the correct option is b) 60°, as the smallest angle is 40°.
Step-by-step explanation:
Let's assume the angles of the quadrilateral are \(a\), \(2a\), \(4a\), and \(5a\), respectively.
According to the given information, the smallest angle is \(a\), which is either 120° or 40°.
a) If \(a = 120°\):
The four angles of the quadrilateral would be 120°, 240°, 480°, and 600°, respectively. However, angles in a quadrilateral cannot exceed 360°, so this option is not valid.
b) If \(a = 40°\):
The four angles of the quadrilateral would be 40°, 80°, 160°, and 200°, respectively. These angles are within the valid range for a quadrilateral.
Therefore, the correct option is b) 60°, as the smallest angle is 40°.
Help me plssss 5 stars to whoever answers
Answer:
f = 65
s = 144
t = 144
u = 77
Step-by-step explanation:
the sum of a triangles angles will always be 180
so we can subtract 37 and 78 from 180 to find f which is 65
in regards to s and t, the sum of those 4 angles will be 360, and we can assume the opposite sides of the angles are the same.
so the other side of the 36 angle will also be 36, so we subtract 36 and 36 from from 380 which gives us 288
then we divide it by 2 because we have 2 unknown angles that are the same size, then we get 144 for s and 144 for t
the sum of the angles of a polygon will always be 360
so we can subtract 86 and 53 and t (which we now know is 144) from 360 to find u
so u = 77
Selina claims single having one exemption. Her state tax deduction is 21% of her federal tax contribution. Calculate the amount of state tax Selina owes if her gross pay for two weeks is $840.
The following federal tax table is for biweekly earnings of a single person.
A 9-column table with 7 rows is shown. Column 1 is labeled If the wages are at least with entries 720, 740, 760, 780, 800, 820, 840. Column 2 is labeled But less than with entries 740, 760, 780, 800, 820, 840, 860. Column 3 is labeled And the number of withholding allowances is 0, the amount of income tax withheld is, with entries 80, 83, 86, 89, 92, 95, 98. Column 4 is labeled And the number of withholding allowances is 1, the amount of income tax withheld is, with entries 62, 65, 68, 71, 74, 77, 80. Column 5 is labeled And the number of withholding allowances is 2, the amount of income tax withheld is, with entries 44, 47, 50, 53, 56, 59, 62. Column 6 is labeled And the number of withholding allowances is 3, the amount of income tax withheld is, with entries 26, 28, 31, 34, 37, 40, 43. Column 7 is labeled And the number of withholding allowances is 4, the amount of income tax withheld is, with entries 14, 16, 18, 20, 22, 24, 26. Column 8 is labeled And the number of withholding allowances is 5, the amount of income tax withheld is, with entries 1, 3, 5, 7, 9, 11, 13. Column 9 is labeled And the number of withholding allowances is 6, the amount of income tax withheld is, with entries 0, 0, 0, 0, 0, 0, 1.
a.
$16.17
b.
$16.80
c.
$32.34
d.
$33.60
The amount of state tax Selina owes is $77.42.
To calculate the amount of state tax Selina owes, we need to follow the given information.
Selina's gross pay for two weeks is $840. We need to determine her federal tax contribution based on the provided tax table.
Looking at the federal tax table, we find that for a gross pay of $840, the federal tax withheld for 0 withholding allowances is $98.
Next, we calculate the state tax deduction, which is 21% of the federal tax contribution:
State tax deduction = 21% of $98
State tax deduction = 0.21 * $98
State tax deduction = $20.58
Finally, we subtract the state tax deduction from the federal tax contribution to find the amount of state tax Selina owes:
State tax owed = Federal tax contribution - State tax deduction
State tax owed = $98 - $20.58
State tax owed = $77.42
Therefore, the amount of state tax Selina owes is $77.42.
None of the provided options (a, b, c, d) match the calculated amount.
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Answer:
B. $16.56
Step-by-step explanation:
Got it right on edge 2023
HELP QUICK PLS, For each of the figures, write Absolute Value equation in the form
|x−c=d|, where c and d are some numbers, to satisfy the given solution set.
pls answer!
x = -8; x = -4
The absolute value equation for x = -4 can be written as:
|x - (-2)| = 2
We have,
For x = -8, the absolute value equation can be written as:
|x - c| = d
Substituting x = -8 into the equation, we have:
|-8 - c| = d
To satisfy the given solution set, we need to determine the values of c and d that make the equation true.
Since x = -8, the absolute value of -8 minus c should be equal to d.
For x = -8, a suitable choice of c would be -12 and d would be 4.
This gives us:
|-8 - (-12)| = 4
|4| = 4
Therefore, the absolute value equation for x = -8 can be written as:
|x - (-12)| = 4
Similarly, for x = -4, the absolute value equation can be written as:
|x - c| = d
Substituting x = -4 into the equation, we have:
|-4 - c| = d
To satisfy the given solution set, we need to determine the values of c and d that make the equation true.
Since x = -4, the absolute value of -4 minus c should be equal to d.
For x = -4, a suitable choice of c would be -2 and d would be 2. This gives us:
|-4 - (-2)| = 2
|-2| = 2
Therefore,
The absolute value equation for x = -4 can be written as:
|x - (-2)| = 2
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What is the meaning of "it is a subset of any X ∈ C"?
The phrase "it is a subset of any X ∈ C" indicates that the subject in question (denoted by "it") is a subset of every element X that belongs to the set C. In other words, whatever "it" refers to is contained within every element of the set C.
The phrase "it is a subset of any X ∈ C" indicates that the subject in question (denoted by "it") is a subset of every element X that belongs to the set C. In other words, whatever "it" refers to is contained within every element of the set C.
To provide a clearer understanding, let's break it down further:
"Subset": A subset is a collection of elements that are all contained within another set. If set A is a subset of set B, it means that every element of A is also an element of B.
"Any X ∈ C": Here, X represents a generic element of the set C. The phrase "X ∈ C" denotes that X belongs to the set C. It implies that X is one of the elements within the set C.
Combining the two parts, "it is a subset of any X ∈ C" means that "it" (referring to a specific set or collection of elements) is included in every element X of the set C. In other words, every element of C contains "it" as a subset.
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Triangle ABC - triangle DEF. Use the image to answer the question. Determine the measurement of DF.
A. DF=3.3
B. DF=2.37
C. DF=2.28
D. DF=1.1
The measure of DF is 2.28.
We have,
Triangle ABC ≅ Triangle DEF
So,
The ratio of the corresponding sides is equal.
Now,
BA/ED = AC/DF
Substitute the values.
11/3.3 = 7.6/DF
DF = (7.6 x 3.3) / 11
DF = 7.6 x 0.3
DF = 2.28
Thus,
The measure of DF is 2.28.
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Somraj had ₹1,78,500 in his bank account and after one year, he withdrew the amount completely along with the interest of 20,489. He bought a laptop for his son worth 36,725, a dining table worth 8,800, a bike worth 56,725 and deposited the rest in his wife's account. a. What is the total cost of the bike and the dining table? Which is costlier, the bike or the dining table? b. c. What is the amount that he deposited in his wife's account?
Answer:
Step-by-step explanation:
Let's calculate the total cost of the bike and the dining table first.
The cost of the bike is ₹56,725.
The cost of the dining table is ₹8,800.
To find the total cost, we add the cost of the bike and the cost of the dining table:
₹56,725 + ₹8,800 = ₹65,525
So, the total cost of the bike and the dining table is ₹65,525.
To determine which item is costlier, we compare the costs of the bike and the dining table. In this case, the bike is costlier as it costs ₹56,725, while the dining table costs ₹8,800.
Now, let's calculate the amount that Somraj deposited in his wife's account.
He initially had ₹1,78,500 in his bank account and withdrew the entire amount along with the interest of ₹20,489. Therefore, the total amount withdrawn is:
₹1,78,500 + ₹20,489 = ₹1,98,989
From this amount, he spent ₹36,725 on the laptop, ₹8,800 on the dining table, and ₹56,725 on the bike. So, the total amount spent on these items is:
₹36,725 + ₹8,800 + ₹56,725 = ₹1,02,250
To find the amount deposited in his wife's account, we subtract the total amount spent from the total amount withdrawn:
₹1,98,989 - ₹1,02,250 = ₹96,739
Therefore, Somraj deposited ₹96,739 in his wife's account.
Answer:
a. 65,525
b. bike
c. 96,739
Step-by-step explanation:
a.
total cost of the bike and the dining table,
= 56,725 + 8,800
= 65,525
b.
bike is costlier than the dining table.
c.
total amount somraj received from bank
= 1,78,500 + 20,489
= 198,989
total expenditures
= 36,725 + 8,800 + 56,725
= 102,250
amount he saved to deposit in his wife's account
= 198,989 - 102,250
= 96,739
Find the volume
1.Cone whose radius is 10cm and the height is 5cm.
2.Sphere whose radius is 5m.
3.Cone whose radius is 6m and the height is 20m.
Answer:
The answers are all in 2d.p
1)523.81cm³
2)166.67m³
3)754.29m³
Step-by-step explanation:
1)V=1/3pir²h
V=1/3×10²×5×22/7
V=523.81cm³
2)V=4/3pir³
V=4/3×5³
V=166.67m³
3)V=1/3pir²h
V=1/3×22/7×6²×20
V=754.29m³
A cylinder has a base diameter of 20 inches and a height of 2 inches. What is its volume in cubic inches, to the nearest tenths place?
Answer:
628.3 cubic inches
Step-by-step explanation:
Since the base diameter of the cylinder is d=20 inches, so its radius r is:
[tex]r=\frac{d}{2}=\frac{20}{2}=10[/tex]
Then, the volume V of the cylinder with radius r=10 inches and height h=2 inches is:
[tex]V=\pi r^{2} h=\pi\times 10^{2}\times 2=628.3[/tex]
Answer:
To find the volume of a cylinder, we need to use the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height. Since we are given the diameter of the base, which is 20 inches, we can find the radius by dividing it by 2. So, r = 20 / 2 = 10 inches. The height is given as 2 inches. Plugging these values into the formula, we get:
V = π(10)^2(2)
V = π(100)(2)
V = 200π
To get the volume in cubic inches, we need to multiply this by the conversion factor of 1 cubic inch per cubic inch. This does not change the value, but it gives us the correct units. So,
V = 200π cubic inches
To round this to the nearest tenths place, we need to look at the hundredths digit. If it is 5 or more, we round up; if it is less than 5, we round down. Using a calculator, we can approximate π as 3.14. So,
V ≈ 200(3.14) cubic inches
V ≈ 628 cubic inches
The hundredths digit is 0, which is less than 5. So we round down and keep the tenths digit as it is. Therefore,
V ≈ 628.0 cubic inches
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A steel manufacturer wants to produce a container in the shape of a rectangular solid with volume 84 m3 . The manufacturer wants the length of the container to be one meter longer than the width, and the height to be one meter greater than twice the width. What should the dimensions of the container be?
Answer:
Step-by-step explanation:
Use cramer's rule to solve this system: 8x+5y= 2x - 4y = - 10
The solution to the system of equations using Cramer's rule is x = -1 and y = 2.
To solve the system of equations using Cramer's rule, we'll need to determine the values of x and y by calculating the determinants of various matrices.
The given system of equations is:
8x + 5y = 2 (Equation 1)
2x - 4y = -10 (Equation 2)
First, let's calculate the determinant of the coefficient matrix, D:
D = |8 5|
|2 -4|
D = (8 * -4) - (5 * 2)
D = -32 - 10
D = -42
Next, we'll calculate the determinant of the matrix formed by replacing the x coefficients with the constants from the right side of the equations, Dx:
Dx = |2 5|
|-10 -4|
Dx = (2 * -4) - (5 * -10)
Dx = -8 + 50
Dx = 42
Similarly, we'll calculate the determinant of the matrix formed by replacing the y coefficients with the constants, Dy:
Dy = |8 2|
|2 -10|
Dy = (8 * -10) - (2 * 2)
Dy = -80 - 4
Dy = -84
Now, we can find the values of x and y:
x = Dx / D
x = 42 / -42
x = -1
y = Dy / D
y = -84 / -42
y = 2
Therefore, the solution to the system of equations is x = -1 and y = 2.
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Amy opened a savings account and deposited $300.00. The account earns 2% interest, compounded continuously. If she wants to use the money to buy a new bicycle in 1 year, how much will she be able to spend on the bike?
Use the formula A=Pert, where A is the balance (final amount), P is the principal (starting amount), e is the base of natural logarithms (≈2.71828), r is the interest rate expressed as a decimal, and t is the time in years.
The final amount is $2203. 2
How to determine the valueFrom the information given, the formula for finding the amount is expressed as;
A=Pert
Such that the parameters are;
A is the balance (final amount), P is the principal (starting amount) e is the base of natural logarithms (≈2.71828) r is the interest rate expressed as a decimal t is the time in years.Substitute the values, we have;
A = 300 × [tex]2.71^(^2^*^1^)[/tex]
Multiply the exponents, we have;
A = 300 × [tex]2.71^2[/tex]
Find the square value and multiply, we get;
A = $2203. 2
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Solve the following system of equations with the substitution method:
y=10/3x-121
y=5/4x-46
Answer:
x = 36
y = -1
Step-by-step explanation:
The substitution method is when the value of one variable from one equation is substituted in the other equation.
y = 10/3x - 121
y = 5/4x - 46
In this case you substitute one of the equations for y.
5/4x - 46 = 10/3x - 121
Lets set the coefficient being multiplied by x to a number with a common demoninator.
15/12x - 46 = 40/12x - 121
Next isolate x and combine like terms.
15/12x - 46 = 40/12x - 121
-15/12x -15/12x
-46 = 25/12x - 121
+121 +121
75 = 25/12x
*12/25 12/25
36 = x
------
Now lets plug x in to solve for y
(you pick either equation to do this)
y = 5/4(36) - 46
y= 45 - 46
y = -1
An investor was afraid that he would become like King Lear in his retirement and beg hospitality from his children, so he purchased grain "tithes," or shares in farm output, for 800 pounds. The tithes paid him 78 pounds per year for 30 years. What interest rate did the he receive on this investment?
as far as I can read it, he bought £800 in shares, who knows how many, is irrelevant in this case, however we also know that he got £78 for 30 years, what was the rate?
well, we can nevermind the 30 years part and keep an eye that every year his earned interest was £78 flat, so we're looking at a simple interest rate, since it's not compounding, so let's reword all that
with an initial investment of £800 yielding £78 per year, what's the interest rate?
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \pounds 78\\ P=\textit{original amount deposited}\dotfill & \pounds 800\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 78 = (800)(\frac{r}{100})(1) \implies 78=8r\implies \cfrac{78}{8}=r\implies \stackrel{ \% }{9.75}=r[/tex]
one serving of vegetables has 96 grams of protein witch is 30% of the recommended daily amount find the recommended daily amount of protein
Answer:
320 g
Step-by-step explanation:
To find the recommended daily amount of protein, we can set up a proportion using the given information:
30% of the recommended daily amount = 96 grams
Let "x" represent the recommended daily amount of protein. We can set up the proportion as:
30/100 = 96/x
To solve for x, we can cross-multiply and solve the equation:
30x = 100 * 96
30x = 9600
Dividing both sides by 30:
x = 9600 / 30
x ≈ 320
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
The probability of landing on purple to the nearest hundredth: 0.15
How to solveThe total number of spins is 84, and the probability of landing on purple is 13/84 = 0.15476.
Rounding to the nearest hundredth, this is 0.15.
Elaborating:
Number of times the spinner landed on purple: 13
Total number of spins: 84
Probability of landing on purple: (13/84) = 0.15476
Probability of landing on purple to the nearest hundredth: 0.15
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The Complete Question
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 18
Blue 15
Green 20
Yellow 18
Purple 13
Based on these results, express the probability that the next spin will land on purple as a decimal to the nearest hundredth.
Geometry
Show work
Please answer fast
Applying the Angle Addition Postulate, the measure of angle BDC is calculated as: 57 degrees.
How to Apply the Angle Addition Postulate?The Angle Addition Postulate establishes that when two angles are adjacent, the measure of the resulting angle formed by their combination is equal to the sum of their individual measures.
Therefore, according to the Angle Addition Postulate, we would have:
(-6x + 11) + (-7x + 15) = 104
Solve for x:
-6x + 11 - 7x + 15 = 104
-13x + 26 = 104
-13x = 104 - 26
-13x = 78
x = -6
Measure of angle BDC = -7x + 15
Plug in the value of x:
Measure of angle BDC = -7(-6) + 15 = 57°
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Calculate the dimensions of an irregular hexagon whose perimeter in 98 cm. Answer will vary.
The dimensions of the irregular hexagon are 17 cm, 15 cm, 14 cm, 13 cm, 22 cm and 17 cm
Calculating the dimensions of the irregular hexagonFrom the question, we have the following parameters that can be used in our computation:
Shape = irregular hexagon
Also, we have
Perimeter = 98 cm
The perimeter of a shape is the sum of its side length
An irregular hexagon has six unequal sides
using the above as a guide, we have the following:
17 + 15 + 14 + 13 + 17 + 22 = 98
This means that the side lengths are 17 cm, 15 cm, 14 cm, 13 cm, 22 cm and 17 cm
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please help if you can answer any it’s helpful thanks so much
Answer:quantom physics x=y
Step-by-step explanation:
need to get oxygen
Simplify each expression. Write your answer in exponential notation.
13. [(-0.5) (-0.5)²12²
14. (3.3³)3
تبر4 + 2( 20) .15
16. (a¹. a)³
(a^)³
Help I really need the extra credit
For simplification the exponent rules must be known to us .
The exponent rules are mentioned below:
a^0 = 1a^1 = aa^m × a^n = a^m+na^m / a^n = a^m−na^−m = 1/a^m(a^m)^n = a^mn(ab)m = a^mb^m(a/b)m = a^m/b^m1)
Now,
Simplifying,
[(-0.5)² *(-0.5)²]²
Apply property 3,
[(-0.5)^4]^2
(-0.5)^8
2)
(3.3³)3
Simplify by property 3
= 3 ^12
3)
(y² × y)²÷4y²
Simplify by rule 3 and 4,
= y^6 ÷ 4 y²
= y^4/4
4)
(a^3 × a^6)^3/(a^4)^5
Simplify by rule 3 and 4,
=a^7
Hence with the use of exponent rules the expressions can be simplified.
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if i were to make 126 dollars a week and i were to work for one year, how much money would i have when the year is over? please hurry
a racer is traveling 150 miles per hour how many feet dose it travel in 5 seconds
150 miles is the same as 150*5280 = 792000 feet, and one hour is equivalent to 60*60 = 3600 seconds. Now we divide 792000 feet by 3600 seconds to get the equivalent rate: 792000 ft/3600 sec = 220 ft/second. Now, we multiply the rate by 5 and get 1100 feet per 5 seconds. So, our answer is 1100 feet.
Write each expression in factored form. If it is not possible, write “not possible.”
a2−36
49−25b2
c2+9
10081−16d2
64+121b2
Expression in factored form
a² - 36 = (a + 6)(a - 6)
49 - 25b² = (7 - 5b)(7 + 5b)
c² + 9 = Not possible (sum of squares)
10081 - 16d² = (101 - 4d)(101 + 4d)
64 + 121b² = Not possible (sum of squares)
Let's factorize each expression:
a² - 36:
This expression is a difference of squares, as it can be written as (a + 6)(a - 6). Therefore, the factored form is (a + 6)(a - 6).
49 - 25b²:
This expression is also a difference of squares. It can be factored as (7 - 5b)(7 + 5b).
c² + 9:
This expression is not factorable because it is a sum of squares. The factored form is not possible.
10081 - 16d²:
This expression is a difference of squares. It can be factored as (101 - 4d)(101 + 4d).
64 + 121b²:
This expression is not factorable because it is a sum of squares. The factored form is not possible.
To summarize:
a² - 36 = (a + 6)(a - 6)
49 - 25b² = (7 - 5b)(7 + 5b)
c² + 9 = Not possible (sum of squares)
10081 - 16d² = (101 - 4d)(101 + 4d)
64 + 121b² = Not possible (sum of squares)
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A spinner with three equal size sections labeled red, green, and yellow is
spun once. Then a coin is tossed, and one of two cards labeled with a 1 or
a 2 is selected. What is the probability of spinning yellow, tossing heads,
and selecting the number 2?
FASTTT (ASAPPP!)
A 13 km 13km13, start text, k, m, end text stretch of road needs repairs. Workers can repair 3 1 2 km 3 2 1 km3, start fraction, 1, divided by, 2, end fraction, start text, k, m, end text of road per week. How many weeks will it take to repair this stretch of road?
you can start by dividing the total length of the road by the distance that can be repaired per week:
13 km ÷ 3 1/2 km/week = 3.71 weeks
Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.
What is the angle of o in the drawing below? Type in numerical answer only
Answer:
[tex]52 + o = 180[/tex]
[tex]o = 128[/tex]
Angle o measures 128°.
What is the co-interior angle x in the drawing below? Type in numerical answer only
Answer:
[tex]58 + x = 180[/tex]
[tex]x = 122[/tex]
Angle x measures 122°.
5/6x - 1/3 > 1 1/3
Solve for x
Answer:
First subtract (4) and (3x) from each side of the equation to isolate the x ... 5x-4=3x-8 One solution was found : x = -2 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation
Step-by-step explanation:
Answer:
x > 2
Step-by-step explanation:
To solve for x, we will first simplify the left side of the inequality by finding a common denominator for the fractions:
5/6x - 1/3 > 4/3
Multiplying both sides by 6 to eliminate the fractions, we get:
5x - 2 > 8
Adding 2 to both sides, we have:
5x > 10
Dividing both sides by 5, the final answer is:
x > 2
Hope this helps!
simplify and write in usual form ((5.5 * 10 ^ - 4)(6 * 10 ^ 7))/((3.3 * 10 ^ - 6) * (2 * 10 ^ 4) ^ 2)
Step-by-step explanation:
Expand the given 10 n and multiply it by the given number. 2. Then the result will be in the usual form.
2021: Sales Revenues = $800,000. Cost of good sold = $350,000
2020: Sales Revenues = $795,000. Cost of good sold = $600,000
Answer:
Step-by-step explanation:
Sales Revenue: $800.00
Cost of good sold: $350,000.00
Subtract: $450,000.00
Sales Revenue: $795,000.00
Cost of good sold: $600,000.00
Subtract Sales $195,000.00
Revenue from Cost
of goods sold.
in aright prism,all the lateral faces are rectangles. true or false
True. In a right prism, all the lateral faces are indeed rectangles.
Given data ,
A right prism is a three-dimensional solid with congruent polygonal bases and rectangular lateral faces that connect the corresponding sides of the bases.
Bases: A right prism has two parallel polygonal bases that are congruent. The bases can be any polygon, such as a triangle, rectangle, square, pentagon, etc. The shape of the bases determines the overall shape of the prism.
Height: The height of a right prism is the perpendicular distance between the two bases. It is the length of the lateral edges connecting the corresponding vertices of the bases.
Lateral Faces: The lateral faces of a right prism are rectangular in shape. They are perpendicular to the bases and connect the corresponding edges of the bases. The lateral faces are always parallelograms, and their opposite sides are equal in length.
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