The angle of depression from point R to point S is ∠1.
The angle of elevation from point S to point R is ∠2.
∠2 is the angle of elevation from S to R.
∠1 is the angle of depression from point R to point S.
What is an angle of elevation?
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
There is an angle of elevation from point R to S. Thus point R is lie above S.
The angle of depression from point R to point S is ∠1.
The angle of elevation from point S to point R is ∠2.
∠2 is the angle of elevation from S to R.
∠1 is the angle of depression from point R to point S.
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a small town in the UK has only 600 high school students. what is the largest possible sample you can take from this town and still be able to calculate the standard deviation of the sampling distribution of p-hat?
To calculate the standard deviation of the sampling distribution of p-hat, the answer will be 59 students.
By calculating,
600/10=60 and 59 students which is less than 10% of the population.
A sampling distribution, also known as a finite-sample distribution, in statistics is the probability distribution of a given random-sample-based statistic. The sampling distribution is the probability distribution of the values that the statistic takes on if an arbitrarily large number of samples, each involving multiple observations (data points), were used separately to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample. Although only one sample is frequently observed, the theoretical sampling distribution can be determined.
Because they offer a significant simplification before drawing conclusions using statistics, sampling distributions are crucial in the field. They enable analytical decisions to be made based on the probability distribution of a statistic rather than the combined probability distribution of all the individual sample values
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the proportions of families with various numbers of children age 18 or under in a small town are given in the following table. one family is randomly selected from this town. x 0 1 2 3 4 5 p(x) .10 .40 .13 .10 .22 .05 find the probability that the selected family has at least 3 children age 18 or under.
The probability that at least 3 children age 18 or under will be selected is 0.50
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Probability = sample space/total possible outcome
at least 3 children means x≥ 3
therefore ;
probability of atleast 3 children age 18 or under are selected =
.13+ .10 +.22 +.05
= 0.50
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Paula works at an appliance store where they make most of their money on commission. She makes 4.25% commission on the price of any appliance she sells. The store was offering 20% off on washers and dryers. Her first customer bought a washer for $685.96 and a dryer for $475.70 before applying the discount. How much money did she lose because of the sale? Round your answer to the nearest cent.
well, let's take a looksie at what it would have been had there not been a sale, so at regular price the washer and dryer are just 685.96 + 475.70 = 1161.66, well hell how much is 4.25% of that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{4.25\% of 1161.66}}{\left( \cfrac{4.25}{100} \right)1161.66} ~~ \approx ~~ 49.37[/tex]
now, since we know the appliances are going to be 20%, that means the appliaces sale price will be 100% - 20% = 80%, so 80% of the original price, well, we know the original price for those two is 1161.66, what's 80% of that?
[tex]\stackrel{\textit{80\% of 1161.66}}{\left( \cfrac{80}{100} \right)1161.66} ~~ \approx ~~ \stackrel{ sale~price }{929.33} \hspace{5em} \stackrel{\textit{4.25\% of 929.33}}{\left( \cfrac{4.25}{100} \right)929.33} ~~ \stackrel{ \textit{Paula's commission} }{\approx ~~39.5}[/tex]
well, Paula could have made 49.37, but she ended up with 39.5, 49.37 - 39.5 ≈ 9.87.
28. In the adjoining figure, what is the value of y? (b) 54 (a) 36 (c) 63 (d) 72
3x=108
and y= 54
by linear pair angle
Explain the types of exponential function.
Exponential functions are mathematical functions that involve an exponent or power. There are two types of exponential functions: growth and decay.
1. Exponential Growth Functions: These functions have the form y = a*b^x, where a > 0 and b > 1. They model exponential growth, where the value of y increases rapidly as x increases. For example, the function y = 2^x is an exponential growth function, as the value of y doubles for each increase in x.
2. Exponential Decay Functions: These functions have the form y = a*b^x, where a > 0 and 0 < b < 1. They model exponential decay, where the value of y decreases rapidly as x increases. For example, the function y = (1/2)^x is an exponential decay function, as the value of y is halved for each increase in x.
Both types of exponential functions are important in many fields, including finance, biology, and physics. They are used to model phenomena such as compound interest, population growth, and radioactive decay.
What are the three first common denominators of 7/9 and 2/3
From the given information provided, the first three common denominators of 7/9 and 2/3 are 9, 18, and 27.
To find the common denominators of 7/9 and 2/3, we need to find the least common multiple (LCM) of their denominators.
The prime factorization of 9 is 3 x 3, and the prime factorization of 3 is 3.
The prime factorization of 2 is 2, and the prime factorization of 3 is 3.
The common factors are 3, so the LCM of 9 and 3 is 9.
Therefore, the common denominator of 7/9 and 2/3 is 9.
To find the next two common denominators, we can continue to find the LCM of the denominators with the added factor of 9.
The prime factorization of 18 (2 x 3 x 3) includes the prime factors of 9, so it is a common denominator.
The prime factorization of 27 (3 x 3 x 3) also includes the prime factors of 9, so it is another common denominator.
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How do you find a tangent line with two equations?
To find the equation of the tangent line to a curve at a given point, we will need the equation of the curve and the place where you want to locate the tangent line in order.
Calculate the derivative by differentiating the curve's equation. This will reveal the tangent line's slope at any point along the curve.
Put the derivative you discovered in step 1's derivative into the x-coordinate of the place where you wish to find the tangent line. This will reveal the tangent line's slope at that particular position.
To determine the equation of the tangent line, use the point-slope form of the equation of a line. A line's point-slope formula is written as y - y1 = m(x - x1), where (x1, y1) is the line's point and m is its slope. Both the slope of the line and the location on the line where you wish to find the tangent line are known to you from step 2.
Put the tangent line's equation in a simpler, more conventional form, as y = mx + b.
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The winning team
in a 400-meter relay race had a time of
198.608 seconds. Suppose all 4 of the split
times were the same. Write and solve an
equation to find the split times.
The equation for split times is 4x= 198.608 and the value of x is 49.652
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
Let x be the split time
all 4 of the split times were the same.
4x= 198.608
=> x= 198.608/4 = 49.652
The equation for split times is 4x= 198.608 and the value of x is 49.652
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Use the drop-down menus to compare −2.25 and −3.
please i need help!!!
When comparing two numbers, there are a few different things you might be interested in: which is larger, which is smaller, or whether they are equal.
In this case, we can see that both numbers are negative, which means they are to the left of zero on the number line. In general, the further left a number is on the number line, the smaller it is. Therefore, we can say that:
-2.25 > -3
In other words, -2.25 is larger (closer to zero) than -3.
Write the solution set of the given homogeneous system in parametric vector form.3x1+3x2+6x3=0−6x1−6x2−12x3=0−4x2+4x3=03x1+3x2+6x3=0−6x1−6x2−12x3=0−4x2+4x3=0 where the solution set is x=⎡⎢⎣x1x2x3⎤⎥⎦x=[x1x2x3]
The solution set of the given homogeneous system in parametric vector form is x = (0, 0, t), where t is a real number
Vectors are an important mathematical tool for representing complex data and equations. In this problem, we are given a homogeneous system of equations and asked to write the solution set in parametric vector form.
The homogeneous system consists of three equations: 3x₁ + 3x₂ + 6x₃ = 0, -6x₁ - 6x₂ - 12x₃ = 0, and -4x₂ + 4x₃ = 0. To solve this system, we need to use linear algebra techniques, such as Gaussian elimination, to find the solution set.
By using Gaussian elimination, we can reduce the system to a simpler system, which has the form x₁ = 0, x₂ = 0, and x₃ = t, where t is a real number. This can be written as a parametric vector form as x = (0, 0, t).
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Luther drew on his graph paper. After performing a series of transformations, Isabella drew What is the sequence of transformations Isabella used to produce ？
Rotate clockwise about the origin; translate 10 units down.
Rotate clockwise about the origin: translate 1 unit up.
The sequence of transformations performed by Isabella is Rotate 90° clockwise about the origin; translate 10 units down.
What is transformation?A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.
Given that, Luther drew on his graph paper. After performing a series of transformations, Isabella drew. we need to find the transformations performed by Isabella,
We see, that, the sequence performed by Isabella is a rotation of 90°, from the origin, also the image is 10 units down to the original figure.
Hence, the sequence of transformations performed by Isabella is Rotate 90° clockwise about the origin; translate 10 units down.
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The complete question :-
can anyone help with this
Answer: -20
Step-by-step explanation:
2(-1 x 3 - 7)
2(-3-7)
2(-10)
-20
Answer:
[tex]\huge\boxed{\sf -20}[/tex]
Step-by-step explanation:
Given expression:= 2(xy - 7)
Put x = -1, y = 3
= 2[(-1)(3) - 7]
= 2(-3 - 7)
= 2(-10)
= -20[tex]\rule[225]{225}{2}[/tex]
a trailer manufacturing company buys screw fasteners in boxes of 5,000. three percent of all fasteners are unusable. the mean and variance of the number x of unusable fasteners in a randomly selected box are about
The mean and variance of the number x of unusable fasteners in a randomly selected box are about 150 and 150 respectively.
How calculate the mean and variance of the number x of unusable fasteners?Poisson distribution is a distribution function useful for characterizing events with very low probabilities of occurrence within some definite time or space. It is used when the number of trials is very large and the probability of success is comparatively small.
In Poisson distribution, the mean is defined as:
λ = np
where n = number of items and p = probability of success
Given: n = 5000 and p = 3/100 = 0.03
Thus, λ = np = 5000 * 0.03 = 150
Since the mean and variance are equal in Poisson distribution. Thus, the variance (σ²) = 150
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Consider the following. x = sin(2t), y = -cos(2t), z = 4t; (0, 1, 2pi) Find the equation of the normal plane of the curve at the given point. Find the equation of the osculating plane of the curve at the given point.
The equation of the osculating plane is (-1/3)(x-0) + (1/3)(y+1) + (2/3)(z-8 π) = 0.
First, we find the point on the curve at
[tex]t = 2\pi[/tex]
[tex]x = sin(2(2\pi)) = 0 \\
y = -cos(2(2\pi)) = -1 \\
z = 4(2\pi) = 8\pi[/tex]
So the point on the curve is
[tex] (0, -1, 8\pi)[/tex]
To find the normal plane, we take the cross product of the partial derivatives:
[tex]r_t = (2cos(2t), 2sin(2t), 4) \\
r_t(2\pi) = (2cos(4\pi), 2sin(4\pi), 4) = (2, 0, 4) \\
r_tt = (-4sin(2t), 4cos(2t), 0) \\
r_tt(2\pi) = (0, -4, 0) \\
n = r_t × r_tt = (-16, -8, -8)[/tex]
So the equation of the normal plane is
[tex]-16(x-0) - 8(y+1) - 8(z-8\pi) = 0.[/tex]
To find the osculating plane, we first find the unit tangent and unit normal vectors:
[tex]T = r_t / ||r_t|| = ( \frac{1}{2})cos(2t)i + ( \frac{1}{2}) sin(2t)j + ( \frac{1}{4})k \\
N = n / ||n|| = ( \frac{2}{3})cos(2t)i + ( \frac{1}{3})sin(2t)j + ( \frac{1}{3})k[/tex]
Then the binormal vector is B = T × N, which is
[tex]( \frac{ - 1}{3})sin(2t)i + ( \frac{1}{3} )cos(2t)j + ( \frac{2}{3} )k[/tex]
Finally, the equation of the osculating plane is
[tex]( \frac{ - 1}{3})(x-0) + ( \frac{1}{3})(y+1) + ( \frac{2}{3})(z-8\pi) = 0[/tex]
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Help me ASAP! Thank you! 25 points
Which expression(s) are equivalent to -2x + 3 + 7y + 4x -5. Select all the correct answers.
A. 2x + 7y - 2
B. 9xy - 2
C. 7y -2 + 2x
D. -x + 10yx - 5
Answer:
[tex] \sf \: a) \: 2x + 7y - 2 [/tex]
[tex] \sf \: c) \: 7y - 2 + 2x [/tex]
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The expression is,
→ -2x + 3 + 7y + 4x - 5
Let's simplify the expression,
→ -2x + 3 + 7y + 4x - 5
→ -2x + 4x + 7y + 3 - 5
→ (-2x + 4x) + (7y) + (3 - 5)
→ (2x) + 7y + (-2)
→ 2x + 7y - 2
→ 7y - 2 + 2x
Hence, option (a) & (c) is correct.
Step-by-step explanation:
-2x + 3 + 7y + 4x - 5 = 2x + 7y - 2
as addition is commutative (= can be done in any sequence of terms), the right answers are variations in the sequence of these 3 terms :
A and C are correct.
B and D disqualify themselves right away by including mixed terms of xy. you can never ever create such a mixed term just out of addition or subtraction of single x and y terms. you need multiplication to do that. but there is none.
The local supermarket had a sale on canned green beans. The green beans sold for 3!cans for $1. 25. One can of green beans usually sells for 50 cents. Find the percent of increase of decrease
The sale price of the green beans represents a decrease of 16.67% compared to the original price of the beans.
To find the percent increase or decrease in the price of a can of green beans during the sale, we need to compare the sale price with the original price.
During the sale, the green beans were sold at a rate of 3 cans for $1.25, or approximately 41.67 cents per can:
Sale price per can = $1.25 / 3 = $0.4167 ≈ 41.67 cents
The original price of a can of green beans was 50 cents.
To find the percent increase or decrease in the price, we can use the following formula:
Percent increase or decrease = ((New value - Old value) / Old value) x 100%
Substituting the values, we get:
Percent increase or decrease = ((0.4167 - 0.5) / 0.5) x 100%
Percent increase or decrease = (-0.0833 / 0.5) x 100%
Percent increase or decrease = -16.67%
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a rectangular room measures 14 feet by 17 feet with a 9 foot high ceiling the room is being painted each wall will be painted with two coats and the ceiling will be painted wih one coat each gallon of paint covers 350 square feet and costs $28 what is the total price for paint with an 8.5% sales tax?
The total price for paint with an 8.5% sales tax is $69.02928.
What is Area?The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure.
Given:
Length = 14 feet
width = 17 feet
Height = 9 foot
So, the area of Four walls
= 2(14 x 9) + 2( 17 x 9)
= 2 x 126 + 2 x 153
= 252 + 306
= 558
Now, Area of ceiling
= lw
= 14 x 17
= 238
So, the total Area = 558 + 238 = 796
Now, the cost of painting room
= 796/350 x 28
= 63.68
and, After sales tax
= 63.68 + 0.085 x 63.68
= $69.02928
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How to convert 93 cm to inches?
93 centimeter is approximately equal to 36.6142 inches ( rounded to four decimal places )
To convert 93 cm to inches, we can use the following formula:
1 cm = 0.393701 inches
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The length in inches = conversion factor × The length in centimeter
Substitute the values in the equation
93 cm = 93 x 0.393701
Multiply the numbers
= 36.6142 inches ( rounded to four decimal places )
Therefore, 93 centimeter is 36.6142 inches
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Miss Chen puts the same number of art supplies at each of 12 work stations. Each work station receives several containers of paints and 3 paint brushes. Miss Chen uses 132 items in all.
Which equation can be used to determine the number of containers of paint, p, at each work station?
Answer:
11 containers of paint and 3 paint brushes
Step-by-step explanation:
The equation that can be used to determine the number of containers of paint, p, at each work station is p = 132 / (12 * 3) = 11. Therefore, each work station receives 11 containers of paint and 3 paint brushes
a rare coin is currently worth $450. the value of the coin increases 4% each year. determine the value of the coin after 7 years.
Answer:310.45
Step-by-step explanation:
what is perpendicular line calculator online
A perpendicular line calculator online is a tool used to find the equation of a line that is perpendicular to a given line and passes through a given point.
A perpendicular line calculator online is a math tool used to find the equation of a line that is perpendicular to a given line and passes through a given point. To use this calculator, users input the slope and y-intercept of the given line, as well as the x- and y-coordinates of the given point.
The calculator then uses the formula for the slope of a perpendicular line to find the slope of the new line and calculates the y-intercept by plugging in the given point. This tool is useful in many applications, such as finding the equation of a perpendicular bisector, a perpendicular tangent line, or a perpendicular distance between two points.
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In the high school graduation class there was 200 students five years later it was 320 the next year it was 400 which five year peroid experinced the greatest perecent change
The greatest percent change occurred in the first five-year period, between the first and second year, with a percent change of 60%.
What is percent ?
Percentage is a number or ratio expressed as a fraction of 100.
We can calculate the percent change between two values using the following formula:
percent change = (new value - old value) / old value x 100%
To compare the percent change over a five-year period, we need to consider the percent change between each pair of values, as follows:
Percent change between the first and second year:
percent change = (320 - 200) / 200 x 100% = 60%
Percent change between the second and third year:
percent change = (400 - 320) / 320 x 100% = 25%
Therefore, the greatest percent change occurred in the first five-year period, between the first and second year, with a percent change of 60%.
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How to convert 750 ml to cup?
The value of volume 750 ml after converting to cups is 3.17 cups.
The conversion is useful when you need to measure liquids in cups instead of milliliters, especially if you are following a recipe that is written in cups instead of milliliters.
To convert 750ml to cups, you need to know that one cup is equal to 236.6ml. Knowing how to make the conversion can help you get the right measurements and produce accurate results in your cooking or baking. To do the conversion, divide 750 by 236.6 to get the answer in cups.
So, 750ml / 236.6ml per cup = 3.17 cups (rounded to the nearest hundredth).
Therefore, volume of 750ml is equivalent to 3.17 cups.
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Consider the initial value problem 5y? , y(0) = yo For what value(s) of yo will the solution have vertical asymptote at t=4 and t-interval of existence C < 4?
the initial value problem dy/dt = 5y, y(0) = y0, the solution has a vertical asymptote at t = 4 only when y0 = 0, and the time interval of existence is the entire real line, (-∞, ∞).
The initial value problem given is: dy/dt = 5y, y(0) = y0
The solution to this differential equation is: y(t) = y0 × e⁽⁵t⁾
To find the value(s) of y0 for which the solution has a vertical asymptote at t = 4, we need to set t = 4 and solve for y0 such that the solution becomes infinite.
y(4) = y0 × e⁽⁵ˣ⁴⁾ = y0 × e²⁰
For the solution to have a vertical asymptote at t = 4, y0 × e²⁰ must be infinite. This means that y0 must be equal to 0.
Next, we need to determine the time interval of existence C<4 for the solution. The solution is continuous and differentiable for all values of t, so the time interval of existence is the entire real line, (-∞, ∞). Therefore, for the initial value problem dy/dt = 5y, y(0) = y0, the solution has a vertical asymptote at t = 4 only when y0 = 0, and the time interval of existence is the entire real line, (-∞, ∞).
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Determine whether the variable is a discrete random variable, continuous random variable, or not a random variable.
a. The height of a randomly selected giraffe.
b. The number of textbook authors now sitting at a computer.
c. The gender of college students.
d. The number of people in a restaurant that has a capacity of 300.
e. The number of bald eagles in a country.
f. The number of people with blood type A in a random sample of 43 people.
a) It is a continuous random variable.
b) It is a discrete random variable.
c) It is not a random variable nor discrete.
d) It is a continuous random variable
e) It is a discrete random variable
f) It is a discrete random variable
What is Continuous Random Variable?A continuous variable has an uncountable range of possible values.
Any value falling inside an interval is acceptable.
What Is Discrete Random Variable?They cannot be stated as decimal numbers and can only accept a discrete value. Counting is used to obtain them rather than measuring.
a). The height of a randomly selected giraffe is a continuous random variable.
b). The random variable is discrete. You can count how many people are sitting at a computer.
c). The gender of college students ⇒ Gender is categorical data. It is neither continuous nor discrete.
d). The number of people in a restaurant that has a capacity of 300 is a continuous random variable
e). The number of bald eagles in a country Since the number of people cannot be expressed as decimals, thus it is a discrete random variable
f). it is a discrete random variable as a number of people is a discrete count, which takes values such as 0 or 1 or 2.
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If θ is an angle in standard position and its terminal side passes through the point (2,7), find the exact value of tan � tanθ in simplest radical form.
Therefore , the solution of the given problem of trigonometry comes out to be the exact value of tanθ in simplest radical form is:
tanθ = 7/2.
What exactly does trigonometry mean?connections between trigonometry and cubic slope The field of mathematics is believed to have been established around the fourth millennium BC, when scientists and professions came together. Many geometric problems can be resolved using precise mathematical techniques, and these techniques can also be used to predict the results of calculations. Trigonometry is the study of the six basic trigonometric operations.
Here,
We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the terminal side of the angle θ and the x and y axes.
The distance from the origin to the point (2,7) is the hypotenuse, so we have:
r = √{2²+7²} = √53
Since $\tan\theta$ is the ratio of the opposite side to the adjacent side, we have:
tanθ = 7/2
Therefore, the exact value of tanθ in simplest radical form is:
tanθ = 7/2.
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What is the probability of Andre choosing a number greater than 5?
1) 0
2) greater than 0 and less than 1/2
3) 1/2
4) greater than 1/2 and less than 1
Answer:
1/2
Step-by-step explanation:
The numbers are: 1, 2, 4, 5, 7, 8, 9, 10
We see that only 7, 8, 9, and 10 are greater than 5
So, 4 possible numbers are greater than 5 in the total of 8 numbers.
So, the probability is 4/8 = 1/2
So, the answer is 1/2.
The scale of a district map is 1/10,000. Find the distance on the mal, in centimeters, for each of the following actual distances.
A) 800m B) 5km
Please help!!
Its in the form of a picture
From the given information the quadrilateral QUAD is a rectangle because opposite sides are of the same length and the adjacent sides are perpendicular to each other.
What is a quadrilateral?
A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry. A closed quadrilateral has four sides, four vertices, and four angles. It is a form of a polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees. The diagonals are obtained by joining the opposing vertices of the quadrilateral.
From finding the lengths of the sides of the quadrilateral, we can see that two sides of the quadrilateral have the same length and the other two sides have the same length.
QU
length = √20
slope = 2
UA
length = √5
slope = -1/2
AD
length = √20
slope = 2
DQ
length = √5
slope = -1/2
Now the lines QU and UA are perpendicular to each other since the product of slopes is -1.
So QU ⊥ UA
similarly,
AD ⊥ UA
AD ⊥ DQ
Also, the lines QU and AD as well as the lines UA and DQ are parallel to each other as the slopes are the same.
Therefore from the given information the quadrilateral QUAD, is a rectangle because opposite sides are of same length and the adjacent sides are perpendicular to each other.
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i need help with part A and part B
