The total volume is 5760cm^3
What is the volume?Here we have a composite figure that can be decomposed into two simpler ones, such that the simpler ones are rectangular prisms of:
12 cm by 20 cm by 8 cm
12 cm by 40 cm by 8cm
We know that the volume is equal to the product between the dimensions, then the volumes are:
v1 = 12cm*20cm*8cm = 1,920 cm^3
v2 = 12cm*40cm*8cm = 3,840cm^3
The total volume is the sum of these two:
V = 1920cm^3 + 3840cm^3 = 5760cm^3
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The country of Sylvania has decided to reduce the number
3
of its illiterate citizens by
5 each year. This year there are
9000 illiterate people in the country.
Write a function that gives the number of illiterate people in Sylvania, P(t), t years from today.
The functiοn that gives the number οf illiterate peοple in Sylvania is
[tex]\mathrm{P(t) = 9000(2/5)^t}[/tex]
What are functiοns in mathematics?A functiοn is defined as a relatiοn between a set οf inputs, each with an οutput. Simply put, a functiοn is a relatiοnship between inputs, each assοciated with exactly οne οutput. Each functiοn has a dοmain and cοdοmain οr scοpe.
Hοw tο identify relatiοn and functiοn?Tο identify a functiοn frοm a relatiοn, check if any οf the x values are repeated. If it's nοt repeated, it's a functiοn. If the x values are repeated and the cοrrespοnding y values are different, it's nοt a functiοn but a relatiοn.
Sοlutiοn accοrding tο the questiοn:
Given, Tοtal number οf illiterate peοple = 9000
Amοunt = 3/5
Fοr the first year = 9000 × (1 - 3/5) = 9000(2/5)
Nοw, fοr "t years":
P(t) = 9000(2/5)
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Drag each set of coordinates to the correct location on the table. Calculate the distance between the pairs of coordinates, and classify them according to the distance between them. (3, 4) and (2, 1) (3, 7) and (5, 2) (5, -2) and (3, 3) (-2, 3) and (1, 2) (-4, -2) and (-3, 1) (4, -1) and (-1, 1)
The distances based on their values, we have:
Distances of approximately 1 to 2 units: (-3, 1) and (-4, -2)
Distances of approximately 3 units: (2, 1) and (1, 2)
Distances of approximately 5 units: (3, 7) and (4, -1), (5, -2) and (3, 3), and (-1, 1) and (4, -1).
Coordinates (3, 4) (3, 7) (5, -2) (-2, 3) (-4, -2) (4, -1)
(2, 1) 3.16
(5, 2) 5.39
(3, 3) 5.1
(1, 2) 3.16
(-3, 1) 1.41
(-1, 1) 5.1
We may use the distance formula to determine the separation between each pair of coordinates:
Distance is equal to sqrt((x2 - x1) + (y2 - y1))
Using the values to categorise the distances, we have:
About 1 to 2 unit distances are (-3, 1) and (-4, -2)
Distances roughly 3 units apart: (2, 1) and (1, 2) Distances roughly 5 units apart: (3, 7) and (4, -1), (5, -2) and (3, 3), and (-1, 1) and (4, -1).
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URGENT!!! A dolphin swims 665,280 feet in 3 hours. Use the formula d = rt, where d represents distance, r represents rate, and t represents time, to answer the following questions. Show your work.
Rearrange the distance formula, d = rt, to solve for time.
Answer:
Step-by-step explanation:
665,280 dived by 3 = 221760
221760 = distance
221760 = per 1 hour
I tried my best :}
Find the measurements of X
pt
Answer:
x = 15°
Step-by-step explanation:
the inscribed angle APB is half the measure of the central angle AOB , so
x = [tex]\frac{1}{2}[/tex] × 30° = 15°
Suppose you own a large grocery store and are trying to save money by controlling
your inventory costs for beans, which you order by the whole case. Each year you
order a total of 675 cases. Suppose that you know that your yearly inventory cost
if you order Q cases of beans at a time is given by , where C is
yearly inventory cost measured in dollars.
a) What is your yearly inventory cost if you order one case at a time? Explain in
context what your answer means.
b) How many cases should you order at a time to minimize your annual inventory
cost? [Be sure to provide evidence supporting your answer.]
c) How much money will you save each year by ordering based on your answer to
part b) instead of ordering one case at a time?
d) When you are minimizing your annual inventory cost as in part b), about how
often should you place your orders? [Be sure to provide evidence supporting
675 cases divided by 135 cases per order equals five orders each year
a) If you order one case at a time, your yearly inventory cost is $6,750. This means that if you order one case of beans each year, it will cost you a total of $6,750.
b) To minimize your annual inventory cost, you should order 135 cases at a time. This is the number of cases that produces the minimum value for the cost equation, C = 200Q + 5,750.
c) By ordering 135 cases at a time instead of one, you will save $3,750 each year in inventory costs.
d) When you are minimizing your annual inventory cost, you should place your orders every five years. This is because 675 cases divided by 135 cases per order equals five orders each year.
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answer quick please!!
Match the following reasons with the statements given.
Prove:
The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.
Given:
RAS is isosceles
AM is median
Prove:
RAM SAM
1. Triangle RAS is isosceles, AM is a median
Reflexive
2. AR = AS
Definition of median
3. AM = AM
Given
4. MR = MS
Definition of isosceles triangle.
5. Triangle RAM congruent to Triangle SAM
SSS
The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.
What is median ?The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Each triangle has three medians, one from each vertex, and they are concurrent at a point called the centroid. The median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.
According to given information :Triangle RAS is isosceles, AM is a median --> Definition of isosceles triangleAR = AS --> Definition of medianAM = AM --> ReflexiveMR = MS --> Median divides the base into two congruent segmentsTriangle RAM congruent to Triangle SAM --> SASTherefore, the median from the vertex angle of an isosceles triangle divides the triangle into two congruent triangles.
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Roland and Vickie are salespeople who earned the same amount this week, although Vickie made 8 more sales than Roland. Roland earns a base of $49 plus $15 per sale. Vickie earns a base of $145 plus $6 per sale. How many sales did Roland make this week?
Roland made 16 sales this week, while Vickie made 8 more sales than Roland.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
Let x represent the number of sales Roland has.
Roland earns a base of $49 plus $15 per sale. HenceL
Total earning by Roland = 15x + 49
Vickie made 8 more sales than Roland. Vickie earns a base of $145 plus $6 per sale.
Total earning by Vickie = 6(x + 8) + 145 = 6x + 193
Roland and Vickie are salespeople who earned the same amount this week, Therefore:
15x + 49 = 6x + 193
9x = 144
x = 16
Roland made 16 sales this week.
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Help!!!!
I’m on the last question
Answer: 28
Step-by-step explanation: Both Of Those Triangles Are Equal. That Means They Both Equal 14. So If We Multiply 14 With 2, We Would Get 28 cm!
Hoped This Helped!
Answer:
28cm
Step-by-step explanation:
its a perfect rectangle so both triangle are Reflexive property so they would be the same size
work Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x)=-5x^(4)-4x^(3)+3x^(2)+5x+10
The answer of possible rational zeros for the given function f(x)=-5x^(4)-4x^(3)+3x^(2)+5x+10 are ±1, ±2, ±5, ±10, ±1/5, and ±2/5
The Rational Zero Theorem states that if f(x) is a polynomial with integer coefficients, then any rational zero of f(x) must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
To find the possible rational zeros for the given function f(x)=-5x^(4)-4x^(3)+3x^(2)+5x+10, we need to list the factors of the constant term (10) and the factors of the leading coefficient (-5).
Factors of 10: ±1, ±2, ±5, ±10
Factors of -5: ±1, ±5
Now, we can list all possible rational zeros by taking each factor of the constant term and dividing it by each factor of the leading coefficient:
Possible rational zeros: ±1/1, ±2/1, ±5/1, ±10/1, ±1/5, ±2/5, ±5/5, ±10/5
Simplifying the fractions gives us the final list of possible rational zeros:
Possible rational zeros: ±1, ±2, ±5, ±10, ±1/5, ±2/5, ±1, ±2
Removing duplicates, we get:
Possible rational zeros: ±1, ±2, ±5, ±10, ±1/5, ±2/5
Therefore, the possible rational zeros for the given function f(x)=-5x^(4)-4x^(3)+3x^(2)+5x+10 are ±1, ±2, ±5, ±10, ±1/5, and ±2/5.
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A (-1,6)
Work out the length of AB.
Give your answer to 3 significant figure
O
B (5, 3)
thagoras' Theorem - Line on a Graph
8
X
Answer:
AB = 6.71
Step-by-step explanation:
The vertical leg of the right triangle
= absolute value of difference in y-coordinates between A(-1, 6) and B(5, 3)
= |6 - 3| = |3|
= 3
The horizontal leg of the right triangle
= absolute value of difference in x-coordinates between A(-1, 6) and B(5, 3)
= |- 1 - 5|
=|- 6|
= 6
By the Pythagorean theorem, the hypotenuse AB is related to each of these two legs by the formula
AB² = 3² + 6²
AB² = 9 + 36
AB² = 45
AB = √45
or
AB = 6.7082039324
= 6.71 significant to 3 significant figures
Significant figures means number of digits excluding leading and trailing zeros
In each case determine whether W is a subspace of R ^ 2 . If W is a subspace, then give a geometric description of W.
1. W = \{x / x_{1} = 2x_{2}\}
2. W = \{x / x_{1} - x_{2} = 2\}
3. W=\ x / x_{1} = x_{2} or x_{1} = - x_{2}
4. W = {x: x₁ and x_{2} are rational numbers}
5. W = \{x / x_{1} = 0\}
6. W = \{x / |x_{1}| + |x_{2}| = 0\}
If W is a subspace, then
1. Geometric description of W is a line passing through the origin with a slope of 2.
2. W is not a subspace of R ^ 2.
3. Here, W is the union of two lines passing through the origin with slopes of 1 and -1.
4. In this case, W is not a subspace of R ^ 2.
5. Geometrically, W is a line passing through the origin with a slope of 0.
6. Here, Geometrically, W is a single point at the origin.
1. W = \{x / x_{1} = 2x_{2}\} is a subspace of R^2 because it satisfies the three conditions of being a subspace: it contains the zero vector (0,0), it is closed under addition, and it is closed under scalar multiplication. Geometrically, W is a line passing through the origin with a slope of 2.
2. W = \{x / x_{1} - x_{2} = 2\} is not a subspace of R^2 because it does not contain the zero vector (0,0). Geometrically, W is a line that does not pass through the origin.
3. W=\ x / x_{1} = x_{2} or x_{1} = - x_{2} is a subspace of R^2 because it satisfies the three conditions of being a subspace. Geometrically, W is the union of two lines passing through the origin with slopes of 1 and -1.
4. W = {x: x₁ and x_{2} are rational numbers} is not a subspace of R^2 because it is not closed under scalar multiplication. For example, if we multiply the vector (1/2, 1/3) by the scalar √2, we get the vector (√2/2, √2/3), which is not in W. Geometrically, W is the set of all points with rational coordinates.
5. W = \{x / x_{1} = 0\} is a subspace of R^2 because it satisfies the three conditions of being a subspace. Geometrically, W is a line passing through the origin with a slope of 0 (the x-axis).
6. W = \{x / |x_{1}| + |x_{2}| = 0\} is a subspace of R^2 because it contains only the zero vector (0,0), which satisfies the three conditions of being a subspace. Geometrically, W is a single point at the origin.
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What is the missing angel
The missing angle as labelled in the task content and required to be determined is; 33°.
What is the measure of the missing angle?It follows from the task content that the missing angle is to be determined from the task content.
By the use of trigonometric ratios;
The missing angle, x can be determined as follows;
tan (x) = 9.09 / 14
x = tan-¹ (9.09/14).
x = 32.995°
The missing angle is therefore; 33°.
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Please answer number 10, make sure to answer both parts. Thank you.
The volume is 3x³ + 16x² + 3x - 10, while when the height is reduced by 50%, the new volume is (1/2)(3x³ + 16x² + 3x - 10)
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.
The volume of the triangular prism is:
Volume = area of base * height
Substituting:
Base area = (1/2) * (2x + 2) * (x + 5) = x² + 6x + 5; height = 3x - 2
Volume = area of base * height = (x² + 6x + 5)(3x - 2)
Volume = 3x³ + 18x² + 15x - 2x² - 12x - 10 = 3x³ + 16x² + 3x - 10
The volume is 3x³ + 16x² + 3x - 10
If the height is reduced by 50%, new height = (1/2)(3x - 2)
Volume = area of base * height = (x² + 6x + 5) * (1/2)(3x - 2)
Volume = (1/2)(3x³ + 16x² + 3x - 10)
The new volume is (1/2)(3x³ + 16x² + 3x - 10)
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help me with this please
Ok, ik this may be impossible without a protractor. But im Still Gonna Ask for Help…
Answer:
You must be really must to answer that paper yho
85% if the sixth graders voted to have outdoor recess. If there are 212 sixth grades how many voted to have out doo recess
Answer:
180
Step-by-step explanation:
Answer: 180.2
Step-by-step explanation: 85% of 212 is 180.2
REVIEW
At a grocery store, Ethan buys 4 bananas and 5 oranges for $5.60. The total cost of one banana and one orange is $1.20.
How much does each orange cost?
Answer:
The answer to your problem is, $0.60
Step-by-step explanation:
1 banana and 1 orange = 1.20.
We divide next:
1.20 / 2 = 0.60.
We know that because in the question it says one banana and one orange is 1.20. Next we divide because two items are sharing the same number.
1.20 / 2 = ? ( ? = 0.60 or 0.6 )
Thus the answer to our problem is, $0.60
anyone knows the answer PLEASE for this question
Answer:
1= b to the second power, 2=a to the second power, 3=b to the fourth power, 4=a to the fourth
Step-by-step explanation: your welcome
Answer: 2)b^2+a^2
Step-by-step explanation:
x and y would have to be the same value since y(sin) and x(cos) of x and y on the unit circle is the same meaning it's the same point. Thus, cos(x-y) = cos(0) = 1. b^2+a^2=cos^2(x)+sin^2(x)= 1.
Use the table below to calculate the average percent change in population in California from 2000-2009.
If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
Answer:
Step-by-step explanation: your hot
For the piecewise function, find the values h(- 8), h(-3), h(2), and h(5). -2x 10, for x< -7 2. x+3, forx22 h(x) = for 7sx<2 h(-8) = h(-3) = h(2) = h(5)
The numeric values of the piece-wise function are given as follows:
h(-8) = 26.h(-3) = 16.h(2) = 4.h(5) = 7.How to calculate the numeric value of a function or of an expression?To obtain the numeric value of a function or of an expression, we replace each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression.
A piece-wise function is a function that has different definitions, based on the input interval of the function.
For x < 2, the function is defined as follows:
h(x) = -2x + 10.
Hence the numeric values on the interval are obtained as follows:
h(-8) = -2(-8) + 10 = 26.h(-3) = -2(-3) + 10 = 16.For x >= 2, the function is defined as follows:
h(x) = x + 2.
Hence the numeric values on the interval are obtained as follows:
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Mike constructed a kite by attaching two congruent triangles as shown in the diagram below.
Which equation can Mike use to determine the amount of material, in square inches, needed to create the kite?
F. A=[12(12)(8)]⋅2
G.A=[12(6)(8)]⋅2
H.A=[(12)(4)]⋅2
J.A=[(6)(10)]⋅2
The amount of material, in square inches, needed to create the kite is A = [1/2(6)(8)].2. Option G is the correct answer.
What is area of an isosceles triangle?Either of a triangle's two sides that are equal in length is said to be isosceles. This characteristic equates to the triangle's two angles being equal. Two of the sides and two of the angles of an isosceles triangle are equal. An isosceles triangle has three sides that are all the same length, have the same angles, and meet at symmetrical corners. Two right-angle triangles are produced if a perpendicular line is traced from the junction of two equal sides to the base of the unequal side.
The area of the triangle is given as:
A = 1/2(b)(h)
Here, the base = 6 and height = 8 in.
Thus, the area of the triangle is:
A = 1/2(6)(8)
The figure consists of 2 similar triangles. So, the area of the second triangle is added to get the final area.
A = [1/2(6)(8)].2
Hence, the amount of material, in square inches, needed to create the kite is A = [1/2(6)(8)].2. Option G is the correct answer.
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Given the linear equation of y=8, comparing to the equation of
the straight line, what is c?
A. 0
B. 1
C. 8
D. Cannot be calculated
The value of c is 8 (option C).
Determine he value of cTo find the value of c in a linear equation, we can compare the given equation to the standard form of a linear equation, which is y = mx + c.
In this case, the given equation is y = 8. If we compare this to the standard form, we can see that m (the slope) is 0 and c (the y-intercept) is 8.
Therefore, the value of c is 8.
So, the correct answer is C. 8
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the sum of series whose n term is 3(2x+1) is
i need detailed answer
The sum of a series whose nth term is 3(2x+1) can be calculated using the formula: S = (n/2)(3a + 3d + a), where a = the first term of the series and d = the common difference between the terms. In the given series, the first term is 3(2x+1), and the common difference is 3. Therefore, the sum of the series is: S = (n/2)(3(2x+1) + 3(3) + (2x+1)) = (n/2)(9x + 10)
her body fat is 14.9% she weighs 172 pounds how much of her weight is made up of fat?
25.628 pounds of her weight is made up of fat.
We can use the formula Weight of Fat = Body Fat % x Body Weight. To find out how much of her weight is made up of fat, we need to multiply her body fat percentage by her weight. We can do this by using the following formula:
Body fat weight = Body fat percentage x Weight
In this case, the body fat percentage is 14.9% and the weight is 172 pounds. Plugging these values into the formula, we get:
Body fat weight = 14.9% x 172 pounds
Body fat weight = 0.149 x 172 pounds
Body fat weight = 25.628 pounds
In this case, 14.9% of 172 pounds is 25.628 pounds.
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A robot can complete 7 tasks in ⅖
hour. Each task takes the same amount of time. How long does it take the robot to complete one task?
Answer: [tex]\frac{2}{35}[/tex] hour
Step-by-step explanation:
We will divide the time it takes it to do 7 tasks (⅖ hour) by the number of tasks it does in that time frame (7 tasks) to find the time per task.
[tex]\frac{2}{5}[/tex] hour / 7 tasks = [tex]\frac{2}{5} *\frac{1}{7}[/tex] = [tex]\frac{2}{35}[/tex] hour or about 3.43 minutes
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A sample is taken from the 15th and 50th items from 100
production lines. Which is this sampling method?
Answer options:
Systematic sampling
Cluster sampling
Convenient sampling
Stratified sampling
A sample is taken from the 15th and 50th items from 100 production lines. The sampling method used in this scenario is Systematic sampling.
Systematic sampling is a method in which a sample is taken at regular intervals from a larger population. In this case, the sample is taken from the 15th and 50th items from 100 production lines, meaning that the sample is taken at regular intervals from the larger population of 100 production lines.
This method is different from cluster sampling, which involves dividing the population into groups and then selecting a sample from each group. It is also different from convenient sampling, which involves selecting a sample based on convenience or accessibility.
Finally, it is different from stratified sampling, which involves dividing the population into strata and then selecting a sample from each stratum. Therefore, the correct answer is Systematic sampling.
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14
Nadia was considering two different vacation packages. For each, she wrote a linear equation
to model the cost of airfare and'n nights in a hotel. She graphed the corresponding lines and
found the two packages cost the same only when the vacation includes 5 nights in a hotel.
Which statement about Nadia's graph must be true?
AThe lines are parallel.
BThe lines are not parallel.
CThe x-intercepts are the same.
D The y-intercepts are the same.
Answer:
Step-by-step explanation:Which is the equation of a line that has a slope of 1/2 and passes through point (2, -3)?
Maya buys greeting cards to give to her friends at school. She buys some greeting cards that cost $2. 50 each and some greeting cards that cost $4 each. She buys 12 cards in all for a total of $40. 50. How many greeting cards that cost $2. 50 did Maya buy?
Maya bought 5 greeting cards that cost $2.50 each and 7 greeting cards that cost $4 each.
Let's use algebra to solve this problem. Let's call the number of greeting cards that cost $2.50 "x" and the number of greeting cards that cost $4 "y". We know that Maya bought 12 cards in total, so:
x + y = 12
We also know that the total cost of the cards was $40.50, so:
2.50x + 4y = 40.50
Now we have two equations with two variables. We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y:
y = 12 - x
Now we can substitute this expression for y in the second equation:
2.50x + 4(12 - x) = 40.50
Simplifying this equation:
2.50x + 48 - 4x = 40.50
-1.50x = -7.50
x = 5
So Maya bought 5 greeting cards that cost $2.50 each. To find out how many cards she bought that cost $4, we can substitute this value of x in the first equation:
x + y = 12
5 + y = 12
y = 7
So Maya bought 7 greeting cards that cost $4 each.
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List in order from least to greatest.
Answer:
56%, 4/5, 1.07, 5/4
Step-by-step explanation:
5/4=1.25
56%=0.56
1.07
4/5=0.8
so the order is
56%, 4/5, 1.07, 5/4
factor by grouping
8v-6vw+4-3w
The fully factored form of 8v - 6vw + 4 - 3w is (2v + 1)(4 - 3w).
How to factor the expressionFrom the question, we have the following parameters that can be used in our computation:
8v - 6vw + 4 - 3w
To factor by grouping, we'll group the first two terms and the last two terms:
(8v - 6vw) + (4 - 3w)
Next, we'll factor out the greatest common factor (GCF) from each group:
2v(4 - 3w) + 1(4 - 3w)
Notice that both groups now have a common factor of (4 - 3w), which we can factor out:
(2v + 1)(4 - 3w)
Hence, the factored expression is (2v + 1)(4 - 3w)
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What is the minimum possible parameter of a rectangle whose length and breadth are whole numbers and area is 60 sq. Units?
The minimum possible parameter of the rectangle is 34 units.
What is a rectangle?
A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
Let's assume the length of the rectangle is L and the width is W. The area of the rectangle is given as 60 sq. units.
Area of rectangle = Length × Width = L × W = 60
We are looking for the minimum perimeter of the rectangle. Perimeter of rectangle = 2(L + W)
To find the minimum perimeter, we need to find the minimum values of L and W that satisfy the condition that the area is 60.
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
If we choose L = 1 and W = 60, then the area is 1 × 60 = 60.
If we choose L = 2 and W = 30, then the area is 2 × 30 = 60.
If we choose L = 3 and W = 20, then the area is 3 × 20 = 60.
If we choose L = 4 and W = 15, then the area is 4 × 15 = 60.
If we choose L = 5 and W = 12, then the area is 5 × 12 = 60.
If we choose L = 6 and W = 10, then the area is 6 × 10 = 60.
The minimum perimeter occurs when L and W are the closest in value, which is achieved when L = 5 and W = 12. Thus, the minimum perimeter of the rectangle is:
Perimeter = 2(L + W) = 2(5 + 12) = 34
Therefore, the minimum possible parameter of the rectangle is 34 units.
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