Hilbert's euclidean parallel postulate implies the converse to the alternate interior angle theorem since if α = β, then l and m cannot be parallel.
Hilbert's Euclidean parallel postulate states that given a line and a point not on that line, there exists exactly one line passing through the point and parallel to given line.
Suppose we have two parallel lines l and m, and a third line n that intersects both l and m, forming alternate interior angles α and β. We want to prove that if α = β, then l and m are not parallel.
Let's assume contrary, that l and m are parallel despite α = β. Then, by Hilbert's parallel postulate, there exists exactly one line passing through any point on n that is parallel to l and m.
Therefore, if we draw a line parallel to l and m through point where n intersects l, it must be same as line passing through point where n intersects m.
But this leads to a contradiction, because if lines are same, then alternate interior angles α and β are congruent.
Thus, we have shown that if α = β, then l and m cannot be parallel. This is converse to alternate interior angle theorem.
Therefore, we have proved that Hilbert's Euclidean parallel postulate implies converse to the alternate interior angle theorem.
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14 Customers into the store over the course of seven minutes how many Internet store after one minute
Answer:
2
Step-by-step explanation:
14 divided by 7 is two customers in one minute
Answer:
After one minute there will be 2 people inside the store.
Step-by-step explanation:
First we put this into a proportion. Aka set up like a fraction.
14 (customers) x
------- ---> ------
7 (minute) 1 minute
In order to find x, we must divide by 7 because in order to make the bottom number one on the bottom, you must divide by 7 , so we do the same to the top.
14/7 is 2.
This means that per minute, there are 2 people inside the store.
After one minute, There will be 2 people inside the store.
A bag contains 11 red M&Ms, 8 green M&Ms, and 6 blue M&Ms.What is the ratio of blue M&Ms to green M&Ms?
Answer:
The answer is 6/25 :8/25
The midpoint of AB is M(-3,-3). If the coordinates of A are (-5, -1), what are
the coordinates of B?
Answer:
The coordinates of B are (-1, -5).
Step-by-step explanation:
Since the x-coodinate of M is 2 greater than that of B (note that -3 = -5 + 2), the x-coordinate of B is found by adding 2 to -3, obtaining -1. The y-coordinate of M is -3, which is 2 less than the y-coordinate of A; Thus, the y-coordinate of B is 2 less than -3, that is, -5.
The coordinates of B are (-1, -5).
usando las propiedades de la igualdad resuelve: 13r=117 y explica el procedimiento
Answer:
r=9
Step-by-step explanation:
13r=117
r=117/13
r=9
please help and explain
is the square root of 16/9 rational or irrational
is 0.30300 rational or irrational?
Answer:
√169
Step-by-step explanation:
its is a rational, thats all I can help with
what is the result of -4+5/3?
Answer:
-2⅓
Step-by-step explanation:
-4 + 5/3 Start out with this sum.
-4 + 1 ⅔ Make 5/3 into a mixed number.
-2 ⅓ Then add them together. The best way to do this is to first add -4 and 1 which makes -3. Then add ⅔ to -3 which is -2 ⅓
a dealer sells a camera to a man and makes 15% profit. The man sells the camera to another man for 414$ with 10% loss. Find the original cost of the camera.
Answer:
$386.75
Step-by-step explanation:
First we must find the price of the camera after the man sold it, with the 10% loss.
To do this we find 10% of 414, which is 41.4 . Meaning the camera was originally bought from the dealer for $455.40, as we have to add the 10% back onto the price.
Now we find 15% of 455 and subtract it, with 15% being 68.25, the original cost was $386.75. My guy was seriously ripped off :(.
Orignal price: $386.75Which of the following statements must be true about the diagram
Answer:
D ) x+y=w
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Which of the following best describes the equation below?
y = -3x - 13
A.
both linear and nonlinear
B.
nonlinear
C.
neither linear nor nonlinear
D.
linear
Answer:
d. linear
Step-by-step explanation:
using the format y=mx+b
You spent m minutes studying on Monday On Tuesday you studied 15 more minutes than you did on Monday. Wednesday, you studied 30 more minutes than you did Tuesday you studied twice as long on Thursday as you did on Monday on Friday you studied 20 minutes less than you did on thursday
Answer: 7m - 40
Step-by-step explanation:
Monday = m
Tuesday = m + 15
Wednesday = m + 15 + 30 = m + 45
Thursday = 2 × m = 2m
Friday = 2m - 20
The expression will now be:
= m + m + 15 + m + 45 + 2m + 2m - 20
= 7m- 40
m> 32
Which of the following could be a possible value for m?
32
33
100
n 31
Solve for x: please help
Answer:
45 because an acute angle is 45 degrees
Answer:
22.5
Step-by-step explanation:
22.5 + 22.5 x 3 =
22.5 + 67.5 =
90
Hope that helps!
There are sixteen girls and twelve boys in block 7 math. At that rate, how many
girls would you expect in a group with two hundred ten boys?
Answer:280
Step-by-step explanation:
If the main group is a ratio of girls to boys 16:12 and the 12 is increased to 210 then do 210/12=17.5 and multiply the 17.5 by 16 to get 280
Divide 9 by t. Then, add 3.
Which of the following expressions matches the statement above?
OA. t + 9 + 3
OB. 9 + 3+ t
C. 9 + (t + 3)
OD. 9+t+3
A translation is shown on the grid below
Answer:
translation of ABC to A'B'C' is 5,3
Help please
|2x + 5| = 11
Step-by-step explanation:
[tex]2x + 5 = 11 \\ 2x = 11 - 5 \\ 2x = 6 \\ x = 6 \div 2 \\ x = 3[/tex]
Which of the following expressions are equivalent to 4 + 36x
Please answer and dont take my points bc i am in a hurry
A
4(1) + 4(36x)
B
4(1 + 36x)
C
2(1) + 4(9x) + 4
D
4(1 + 9x)
Answer:
The answer would be D.
Answer:
The answer is D 4(1 + 9x) or C depending on what school website you use.
Step-by-step explanation:
Help me pleaseeee I don’t know what to do!!
Answer:
the answer is the M
Step-by-step explanation:
angle A and M both have 2 arcs which means they are congruent(equal)
0510006 please answer this
what is 8*29
Answer:
8*29=232
Step-by-step explanation:
if you take 8*20 you get 160
if you take 8*9 you get 72
Add them and you get 232
help me plz! The one with the correct answer gets brainliest!
What is the number for the variable "x"? : ( x+29= −11)
Answer:
x=(-40)
Step-by-step explanation:
x+29= (-11)
x+29=(-11)
-29=-29
x=(-40)
Answer:
x=-11+29
x=18
Step-by-step explanation:
find JQ if Q is the incenter of JLN
Answer:
Find each measure. 9. NP. ANSWER: 14. 10. PS.
Step-by-step explanation:
The length of JQ is 18.79 unit.
What is Pythagoras theorem?According to the Pythagoras theorem, a triangle's hypotenuse square equals the sum of its other two sides' squares.
Given:
Q is the incenter of JLN
QP= QK= QM= 9 units
Now, In Δ JPQ
JP= 16.5, QP =9 , QP⊥ JP
So, JQ = √JP² + QP²
JQ= √16.5²+ 9 ²
JQ= 18.79 units
Hence, the length of JQ is 18.79 unit.
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how many degrees is a 12-gon
Answer:
150 degrees
Step-by-step explanation:
The degrees of a n-sided polygon is given by the expression:
180 ( n − 2 )
where n is the number of sides. As we know that it ahs 12 sides, so
=180 ( 12 − 2 )
=180 ( 10 )
=1800 i.e. Therefore, there are 1800 degrees in a 12
-gon.
To find the measure of the angles, we know that the sum of all the angles is 1800 degrees, and there are 12 angles. So,
1800/12 = 150
So, the measure of the interior angle of a 12-gon is 150 degrees.
5. What are the values of x and y?
O x=2sqrt3 y=4
O x=8sqrt7 y=4sqrt21
O x=8sqrt3 y=8sqrt3
O x=4sqrt21 y=8sqrt7
Answer:
x= 90 degree
y= 43 degree
Step-by-step explanation:
We have been given an isosceles triangle being two sides equal AB and AC
By the property of isosceles triangle
The sides which are equal will have same base angle
Hence, ∠ABC=∠ACB=
We know that sum of angles of triangle is
∠ABC+ ∠ACB+∠BAC= (1)
Since, ∠BAC is the bisector so, ∠BAD and ∠DAC are equal which is
Now, substituting the values in (1) we get:
Now, we will consider ΔABD to find x
,∠ADB=∠ABD=
Now, Apply the sum of angles of triangle is we get:
Answer:
x = 8[tex]\sqrt{7}[/tex]
y = 4[tex]\sqrt{21}[/tex]
Step-by-step explanation:
use the altitude rule to find the height of the triangle first
12/h = h/16
h² = 12x16
h = [tex]\sqrt{192}[/tex]
h = [tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{3}[/tex] = 8[tex]\sqrt{3}[/tex]
now you can use the Pythagorean Theorem with height of 8[tex]\sqrt{3}[/tex] along with the other leg of 12 to find 'y'; which comes out to be [tex]\sqrt{336}[/tex] or [tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{21}[/tex]
then use the Pythagorean Theorem with height of 8[tex]\sqrt{3}[/tex] along with the other leg of 16 to find 'x'; which comes out to be [tex]\sqrt{448}[/tex] or [tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{4}[/tex][tex]\sqrt{7}[/tex]
-3r+5r
What is the answerrr i need helpp :((((
Answer:
2r
Step-by-step explanation:
2r is the answer because:
We have to switch the -3r in to +3r and positive + positive = positive.
Then we change the add sign in to subtracting sign and we subtract:
3r-5r and it will give us:
2r
And we keep the answer positive because our answer was a +5r so the bigger number keeps the sign the same.
Katherine has a fish tank shaped like a triangular prism in her living room. The triangle that forms the base of the tank has a base of 24 inches and a height of 20 inches. The entire tank is 36 inches tall. What volume of water is needed to fill the tank if the tank is only filled to 6 inches below the top?
Answer:
[tex]Volume = 7200in^3[/tex]
Step-by-step explanation:
Given
[tex]B = 24[/tex] --- base of the tank base
[tex]h = 20[/tex] --- height of the tank base
[tex]H = 36[/tex] --- height of the tank
Required:
Determine the volume of water needed for 6 inches below the top
First, calculate the area of the tank base.
[tex]Area = \frac{1}{2}Bh[/tex]
[tex]Area = \frac{1}{2}*24*20[/tex]
[tex]Area = 12*20[/tex]
[tex]Area = 240[/tex]
If the tank is filled 6 inches below the top, this means that the height of the water is H - 6.
So, the volume is:
[tex]Volume = Area * (H - 6)[/tex]
Substitute 240 for Area and 36 for H
[tex]Volume = 240 * (36 - 6)[/tex]
[tex]Volume = 240 * 30[/tex]
[tex]Volume = 7200in^3[/tex]
Fay has a lemonade stand.
She spends £42 on ingredients.
She sells each glass of lemonade for £1.20.
If she sells 50 glasses of lemonade, what is her total profit?
Answer:
she made a profit of 18$
50*1.2=60-42=18
Step-by-step explanation:
Please help with this!?!?!?
Answer:
2$
Step-by-step explanation:
you can see that for every mile, the cost goes up 1.5 dollars, and if you tale the lowest amount, 2 miles, multiply by 1.5 = 3, and then subtract that from 5, you get 2
Can someone please help me on this question? Question: What percent of a dollar is a quarter, a nickel, a dime, and two pennies?
Answer:
Its 42 percent
Step-by-step explanation:
0.25+0.5+0.10+0.2=0.42 or 42%
All the change added together is 42/100 because a dollar is just 100 cents.
help help help plz plz plz
Answer:
x = 7
All 8 angles measure 135°
Step-by-step explanation:
(n-2)·180 = (8-2)·180 = 1,080°; this is the total of all interior angles
each angle is equal so we can divide 1080 by 8 and find that each angle measures 135°
to solve for 'x':
16x + 23 = 135
16x = 112
x = 112/16
x = 7
check: 16(7) + 23 = 135
112 + 23 = 135
135 = 135
If = 58° and m = 120 in, what is the value of p to the nearest tenth of an inch?
Answer:
141.5 in
Step-by-step explanation:
sin 58 = m/p = 120/p
120 = psin58
120/sin 58 = p
p = 141.5 in.
Another way to look at this problem is to remember that the hypotenuse of a right triangle is the longest side. Since 141.5 is the only answer greater than 120, it would have to be the logical choice for the length of p