To prove the statement using neutral geometry, we'll rely on the properties of triangles and the parallel postulate in neutral geometry.
Let's assume we have a triangle ABC, where angle A is right or obtuse.
Case 1: Angle A is right:
If angle A is right, it means it measures exactly 90 degrees. In neutral geometry, we know that the sum of the interior angles of a triangle is equal to 180 degrees.
Since angle A is right (90 degrees), the sum of angles B and C must be 90 degrees as well to satisfy the property that the angles of a triangle add up to 180 degrees. Thus, angles B and C are acute.
Case 2: Angle A is obtuse:
If angle A is obtuse, it means it measures more than 90 degrees but less than 180 degrees. Again, in neutral geometry, the sum of the interior angles of a triangle is equal to 180 degrees.
Since angle A is obtuse, the sum of angles B and C must be less than 90 degrees to ensure the total sum is 180 degrees. Therefore, angles B and C must be acute.
In both cases, we have shown that if one interior angle of a triangle is right or obtuse, then the other two interior angles are acute. This conclusion is derived solely from the properties of triangles and the sum of interior angles, without relying on any Euclidean-specific axioms or theorems.
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At a 95-percent confidence level, what should be the cutoffs from the left and right sides of a normal distribution?
The cutoffs from the left and right sides of normal distribution at a 95-percent confidence level are 1.96.
What is the confidence level?The confidence level, which is used in statistics, describes the likelihood that the estimation of a statistical parameter's location in a sample survey is also true for the population.
Confidence levels must be decided upon in advance when surveying since they affect the survey's essential scope and error margin. Confidence intervals of 90, 95, and 99 percent are widely employed in surveys.
If the confidence level were set at 95%, there is a very good likelihood that the population's arithmetic mean, as a statistical number, will fall within the survey's established margins of error.
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Which is the best first step to factor….?
Answer:
A
Step-by-step explanation:
By using greatest common factor you are able to take a 2 out of all the numbers
GCSE MATHS PLEASE HELP
Answer:
A) y = 16/(x^2), B) 4/5
Step-by-step explanation:
For A, we can plug in some of the table values to check it. I will try 2 and 3
2. 4 = 16 / (2^2)
16/4 = 4
3. 16/9 = 16 / (3^2)
16/9 = 16/9
B) We can just input y into the formula 25 = 16 / (x^2)
This leaves us with +-4/5
Answer:
see explanation
Step-by-step explanation:
(a)
given y varies inversely as x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
to find k substitute any ordered pair from the table into the equation
using (2, 4 ) , then
4 = [tex]\frac{k}{2^2}[/tex] = [tex]\frac{k}{4}[/tex] ( multiply both sides by 4 )
16 = k
y = [tex]\frac{16}{x^2}[/tex] ← equation of variation
(b)
when y = 25 , then
25 = [tex]\frac{16}{x^2}[/tex] ( multiply both sides by x² )
25x² = 16 ( divide both sides by 25 )
x² = [tex]\frac{16}{25}[/tex] ( take the square root of both sides )
x = ± [tex]\sqrt{\frac{16}{25} }[/tex] = ± [tex]\frac{4}{5}[/tex]
the positive value of x is x = [tex]\frac{4}{5}[/tex]
Suppose the shipping weight of your cheese shop's customized gift baskets is asymmetrically distributed with unknown mean and standard deviation. For a sample of 70 orders, the mean weight is 57 ounces and the standard deviation is 7.1 ounces. What is the lower bound of the 90 percent confidence interval for the gift basket's average shipping weight
The lower bound of the 90% confidence interval for the gift basket's average shipping weight is 55.605.
Given mean weight of 57 ounces ,sample size 70 ,confidence level 90% and standard deviation of 7.1 ounces.
We have to find the lower bound of the confidence interval for the gift's basket's avrage shipping weight.
We can easily find the confidence interval and its lower bound through theformula of margin of error.
Margin of error is the difference between real values and calculated values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where z is the critical value of confidence level
σ is standard deviation,
n is the sample size
We have to first find the z value for 90% confidence level which is 1.645.
Margin of error=1.645*7.1/[tex]\sqrt{70}[/tex]
=11.6795/8.3666
=1.395
Lower bound of the confidence interval = Mean - margin of error
=57-1.395
=55.605.
Hence the lower bound of the confidence interval for the gift basket's average shipping weight is 55.605.
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What is the measure of angle g, in terms of x? x° x° x° 90° 180° – x° 180° – 2x°
The measure of angle G in terms of x is x+x degrees
Circle theoremThe measure of angle F and angle D is 90 degrees so that;
<GFD = <GDF = 90 - x
Since the sum of angle in a triangle is 180 degrees, hence;
<G + 90 - x + 90 - x = 180
<G + 180 - 2x = 180
<G = 2x
<G = x + x
Hence the measure of angle G in terms of x is x+x degrees
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Answer:A
Step-by-step explanation: math and me go together like mustard and pees
I need this problem solved
Answer:
AP = 12, and FQ = 8
Step-by-step explanation:
The proportion between AB:FG and AP:FQ is the same.
--> 9:6 = AP:FQ
I'll say that FQ is x and AP is x+4 (since AP is 4 longer than FQ)
--> 9:6 = x+4:x
--> 6(x+4) = 9x
--> 6x + 24 = 9x
--> 24 = 3x
--> x = 8
Since AP= x+4 and FQ= x. AP becomes 12 and FQ becomes 8.
The hotel staff is decorating the lobby by placing one row of string lights along the outer edge of the rectangular ceiling. A member of the staff maps the ceiling on a coordinate grid as shown, where each unit represents 1 meter.
The length of string used to decorate the ceiling = 40.5 meters.
According to the statement
we have given that the hotel staff is decorating the lobby by placing one row of string lights along the outer edge of the rectangular ceiling.
And the coordinates of rectangular ceiling is A(5,16), B(17,10), C(14,4), D(2,10).
And we have to find the total length for string is used to decorate the rectangular ceiling.
We know that the Total length of string = Area of the rectangular ceiling.
And area of rectangular ceiling = L*B
So, Length of rectangular ceiling = A+B
Length of rectangular ceiling = (17-5) + (16-10)
Length of rectangular ceiling = (12+6)/2
Length of rectangular ceiling = 9.
So,
Breadth of rectangular ceiling = B+C
Breadth of rectangular ceiling = (17-14)+(10-4)
Breadth of rectangular ceiling = (3+6) /2
Breadth of rectangular ceiling = 4.5
So, the length of string used = 4.5*9
the length of string used = 40.5 meters.
The length of string used to decorate the ceiling = 40.5 meters.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
The hotel staff is decorating the lobby by placing one row of string lights along the outer edge of the rectangular celling. A member of the s⊥aff maps the celling on a coordinate grid as shown, where each unit represents . What is the approximate length of string lights the staff needs to decorate the ceiling?
A 20.25 meter
B. 35 meter
C. 40.5 meter
D. 14 meter
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Move the sliders to set the values of r, h, and k, and record at least three different sets of data. also record the equations of the corresponding circles.
The equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .
The question seems incomplete and complete question given in the image !!!!
A circle is the set of all points in a plane at a given distance (called the radius) from a given point (called the center.)
We know that the general equation for a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where ( h, k ) is the center and r is the radius.
According to the question
The equation of circle given is [tex]x^2+y^2=1[/tex]
Center at origin
i.e
(h,k) = (0,0)
and radius = 1 unit
Now ,
By changing changing center (h,k) and radius of equation it will give following equations
h k r equation of circle
0 1 3 [tex](x-0)^2+(y-0)^2=3^2[/tex]
2 2 3 [tex](x-2)^2+(y-2)^2=3^2[/tex]
1 1 1 [tex](x-1)^2+(y-1)^2=1^2[/tex]
-2 -1 2 [tex](x+2)^2+(y+1)^2=2^2[/tex]
3 2 1 [tex](x-3)^2+(y-2)^2=1^2[/tex]
-5 1 3 [tex](x+5)^2+(y-1)^2=3^2[/tex]
Hence, the equations of the corresponding circles can be any equation only have to satisfy the general equation for circle .
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George is driving at an average speed of 707070 miles per hour. At this rate, how long, in minutes, will it take him to complete a 400400400-mile road trip
Given the average speed and distance covered, the time taken for the driver to complete the road trip is 5.7 hours
How long will it take the driver to complete a 400-mile road trip?Speed is simply referred to as distance traveled per unit time.
Mathematically, Speed = Distance ÷ time.
Given the data in the question;
Speed = 70 miles per hourDistance traveled = 400 mileElapsed time = ?We substitute into our equation above.
Speed = Distance ÷ time
70 miles per hour = 400 mile ÷ Elapsed time
Elapsed time = 400 miles ÷ 70 miles per hour
Elapsed time = 5.7 hours
Given the average speed and distance covered, the time taken for the driver to complete the road trip is 5.7 hours.
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Three less than a number x is more than 15. an inequality that represents this word sentence is
Answer:
x - 3 > 15
Step-by-step explanation:
A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 123 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.)
The height of package is 34 inches.
According to the statement
we have given that the perimeter of cylinderical package is 123 inches.
and we have to find the volume of this package.
So,
According to the perimeter
2(Pi)r + h = 123
and then
h = 123 - 2(Pi)r
then the volume become
V = (Pi) r^2h
V= (Pi) r^2 * [ 123 - 2(Pi)r ] = 123 (Pi) r^2 - 2(Pi)r^3
then differentiate it
dV/dr = 246(Pi) r - 6(Pi)r^2
Now take
r(246(Pi) - 6(Pi)r) = 0
then neglect r=0 and then find another value of r.
r = 246(Pi) / 6(pi)
here r=41 then
h = 123 - 2(Pi)r
h = 123 - 2(3.14)41
h = 123 - 2(Pi)r
Then put the value of r then h = 34 inches.
So, The height of package is 34 inches.
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Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U.
Next, draw PT, QU, and RS.
Which statements are true?
m∠Q = m∠R
The length of QU is half the length of RP.
m∠P + m∠Q + m∠R = 180°
QU ≅ RS
PT, QU, and RS intersect at the same point.
The sum of the lengths of QU and RS is equal to the length of PT.
Step-by-step explanation:
1. Not neccesarily true
2. Not necessarily true
3. True because angles in a triangle add to 180°
4. Not necessarily true
5. True because the medians are being constructed, and the three medians of a triangle are always concurrent.
6. Not necessarily true
The statements that are true about the triangle are:
Option C: m∠P + m∠Q + m∠R = 180°
Option E: PT, QU, and RS intersect at the same point.
How to find the true statements of the triangle?1. m∠Q = m∠R: This is not true because there is no indication that the angles are equal.
2.The length of QU is half the length of RP: This is not true because there is no length given to show that measurement.
3. m∠P + m∠Q + m∠R = 180°:
This is true because the sum of angles in a triangle add to 180°
4. QU ≅ RS:
This is not true because we are not told that they are congruent
5. PT, QU, and RS intersect at the same point:
This is true because the medians are being constructed, and the three medians of a triangle are always concurrent.
6. The sum of the lengths of QU and RS is equal to the length of PT: This is not true because we are not told that.
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In a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 50 and a standard deviation of 3. using the empirical rule, what is the approximate percentage of daily phone calls numbering between 47 and 53?
68% of the daily phone calls answered by the company are between 47 and 53.
What is empirical rule?Empirical rule states that for a normal distribution, 68% of the data are within one standard deviation from the mean, 95% of the data are within two standard deviation from the mean and 99.7% of the data are within three standard deviation from the mean.
Given mean of 50 and a standard deviation of 3
68% are within one standard deviation from mean = mean ± standard deviation = 50 ± 3 = (47, 53)
68% of the daily phone calls answered by the company are between 47 and 53.
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18. The area of a right triangle is 30 cm². The length
of one leg of the triangle is 5 cm. What is the
length of the other leg?
(A) 6 cm
(B) 12 cm
(C) 18 cm
(D) 24 cm
Answer:
12
Step-by-step explanation:
The area of a triangle is calculated with the following formula:
[tex]\frac{1}{2} *b*h[/tex] (b: base, h: height (or legs))
We can use this formula to find the length of the other leg:
30 = [tex]\frac{1}{2} *b*h[/tex] multiply both sides with 2 to get rid of fraction
60 = b*h one of the leg's length is given as 5 so
60 = 5*h divide both sides by 5
12 = h is the length of the missing leg.
Prediction of the value of the dependent variable outside the experimental region is called _____. Group of answer choices interpolation forecasting averaging extrapolation
Prediction of the value of the dependent variable outside the experimental region is called extrapolation.
According to the question,
Prediction of the value of the dependent variable outside the experimental region is called extrapolation.
Extrapolation is the statistical method beamed at understanding the unknown data from the known data.
Hence, prediction of the value of the dependent variable outside the experimental region is called extrapolation.
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Convert the exponential to a logarithmic form: 10 ^ 4 = 10000
Answer:
10^4 = 10 × 10 × 10 × 10
= 10000
Using the table below, find the mean and median of the set of data.
Note: Round all numbers to the nearest tenth
The mean of the data set is 81.6.
The median of the data set is 80.
What is mean?The mean is the average of a data set. Therefore,
Mean = (70 x 2 + 75 x 8 + 80 x 6 + 85 x 3 + 90 x 9) / 28 = 81.6.
Hence,
mean = 81.6
What is a median?Median is a statistical measure that determines the middle value of a dataset listed in ascending order .
Therefore,
28 / 2 = 14
median = 80 + 80 / 2 = 160 / 2 = 80
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What is the equation of the line that passes through (4,11) and is perpendicular to the line with the following equation
Your question is incomplete. please read below for the missing content
y = -3/4x + 14 is the answer.
y = 4/3x+ 7...slope here is 4/3. A perpendicular will have a negative reciprocal slope. All that means is to flip the slope and change the sign.
4/3....flip it....3/4....change the sign....-3/4. So our perpendicular equation has to have a slope of -3/4
y = mx + b
slope(m) = -3/4
(4,11)...x = 4 and y = 11
now we sub and find b, the y int
11 = -3/4(4) + b
11 = - 3 + b
11 + 3 = b
14 = b
so ur line is : y = -3/4x + 14
The perpendicular line has the opposite slope of the reciprocal, so the slope of the line you want to find is 1/2. Inserting the given points into the equation y = 1 / 2x + b and solving b yields b = 6. Therefore, the linear equation is y = ½x + 6. When relocated, it becomes –x / 2+. y = 6.
Q) What is the equation of the line that passes through the point (4,11) and is perpendicular to the line with the following equation y = 4/3x + 7
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Select all the correct answers.
The table shows points on the graph of the function f (x) = 3 sin (x- pi/2) + 1
Answer:
B,C and E
Step-by-step explanation:
The period can be calculated by dividing 2pi by the coefficfient of the x, so in this case 1. And we'll get 2pi/1 = 2pi.
The function clearly has a minimum of -2, you can see that from the table.
Same thing for the maximum = 4.
Answer:
See Photo
Step-by-step explanation:
Plato/Edmentum
Drag each statement to the correct location on the flowchart. Not all statements will be used.
Given: AB||CDand AD||BC
Prove: ZA ZC
D
B
Complete the flowchart proof.
m/ADC = m/ADB+ m/CDB m/BCD= m/DAC+m/ACD
m/DAB= m/BCD m/ABC= m/ABD+m/CBD
entum. All rights reserved.
pe here to search
m/DAB = m/DAC+m/ACD
C
m/DAB-m/DAC+m/BAC
MI
whetitution
The information to fill one the box regarding the proof include:
AB = CDAD = CBBD is common to both trianglesHow to illustrate the proof?It should be noted that when two triangles of each corresponding sides are equal, then it's said that they are similar.
Here AB = CD, and AD = CB as they illustrate the fact that they are parallel.
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Triangle DEF is congruent to triangle UVW. The length of side DE is 6 cm, EF is 7.5 cm, and DF is 5 cm. What is the length of side VW?
The length of side VW is 7.5 cm
What is the length of side VW?The given parameters are:
DE is 6 cm, EF is 7.5 cm, and DF is 5 cm
Since the two triangles are congruent, then it means that:
D corresponds to UE corresponds to VF corresponds to WSo, we have:
VW= EF
The side EF is
EF = 7.5 cm
So, we have:
VW = 7.5 cm
Hence, the length of side VW is 7.5 cm
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When the bus leaves the station there are 29 passengers on board. at the first stop, 4 people get off and 11 get on. at the second step, 7 people get off and 23 get on. if the bus has 78 passenger seats and everyone is seating down, how many seats are now free?
When everyone is sitting down, the number of free seats is 26, using arithmetic addition and subtraction.
What is arithmetic addition and subtraction?The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are arithmetic addition and subtraction. The addition symbol is the plus sign (+), and the subtraction symbol is the minus sign (-). (minus sign).
The initial number of passengers on board=29
After 4 people get off at the first stop,
Using arithmetic addition and subtraction, we get,
Number of passengers left=29-4=25
After 11 people get on,
Number of passengers=25+11=36
At the second stop, when 7 people get off,
Number of passengers=36-7=29
When 23 people get on,
Number of passengers=29+23=52
Total number of passenger seats in the bus=78
Number of free seats, when everyone is sitting=78-52
=26
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HELP ASAP!!
Select the two values of x that are roots of this equation.
x²+2x-5=0
A. x--1+2√√6
B. x=-1+√6
C. x=-1-√6
D. x=-1-2√6
Answer:
Step-by-step explanation:
hello:
here an solution
The field width of thestadium is 40m lessthan its length. The total length of the rectangular boundary of the open space in canopy is 420m. Frame a suitable
equation for the given situation and also find the length and width of the field in the stadium.
Answer:
I may have misubderstood the question, so review carefully.
width = 380 m
length is 420 m
Step-by-step explanation:
Let w and l stand for the width and length of the stadium.
We are told that w = l - 40 m
We also learn that l = 420 m
w = l - 40 m
w = (420 m) - 40 m
width = 380 m
length is 420 m
Total area=
Help me please;! Asap thanks so much
The total area of the square based prism is 413.7 square units
How to determine the surface area?The given parameters are:
Base length, a = 10
Height, h = 11
The total surface area is calculated as:
[tex]A = a^2 + 2a\sqrt{\frac{a^2}{4} + h^2[/tex]
This gives
[tex]A = 10^2 + 2 *10\sqrt{\frac{10^2}{4}+11^2[/tex]
So, we have:
[tex]A = 100 + 20\sqrt{246[/tex]
Evaluate
A = 413.7
Hence, the total area of the square based prism is 413.7 square units
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Order the set of numbers from least to greatest: -
--5, -√26.-31
6
Answer:
-31, /~26, -5, 6
Step-by-step explanation:
Sam is rowing a boat away from a dock. The graph shows the relationship between time and Sam’s distance from the dock. Evaluate the function for an input of 6.
Answer:
See below
Step-by-step explanation:
Go across the 'x' axis to '6'....then go UP to the graph to find y = 60
after 6 minutes he has rowed 60 meters
please give the answer
The function can be solved as follows:
f(6 + 4) = 25f(6) - f(4) = 20f(6 - 4) = 1f(6) - f(4) = 6f(6) . f(4) = 91How to solve function?f(x) = 3x - 5
Therefore, the function can be solved as follows:
f(6 + 4) = f(10) = 3(10) - 5 = 25
f(6) + f(4) = 3(6) - 5 + (3(4) - 5)
f(6) - f(4) = 13 + 7
f(6) - f(4) = 20
f(6 - 4) = f(2) = 3(2) - 5 = 6 - 5 = 1
f(6) - f(4) = 3(6) - 5 - (3(4) - 5)
f(6) - f(4) = 18 - 5 - (12 - 5)
f(6) - f(4) = 13 - 7
f(6) - f(4) = 6
f(6.4) = f(24) = 3(24) - 5 = 72 - 5 = 67
f(6) . f(4) = (3(6) - 5 ) (3(4) - 5)
f(6) . f(4) = (18 - 5)(12 - 5)
f(6) . f(4) = (13)(7) = 91
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What is the range of the following set of ordered pairs?
{(-1,7), (6,2), (0,4), (5,2), (-3,1)}
O a. {7,2,4,1}
b.
O c.
O d.
{-1,6, 0, 5, -3}
{-1, -3, 1, 7,6}
{2, 0, 4, 5)
Answer:
range of the given set is { 7,2,4,2,1}
Step-by-step explanation:
. Hello !
When the above kind of set is given the second values of each elements belongs to the range or the y whereas, the first values of the elements belongs to the domain or x.
Thus, domain = {-1,6,0,5,-3}range ={7,2,4,2,1}DOES ANYONE KNOW THE ANSWER
Answer:
D. none
Step-by-step explanation:
we only know about the right angle at the bottom right.
that is not enough information.
we always need 3 pieces of confirmed information of each triangle to be able to say that the 2 triangles are indeed of the same shape and size.
like the other answer options would indicate :
SAS : side - angle - side.
2 sides and the enclosed angle. if we know they are equal, then the rest of the triangles follow automatically.
SSS : all 3 sides. with 3 defined sides there is only one possible shake and size for that triangle.
HL : Hypotenuse and a leg of a right-angled triangle (also 3 pieces of information - 2 sides and the right angle).
since we have only the right angle and nothing else, we cannot prove that the triangles are congruent.