The ratio of the areas of two similar polygons can be found by squaring the ratio of their perimeters or corresponding linear dimensions, but this method only works sometimes, specifically with similar polygons, and not with non-similar ones.
The ratio of the areas of two similar polygons is indeed found by taking the ratio of their corresponding linear dimensions and squaring it. This is because the area is a two-dimensional measurement, whereas perimeter and linear dimensions are one-dimensional. For similar polygons, which are polygons that have the same shape but may have different sizes, any linear dimensions (such as sides, perimeters, diagonals) are proportional.
When you have two similar polygons and you know the ratio of their perimeters, you can use this perimeter ratio to find the ratio of their corresponding side lengths since the ratio of the perimeters of similar polygons is equal to the ratio of their corresponding linear dimensions. After finding this linear ratio, you square it to obtain the ratio of their areas because if one dimension is multiplied by a scale factor 's', the area is multiplied by 's' squared (scale factor squared).
It is important to note, however, that this rule only applies to similar polygons (similarity) and not to polygons that aren't similar, since non-similar polygons do not have a constant ratio of corresponding linear dimensions. Therefore, to answer the original question, the method works sometimes, specifically when dealing with similar polygons.
what is 3 fifths times one and 1third
Find a recurrence relation for the number of n-digit ternary sequences in which no 1 appears anywehere to the right of a 2
To find a recurrence relation for the number of n-digit ternary sequences in which no 1 appears anywhere to the right of a 2, we can consider two cases depending on the last digit being 0 or 2.
Explanation:To find a recurrence relation for the number of n-digit ternary sequences in which no 1 appears anywhere to the right of a 2, we can break the problem down into two cases: when the last digit is 0 or when the last digit is 2. If the last digit is 0, then the number of n-digit ternary sequences is equal to the number of (n-1)-digit ternary sequences in which no 1 appears anywhere to the right of a 2. If the last digit is 2, then the number of n-digit ternary sequences is equal to the number of (n-1)-digit ternary sequences in which no 1 appears anywhere to the right of a 2, plus the number of (n-1)-digit ternary sequences in which no 1 appears anywhere to the right of a 2.
Simplify: 4w(to the power of 9)+(-2w(to the power of 9)) enter the original expression if it cannot be simplified
What is the rule for this pattern of numbers?
28 is 12 less than k
the value of k is 40.
to solve for k when 28 is 12 less than k, we set up an equation and then solve it.
Let's denote k as the unknown number. According to the problem, 28 is 12 less than k, which can be written as:
28 = k - 12
To solve for k, we need to isolate k on one side of the equation.
28 = k -12
28 + 12 = k
40 = k
k = 40
So, the value of k is 40.
The complete question is:
28 is 12 less than k. 28=12-k Solve for k.
A bakery makes 640 muffins everyday. which equation shows how to find the number of muffins the bakery makes in a week?
Mel Sturbridge needs $24,700 to remodel his home.
Find the face value of a simple discount note that will provide the $24,700 in proceeds if he plans to repay the note in 180 days and the bank charges an 8% discount rate.
Round to the nearest cent.
To find out the face value of a simple discount note that will provide a proceed of $24,700 with an 8% discount rate for 180 days, use the formula FV = P / (1 - (r * t)). Plug in the given values and compute the answer. The result is the required face value and should be rounded to the nearest cent.
Explanation:To find out the face value of a simple discount note, we can use the formula FV = P / (1 - (r * t)) where FV represents the face value, P is the proceeds, r is the discount rate, and t is the time in years.
In the problem, P = $24,700, r = 8% or 0.08 (expressed as a decimal), and t = 180/365 because there are 365 days in a year and the note is for 180 days. Let's substitute these values into the formula:
FV = 24700 / (1 - (0.08 * (180/365))
When you calculate the expression on the right, the answer will be the face value required to get a proceed of $24,700 with an 8% discount rate for 180 days. Round to the nearest cent for your final answer.
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1.find the slope between these 2 points:(5,-5) and(3,-5)
2.find the slope between these two points:(2,3)and (4,5)
3.find the slope between the two points (-5,5)and (3,-5)
4.find the slope between these two points (9,9) and (12,15)
Final answer:
To find the slope between two points, use the formula m = (Y2 - Y1) / (X2 - X1) where (X1, Y1) and (X2, Y2) are the coordinates of the two points. The slopes for the given point sets are: 0, 1, -5/4, and 2.
Explanation:
To find the slope between two points, we can use the formula:
m = (Y2 - Y1) / (X2 - X1)
where (X1, Y1) and (X2, Y2) are the coordinates of the two points.
For the first set of points (5, -5) and (3, -5), the slope is:
m = (-5 - (-5)) / (3 - 5) = 0 / -2 = 0
For the second set of points (2, 3) and (4, 5), the slope is:
m = (5 - 3) / (4 - 2) = 2 / 2 = 1
For the third set of points (-5, 5) and (3, -5), the slope is:
m = (-5 - 5) / (3 - (-5)) = -10 / 8 = -5/4
For the fourth set of points (9, 9) and (12, 15), the slope is:
m = (15 - 9) / (12 - 9) = 6 / 3 = 2
A rectangle is dilated by a scale factor of 4.
a) The original rectangle is 8 cm by 3 cm. What are the dimensions of the new rectangle?
b) Is the new image a reduction or enlargement? Explain.
HELP PLEASE
What is the mean absolute deviation for the set of data below?
2, 8, 10, 16
Solution: We are given below data:
[tex] 2, 8, 10, 16 [/tex]
Now to find the mean deviation, we use the below formula:
[tex] MD= \frac{\sum|X-\bar{X}|}{N} [/tex]
Where:
[tex] \sum, [/tex] represents the summation
X, represents the observation.
[tex] \bar{X}, [/tex] represents the mean
N represents the number of observation.
[tex] \bar{X}= \frac{\sum{X}}{N}= \frac{2+8+10+16}{4}=9 [/tex]
[tex] \sum |X-\bar{X}| = |2-9| + |8-9| +|10-9| +|16-9|=7+1+1+7=16 [/tex]
Therefore, the mean deviation is:
[tex] MD= \frac{16}{4} [/tex]
= 4
Answer:
4 \
Step-by-step explanation:
There is only one granola bar left out of a pan of 10 bars. If will and Rachel decide to split the last granola bar, what fraction of the entire pan of granola bars will each friend receive?
A local park rents cabins for people who want to vacation by the forest. The fee for the rental is $27 per night.There is also $55 cleaning and maintenance charge that is added to the total bill.
Define variables for the number of days that a cabin is rented and the cost of the rental. Use the variables to write an equation that represents the cost to the rent the cabin,given the number of days that the cabin is rented.
Please answer as quickly as possible this is URGENT
If x = 30, what does 55 + x - 27 equal?
Answer:
58
Step-by-step explanation:
Put 30 where x is in the expression and do the arithmetic.
55 + 30 - 27 = 85 - 27 = 58
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It can be advantageous to use the associative property of addition to evaluate the expression as ...
55 + (30 -27) = 55 +3 = 58
Find two numbers, if Their sum is 3/5 and their difference is 7 1/5
Answer:
3.9 and -3.3
Step-by-step explanation:
A patio has an area of 432 square feet the width of the patio is 3/4 its length what is the length
24r3-64r2-21r+56 answer
Mr. Harrow has eight boys and six girls in his Honors Precalculus class. If he randomly chooses two students, one at a time, what is the probability that they are both girls
Find |p|.....................
Make a line graph of the data in the table and conjecture on the minimum degree of a polynomial model...
Write 4/10 as a fraction with a denominator of 100. Then write 4/10 as a decimal.
Would it be 4/100 or 40/100? The decimal would be 0.4 ?
PLEASE HELP ME!
Find each value. Use a calculator if needed.
ORDER MATTERS!
a) P(12, 5)
= A. 60 B. 248,832 C. 95,040 D. 300
b) P(8, 8)
= A. 64 B. 40,320 C. 30,555 D. 16
You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound event. Write your answer as a fraction or percent. If necessary round your answer to the nearest hundredth.
The probability of spinning an odd number, flipping heads, then spinning a yellow is ????
probability = number of favourable outcomes / total number of outcomes
probability of spinning any number = 1/3
probability of tossing a coin = 1/2
probability of compound event = 1/3 * 1/2 * 1/3 = 1/18
probability of spinning an odd number, flipping heads, then spinning a yellow is = 2/3*1/2*1/3 = 1/9
a bowl of soup holds 7 ounces. If a spoonful holds 1/6 ounce, how many spoonfuls are in 3 bowls of soup? Tell the operation and explain how you got your answer
complete the ordered pair for the given equation. (_,-1);y=-3/5x-7
max has 2/3 lb. of chocolate. He wants to hand out the chocolate in packages to give to his friends he would like to put 1/6 lb. of chocolate. How many packages can Max make? solve with a visual model
need help solving this
The quadratic equation y = 2(x – 2)2 + 2 with no real solution is graphed. Which value of k will change the function to one with exactly one solution?
On the attached diagram red curve is the graph of the quadratic function [tex]y = 2(x - 2)^2 + 2.[/tex] As you can see this graph has no intersections with x-axis, this means that there are no solutions.
If you translate red curve 2 units down, you obtaine the graph (blue curve) of the function [tex]y = 2(x - 2)^2[/tex] and this graph has one common point with x-axis. This means that there will be exactly one solution.
Answer: k=-2 (you add -2 to the function [tex]y = 2(x - 2)^2 + 2[/tex] to obtain the function [tex]y = 2(x - 2)^2[/tex]).
Answer: 0 ZERO
Step-by-step explanation:
25 less than 6 time a number is 107. What is the number? How do you do that?
25 less than 6 times a number is 107 then that number will be 22 it can be determined by the formation of the equation.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say that number is x
6 times x number
⇒ 6x
25 less than 6x
⇒ 6x - 25
It is equal to 107
So,
6x - 25 = 107
6x = 132
x = 132/6
x = 22
Hence "25 less than 6 times a number is 107 then that number will be 22".
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The Philips family had 3 cats. They needed to split 20 ounces of cat food among the three cats. How much cat food would each cat get? between what two whole numbers does your answer lie?
Each cat would get approximately 6.67 ounces of cat food, which falls between 6 and 7 ounces. The calculation is done by dividing the total amount of food (20 ounces) by the number of cats (3).
Explanation:The Philips family had to split 20 ounces of cat food among their 3 cats. To find out how much food each cat gets, we need to divide the total amount of food by the number of cats. Calculating this, 20 ounces ÷ 3 cats equals approximately 6.67 ounces per cat. Even though this is a decimal, if we consider whole numbers, the amount each cat gets falls between 6 and 7 ounces, since 6.67 is more than 6 and less than 7.
When dealing with fractions and division, it's essential to understand the concept of division and be able to find averages. The task at hand may often find itself related to dividing a quantity evenly among a number of recipients, much like in scenarios where we have to split a pie or determine individual portions.
To divide 20 ounces of cat food equally among three cats, each cat gets approximately 6.67 ounces. The amount of food per cat lies between the whole numbers 6 and 7.
Explanation:The question is asking how to divide 20 ounces of cat food equally among three cats. To find out how much each cat would get, you divide the total amount of cat food by the number of cats:
Determine the total amount of food: 20 ounces.Count the number of cats: 3 cats.Divide the total amount of food by the number of cats: 20 ounces ÷ 3 cats = approximately 6.67 ounces per cat.This calculation shows that each cat would get approximately 6.67 ounces of food. This value lies between the whole numbers 6 and 7. Therefore, when the Philips family divides the cat food, each cat gets a little more than 6 ounces but less than 7 ounces of food.
What is the completely factored form of x2y – 2xy – 24y?
Answer:
C: y(x + 4)(x – 6)
Step-by-step explanation:
I took the test on Edge -2022