1. If SW = 25 and ST = 24, find the area of rectangle RSTW.
2. If SZ = 25 and WT = 14, what is ST?
Answers
1. Using the Pythagoras theorem, the area of the rectangle RSTW is 168 units².
2. Using the Pythagoras theorem, the measure of line segment ST is 48 units.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The diagonal SW measures = 25 units
The breadth ST measures = 24 units.
Applying the Pythagoras theorem -
(Hypotenuse)² = (Base)² + (Perpendicular)²
Substituting the values in the equation -
(SW)² = (ST)² + (WT)²
(25)² = (24)² + (WT)²
(WT)² = (25)² - (24)²
(WT)² = 625 - 576
(WT)² = 49
WT = √49
WT = 7 units
The length WT measures = 7 units
The formula for the area of the rectangle is -
Area = Length × Breadth
Area = WT × ST
Area = 7 × 24
Area = 168 units²
Therefore, the area of the rectangle is obtained as 168 units².
The line segment SZ measures = 25 units
According to the properties of rectangle the diagonals bisect each other.
So, the measure of SW = 2(SZ) = 50 units
The length WT measures = 14 units
Applying the Pythagoras theorem -
(Hypotenuse)² = (Base)² + (Perpendicular)²
Substituting the values in the equation -
(SW)² = (ST)² + (WT)²
(50)² = (ST)² + (14)²
(ST)² = (50)² - (14)²
(ST)² = 2500 - 196
(ST)² = 2304
ST = √2304
ST = 48 units
Therefore, the breadth ST measures = 48 units.
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Related Questions
A piece of material measures 38 inches. Courtney cuts the piece of material into two pieces. One piece measures 19 inches. Write an addition equation that could be used to find the length, m, of the other piece of material.
Answers
Answer:
As a whole, the piece first measured 38 inches. No matter how many times you cut it, all of the pieces will still add up to 38 inches. You know that 19 inches is the length of one of the two pieces, so all you need to find is the other unknown piece. Add the two together, with m being the unknown length.
19+m=38
If you want to solve the equation, just subtract 19 from both sides.
19+m=38
m=19
You and your family go to dinner at a local restaurant in Rexburg, Idaho and your online banking report shows that the total dinner bill (food, tax, and tip) was for $42. Suppose that you did not keep your receipt, but you remember you paid a 20% tip for the service.
What was your bill (food and tax) prior to calculating the tip? (tip was paid on the total of food and tax)
$
Number
(Round your answer to the nearest cent.)
Answers
bill (food and tax) = total bill (food, tax, and tip) / 1.2
We know that the total bill was $42 and the tip was 20%, so we can substitute those values into the equation:
bill (food and tax) = 42 / 1.2
To solve for bill (food and tax), we divide 42 by 1.2:
bill (food and tax) = $35
So the bill (food and tax) prior to calculating the tip was $35.
find the area under the normal distribution curve whose mean is and whose standard deviation is using the given value for as a boundary.
Answers
The area under the normal curve with a mean of 20 and a standard deviation of 5 is 0.8413 when x = 25.
The area under the normal distribution curve is calculated using the z-score, which is the number of standard deviations a value is from the mean. To calculate the area under the normal curve for a given mean and standard deviation, one must use the formula:
Area = ½[1 + erf(z)]
Where erf is the Gaussian error function, and z is the z-score.
To calculate the area under the curve given a boundary x, the z-score must be calculated first. This is done using the formula:
z = (x - mean) / standard deviation
Substituting this into the formula above gives:
Area = ½[1 + erf((x - mean) / standard deviation)]
For example, if the mean is 20 and the standard deviation is 5, and the boundary value is x = 25, the area under the normal curve is calculated as follows:
z = (25 - 20) / 5 = 1
Area = ½[1 + erf(1)] = 0.8413
Therefore, the area under the normal curve with a mean of 20 and a standard deviation of 5 is 0.8413 when x = 25.
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What is 0.55 times 20.1?
(With work pls)
Answers
Answer:
0.55 times 20.1 is equal to 11.055
Step-by-step explanation:
To show work, we can simply multiply 0.55 by 20.1 using long multiplication.
0.55
20.1
0.55
+11.05
11.055
So 0.55 times 20.1 is equal to 11.055
a movie theater has 7 shows a day 4 days per week and 11 shows a day 2 days per week together how many shows in 6 days
Answers
The movie theater will have 50 shows in 6 days
To find the total number of shows in 6 days, we need to calculate the number of shows for each type of day (4 days per week with 7 shows per day and 2 days per week with 11 shows per day) and then add them together.
First, let's calculate the number of shows for the 4 days per week with 7 shows per day:
4 days per week x 7 shows per day = 28 shows per week
Next, let's calculate the number of shows for the 2 days per week with 11 shows per day:
2 days per week x 11 shows per day = 22 shows per week
Now, we can add the number of shows for each type of day together to find the total number of shows in 6 days:
28 shows per week + 22 shows per week = 50 shows in 6 days
We used multiplication to calculate the number of shows per week for each type of day (by multiplying the number of days by the number of shows per day) and then added the two results together to find the total number of shows in 6 days.
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Find the measure of the angle. Round to the nearest degree
Answers
Answer:
59.036
Step-by-step explanation:
tanΘ = opposite/adjacent
Θ =tan⁻¹(opposite/adjacent)
tan⁻¹(10/6) - 59.03624347
An aspiring figure skater named Anthonia has been working on her triple axel jump. She lands it 33.33% on average. Her competition, Zahra, has also been working on her triple axel jump averaging 45% of successful lands. If both are competing at the same event, what is the probability that Anthonia will land her jump and Zahra will not land her axel jump?
Answers
If Anthonia and Zahra compete at the same event, the probability that Anthonia will successfully land her jump and Zahra will not land hers is 18.33%.
What is the probability?We describe probability as the chance or likelihood that an expected event occurs when there are many possible outcomes.
Probability lies between one and zero when it is not 100% certain or uncertain.
The probability that Anthonia lands her triple axel jump = 33.33%
The chance that Anthonia does not land her jump = 66.67% (1 - 33.33%)
The likelihood of Zahra landing her jump successfully = 45%
The odds that Zahra will not successfully land her jump = 55% (1 - 45%)
The probability that Anthonia lands successfully while Zahra does not = 18.33% (33.33% x 55%)
Thus, Anthonia has the chance of winning Zahra at 18.33%.
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Dr. Leona Williams, a well-known plastic surgeon, has a reputation for being one of the best surgeons for reconstructive nose surgery. Dr. Williams enjoys a rather substantial degree of market power in this market. She has estimated demand for her work to be: Q = 480 – 0.2P where Q is the number of nose operations performed monthly and P is the price of a nose operation. What is the inverse demand function for Dr. Williams’ services? What is the marginal revenue function? The average variable cost function for reconstructive nose surgery is estimated to be:
AVC = 2Q2 – 15Q + 400
where AVC is the average variable cost (measured in dollars), and Q is the number of operations per month. The doctor’s fixed cost per month is $8,000. If the doctor wishes to maximize her profit, how many nose operations should she perform each month? What price should Dr. Williams charge to perform a nose operation? How much profit does she earn each month?
Answers
We can conclude that -
The inverse demand function for Dr. Williams’ services is -Q = 5(280 - P)
For maximum profit, she should perform 4 operations.What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is a story of Dr. Leona Williams who is a well-known plastic surgeon.
{ 1 } -
Dr. Williams estimated demand for her work is -
Q = 280 - 0.2P
Inverse of a function can be calculated by following the steps mentioned below -
Step 1 - Replace 'y' with 'x' and vice - versa.Step 2 - Rewrite the equation by solving for 'y'.Step 3 - Replace 'y' with f⁻¹(x).So, we can write -
P = 280 - 0.2Q
P - 280 = - 0.2Q
- (280 - P) = - 0.2Q
(280 - P) = 0.2Q
Q = (280 - P)/0.2
Q = 5(280 - P)
{ 2 } -
The average variable cost function for reconstructive nose surgery is -
AVC = 2Q² – 15Q + 400
Let AVC = A{Q}
For maximum profit -
d/dQ (A{Q}) = 0
d/dQ (2Q² – 15Q + 400) = 0
d/dQ (2Q²) - d/dQ (15Q) + d/dQ (400) = 0
4Q - 15 = 0
4Q = 15
4Q = 15
Q = 3.7
Q = 4 {approx.}
Therefore, we can conclude that -
The inverse demand function for Dr. Williams’ services is -Q = 5(280 - P)
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please help will mark BRAINLIEST
Answers
The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°
What exactly is the degree formula?
Yes, we can use the radian-to-degree formula to convert a negative radian to a degree. Degrees = Radians 180 / is the formula, and it may be used for both positive and negative values. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that connect at a straight angle (90 degrees).
These are referred to as parallels. A circle of latitude is an imaginary ring that connects all places that share a parallel. The Equator is the 0 degree latitude line. Each parallel is one degree north or south of the Equator, with 90 degrees north and 90 degrees south respectively.
Hence, The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°
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given that we assume that all numbers are distinct, explain why it is without loss of generality to assume that a > d
Answers
Since it has no impact on the result or solution of the problem, assuming that a > d does not reduce the generality of the statement. If a > d, the issue can be solved by simply swapping the values of a and d.
It makes no difference to the problem whether an is more or less than d because we are presuming that each integer is distinct. Furthermore, by supposing that a > d, the problem's variables can be arranged consistently, making it simpler to comprehend and resolve. As a result, making the assumption that a > d does not reduce the generality of the solution because the problem remains the same and the assumption may be readily changed if necessary.
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please solve quickly! (15 points)
Answers
Answer:
Step-by-step explanation:
36
(
x
+
3
)
2
(
x
−
3
)
2
(X-3)^2(x+3)^2
So we get
(X+3)^2 - 2(x^2-9)+(x-3)^2 / (x-3)^2)(x+3)^2
= x^2 +6x+9-2x^2+18+x^2-6x+9 / (x-3)^2(x+3)^2
= 36/(x-3)^2(x+3)^2
32.- The high costs of the California real estate market have caused families who cannot afford to buy larger houses to consider backyard sheds as an expansion option. Many are using their patio structures to build their studios, art rooms, and hobby areas, as well as for additional storage. The median price for a custom-built backyard clapboard frame is $3,100 (Newsweek, September 29, 2003). Assume that the standard deviation is $1,200.
A)¿Cuál es el valor z para una estructura de patio trasero que cuesta $2 300?
b) ¿Cuál es el valor z para una estructura que cuesta $4 900?
C) Interprete los valores z en los incisos a) y b). Comente si alguna debe considerarse una observación atípica.
D) El artículo de Newsweek describió una combinación de oficina en el cobertizo del patio trasero construida con $13 000 en Albany, California. ¿Esta estructura debe considerarse una observación atípica? Explique por qué.
Answers
a) The z-score for a structure costing $2,300 is given as follows: -0.67.
b) The z-score for a structure costing $4,900 is given as follows: 1.5.
c) The interpretation of each z-score is given as follows:
A structure costing $2,300 has the price 0.67 standard deviations below the mean, and the cost is not unusual.A structure costing $4,900 has the price 1.5 standard deviations above the mean, and the cost is not unusual.d) The structure would have an unusual price, as the z-score has an absolute value greater than 2.
How to obtain the z-scores?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.A mesure X is considered unusual if the z-score has an absolute value greater than 2.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 3100, \sigma = 1200[/tex]
For item a, the z-score is then given as follows:
Z = (2300 - 3100)/1200
Z = -0.67.
For item b, the z-score is then given as follows:
Z = (4900 - 3100)/1200
Z = 1.5.
For the price of $13,000, the z-score is given as follows:
Z = (13000 - 3100)/1200
Z = 8.25.
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Tarmu run 30 min and burned 170 calories. Write an equation that represents the number of calories,c, burned per min
Answers
c=170/30 is the equation that represents the number of calories,c, burned per min.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given that Tarmu run 30 min and burned 170 calories
We need to find the equation that represents the number of calories, c, burned per min.
To find the calories burned in each minute we have to divide one hundred seventy by thirty.
c=170/30
c=5.66 cal/min
Hence, c=170/30 is the equation that represents the number of calories,c, burned per min.
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Tyrone put 1/3 teaspoon of salt in a batch of cookie dough. He thought that might not been enough salt, so he added another 1/4 teaspoon. How much salt did Tyrone use in total?
Answers
Answer:
7/12 of salt.
1/4 + 1/3 =
1/3 + 1/4 =
4/12 + 3/12 = 7/12.
Step-by-step explanation:
Hope it helps! =D
Chapter 6
Lesson 2 skills practice numerical expressions
Answers
The Numerical Expressions answers are shown below:
What is Integers?Integers come in three types:
Zero (0)Positive Integers (Natural numbers)Negative Integers (Additive inverse of Natural Numbers)Given:
1. 7-6+ 5
= 7 -1
= 6
So, the value of 7-6+ 5 is 6.
2. 31 +19 -8
= 31 + 11
= 42
So, the value of 31 +19 -8 is 42.
3. 64-8+21
= 56 + 21
= 77
So, the value of 64-8+21 is 77.
4. 17+34-2
= 51-2
= 49
So, the value of 17+34-2 is 49.
5. 28+ 89 -67
= 117-67
= 50
So, the value of 28+ 89 -67 is 50.
6. (8+1) x 12- 13
= 9 x 12 -13
= 108 - 13
= 95
So, the value of (8+1) x 12- 13 is 95.
7. 63/9 +8
= 7 +8
= 18
So, the value of 63/9 +8 is 18.
8. 5 x 6 -(9-4)
= 5x 6 - 5
= 30- 5
= 25
So, the value of 5 x 6 -(9-4) is 25.
9. 13x 4 -72 /8
= 13 x 4 - 9
= 52- 9
= 43
So, the value of 13x 4 -72 /8 is 43.
10. 16/2 + 8 x 3
= 8 + 8 x 3
= 8+24
= 32
So, the value of 16/2 + 8 x 3 is 32.
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A bakery used 30% more sugar this month than last month.If the bakery used 560 kilograms of sugar lost month,how much did it use this month?
Answers
728 kilograms of sugar is used in this month.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that a bakery used 30% more sugar this month than last month.
Let us convert 30% to decimal.
Divide 30 by 100
30/100=0.3
the bakery used 560 kilograms of sugar last month we have to find the amount of sugar used this month.
Now multiply 30% of 560
0.3×560
168.
So now 560+168=728 is the amount of sugar used this month.
Hence, 728 kilograms of sugar is used in this month.
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in the x y coordinate plane, which of the following points must lie on kx + 3y + 6 if k = -1/2
Answers
Answer:
honestly, I got no idea. I can tell you though - go us Desmos kid. it'll help you more than any person in this platform.
don't thank me
Step-by-step explanation:
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A line passes through the point(-8, -9) and has a slope of Write an equation in slope-intercept form for this line. -5/4
Answers
Answer:
y = (-5/4)x - 19
Step-by-step explanation:
Given information,
→ Slope(m) = -5/4
→ Point = (-8, -9)
→ y-intercept = b
The slope-intercept form is,
→ y = mx + b
Now the y-intercept will be,
→ y = mx + b
→ -9 = (-5/4)(-8) + b
→ -9 = 10 + b
→ b = -9 - 10
→ [ b = -19 ]
Then the required equation is,
→ y = mx + b
→ [ y = (-5/4)x - 19 ]
Hence, this is the equation.
Using the theory vectors, find all possible fourth corners to parallelograms that have vertices (1,1), (4,2), and (1,3)
Answers
So, the possible fourth corners are (4,4) and (-2,2).
Given the three vertices of a parallelogram (1,1), (4,2), and (1,3), we can use vector algebra to find the fourth corner. We know that opposite sides of a parallelogram are parallel, and therefore have the same vector direction. We can use this property to find the vector pointing from one corner to another and then use this vector to find the fourth corner.
One possible method is:
Find the vector pointing from (1,1) to (4,2) by subtracting the coordinates of the first point from the coordinates of the second point: (4,2) - (1,1) = (3,1)Find the fourth corner by adding this vector to the third point: (1,3) + (3,1) = (4,4)Another possible method is:
Find the vector pointing from (4,2) to (1,3) by subtracting the coordinates of the second point from the coordinates of the third point: (1,3) - (4,2) = (-3,1)Find the fourth corner by adding this vector to the first point: (1,1) + (-3,1) = (-2,2)So, the possible fourth corners are (4,4) and (-2,2).
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vertex to standard form
Answers
The quadratic function y = 7(x + 1)² + 1 in standard form is y = 7x² + 14x + 2.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The given quadratic function is -
y = 7(x + 1)² + 1
Solve the equation to get the standard form.
First solve using the formula (a + b)² = (a² + 2ab + b²) -
y = 7(x + 1)² + 1
y = 7(x² + 2x + 1) + 1
Now, open the brackets -
y = 7x² + 14x + 1 + 1
Now, add the like terms -
y = 7x² + 14x + 2
Therefore, the value is obtained as 7x² + 14x + 2.
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Please help!!
Find the third, fourth, and tenth terms of the sequence described by the rule.
A(n) - 3+ (n-1)(5)
A(3)=
A(4)=
A(10)=
Answers
Answer:
A(3) = 13
A(4) = 18
A(10) = 48
Step-by-step explanation:
This seems like a plug and play.
Starting with A(3). Everywhere you see an n, you'll replace it with a 3, as follows;
3 + (3-1)(5) = ?
We'll solve it step by step. First is 3-1. That's 2, bringing it to
3 + (2)(5).
2 times 5 is 10, bringing it to
3 + 10.
3 + 10 = 13, which concludes
A(3) = 13.
Now doing it for the remaining 2.
3 + (4-1)(5)
3 + (3)(5)
3 + 15
A(4) = 18
Last one...
3 + (10-1)(5)
3 + (9)(5)
3 + 45
A(10) = 48
Kimiyo earns a weekly salary of $675 plus a 6.5% commission on sales at a gift shop. How much would she make in a work week if she sold $4,800 worth of merchandise?
Answers
Kimiyo would make $987 in a work week if she sold $4,800 worth of merchandise.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Kimiyo earns a weekly salary of $675 plus a 6.5% commission on sales at a gift shop.
She sold $4,800 worth of merchandise.
That means,
the commissioned amount = 4800 x 6.5 /100
The commissioned amount = $312
In a week,
Kimiyo's total earning is,
= $675 + $312
= $987
Therefore, $987 is the total salary.
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Find the plane determined by the intersecting lines.
L1 x= -1 + 3t y = 2+2t z=1-t
L2 x=1-4s y=1+2s z=2-2s
Answers
In a plane, intersecting lines are any two or more lines that cross each other. The point of intersection is the common point shared by all intersecting lines.
What are Intersecting Lines?In a plane, intersecting lines are those that cross one another three times or more. The point of intersection is the shared location between all intersecting lines that exists on all intersecting lines.Point O represents the point of intersection where lines P and Q meet in this instance.Specifications of intersecting linesWhen two or more lines intersect, they always do so at the same location.Any angle may be used to intersect the lines. Always more than 0° and less than 180° is the angle that is generated.Vertical angles are created by two intersecting lines. There is a common vertex between the opposing vertical angles (which is the point of intersection).Vertical angles a and c are equivalent in this case. Additionally, b and d have equal vertical angles and are vertical angles.A plus D equals a straight angle of 180 degrees.To Learn more About intersecting lines refer To:
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QUICK!!! WHAT IS -2 2/5 times -1/3
(Please show work)
Answers
-2 2/5 = -12/5 x -1/3
= 4/5
the answer is 4/5 or 0.8 in decimal form if you need it
6-7 Collisions and Explosions (1-D)
1. A flatcar with mass M, traveling at speed v, collides with and couples to a parked
boxcar. They move off together with a speed of 1/3 v. What is the mass of the boxcar?
Answers
They move off together with a speed of 1/3 v,The mass of the boxcar is m/3 (V₁ - V₂)².
What is mass?A body's mass is an inherent quality. Prior to the discovery of the atom and particle physics, it was widely considered to be tied to the amount of matter in a physical body.
in Kinetic energy 4 system, the
K = Kf-Ki
K = 1 (Mcar + Mtruck) Vp ² + mcarv₁_ J 2 2 + Mtruck V2 2 2
K = +(m+2m) (V₁+2√2)² +mv₁² - 1 x 2m v₂ ² 2 2 9
K m (v, ² + 4 √₂ ² + AV₁ V2 ) - { mv, ² - tn v₂ 2 2 6
K = m (V₁²+ 4V₂² + 4 V₁ V2 -1/3V, ² - 6V, ²) /6.
K = m/6 (4V₁V2.-2V₁2-2√22)
k = + m/3 (V₁ - V₂)²
They move off together with a speed of 1/3 v, The mass of the boxcar is m/3 (V₁ - V₂)².
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What is the equation of the line that passes through the point (8, 4) and has a slope
of o?
Answers
The equation of the line passing through the point (8, 4) and having a slope of 0 is y = 4.
What is the slope intercept?
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
The line passing through the point (8, 4) and having a slope of 0 is a horizontal line which is parallel to the x-axis. The slope (m) of this line is 0.
The point-slope form of this line would be:
(y - 4) = 0(x - 8)
Simplifying this, we get:
y = 4
Hence, the equation of the line passing through the point (8, 4) and having a slope of 0 is y = 4.
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ow many ways can you select 7 cookies to buy from a bakery that sells cookies of 3 different flavors (oatmeal, chocolate chip, almond)? we assume that more than 7 cookies are displayed for each flavor. for example, one way is to choose 7 chocolate chip cookies
Answers
There are 2187 combinations to select 7 cookies from a bakery that sells cookies of 3 different flavors (oatmeal, chocolate chip, almond).
When selecting 7 cookies from a bakery that sells 3 different flavors, each cookie selected can be one of the 3 different flavors. This means that for the first cookie, there are 3 choices, for the second cookie, there are also 3 choices, and so on for the 7th cookie. This is known as the combinations formula and it can be represented as 3 x 3 x 3 x ... x 3 (3 being repeated 7 times).
Using the 3⁷ formula, we can calculate that there are 2187 ways to select 7 cookies from a bakery that sells cookies of 3 different flavors. This means that there are 2187 unique combinations of cookies that can be selected, assuming that more than 7 cookies are available for each flavor.
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Your question seems incomplete, but I assume the question was:
"How many ways can you select 7 cookies to buy from a bakery that sells cookies of 3 different flavors (oatmeal, chocolate chip, almond)? We assume that more than 7 cookies are displayed for each flavor. For example, one way is to choose 7 chocolate chip cookies."
Can someone explain to me why the answer is 90 and not 1080? I think it has to do with the inches and ft. But I don’t remember how you solve it.
Answers
Answer:
You are correct
Step-by-step explanation:
You are correct sir. They want the answer in feet, so everything on that triangle has to be converted into feet.
There are 12 inches in a foot. If we do 108/12 we get 9 feet.
If the coordinates of a quadrilateral composed in the first quadrant of the coordinate plane are (0,0), (a,b), (a+c,b), and (c,0), which is the most accurate classification of the quadrilateral?
a. trapezoid
b. rectangle
c. parallelogram
d. square
Answers
the opposite sides of the quadrilateral PQRS are equal and parallel and so PQRS is a PARALLELOGRAM.
Option (C) is CORRECT.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, that the coordinates of the vertices of a quadrilateral composed in the first quadrant of the coordinate plane are (0,0) (a, b), (a + c, b), and (c, 0).
We are to select the most accurate classification of the quadrilateral.
Let the coordinates of the vertices of the quadrilateral be P(0,0), Q(a, b), R(a + c, b), and S(c, 0).
The lengths of the sides are calculated using the distance formula as follows :
PQ = √(a² + b²)
QR = √(a +c -a)² + (b-b)² = √c² = c
RS = √(a² + b²)
SP = c
So, the opposite sides are equal in length.
And, the slopes of the sides are calculated as follows :
The slope of PQ(m₁) = (b-0)/(a-0)
The slope of QR(m₂) = (b-b)/(c-a-c) = 0
The slope of RS(m₃) = 0-b/(c-a-c) = 0
The slope of SP(m₄) = (0-0)/(0-c) = 0
So, the slopes of the opposite sides are equal but:
m₁ *m₂ = 0 ≠ -1
m₃ *m₄ = 0 ≠ -1
Therefore, the opposite sides of the quadrilateral PQRS are equal and parallel and so PQRS is a PARALLELOGRAM.
Option (C) is CORRECT.
Learn more about coordinates here:
https://brainly.com/question/20282507
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Which group cannot form 8 lines with an equal number of members in each line? A. 881 B. 440 C. 353 D. 224
Answers
Answer:
A. 881
C. 353
Step-by-step explanation:
In order to form 8 lines with each line having equal length, the total number of members has to be divisible by 8:
440/8 = 55, so 440 isn't the answer
224/8 = 28, so 224 isn't the answer
881/8 = 110.125. In addition, even numbers can't be divided evenly by odd numbers like 881, so A. 881 is the answer.
Same goes to 353 since 353 is also an odd number that can't evenly divide the even number 8. Hence, C. 353 is the answer as well.