreads 15 pages in 2 hours for $40. What is her proofreading rate in pages per hour? How much does she earn per hour?
Answers
The proofreading rate will be ( 7.5 pages/ hour) and the cost per hour will be $20.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Karyn proofreads 15 pages in 2 hours for $40. The rate will be calculated as:-
Rate of reading = ( 15 / 2 )
Rate of reading = ( 7.5 ) pages per hour
The cost will be calculated as:-
For 2 hours = $40
For 1 hour = ( 40 / 2 )
For 1 hour = $20
Therefore, the proofreading rate will be ( 7.5 pages/ hour) and the cost per hour will be $20.
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can someone pls help? thx i appreciate it :)
Answers
The scale factor from the ΔABC to ΔDEF is 3/2 cm.
Given that, in triangle ABC, side AB measures 12 cm and is the longest side and in triangle DEF, side DE measures 8 cm and is the longest side.
What is the scale factor?To adjust the size of a figure without altering its shape, a scale factor is a number or conversion factor that is utilized.
The fundamental equation to determine a figure's scale factor is written as, Scale factor is equal to the difference between the dimensions of the new and old shapes.
The scale factor from the triangle ABC to triangle DEF is 12/8 = 3/2 cm
The scale factor from the triangle DEF to triangle ABC is 8/12 = 2/3 cm
Therefore, the scale factor from the ΔABC to ΔDEF is 3/2 cm.
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11. Find all missing angles
Answers
The angle ∠1=62° ,∠2=71° ,∠3=109° ,∠4=35° ,∠5=109° ,∠6=29° ,∠7=47° and ∠8=62° for the given quadrilateral by using different laws for angle and lines.
What is quadrilateral?A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.
What is polygon?A polygon is a two-dimensional, closed shape that is flat or plane and is bounded by straight sides. Its sides are not curved. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.
∠1=62° by parallel line properties.
∠2=71° by alternate angles.
∠3=109° by alternate angles
∠4=35° by triangle properties
∠5=109° by alternate angles
∠6=29° by triangle properties
∠7=47° by parallel line properties.
∠8=62° by parallel line properties.
for the given quadrilateral by using different laws for angle and lines, The angles are ∠1=62° ,∠2=71° ,∠3=109° ,∠4=35° ,∠5=109° ,∠6=29° ,∠7=47° and ∠8=62°.
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Physical Science: A ball was dropped from a height of 100 meters. Its height above the ground
in meters at different times after its release is given in the table. Do these ordered pairs satisfy a
linear function? Explain.
Time (s)
Height (m)
0
1
2
100 90.2 60.8
3
11.8
Answers
Answer: Yes they do.
The figure shows rectangle RSTW. Which of the following conditions satisfies the criteria for rectangles?
a. m∠SRZ = 40°
b. m∠STZ = 40°
c. m∠SRW = 80°
c. m∠TWR = 80°
Answers
For the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to m ∠SRZ = 40°.
As given in the question,
In the given figure of rectangle RSTW,
Conditions satisfies the criteria of the rectangles are as follow:
a. m ∠SRZ = 40°
Line segment SR is parallel to TW. TR is the transversal.
m ∠SRT = m ∠WTR ( Alternate interior angles)
T -Z - R
m ∠SRZ = m ∠WTZ = 40°
Given criteria is satisfies the criteria of rectangles.
b. m ∠STZ = 40°
All the interior angles of rectangle are of measure 90°
m ∠STW = 90°
m ∠WTZ = 40° (given)
m ∠STZ + m ∠WTZ = 90°
⇒ m ∠STZ = 50°
Given option does not satisfies the criteria of rectangles.
c. m ∠SRW = 80°
All the interior angles of rectangle are of measure 90°
Given option does not satisfies the criteria of rectangles.
d. m ∠TWR = 80°
All the interior angles of rectangle are of measure 90°
Given option does not satisfies the criteria of rectangles.
Therefore, for the given rectangle RSTW, the condition satisfies the criteria of rectangles is equal to m ∠SRZ = 40°.
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If A=B and B=C, which property let's us say A=C?
Answers
Answer:
By using commutative property, if a = b and b = c, then a = c.
Step-by-step explanation:
Answer:
translative property
Step-by-step explanation:
I need help with this math problem. Find the distance between points J and M
Answers
Answer:
0.75
Step-by-step explanation:
in the pic
goodluck
rewrite this expression as an addition equation -4 3/8 - (-1 1/4)=
Answers
Given the equation:
[tex]\text{ - 4 }\frac{3}{8}\text{ - (-1 }\frac{1}{4})[/tex]8. Give the slope of y + 2 = 3(x-7) and a point on the line.
a. The slope is 3 and (-7, 2) is on the line.
b. The slope is 3 and (7, -2) is on the line.
c. The slope is 2 and (7, 3) is on the line.
d. The slope is 7 and (3, 2) is on the line.
9. What is the point-slope equation of the line containing the points (3, 3) and
(6,5)?
a. y - 3=(x-3)
b. y 3 = (x + 3)
c. y + 3 =(x-3)
d. y + 3 = 3(x - 2)
10. The slope of a given line is 3. The line that is parallel to it has a slope of:
a. -3
b. ½
C. -1
d. 3
11. The slope of a given line is 4. The line that is perpendicular to it has a slope of:
a. -4
b. -
C. 4
Answers
Answer: b c
Step-by-step explanation:
HELP IS DUE AT 10pm AND IM IN THE LAST QUESTION SOMEBODY PLEASE SOS
Answers
Notice how the graph has a sudden drop, and then slowly makes its way back up.
Ava is trying to add together 3/5 and 2/9
Her first step is to rewrite the fractions using their lowest common denominator.
What denominator should she use?
Answers
Explanation:
The LCM of 5 and 9 is 5*9 = 45
This is the LCD of the two fractions.
3/5 = 27/45 after multiplying top and bottom by 92/9 = 10/45 after multiplying top and bottom by 5So,
3/5 + 2/9 = 27/45 + 10/45 = 37/45
how dose parallelogram work
Answers
Answer:
Parallelograms are shapes with 2 pairs of parallel sides, like a square or a rhombus. Parallel means lines on a shape that never touches.
Step-by-step explanation:
Hope this helps!
P.S, brainliest? Thanks!
Rectangle 1 has an area on 60.81 square centimeters. Rectangle 2 has an area of 61.44 square centimeters. Rectangle 3 has an area of 35.52 square centimeters. Rectangle 4 has an area of 47.88 square centimeters. Part A “which two rectangles have the greatest difference in area?” Part B “Look at your answer to part A. What is the difference between those two rectangles areas?”
Answers
The most appropriate choice for area of rectangle will be given by-
Difference between area of rectangle 2 and area of rectangle 3 is the largest.
Difference is 25.92 [tex]cm^2[/tex]
What is area of rectangle?
Area of rectangle is the total space taken by the rectangle.
If l is the length of the rectangle and b is the breadth of the rectangle, then area of rectangle is given by
Area of rectangle = [tex]l \times b[/tex]
Here,
Area of rectangle 1 = 60.81 [tex]cm^2[/tex]
Area of rectangle 2 = 61.44 [tex]cm^2[/tex]
Area of rectangle 3 = 35.52 [tex]cm^2[/tex]
Area of rectangle 4 = 47.88 [tex]cm^2[/tex]
Difference between Area of rectangle 1 and rectangle 2 =
(61.44 - 60.81)[tex]cm^2[/tex]
= 0.63 [tex]cm^2[/tex]
Difference between Area of rectangle 1 and rectangle 3 =
(60.81 - 35.52)[tex]cm^2[/tex]
= 25.29 [tex]cm^2[/tex]
Difference between Area of rectangle 1 and rectangle 4 =
(60.81 - 47.88)[tex]cm^2[/tex]
= 12.93 [tex]cm^2[/tex]
Difference between Area of rectangle 2 and rectangle 3 =
(61.44 - 35.52)[tex]cm^2[/tex]
= 25.92 [tex]cm^2[/tex]
Difference between Area of rectangle 2 and rectangle 4 =
(61.44 - 47.88) [tex]cm^2[/tex]
= 13.56 [tex]cm^2[/tex]
Difference between Area of rectangle 3 and rectangle 4 =
(47.88 - 35.52) [tex]cm^2[/tex]
= 12.36 [tex]cm^2[/tex]
Difference between area of rectangle 2 and area of rectangle 3 is the largest.
Difference is 25.92 [tex]cm^2[/tex]
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