The perimeters of two rhombi with equal areas are sometimes equal, but not always.
Let's consider the formula for the area of a rhombus, which is given by [tex]\( A = \frac{1}{2} \times d_1 \times d_2 \), where \( d_1 \) and \( d_2 \)[/tex] are the lengths of the diagonals. For the perimeter P, we have [tex]\( P = 4 \times s \)[/tex], where s is the length of one side of the rhombus.
For two rhombi to have equal areas, the product of their diagonals must be the same. That is, if we have two rhombi with diagonals [tex]\( (d_1, d_2) \) and \( (d_1', d_2') \), then \( d_1 \times d_2 = d_1' \times d_2' \)[/tex].
However, the perimeter depends only on the length of one side, s, and not on the diagonals. Therefore, two rhombi with the same area can have different side lengths and thus different perimeters.
Let's consider an example:
Rhombus 1:
[tex]- Diagonals \( d_1 = 8 \) units and \( d_2 = 4 \) units[/tex]
[tex]- Area \( A = \frac{1}{2} \times 8 \times 4 = 16 \) square units[/tex]
[tex]- Side length \( s \), using the Pythagorean theorem (since the diagonals bisect each other at right angles), is \( s = \sqrt{4^2 + 2^2} = \sqrt{16 + 4} = \sqrt{20} \) units[/tex]
[tex]- Perimeter \( P = 4 \times s = 4 \times \sqrt{20} \) units[/tex]
Rhombus 2:
[tex]- Diagonals \( d_1' = 10 \) units and \( d_2' = 3.2 \) units[/tex]
[tex]- Area \( A' = \frac{1}{2} \times 10 \times 3.2 = 16 \) square units (equal to the area of Rhombus 1)[/tex]
[tex]- Side length \( s' \), using the Pythagorean theorem, is \( s' = \sqrt{1.6^2 + 2.56^2} = \sqrt{2.56 + 6.5536} = \sqrt{9.1136} \) units[/tex]
[tex]- Perimeter \( P' = 4 \times s' = 4 \times \sqrt{9.1136} \) units[/tex]
Comparing the perimeters:
[tex]- \( P = 4 \times \sqrt{20} \approx 4 \times 4.472 = 17.888 \) units[/tex]
[tex]- \( P' = 4 \times \sqrt{9.1136} \approx 4 \times 3.0188 = 12.0752 \) units[/tex]
Clearly, the perimeters are not equal, even though the areas are the same.
However, it is possible for two rhombi with equal areas to have equal perimeters if their side lengths are the same. For instance, if Rhombus 1 and Rhombus 2 both had side lengths of s = s' = 4 units, then their perimeters would both be P = P' = [tex]4 \times 4 = 16 \)[/tex] units, regardless of the lengths of their diagonals, as long as the diagonals satisfy the area condition [tex]\( d_1 \times d_2 = d_1' \times d_2' \)[/tex].
In conclusion, the perimeters of two rhombi with equal areas can sometimes be equal, specifically when the side lengths are the same, but they are not always equal, as demonstrated by the example above.
PLEASE ANSWER QUICKLY! Suppose that there were a strong correlation between the variables n and p. Which of these is a true statement?
A. n may cause p.
B. p must cause n.
C. n must cause p.
D. n must not cause p.
The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times the first. What are the numbers?
brainly The point (−4, 2) is on the terminal side of angle Θ, in standard position. What are the values of sine, cosine, and tangent of Θ? Make sure to show all work. (10 points)
help me 15p for an answer and brainliest
help mme please
the true it is 20p
Answer:
Option 4.
Step-by-step explanation:
What is the area of the parallelogram?
For a circle with a radius of 6 feet, find the arc length of a central angle of 45 degrees
quando o Ângulo de elevação do sol e de 70 a sombra de um edifício medes 20 cm calcule a altura do edifício
dados : sen 70=0,93 cos 70=0,3 e tg70=2,74?
Simplify. x + 4.7 = −9.2 A. −13.9 B. 13.9 C. −12.9 D. 12.9
Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want to work over 65 hours per week combined. Jane is paid $14 per hour at her job, and Jack is paid $7 per hour at his. Neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. If they need to make a minimum of $770 per week before taxes, what is the maximum amount of hours that Jack can work per week according to these limits?
Answer:
20
Step-by-step explanation:
PLEASE SOMEONE I AM SO DESPERATE like actually crying
1. The equation of a parabola is given. y=−1/6x2+7x−80 What is the equation of the directrix of the parabola?
2. (y+2)^2= 129X-5)
What is the equation of the directrix of the parabola?
y= (−1/6)x^2+7x−80 multiply both sides by -6
-6y = x^2 - 42x + 480 subtract 480 from both sides
-6y - 480 = x^2 - 42x take (1/2) of 42 = 21.....square this = 441 and add to both sides
-6y - 480 + 441 = x^2 - 42x + 441 simplify the left, factor the right
-6y - 39 = (x - 21)^2 factor the left side as
-6 (y + 39/6) = ( x - 21)^2 (1)
Using the form
4p (y - k) = ( x - h)^2 we can write (1) as
4 (-3/2)(y - (-39/6) ) = ( x - 21)^2
The vertex = ( h, k) = ( 21, -39/6) and p = -3/2
And the directrix is given by
y = k - p → y = -39/6 - (-3/2) = -39/6 + 3/2 = -39/6 + 9/6 =
-30/6 = - 5-------> y=-5
the answer Part 1) is
y=-5
Part 2) (y+2)^2= 129X-5
What is the equation of the directrix of the parabola?Using the form
4p (x - h) = ( y - k)^2 we can write (1) as
4*(129/4)*(x-5/129)=(y+2)²
The vertex = ( h, k) = ( 5/129, -2) and p = 129/4
And the directrix is given by
x = h - p → x = 5/129 - (129/4) = (20-16641)/516-----> -16621/516
x=-32.21
the answer part 2) is
x=-32.21the equation 3sinx+cos^2x=2 is solved below
Please help! Thanks!
Group terms that contain the same variable, and move the constant to the opposite side of the equation
(A²-3A)=-1Complete the square. Remember to balance the equation by adding the same constants to each side.
(A²-3A+2.25)=-1+2.25
Rewrite as perfect squares
(A-1.5)²=1.25(+/-)(A-1.5)=1.12
first solution
(A-1.5)=1.12--------> A=1.12+1.5-----> A=2.62-----> sin x=2.62
second solution
-(A-1.5)=1.12----> -A+1.5=1.12----> A=1.5-1.12----> A=0.38---> sin x=0.38
the answer is
the equation was factored incorrectly
Its is b. hope this halps
Create a function to model the height of a firework when shot in the air. Explain whether the function will have a maximum or a minimum value.
Rachel enjoys exercising outdoors. Today she walked5 2/3 miles in2 2/3 hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile
the answer to your question is
Unit walking rate in miles per hour = 5 2/3 / 2 2/3 = 17/3 / 8/3 = 17/3 x 3/8 = 17/8 = 2 1/8 miles per hour.
Unit walking rate in hours per mile = 1/ 17/8 = 8/17 hours per mile
Answer:
Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles or 5.67 miles in 2 2/3 hours or 2.67 hours.
Rachel’s unit walking rate in miles per hour is = [tex]\frac{5.67}{2.67}[/tex] = 2.125 miles per hour or 2 1/8 miles per hour.
Rachel’s unit walking rate in hours per mile = [tex]\frac{2.67}{5.67}[/tex] = 0.47 hours per mile.
How do I convert 2.4 x 10^21 formula units of magnesium hydroxide to grams?
A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by: P(x)=-3(x-5)^2+12 . What sock price should the company set to earn a maximum profit?
To obtain the maximum profit, the company should set the price of each pair of socks to $5. This answer is derived from the vertex of the given quadratic profit function.
Explanation:The student question asks at which price the sock selling company should sell its product to earn a maximum profit, given the profit function: P(x)=-3(x-5)^2+12. This function is a standard form of a quadratic equation, and in such equation, the maximum value is achieved at the vertex.
In this case, the vertex (h,k) of the quadratic function is (5,12), where 'h' is the value of 'x' that gives the maximum profit 'k'. So the company should set the price at $5 to earn a maximum profit.
This economic model analysis' underlying principle relies on the assumption of maximizing total revenues and minimizing total costs to yield the maximum profit. Hence, recognizing the nature of the profit function is crucial.
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How many distinct permutations are there of the letters of the word BOOKKEEPER?
There are __[blank]__ distinct permutations of the letters of the word BOOKKEEPER.
A group of 3 English majors, 2 anthropology majors, and 5
history majors are going out to dinner, where they will sit at a circular table. If students with the same major need to sit together, how many different ways can the students be seated around the table?
The word BOOKKEEPER has 10 letters, but with repetitions. There are 30240 distinct permutations. On the circular table, with students of the same major sitting together, there are 1440 different ways to seat the students.
Explanation:The word BOOKKEEPER has 10 letters, but the letter O appears twice, the letter K appears twice, and the letter E appears three times. To find the number of distinct permutations, we need to divide the total number of permutations by the repetitions. So, we have 10!/(2!2!3!) = 30240 distinct permutations.
In the second question, we need to consider the students with the same major sitting together as a single entity. We can treat the circular table as a linear arrangement by fixing one student in a position and arranging the rest. So, the total number of different ways the students can be seated around the table is (3!2!5!) × 2! = 1440.
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The depreciating value of a semi-truck can be modeled by y = Ao(0.87)x, where y is the remaining value of the semi, x is the time in years, and it depreciates at 13% per year.
An exponential function comes down from the positive infinity and passes through the points zero comma eighty-seven thousand. The graph is approaching the x-axis.
What is the value of the truck initially, Ao, and how would the graph change if the initial value was only $67,000?
$90,000, and the graph would have a y-intercept at 20,000
$87,000, and the graph would have a y-intercept at 67,000
$87,000, and the graph would fall at a slower rate to the right
$87,000, and the graph would fall at a faster rate to the right
Answer:
I just took the test the answer is
Step-by-step explanation:
B. 87,000, and the graph would have a y-intercept at 67,000.
10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!
Please help with geometry
What is the answer for this equation?
36^-x+3=(1/216)^x+1
Anyone know the answer?
Find the determinant of G
Three added to eight times a number is the same as three times the value of two times the number minus one
Choose the example that correctly shows the mean population density of a region.
A. 678 people per cubic meter
B. 678 cubic meter per number of people
C. 678 people per square mile
D. 678 square mile per people
Please answer ASAP!!! How many vertical asymptotes does the graph of this function have ?
Answer:
The answer is 1.
Got it from Apex
Step-by-step explanation:
If an airplane travels 15 miles in 2 minutes what is the speed in miles per hour
A rectangular wall has a length of 12ft and a width of 8ft. The wall has two rectangular windows. Each window has a width of 3ft and a height of 5ft. Andrea chooses a point on the wall at random to test a new paint color. What is the probability she could choose a point on a window
A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds: f(t) = −16t2 + 48t + 160 The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____ feet per second.
The Average rate of change of f(t) from t = 3 seconds to t = 5 seconds is - [tex]v_{avg} = -80\;ft/s[/tex]
We have a equation -
[tex]f(t) = -16t^{2} +48t+160[/tex]
that calculates the height of the ball from sea level in feet at different times.
We have to find the average rate of change of f(t) from t = 3 seconds to t = 5 seconds.
What is Average velocity?The rate of change of displacement per unit time is called average velocity. Mathematically -
[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]
We have -
[tex]f(t) = -16t^{2} +48t+160[/tex]
For time t = 3 seconds, f(t) is -
[tex]f(3) = -16(3)^{2} + 48(3) + 160\\f(3) = -144 +144 +160\\f(3) = 160\; feets\\[/tex]
For time t = 5 seconds, f(t) is -
[tex]f(5) = -16(5)^{2} + 48(5) + 160\\f(5) = -400+240+160\\f(5) = -400 + 400\\f(5) = 0 feet[/tex]
The formula for average velocity is -
[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]
According to question -
[tex]t_{2} = 5s[/tex] and [tex]t_{1} = 3s[/tex]
[tex]d_{2} = f(5) = 0 feet[/tex] and [tex]d_{1} = f(3)=160[/tex]
Substituting the values in the formula of average velocity, we get -
[tex]v_{avg} = \frac{0 - 160}{5 - 3} \\v_{avg} = \frac{-160}{2\\} \\v_{avg} = -80\;ft/s[/tex]
Hence, average rate of change of f(t) from t = 3 seconds to t = 5 seconds is [tex]v_{avg} = -80\;ft/s[/tex].
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Find the domain of the function :
Can you show the steps
I need to answer three questions about y = x^(-2) on the interval [-4, -1/2]. I have attached my questions and my answers as screenshots:
Part 1 - ANSWER C
Part 2 - ANSWER A
Part 3 - ANSWER B
I am referring to each part in the order that I uploaded the screenshots. You will see that my answers are highlighted in blue. I like second opinions!