The properties of midpoints and rectangles to show that a quadrilateral with vertices at the midpoints of the sides of a rectangle is a rhombus.
In this problem, we will prove that a quadrilateral with vertices at the midpoints of the sides of a rectangle is a rhombus. This is an important result in geometry and is often used in solving more complex problems.
Let us consider a rectangle ABCD with sides AB, BC, CD, and DA. Let P, Q, R, and S be the midpoints of the sides AB, BC, CD, and DA, respectively.
We need to prove that PQRS is a rhombus, which means we need to show that all sides of PQRS are equal.
First, we can observe that PQ and SR are parallel to AD, and QR and PS are parallel to AB. This is because P and S are midpoints of AB and AD, and Q and R are midpoints of BC and CD, respectively. Therefore, PQ and SR are both half the length of AD, and QR and PS are both half the length of AB.
Next, we can use the fact that the opposite sides of a rectangle are equal. This means that AD = BC and AB = CD. Therefore, PQ and SR have the same length, as they are both half of AD. Similarly, QR and PS have the same length, as they are both half of AB.
Thus, we have shown that all sides of PQRS are equal, which means that PQRS is a rhombus.
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Complete Question:
ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.
write the set b=1/10 1/100 1/1000 in set builder form
The set builder form of the set b = {1/10, 1/00, 1/1000} is b = {x | x = 1/10ⁿ, where n is a positive integer}
In mathematics, set builder notation is a concise way of describing a set using a rule or a formula.
Let's explore how we can use set builder notation to write the set b={1/10, 1/100, 1/1000}.
To begin, we need to identify the common property that these elements share. In this case, we can observe that each element is a rational number with a power of ten as the denominator. So, we can write the set b as follows:
b = {x | x = 1/10ⁿ, where n is a positive integer}
In this notation, the vertical bar represents "such that" and separates the description of the element from the rule that defines the set. The letter x is a variable that represents any element that satisfies the rule. We use the power of ten as a common property to describe the set b.
In this set builder form, we can see that b is a set of elements that can be expressed as 1/10 to the power of a positive integer. We can also use set builder notation to define other sets with different properties, such as sets of even numbers or sets of prime numbers.
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This is the correct answer
Answer: yes
Step-by-step explanation:
A snail moves at a speed of 2 feet per minute. How many yards will the snail have moved in one hour? The snail has moved a total of
3
yards
The snail moves a distance of 40 yards in one hour as it moves at a speed of 2 feet per minute.
We can start by converting the speed of the snail from feet per minute to yards per hour, since the distance moved is given in yards per hour.
There are 60 minutes in an hour, so the snail's speed in yards per hour is:
2 feet per minute * 60 minutes per hour * (1/3) yards per foot = 40 yards per hour
Hence,
The snail moves a distance of 40 yards in one hour.
Since we are given that the snail has moved a total of 3 yards, we can find the amount of time it took by dividing the distance by the rate:
time = distance / rate
time = 3 yards / 40 yards per hour
time = 0.075 hours or 4.5 minutes
Therefore, the snail will move a distance of 3 yards after 4.5 minutes and distance of 40 yards in one hour.
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In △ABC, m∠A = x, m∠B = 2x + 2, and m∠C = 3x +4. What is the value of x?
1) 29
2) 31
3) 59
4) 61
Answer: 1) 29 (look at the image for the solution)
Step-by-step explanation:
Pls help thank you will mark the Brainliest
Online math courses can also offer some benefits, such as the flexibility to work at your own pace and the ability to review lectures and assignments as needed. Overall, taking an online math course requires self-discipline, motivation, and a willingness to seek help when needed.
Describe Online classes?Online classes are virtual classrooms that offer students the opportunity to learn from anywhere, at any time, with a reliable internet connection. The primary focus of online classes is to provide students with the same level of academic instruction as they would receive in a traditional classroom setting. Many educational institutions and organizations offer online classes, including colleges, universities, and K-12 schools.
One of the significant advantages of online classes is that they offer flexibility, which means students can manage their coursework according to their schedule. Students can also access course material, lectures, and assignments from anywhere, which eliminates the need to attend a physical classroom. Online classes also offer students the ability to work at their own pace and review course material as often as they need to.
Online classes provide students with access to a wide range of educational resources, including video lectures, interactive quizzes, discussion forums, and other learning tools. Many online classes also provide students with personalized support, including one-on-one virtual sessions with instructors or teaching assistants.
Taking an online math course can be different from taking other subjects online. Typically, online math courses involve watching pre-recorded video lectures, completing online assignments, and participating in online discussions or forums. Online math courses may also use virtual tools, such as interactive graphs or calculators, to enhance the learning experience.
Compared to other online courses, learning math online may require more self-discipline and motivation, as it can be challenging to stay engaged with the material without the structure of a traditional classroom. Additionally, math is a subject that often builds on previous concepts, so it is essential to stay on top of the material and seek help if needed.
However, online math courses can also offer some benefits, such as the flexibility to work at your own pace and the ability to review lectures and assignments as needed. Overall, taking an online math course requires self-discipline, motivation, and a willingness to seek help when needed.
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$22 if it has 11 attendees. If there are 48 attendees, how much will picnic cost? Assume the relationship is directly proportional.
Answer:
$96
Step-by-step explanation:
We know
$22 if it has 11 attendees.
$22 divided 11 = $2 per attendee
So, we know per attendee costs $2
If there are 48 attendees, how much will the picnic cost?
2 x 48 = $96
So, the picnic cost $96.
Convince Me! Use Patterns and Structure Sue knitted a scarf for her
friend June that was also 4 feet long. After a month, the length of June's
scarf could be represented by the expression 0.5 x 4. How did the length
of June's scarf change? Explain.
The length of June's scarf change using patterns and structure is 4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given that;
The length of friend june scarf= 4 feet
The representation of length of june after a month= 0.5x4
Now,
Sue knitted a scarf for her friend June that was also 4 feet long and, after a month, the length of June's scarf is given by the expression 3/3 x 4, to know how did the length of June's scarf change you must perform the following calculation;
Month; 1 = 4
Month; 2 = 3/3 x 4 = 1 x 4 = 4
Therefore, by algebra the the answer will be 4.
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QUESTION FOR FOR LIH04
4 red bricks have a mean weight of 5 kg.
5 blue bricks have a mean weight of 9 kg.
1 green brick has a weight of 6 kg.
Donna says,
"The mean weight of the 10 bricks is less than 7 kg. "
Is Donna correct?
You must show how you get your answer.
Donna is not correct, as the mean is of 7.1 kg, which is greater than 7 kg.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
The sum of the data-set in this problem is given as follows:
4 x 5 + 5 x 9 + 1 x 6 = 71 kg.
The number of observations is given as follows:
10.
Hence the mean is given as follows:
71/10 = 7.1 kg > 7 kg.
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There is a total of
wholes in 72
.
The remaining fractional part is .
2
The whole number whose sum is 72 cannot be in the ratio C. 3/4.
How to explain the ratioRatio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them
The whole number must be divided by sum of two ratio particularly
A.5 + 7=12
72 can be divided by 12
B.3+5=8
72 can be divided by 8
C.4+3=7
72 can not be divided by 7
D.4+5=9
72 can be divided by 9
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The whole number whose sum is 72 cannot be in the ratio
A. 5/7
B. 3/5
C. 3/4
D. 4/5
A recipe for flapjacks uses only syrup sugar butter and oats in the ratio 1:2:2:4 Using this recipe 250g of syrup are needed to make 12 flapjacks find the quantity of oats needed to make 18 of these flapjacks?
A recipe for flapjacks uses only syrup sugar butter and oats in the ratio 1:2:2:4. Using this recipe 250g of syrup are needed to make 12 flapjacks. The quantity of oats needed to make 18 of these flapjacks is 375g.
The recipe for flapjacks has a ratio of syrup to sugar to butter to oats of 1:2:2:4. This means that for every 1 unit of syrup, there are 2 units of sugar, 2 units of butter, and 4 units of oats.
We know that 250g of syrup are needed to make 12 flapjacks. To find out how much oats are needed to make 18 flapjacks, we can set up a proportion:
syrup: sugar: butter: oats = 1:2:2:4
250g:x = 12:18
To solve for x, we can cross-multiply and simplify:
250g * 18 = 12x
4500g = 12x
x = 375g
Therefore, we need 375g of oats to make 18 flapjacks using this recipe.
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please help i’ll mark brainliest
Answer:
Step-by-step explanation: umm hard the question doesn't sound like a question
ASAP Select the correct answer.
What is the slope of the line that goes through the points (-4,2) and (8,5)?
A.-4
B.-1/4
C.1/4
D.4
the scores on a standardized test are normally distributed with a mean of 100 and standard deviation of 5. what test score is 1.4 standard deviations
A test score that is 1.4 standard deviations above the mean is 107. This means that a student who scored 107 on this standardized test would be above average, as the mean is 100 and the standard deviation is 5.
To find the test score that is 1.4 standard deviations above the mean, we need to use the formula:
z = (x - μ) / σ
where z is the number of standard deviations from the mean, x is the test score, μ is the mean, and σ is the standard deviation.
In this case, we know that z = 1.4, μ = 100, and σ = 5. So we can rearrange the formula to solve for x:
x = z * σ + μ
Substituting the values we know, we get:
x = 1.4 * 5 + 100 = 107
Therefore, a test score that is 1.4 standard deviations above the mean is 107. This means that a student who scored 107 on this standardized test would be above average, as the mean is 100 and the standard deviation is 5.
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an inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per second. the pyramid, at the top, has the shape of a square with sides of length 2 cm, and the height is 10 cm. find the rate at which the water level is rising when the water level is 2 cm.
The rate at which the water level is rising when the water level is 2 cm is 8 cm.
A pyramid's volume is equal to 1/3 of B, where B is the base's area and h is its height. Given that the base is square, B = s2, where s is a base side The volume is therefore 1/3 s2h.
We are aware that the base's side is 8 cm long and the whole pyramid's height is 11 cm. Also, no matter how high the water is, its surface will always form a square with the same proportion to the water's depth as a side of the pyramid's top has to the pyramid's total height. This indicates that s = 8/11 h regardless of the water depth.
So that means that the formula for the volume of the pyramid formed by the water is V = 1/3 (8/11 h)2 h = 64/363 h3.
Separate this as a function of time to get the rate of change of the volume of water :
V = 64/363 h3
dV/dt = 3 (64/363) h2 dh/dt = 192/363 h2 dh/dt
Nonetheless, we are aware that the volume is shifting at a speed of 65 cc every second. So at any point in time,
65 = 192/363 h2 dh/dt
65 * 363 / 192 = h2 dh/dt
23595 / 192 = h2 dh/dt
(23595 / 192) / h2 = dh/dt
When the level of water (h) is 8, that indicates:
(23595 / 192) / 64 = dh/dt
1.92 = dh/dt
So the water level is rising at the rate of 1.92 cm per second when the water level is 8 cm.
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Brian and Mason buy cars at the same time.
The function f(t) = 21,500(0.87)t models the value of Brian’s car t years after purchase.
The function g(t) = 19,200(0.91)t models the value of Mason’s car t years after purchase.
What is the approximate difference between the values of the cars after 4 years?
The approximate difference between the values of the cars after 4 years is $134.82.
What is Function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
According to question:To find the difference between the values of the cars after 4 years, we can subtract the value of Mason's car from the value of Brian's car at t = 4.
f(4) = 21,500(0.87)^4 ≈ 11,426.91
g(4) = 19,200(0.91)^4 ≈ 11,292.09
Therefore, the approximate difference between the values of the cars after 4 years is:
f(4) - g(4) ≈ 11,426.91 - 11,292.09 ≈ 134.82
So the approximate difference is $134.82.
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what is the cost of fencing a circular garden of radius 28 with five rounds of wire if the wire cost Rupees 50 per metre.
Answer:
7,000 Rupees
Step-by-step explanation:
A principal of $900 was invested at 2.5% interest, compounded annually. Let t be the number of years since the start of the investment. Let y be the value of the investment in dollars. Write an exponential function showing the relationship between y and t.
Group of answer choices
Answer: 900 x (2.5 x t) = y
900 hundred dollars originally invested, times the number of years multiplied by the yearly interest rate, equals Y, or the amount of the investment in dollars.
I hope this helps & good luck <3 !!!
5. Ella checks out a book from the library. She does not read any pages that day. Starting the next day, she reads the same number of pages each day. The graph shows the number of pages Ella has left to read to finish the book. Determine the number of pages in the book. Assume that the relationship between the two quantities is linear. Library Book Number of Pages Unread 60 54 48 42 36 30 24 18 12 6 0 1 2 3 4 5 6 7 8 9 10 x Number of Days a. b. C. d. 5 5 8 48 58
The number of pages in the book is given as follows:
58 pages.
How to obtain a linear function?
The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.From the graph, two points are given as follows:
(2,48) and (8, 18).
When x increases by 6, y decays by 30, hence the slope m is given as follows:
m = -30/6
m = -5.
Hence:
y = -5x + b.
When x = 2, y = 48, hence the intercept b, representing the number of pages in the book, is given as follows:
48 = -10 + b
b = 58.
Missing InformationThe graph is given by the image presented at the end of the answer.
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A population of a town is 18,000 it decreases at a rate of 8% per year
Approximately it takes 6 years to the population be fewer than 11,000.
What is population growth and population decrease formula?If the constant decrease in population be R% per annum, then the population after n years = P(1-R/100)ⁿ.
Given that, A=11,000, rate of interest=8% and P=18,000.
Here, 11,000=18,000(1-8/100)ⁿ
11/18=(1-0.08)ⁿ
0.611=(0.92)ⁿ
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
n=ln(0.611)/ln(0.92)
Decimal Form: n=5.90847701…
n=6
Therefore, approximately it takes 6 years to the population be fewer than 11,000.
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"Your question is incomplete, probably the complete question/missing part is:"
The population of a town is 18,000. it decreases at a rate of 8% per year. In about how many years will the population be fewer than 11,000?
Pls show your work thank you will mark the Brainliest
Answer: A
Step-by-step explanation: There isn't much work to be shown here, however you can look at graphical patterns to get your answer. It says the initial value is $200000 so you can eliminate B and D because they start at $100000. That leaves A and C. C is increasing at a higher rate and is greater than 100% per year. That leaves option A.
Please help :) 10 points (Geometry)
Answer: (2,0)
Step-by-step explanation:
Midpoint formula( [tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])
P(-4, 6)
Q(8, -6)
Substitute into formula
-4+8/2
4/2
x = 2
6-6/2
0/2
y = 0
Answer (2,0)
Determine the period.
10
Check the picture below.
we now are using two z score formulas. the denominator is the standard deviation on the first one we learned. the denominator is the standard error on the second one we learned. how do you know which z score formula to use? g
The choice between using the standard deviation and standard error in the denominator of a z-score formula depends on the context of the problem and the type of data being analyzed.
To determine which z-score formula to use, consider the type of data and the context of the problem. If you have a sample with a known population standard deviation, use the first formula. If the data represents a random sample of a larger population, the standard error is typically used to account for the variability in estimating the population mean. On the other hand, if the data represents the entire population, the standard deviation is used as the denominator. It's important to understand the distinction between a sample and a population and to choose the appropriate formula accordingly.
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Two simultaneous equations are given below, where p and q are constants.
3x-py = 4
4x - 3y + q = 0
The solution to these equations is x = 1, y = 2.
Find the value of p and q.
Answer:
p = -1/2
q = 2
Step-by-step explanation:
Equations are:
3x - py = 4 [1]
4x - 3y + q = 0 [2]
If x = 1 and y = 2, then substituting for these values in each equation will provide a solution for p and q
Plugging x = 1 in Equation [1]:
3(1) - p(2) = 4
→ 3 - 2p = 4
→ -2p = 4 - 3
-2p = 1
-2p/-2 = 1/-2
p = -1/2
For the second equation 4x - 3y + q = 0
x = 1, y = 2
→ 4(1) -3(2) + q = 0
→ 4 - 6 + q = 0
→ -2 + q =0
→ q = 2
Original Price Percent of Discount Sale Price
$
64% $72
The original price when 64% is applied to the item will be $200.
What is the percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentile in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value × 100
Let 'x' be the Original Price. Then the equation is given as,
(1 - 0.64) x = $72
0.36 x = $72
x = $200
The original price when 64% is applied to the item will be $200.
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Rewrite in simplest rational exponent form square root of x times the fourth root of x. Show each step of your process.
The simplified form of the expression √x × ⁴√x in rational exponent form is x^3/4.
What is the simplified form of the expression?Given that, square root of x times the fourth root of x.
√x × ⁴√x
To simplify the expression, rewrite using the least common index of 4.
Since ⁿ√xᵃ = x^(x/n)
√x = x^(1/2)
and
⁴√x = x^(1/4)
Hence, we have;
x^(1/2) × x^(1/4)
Using exponent rule
x^( 1/2 + 2/4 )
Add 1/2 and 1/4
x^( 1/2 + 1/4 )
x^3/4
Therefore, the simplified form is x^3/4.
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the perimeter of a ractangle is 280cm the ratio of the width to the length is 3:4. what is the length of the rectangle?
For the given width length ratio and perimeter of rectangle, the length of rectangle is 80 cm.
The perimeter of a shape is defined as the total length of its boundary. The perimeter of a shape is determined by adding the length of all the sides and edges enclosing the shape.
Let the width of the rectangle be 3x, and the length be 4x (since the ratio of the width to the length is 3:4).
The perimeter of a rectangle is the sum of the lengths of all four sides, so we have:
Perimeter = 2(length + width)
Substituting the expressions for the length and width, we get:
280cm = 2(4x + 3x)
Simplifying the right-hand side, we get:
280cm = 14x
Dividing both sides by 14, we get:
x = 20
Therefore, the length of the rectangle is 4x = 4(20) = 80 cm
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Which one of the following absolute value equations and inequalities have a solution set that is NOT the empty set?
O |2x-1|-7<-6
O |4x+5| -4=-5
O 3|x+2|-2=-3
O 2|x-5|-4 <-8
Uber charges $5.00 plus $.35/mile to take someone to a destination. Jen needed a
ride to the airport. Her total cost was $17.60. How many miles was she away from the
airport?
Answer:
36
Step-by-step explanation:
First you have to do 17.60 minus the fee ($5) giving you 12.6
after that you want to X the .35 by 36 which will make you reach 12.6
so by that it is 36 miles X the .35 Per mile fee giving you 36 miles (sorry if that made no sense)
