Prove that the following statements are false provide counter examples to disprove them: (1) If two angles have common vertex and their bisectors create one line, then these angles are vertical. (2) If the angle bisectors of two equal angles belong to the same line, then these angles are vertical.
Answers
Answer:
Examples to disprove them are as follows;
1) Angles of two different inscribed regular polygon in contact at their vertices
2) Angles on the opposite corners of a regular even sided polygon
Step-by-step explanation:
The statement to be disproved can be presented as follows;
1) ∠A and ∠B share a common vertex
2) The bisectors of ∠A and ∠B create one line then
∠A and ∠B are vertical, that is ∠A and ∠B are on the opposite sides of the point where two lines cross or ∠A = ∠B
Given that ∠A = Interior angle of a inscribed square = 90°
∠B = Interior angle of an inscribed equilateral triangle = 60°
Therefore the two circles can be arranged such that the line connecting the centers of both circles, are the bisectors of ∠A and ∠B
However, ∠A ≠ ∠B hence the two angles are not vertical QED
(2) The angles ∠A and ∠B where ∠A = ∠B are on the opposite corners of an even sided regular polygon are equal and their bisectors belong to the same line, however, it can be shown that ∠A and ∠B are not vertical.
Related Questions
Please help me. Mark me the branliest.
Topic: Percentage
Q1) 80% of a dog's mass is equal to 24% of the mass of a lion. If the mass of the lion is 105 kg more than the mass of the dog, find the total mass of the dog and the lion.
Answers
We are given that 80% of the dog's mass is equal to 24% of the lion's mass. Mathematically, this can be expressed as:
0.80D = 0.24L
We are also given that the mass of the lion is 105 kg more than the mass of the dog:
L = D + 105
We can use these two equations to find the values of D and L.
Substituting the value of L from the second equation into the first equation:
0.80D = 0.24(D + 105)
Now, let's solve for D:
0.80D = 0.24D + 0.24(105)
0.80D - 0.24D = 25.2
0.56D = 25.2
D = 25.2 / 0.56
D ≈ 45
Now that we have the value of D, we can find the value of L by substituting it back into the second equation:
L = 45 + 105
L = 150
Therefore, the total mass of the dog and the lion is:
D + L = 45 + 150 = 195 kg
So, the total mass of the dog and the lion is 195 kg.
please write a function for the points (1/3,0) (-2 3/4,0) and (0,-5) and explain the steps.
thank you!
Answers
The function for the points are y = -15x - 5
How to determine the functionFrom the information given, we have that;
The points are;
(1/3,0) (-2 3/4,0) and (0,-5)
Using the point-slope form of a linear equation, we have;
y - y₁ = m(x - x₁)
Such that;
m is the slope of the liney - y₁ and (x - x₁) are the pointsUsing (1/3, 0) and (0, -5), we have that the slope is;
m = (0 - (-5))/0 -1/3)
expand the bracket
= 5 / (-1/3)
= -15
Now, take any of the given points and substitute the values
Using (1/3, 0), we get;
y - 0 = -15(x - 1/3).
y = -15x - 5.
Learn more about functions at: https://brainly.com/question/25638609
#SPJ1
The function for the points solved by (1/3,0) (-2 3/4,0) and (0,-5) solved by point slope form is \(a=-15b-5\)
We have given the points:
(1/3,0) (-2 3/4,0) and (0,-5)
Using the formula of linear equation
\(a-\)\(a_{1}\)\(=x[b-b_{1}]\)
Where we will consider (1/3,0) = \(a-a_{1}\) and (0,-5) = \(b-b_{1}\)
that is 1/3 = \(a\), 0 = \(a_{1}\) and
0 = \(b\), -5 = \(b_{1}\)
\(x\) refers to the slope of line (take any variable)
Now for finding the value of \(x\),
\(x=a-a_{1}/b-b_{1}\)
inserting the values,
\(x=[0-[-5]]/[0-1/3]\\x= -15\)
Substitute the value of \(x\) in the equation
\(a-0=-15[b-1/3]\)
By simplifying the equation, we get
\(a=-15b-5\)
To know more about functions and points:
https://brainly.com/question/30721594
You pick a card at random. 6 7 8 9 What is P(divisor of 70)? Write your answer as a percentage. %
Answers
Answer:
Step-by-step explanation:
Evaluate this problem and show the work
Answers
Answer: 103
Step-by-step explanation:
\(3+5^{2} *4\\=3+(25*4)\\=3+100\\=103\)
Alex painted 178 ft2 of his 1/3 apartment's walls with gallon of paint. He has 2 gallons of paint in all. If he wants to cover 1,000 f2 of his apartment, does he have enough paint? Complete a true statement.
2 gallons of paint will cover
A. 968
B. 996
C. 1,068
f2 and Alex needs to cover 1,000 f2 so he
D. will
E. will not
have enough paint.
Answers
Answer:
Step-by-step explanation:1 gallon of paint paints 1/3 of the house and he had already painted 1/3 of the house with 1 gallon of paint. so the left is 2/3 of the house. and 2 gallon of paint paints 2/3 of the house so,2/3=2/3 which means D. he will cover 1,000 f2 of his apartment.
The equation c = 5m represents how many ice cream cones (c) are sold within a certain number of minutes (m) at a certain ice cream shop.
Determine the constant of proportionality.
5
1
one fifth
25
Answers
Answer:
The COP of problem is 5 because the 5m means 5 per minute, which means that the cop is 5.
Answer: 5
Step-by-step explanation:
The constant of proportionality is 5 because here is the formula for this sort of question.
y=kx The k is the constant of proportionality and we can substitute the k for 5.
Ok, maybe that wasn't very helpful but the simplest way to know is this.
The 5 is the constant of proportionality because the constant of proportionality is the same thing as the slope (hopefully you know what slope is). The slope is the rate of change.
C is the y because the number of cones DEPENDS on the number of minutes (the number of minutes is X). The number of cones change by each minute.
Example:
c=5(3)
c=15 (15 cones)
or
10=5x
10/5=5x/5
2=x
Just use substitution.
Okay sorry if this was confusing, I just am not good at explaining this even though I know what it is.
Simple answer: It's 5
ANSWER FAST YO
An English test has 20 questions. A student answers 75% correctly.
How many questions does the student answer correctly?
Enter your answer in the box.
_____ questions
Answers
Answer:
The student answers 15 answers correctly.
Answer:
15
Step-by-step explanation:
hope it helps
can someone help me with this please?
Answers
Answer:
Big triangle= 4*1.5=6
Small Triangle= 7.5/1.5=5
Ratio=7.5/5 or 1.5
Step-by-step explanation:
\(\frac{7}{10.5}\)=\(\frac{x}{7.5}\)
cross multiply
10.5x=52.5
divide both sides by 10.5
x=5
7.5/5= ratio
PLease solve it as fast has you can
Answers
Answer:
\(f^{-1}\left(f(576)\right)=\boxed{576}\)
\(f^{-1}(-7)+f(-7)=\boxed{13}\)
Step-by-step explanation:
The inverse of an invertible function with the domain of all real numbers is obtained by reflecting the original function across the line y = x, which swaps the input and output values of the function. Therefore, (x, y) → (y, x).
Given table:
\(\begin{array}{lrrrrrr}\vphantom{\dfrac12}x&-7&11&-13&6&5&-9\\\cline{1-7}\vphantom{\dfrac12}f(x)&7&12&8&-7&13&5\end{array}\)
Inverse function:
\(\begin{array}{lrrrrrr}\vphantom{\dfrac12}x&7&12&8&-7&13&5\\\cline{1-7}\vphantom{\dfrac12}f^{-1}(x)&-7&11&-13&6&5&-9\end{array}\)
If we have a function f(x), the inverse function is denoted as f⁻¹(x), and it has the property that f⁻¹(f(x)) = x for all valid inputs x in the domain of f(x).
Therefore:
\(\large\boxed{f^{-1}\left(f(576)\right)=576}\)
The value of f(-7) is the value of f(x) when x = -7. Therefore, reading from the original table, f(-7) = 7.
The value of f⁻¹(-7) is the value of f⁻¹(x) when x = -7. Therefore, reading from the inverse function table, f⁻¹(-7) = 6.
Therefore:
\(\large\boxed{\begin{aligned}f^{-1}(-7)+f(-7)&=6+7\\&=13\end{aligned}}\)
Cans someone help me with 6 and 7 please I am very confused on this two so I’ll appreciate it if u help me!
Answers
Answer:
6. $127.50
7. 275c
Step-by-step explanation:
Q6)
Kerry's workday is 10 hrs. and works 40 hrs. per week, Kerry works for 4 days
Watson's workday is 8 hrs. and works 40 hrs. per week, Watson works for 5 days
Kerry: works 4 days and gets paid $ 12.75 per cat & grooms 15 cats per day, so Kerry makes = 4(12.75 × 15) = 4(191.25) = $ 765
Watson: works 5 days and gets paid $ 12.75 per cat & grooms 10 cats per day, so Watson makes = 5(12.75 × 10) = 5(127.50) = $ 637.50
∴ The difference between their weekly earning is 765 - 637.50 = $ 127.50
Q7)
Given:
There are 'c' number of conferences rooms in the Texas Hotel
Number of foldable chairs in each room = 275
Solution:
So, the total number of chairs in all conference rooms would be c X 275
= 275c
find area of a right triangle with a width of 4cm and a length of 10cm
Answers
Answer:
I'm almost sure 10 times 4
ILL GIVE 50 + 25 POINTS AND BRAINLIEST TO CORRECT ANSWER!!
x is indirectly proportional to y, if x = 32 and y = -10, write the proportional constant and equation. Then if y = -51, find x.
TYVM!!
Answers
Answer: 10
Step-by-step explanation:
add subtract and add again
Frank's Auto Corner recorded its sales for the second quarter (April, May, and June) of 1999. April sales were 89 cars, May sales were 98 cars, and June sales were 115 cars. During the same quarter in the previous year, 1998, the total sales were 287 cars. How many cars were sold at Frank's Auto Corner during the second quarter of 1999? How many more cars were sold during the second quarter of 1999 than in the second quarter of 1998? Explain how you got your answer. (2-step question)
Answers
Answer:
Part 1: How many cars were sold at Frank's Auto Corner during the second quarter of 1999? 302 cars
Part 2: How many more cars were sold during the second quarter of 1999 than in the second quarter of 1998? 15 cars
Step-by-step explanation:
Part 1: How many cars were sold at Frank's Auto Corner during the second quarter of 1999?
How to: Add the number of cars sold during April, May, and June of 1999. This would be: 89 + 98 + 115 = 302 cars
Part 2: How many more cars were sold during the second quarter of 1999 than in the second quarter of 1998?
How to: Subtract the number of cars sold in the second quarter of 1998 from the number sold in second quarter 1999. We are given that 287 cars were sold in the second quarter of 1998 so: 287 - 302 = 15 cars
Please help me answer please actually answer
Answers
Answer:
your answer will be 29*
am not sure
Step-by-step explanation:
you would have to add the 97 and 54 and then subtract that number from 180 because 180 is the total degree of every triangle and then after the subtraction you get 29. also love shoto in the back :D
1,725 couch, 15% markup
Answers
Answer: 1,983.75
First option
Step-by-step explanation:
In order to find markup you convert the percentage to a decimal: 0.15.
You multiply 1725 by 0.15 and you get 258.75. This is the markup. In order to get the total cost, you add the original price with the markup price.
1725 ( original price ) x 258.75 ( markup price ) = 1,983.75 ( total cost with the markup )
how does factoring relate to determining whether expressions are equivalent?
Answers
Answer:
Two expressions are equivalent if they can be simplified to the same third expression or if one of the expressions can be written like the other. In addition, you can also determine if two expressions are equivalent when values are substituted in for the variable and both arrive at the same answer.
The equation below shows the total volume (V), in cubic units, of 7 identical boxes with each side equal to s units:
V = 7s3
If s = 2.3 units, what is the value of V? (1 point)
Answers
Answer:
48.3
Step-by-step explanation:
multiply 7by 2.3 then multiply the whole thing by3 and that’s your answer
Answer: 48.3
Step-by-step explanation:
Can someone pls help?
Answers
Answer:
4. Drawing 2 is a scale of Drawing 1
A) is 2.5
B) is 7.8
Step-by-step explanation:
13/5.2=2.5
5.2 x 2.5=13
And since we have the scale factor 2.5
and since it decreases in size we divide
19.5/2.5= 7.8
:D correct
Please solve this equation
-3(5-2z)=z+10
Answers
-15 -10 = -6z + z
-25 = -5z
5 = z
z = 5
____
(Let's now put z=5)
-3(5-10) = 5+10
-15+30 = 15
15 = 15
___
Therefore, we now have double-checked that z=5
The following system of linear equations is shown in the graph.
y equals one fourth times x minus 1
x − 4y = 4
a coordinate plane with two lines that pass through the points 0 comma negative 1 and 4 comma 0
How many solutions does the system of linear equations have?
No solution
Infinitely many solutions
One solution at (4, 0)
One solution at (0, −1)
Answers
The system of linear equations is given as:
y = 1/4x - 1
x - 4y = 4
To find the solution, we can substitute y in the second equation with 1/4x - 1:
x - 4(1/4x - 1) = 4
x - x + 4 = 4
4 = 4
The equation 4 = 4 is always true, which means that the system of linear equations has infinitely many solutions.
Therefore, the answer is:
Infinitely many solutions.
If m∠2 = 80°, what is m∠4?
Answers
Answer:
80
Step-by-step explanation:
Answer:
80 because its a vertical angle
Step-by-step explanation:
Use the original price and the markup to find the retail price.
Original price: $36; Markup: 12.5%
Answers
Answer:
40.5
Step-by-step explanation:
mark up =36×(12.5/100)=4.5
retail price = 36 + 4.5 = 40.5
What is the slope of the line on the graph?
Enter your answer in the box.
Answers
Answer:
The slope is 6/1 or just 6
Step-by-step explanation:
What is the difference of 16 and a number, divided by 2 ?
Answers
Answer:
it is 16 - 1/2n
Step-by-step explanation:
if we considered the number as n
Step by step explanation:
Difference meaning subtracting and we have to subtract 16 by a number (in this case we don’t know what the number is) therefore we can use X. Then we know that whatever answer you get from 16-x, it’s being divided by 2
Simplify the expression.
3.1 -5.7n - 4n+6=
Answers
Answer:
-89
Step-by-step explanation:
m
semsee45 this is your question.
In the equation x = ky^2 + m/y + 4, when x = 18 and y = 2, and when x = -3 and y = 1, find x when y = 4.
TY :) !
Answers
Solution is in da attachment mate!! :D
in the solution to this system, what is the value of y?
x + y + x = 0
2x + y - z = 7
x - y + z = -4
y = _______
The solution is: _______
Answers
Answer:
0
Step-by-step explanation:
x+0+x = 0 so y must equal 0
I need help Right Now!!!!!!!!!!
Answers
Subtract 10 and 6 1/2 to get 3 1/2
When astronauts Neil Armstrong and Buzz Aldrin first walked on
the moon in 1969, they were able to bounce from step to step!
This is because the gravitational force of the moon is about
16.5% of that of the Earth. If you visited the moon,
weighing 100 pounds on Earth, what would your weight be?
Answers
Answer:
16.5 pounds
Step-by-step explanation:
16.5% as a decimal is 0.165
0.165 x 100 = 16.5
So in conclusion you will weigh about 16.5 pounds on the moon.
i need help with no. 18. can someone help me? like with how its solved, not just answer
Answers
Answer:
the answer is 7.22
Step-by-step explanation: