The simplified expression is -7.1y - 7.8x + 14.8.
The given expression is 2.6y + 14.8 - 7.8x - 9.7y. To combine like terms, we first identify the terms that have the same variable with the same exponent. In this case, we have two terms with y, and they both have the exponent 1. So, we can combine these terms together by adding their coefficients, which are 2.6 and -9.7.
2.6y - 9.7y can be simplified as (2.6 - 9.7)y, which is equal to -7.1y. Therefore, the expression can be written as:
-7.1y - 7.8x + 14.8
We cannot combine any other terms in this expression since they do not have the same variable or exponent.
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Answer explication question
The solution is:
The equations are;
4(2x + 5) = 3(2x + 8)
x = 2
Perimeter of each shape is 36
Here, we have,
Mathematically;
The perimeter of a square is 4L
while the perimeter of an equilateral triangle is 3L
where L represents the lengths of the sides
Mathematically, from what we have in the question, since the perimeter are equal;
4(2x + 5) = 3(2x + 8)
8x + 20 = 6x + 24
8x-6x = 24-20
2x = 4
x = 4/2
x = 2
The side of the square will measure;
2(2) + 5 = 9
Its perimeter is 4(9) = 36
The side of the triangle will measure
2(2) + 8 = 12
Its perimeter will be 3(12) = 36
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Please answer this as quick as possible, wrong answers or chatgpt will be reported:
Q3. A Ferris wheel reaches a maximum height of 60 m above the ground and takes twelve minutes to complete one revolution. Riders have to climb a 4 m staircase to board the ride at its lowest point.
(a) [4 marks] Write a sine function for the height of Emma, who is at the very top of the
ride when t = 0.
(b) [2 marks] Write a cosine function for Eva, who is just boarding the ride.
(c) [2 marks] Write a sine function for Matthew, who is on his way up, and is at the same height as the central axle of the wheel.
For Matthew, the height is given as [tex]52 + 8 sin (\pi/6t)[/tex]
What is a Sine Function?To express the characteristic repetition of certain actions or events, a sine function is often employed.
This mathematical function links a position on the edge of a unit circle with the height of its corresponding y-coordinates. Conveyed generally as sin(x), it represents angle measurement in radians.
This repeatable pattern attains values between -1 to 1 and reappears once per every 2π radians. There are numerous applications of this type of sinusoidal oscillation pattern, including signal processing, engineering, and physics among others.
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PLEASE HELP I DO NOT UNDERSTAND!
A high school baseball player has a 0.197 batting average. In one game, he gets 8 at bats. What is the probability he will get at least 2 hits in the game?
The probability of the high school baseball player getting at least 2 hits in a game with 8 at bats, given his 0.197 batting average, is approximately 0.378.
To calculate the probability of the player getting exactly 2 hits in the game, we can use the binomial probability formula:
P(X = x) = (n choose x) x pˣ x (1-p)ⁿ⁻ˣ
Where:
P(X = x) is the probability of getting exactly k hits
n is the number of trials (in this case, 8 at bats)
k is the number of successful trials (in this case, 2 hits)
p is the probability of a successful trial (in this case, 0.197)
Using this formula, we can calculate the probability of the player getting exactly 2 hits in the game:
P(X = 2) = (8 choose 2) x 0.197² x (1-0.197)⁸⁻² = 0.214
So the probability of the player getting exactly 2 hits in the game is 0.214.
To calculate the probability of the player getting at least 2 hits in the game, we need to add up the probabilities of getting exactly 2 hits, exactly 3 hits, exactly 4 hits, and so on, up to 8 hits. This can be a bit cumbersome to do by hand, but fortunately, there are tools available to help us with this.
Using a binomial probability calculator or a statistical software program, we can find that the probability of the player getting at least 2 hits in the game is approximately 0.378.
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The maximum grade allowed between two stations in a rapid transit rail system is 2.6% between station and station B, which are 260 feet apart. The tracks rise 5 feet. What is the grade of the track between the stations round answer to the nearest 10th.
The grade of the track between the stations is approximately 1.9%.
How to calculate the grade of the track between the stations round answer to the nearest 10th.The grade of the track is given as a percentage by the change in elevation (climb) divided by the horizontal distance (run) between the two stations:
(climb / run) x 100% = grade
We are given a 5 foot ascent and a 260 foot horizontal distance (run). When we enter these values into the formula, we get:
1.92% = (5/260) x 100% = grade
Rounding to the nearest tenth, the grade of the track between the stations is approximately 1.9%.
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PLEASE HELP!! THIS IS URGENT!!
A rectangular prism is shown in the image.
A rectangular prism with dimensions of 3 yards by 5 yards by six and one-half yard.
What is the volume of the prism?
195 yd3
ninety seven and one half yd3
forty eight and three fourths yd3
thirty five and one half yd3
The volume of the rectangular prism is 97.5 cubic yards. (option b).
In this case, the rectangular prism has dimensions of 3 yards by 5 yards by 6 and one-half yard. To find its volume, we need to multiply these three dimensions together.
First, we need to convert the height of the prism to yards, as the other two dimensions are already given in yards. We know that 1 yard is equal to 3 feet, so 6 and one-half yards is equal to (6 x 3) + (1/2 x 3) = 18 + 1.5 = 19.5 feet. We then convert this to yards by dividing by 3, which gives us 6.5 yards.
Now, we can find the volume of the rectangular prism by multiplying the three dimensions together:
Volume = length x width x height
Volume = 3 yards x 5 yards x 6.5 yards
Volume = 97.5 cubic yards
Hence the correct option is (b).
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Sofie makes and sells scarves. Her profit depends on what price she charges for a scarf.
She writes the expression (x−5)(50−2x)
to represent her profit based on the price per scarf, x
.
Enter Sofie's average change in profit for two different sections of the graph.
A graph has price per scarf (dollars) on the x-axis, and profit (dollars) on the y-axis. A parabola with equation f (x) = (x minus 5) (50 minus 2 x) opens down and goes through (5, 0), has vertex (15, 200), and goes through (25, 0).
CLEAR CHECK
What is Sofie's average change in profit from x=5
to x=15
?
For every $1
increase in the price per scarf, Sofie's profit changes by an average of $
.
What is Sofie's average change in profit from x=15
to x=25
?
For every $1
increase in the price per scarf, Sofie's profit changes by an average of $
.
Which expression is equivalent to 7m+5.5(2+m)
?
Pour développer il faut appliquer la distributivité de la multiplication :
7m + 5.5(2+m) = 7m + 5.5 x 2 + 5.5m
= 7m + 11 + 5.5m
Il faut combiner les termes contenant m :
= 7m + 5.5m + 11
= (7 + 5.5)m + 11
= 12.5m + 11
solve for 8v = 3v + 25
Answer:
v = 5
Step-by-step explanation:
Collect like-terms:
[tex]8v = 3v + 25[/tex]
[tex]8v - 3v = 25[/tex]
[tex]5v = 25[/tex]
Divide both sides by 5 to make v the subject:
[tex]v = 5[/tex]
What is the height of the cylinder?
Answer: 6.996
Step-by-step explanation:
As given in the problem, V = πr²h
We are given V and r, so all we must do is plug them in and solve for h
[tex]351.68=\pi (4)^2h\\351.68=\pi 16h\\h=6.996[/tex]
please and thank you for helping
I have to divide
to find the area of each wing to founds the total area In square inches
And to find the wing area in square meters inches
The area of each wing to founds the total area as; 26000 square inches
We need to find the area of each wing to founds the total area In square inches
The dimensions are;
Length = 100 + 100 = 200 unit
Width = 70 + 70 = 130
Now the area of the wing
= Length x width
= 200 x 130
= 26000
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24. Brittany is making lemonade from
a mix. The instructions say to mix
8 scoops of powder per gallon, but
she is only making a quart. How
many scoops should Brittany use?
A. 1
B. 2
C. 4
D. 16
Answer:
B 2
Step-by-step explanation:because a quart is 0.25 of a gallon
A local wine equipment manufacturer is planning to issue stocks. The company just paid a dividend of $3.60. They now expect to pay dividends to grow at 15% for the next 3 years and thereafter grow at an annual rate of 8%. What should be the price of the stock given these revised forecasts? Assume a rate of return of 16%
a.How does a cumulative voting system allow minority representation in corporations?
Based on these expected future dividends and the rate of return required by investors, the price of the stock should be $414 in year 1, $476 in year 2, $547 in year 3, $93.24 in year 4, $114.53 in year 5, and $138.49 in year 6.
To calculate the price of the stock, we need to first determine the expected future dividends. We know that the current dividend is $3.60, and we can use the dividend growth rate to calculate the expected future dividends.
For the first three years, we can use the 15% dividend growth rate to calculate the expected dividends as follows:
Year 1: $3.60 x 1.15 = $4.14
Year 2: $4.14 x 1.15 = $4.76
Year 3: $4.76 x 1.15 = $5.47
The Gordon growth model is as follows:
P = D / (r - g)
where:
P = price of the stock
D = expected dividend payment
r = rate of return required by investors
g = expected dividend growth rate
Using the formula, we can calculate the price of the stock as follows:
Year 1: P = $4.14 / (0.16 - 0.15) = $414
Year 2: P = $4.76 / (0.16 - 0.15) = $476
Year 3: P = $5.47 / (0.16 - 0.15) = $547
After year 3, the expected dividend growth rate is 8%, so we can use this rate to calculate the price of the stock beyond year 3.
Year 4: P = $5.47 x 1.08 / (0.16 - 0.08) = $93.24
Year 5: P = $5.96 x 1.08² / (0.16 - 0.08) = $114.53
Year 6: P = $6.47 x 1.08³ / (0.16 - 0.08) = $138.49
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Given the geometric sequence an with the following information, find a10.
a2=-36 a7=128/27
The 10th term of the sequence is 1024/729
Finding the 10th term of the sequenceFrom the question, we have the following parameters that can be used in our computation:
a2 = 36
a7 = 128/27
The nth term of a geometric sequence is
an = a1 * r^(n -1)
So, we have
a2 = a1 * r = 36
a7 = a1 * r^6 = 128/27
Divide the equations
r^5 = (128)/(27 * 36)
This gives
r = [(128)/(972)]^1/5
So, we have
r = [(32)/(243)]^1/5
r = 2/5
Also, we have
a1 = 128/(27r^6)
The 10th term of the sequence is
a10 = a1 * r^9
So, we have
a10 = 128/(27r^6) * r^9
This gives
a10 = 128/(27) * r^3
This gives
a10 = 128/(27) * [2/3]^3
Evaluate
a10 = 128/27 * 8/27
This gives
a10 = 1024/729
Hence, the 10th term is 1024/729
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HELP PLS ASAPPP
I don't want to restart this entire thing so someone pls help
Answer:y=4/3x-14/3
Step-by-step explanation:
1. Find the slope of the original line
3/4x-y=7/2
-y=-3/4+7/2
y=3/4x-7/2
2. Using this find the negative reciprocal
3/4 -------- -4/3
3. Now insert -2,-2 in the equation y=-4/3x
-2=-4/3(-2)
-2=8/3
4. Find the needed intercept to make true.
-2=8/3-14/3
Therefore, y=-4/3x-14/3
What are the domain and range of the inequality? Refer to photo
The domain and the range of the given function is x ≥ 1 and y ≥ -4 respectively.
Given is a function, y ≤ √(x-1) -4, we need to find the domain and the range,
Domain = all the input values.
Range = all the output values.
So, the function is =
y ≤ √(x-1) -4
The related function can be written as =
y = √(x-1) -4
The function is defined if =
√(x-1) ≥ 0
∴ (x-1) ≥ 0
x ≥ 1,
In the given inequality, the sign of inequality is ≥, it means the points on the boundary line are included in the solution set. Thus, 1 is included in the domain.
So, the domain of the given inequality is x ≥ 1.
Now,
√(x-1) ≥ 0
√(x-1) -4 ≥ 0 - 4
y ≥ -4
The points on the boundary line are included in the solution set. Thus, -4 is included in the range.
So, the range of the given inequality is y ≥ -4.
Hence, the domain and the range of the given function is x ≥ 1 and y ≥ -4 respectively.
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In casino games the player roll a pair of dice . If the first throw is a 7or 11 the player wins automatically what is the probability that theplayer will win on the first throw
The probability of winning on the first roll is 0.22
Solution-
As in the game of casino, two dice are rolled simultaneously.
So the sample space would be,
|S| = 36
Let E be the event such that the sum of two numbers are 7, so
E = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)}
|E| = 6
P(E) = 6/36
Let F be the event such that the sum of two numbers are 11, so
F = {(6,5), (5,6)}
|F| = 2
P(F) = 2/36
Now,
P(E∪F)= 0.22
The probability of winning on the first roll is 0.22
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Find the mode of these numbers:4,2,4,2,3,0,1,2,4,1,3,4,2
Answer:
2 and 4
Step-by-step explanation:
Answer: 4,2
Step-by-step explanation:
Mode: Number that repeats itself more
If there are 2 or more numbers that repeat themself the same amount you put both.
4,2,4,2,3,0,1,2,4,1,3,4,2
4: 4 times
2: 4 times
3: 2 times
0: 1 time
1: 2 times
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500.
the voltage V in a circuit is given by V=\sprt(PR) where P is the power and R is the resistance in ohms. a. if the voltage circuit is 120 volts and the circuit produces 1500 watts of power, what is the resistance in the circuit?
The resistance in the circuit is 9.6 Ohms.
What is the resistance in the circuit?Ohm’s law states that the potential difference between two points is directly proportional to the current flowing through the resistance.
Given that:
V = √(PR)
Where P is the power and R is the resistance in ohms.
Make the resistance R, the subject of the formula.
V = √(PR)
V² = (√(PR) )²
V² = PR
PR = V²
R = V²/P
Plug in Voltage V = 120V and Power P = 1500 watts
R = V²/P
R = (120)² / 1500
R = 14400 / 1500
R = 9.6 Ω
Therefore, the resistance is 9.6 Ω.
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Bernice made 950 ml of gravy to go with her 5 kg turkey. The capacity of the gravy dish is 540 ml. How much gravy will be left in the pot after Bernice fills up the gravy dish?
After filling up the gravy dish, Bernice will have 410 ml of gravy left in the pot.
We have,
Determine the amount of gravy needed to cover the turkey:
We know that Bernice made 950 ml of gravy to go with a 5 kg turkey.
There are different ways to estimate how much gravy is needed to cover a turkey, but a common rule of thumb is to allow for about 1/2 cup (or 120 ml) of gravy per serving.
Assuming that the turkey will be served to about 8 people, we can estimate that Bernice will need:
We can write it as an expression:
= 120 ml/serving x 8 servings
= 960 ml of gravy
This means that Bernice made just enough gravy to cover the turkey and have a little bit left over.
Calculate how much gravy will be left in the pot:
We know that the capacity of the gravy dish is 540 ml.
If Bernice fills up the gravy dish with gravy, she will have.
= 950 ml - 540 ml
= 410 ml of gravy left in the pot.
Therefore,
After filling up the gravy dish, Bernice will have 410 ml of gravy left in the pot.
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−3a+6b=a+4b, what does A =
Answer:
a= b/2
Step-by-step explanation:
it is in internet
4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f4.67 f
The representation of 4.67 on the number line upto 4-decimal places. can be given in image. A picture of numerals along a straight line is called a number line.
A picture of numerals along a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.
Just to refresh your memory, the entirety of a number is a collection of numbers that contains both zero (0) and all the numbers that count (1, 2, 3,4,5,6), while the number that is natural is a collection of all counting values (1, 2, 3,4, 5, 6). The representation of 4.67 on the number line upto 4-decimal places. can be given in below image.
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Your question is incomplete but most probably your full question was,
Visualise the representation of 4.67 on the number line upto 4-decimal places.
Shandin looks at the prices of 5 skateboards. The prices are $65, $79, $95, $80, and $175. These prices contain one extreme value ($175). Which measure of center should Shandin use to describe the prices? A. Mean absolute deviation (MAD) OB. Mean O C. Range O D. Median
Answer:
Shandin should use the median to describe the prices since it is a more robust measure of center that is not affected by extreme values. In this case, the median is $80, which represents the middle value when the prices are arranged in ascending order: $65, $79, $80, $95, and $175. The mean and range can be affected by the extreme value of $175, and the MAD is a measure of dispersion rather than center.
Answer:
D
Step-by-step explanation:
Solve the following simultaneous equation using algebra
6x+3y=45
The solution to the simultaneous equation is x = 6 and y = 3.
To solve this system of equations, we can use the method of elimination. First, we want to eliminate one of the variables, either x or y. In this case, it is easiest to eliminate y. To do so, we can multiply the second equation by 3, which gives us:
6x + 3y = 45
6x - 6y = 18
Now, we can subtract the second equation from the first:
6x + 3y - (6x - 6y) = 45 - 18
Simplifying this expression, we get:
9y = 27
Dividing both sides by 9, we get:
y = 3
Now that we know the value of y, we can substitute it into either equation to find the value of x. Let's use the first equation:
6x + 3y = 45
6x + 3(3) = 45
6x + 9 = 45
Subtracting 9 from both sides, we get:
6x = 36
Dividing both sides by 6, we get:
x = 6
Correct Question :
Solve the following simultaneous equation using algebra
6x+3y=45
2x-2y=6
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Please answer the question
The correct statement about the product of 5/12 and 7 is given as follows:
C. The product is greater than 5/12 but less than 7.
How to calculate the product?The multiplication operation for this problem is given as follows:
5/12 x 7.
The factors of the operation are given as follows:
5/12 and 7.
When two fractions multiply each other, the product is given by the multiplication of the numerators divided by the multiplication of the denominators, hence:
5/12 x 7 = (5 x 7)/(12 x 1) = 35/12.
35/12 is a number close to 3, which is:
Greater than 5/12.Less than 7.Hence option C is the correct statement.
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Which addition equation can you make a 10 to add choose 2 that apply
13+15=
49+28=
20+47=
45+35=
We can add 13 and 15, or 49 and 28, or 20 and 47, or 45 and 35 to make 10 in the equations
To add choose 2 numbers to make 10, we can use the fact that 10 is the sum of 6 and 4.
Therefore, we can add a number that is 6 more than 10 and another number that is 4 less than 10.
This gives us the following equations:
13 + 15 = 28, since 13 + 15 = 28 and 10 = 6 + 4
49 + 28 = 77, since 49 + 28 = 77 and 10 = 6 + 4
20 + 47 = 67, since 20 + 47 = 67 and 10 = 6 + 4
45 + 35 = 80, since 45 + 35 = 80 and 10 = 6 + 4
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Michelle works for 33 hours this
week. She earns $10 per hour.
Her pay after taxes is $277.11.
How much does she pay in
payroll tax?
This week, Michelle works 33 hours. She is paid $10 per hour. Her take-home pay is $277.11 after taxes. She pays $ 52.89 in payroll tax.
We know that Michelle works for 33 hours this week and her pay for one hour is $10. So, firstly we will calculate her total pay for this week.
Total pay for week = pay for one hour × hours worked
= 10 × 33
= $ 330
Now, after taxes her pay is $277.11. So,
Tax = Pay before tax - pay after tax
= 330 - 277.11
= $ 52.89
A payroll tax is a tax paid by both employees and employers on wages, tips, and salaries. Employers withhold taxes from employees' paychecks and pay them to the government.
Federal, state, and municipal income taxes, as well as the employee's contribution of Social Security and Medicare taxes (FICA), are all included.
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Please answer this Calculus webwork question about differential equations:
The area of the enclosed region is 16√2 - 8 squared units
We have,
The region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π consists of two parts, one above the x-axis and one below the x-axis. We can find the area of each part separately and then add them to get the total area.
First, let's find the x-coordinates of the points where the curves intersect. These are the points where 4 sin(x) = 4 cos(x), or sin(x) = cos(x), which occurs when x = π/4 + kπ/2 for any integer k. Since we are only interested in the intersection points between x = 0 and x = 0.9π, we only need to consider the case k = 0. So the intersection point is x = π/4.
Now, let's consider the part of the region above the x-axis. We need to find the area between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = π/4. This is given by the integral:
A1 = ∫[0, π/4] (4 sin(x) - 4 cos(x)) dx
Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:
A1 = ∫[0, π/4] (4 sin(x) - 4 sin(x + π/2)) dx
= ∫[0, π/4] (4 sin(x) + 4 sin(x)) dx (since sin(x + π/2) = sin(x))
= 8 ∫[0, π/4] sin(x) dx
= 8 [-cos(x)] [0, π/4]
= 8 (1 - 1/√2)
= 8√2 - 8
Next, let's consider the part of the region below the x-axis. We need to find the area between the curves y = 4 cos(x) and y = 4 sin(x) from x = π/4 to x = 0.9π. This is given by the integral:
A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 sin(x)) dx
Using the identities sin(x) = cos(x - π/2) and cos(x) = sin(x + π/2), we can rewrite this as:
A2 = ∫[π/4, 0.9π] (4 cos(x) - 4 cos(x - π/2)) dx
= ∫[π/4, 0.9π] (4 cos(x) + 4 sin(x)) dx (since cos(x - π/2) = sin(x))
= 4 ∫[π/4, 0.9π] (2 cos(x) + 2 sin(x)) dx
= 4 [2 sin(x) - 2 cos(x)] [π/4, 0.9π]
= 4 (2/√2 + 2) - 4 (1 - 1/√2)
= 8√2
So the total area of the region enclosed between the curves y = 4 sin(x) and y = 4 cos(x) from x = 0 to x = 0.9π is:
A = A1 + A2
A = 8√2 - 8 + 8√2
A = 16√2 - 8 squared units
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Find the surface area of the prism shown below. You can assume that this prism has all faces, including the bottom.
Show all formulas, work, and drawings that you made to answer the question, and do not forget to include appropriate units.
The surface area of the prism including rectangles and triangles is equal to 13920 square units.
Prism has,
Two rectangles with side length 20 and 120.
Area of rectangle = length × width
= 20 × 120
= 2400
2400 × 2 = 4800
Two rectangles with side length 20 and 30.
Area of rectangle = length × width
= 20 × 30
= 600
600 × 2 = 1200
Two rectangles with side length 17 and 120.
Area of rectangle = length × width
= 17 × 120
= 2040
2040 × 2 = 4080
One rectangle with side length 120 and 30
Area of rectangle = length × width
= 30 × 120
= 3600
Two triangles with base 30 and height 8.
area of triangle = ( 1/2) × 30 × 8
= 120
120 × 2 = 240
Surface area of the prism
= Area of all rectangles + Area of two triangles.
= 4800 + 1200 + 4080 + 3600 + 240
= 13920
Therefore, the surface area of the prism is equal to 13920 square units.
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