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 1

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

I need help idk if it’s right

Answers

Answer:

A, f(x)=x-4

Step-by-step explanation:

f(x) is basically just another way to write y.

So we have the slope is 1, and the y intercept is -4, thus the equation is f(x)=x-4

Find the surface area and volume of a cube with sides that are 6 inches.

Answers

Answer:

Step-by-step explanation:

Surface Area S=6s²

S=6(36)

S=216 in²

Volume V=s³

V=6³

V=216 in³

Plz I need help with this

Simplify 12c+14b+3c-22

Answers

Answer:

15c +14b -22

Step-by-step explanation:

12c+14b+3c-22

Combine like terms

12c+3c+14b-22

15c +14b -22

Mrs. Jackson gives the table below to her students.
In order for the function to be linear, what must a be and
why?
Х
4
5
6
y
26
23
a = 22 because the rate of change is 1.
a = 20 because the rate of change is 3.
a = 22 because the rate of change is -1.
a = 20 because the rate of change is -3.
a

Answers

Answer:

  a = 20 because the rate of change is -3

Step-by-step explanation:

In order for the function to be linear, sequential values of x must match values of y that have the same first differences. Here, 23-26 = -3, so we must have a-23 = -3. That is to say, the value of "a" must be 20.

The "rate of change" is the ratio of the differences in y to the differences in x. Here, that is -3/1 = -3. The appropriate choice is ...

  a = 20 because the rate of change is -3

The total population of students was 380. Based on the data, what is the best approximation for the total number of students who have a cell phone plan with company Y?

Answers

Answer:

114

Step-by-step explanation:

Which system of equations best represents the situation below?
A farmer grew his own tomatoes (a), eggplants (b), and potatoes (c). He decided to package his vegetables and price them as follows:
2 tomatoes, 1 eggplant, 3 potatoes for $10
3 tomatoes, 2 eggplants, 4 potatoes for $14
4 tomatoes, 2 eggplants, 6 potatoes for $20

Answers

Answer:

A.

2a +b+3c =10

3a+2b+4c=14

4a+2b+6c=20  

Step-by-step explanation:

Hi, to answer this question we have to write a system of equation with the information given:

The price of each package will be equal to sum of the products of each vegetable (a,b or  c) and their respective amount :

So:

2 tomatoes, 1 eggplant, 3 potatoes for $10

2a +1b+3c =10

3 tomatoes, 2 eggplants, 4 potatoes for $14

3a+2b+4c=14

4 tomatoes, 2 eggplants, 6 potatoes for $20

4a+2b+6c=20

The system is:

2a +b+3c =10

3a+2b+4c=14

4a+2b+6c=20  

(option A)

Feel free to ask for more if needed or if you did not understand something.

Yolanda participated in a walkathon in which each kilometer walked raised $10 for charity. Her goal was to raise more than $300 on Saturday and Sunday. She raised $50 on Saturday. Which graph shows all the distances, in kilometers, that Yolanda could have walked on Sunday to reach her goal?

Answers

Answer:

B

Step-by-step explanation:

She needed to raise at least $250

$250 divided by $10 equals 25 km

So she need more than 25km to raise over $300

Monique made several batches of soup for a potluck supper. Each batch required 3/4 of a pound of potatoes, and she used a total of 6 1/2 pounds of potatoes. How many batches of soup did Monique make?

Which division and multiplication problems could represent this scenario? Check all the apply.

A)3/4 divided by 13/2

B)13/2 divided by 3/4

C)3/4(13/2)

D)13/2(3/4)

E)13/2(4/3)

Answers

Answer:

B and E

Step-by-step explanation:

Answer:

B) 13/2 divided by 3/4 and E) 13/2(4/3)

Chantelle takes out a loan of $3,500 with an APR of 4.25%. She will repay the loan in monthly payments for 6 months. To find the total amount of interest she will pay, Chantelle uses an online calculator. What are the correct numbers she should enter?

Answers

Answer:

P = 3,500   r = 0.0425    n = 12    t = 0.5

Step-by-step explanation:

P is the principal amount, which in this case is $3,500, or the start amount.

r is the interest rate, which is 4.25%. Change 4.5% to decimal form and it will be 0.0425.

n is the number of times the loan is repaid, or 12.

t is the time. In this case, the loan will be for 6 months, or half a year. Remember that variable t is always in term of years. In decimal form, half a year is 0.5.

A line passes through the points (–2, –8) and (–4, –8). Which shows the graph of this line? On a coordinate plane, a vertical line is at x = negative 2. On a coordinate plane, a horizontal line is at y = negative 2. On a coordinate plane, a vertical line is at x = negative 8. On a coordinate plane, a horizontal line is at y = negative 8.

Answers

Answer:

Its D

Step-by-step explanation:

just put the answear stop putting this bs

Answer:

The Correct answer you are looking for is (D) - On a coordinate plane, a horizontal line is at y = negative 8.

Step-by-step explanation:

Hope this helped all of you!

Answer is letter (D) the bottom graph.

A thousand dollars is left in a credit union drawing 7% compounded monthly.
What is the balance at the end of 10 years?




Please show the work to answer compound interest work

Answers

Answer: $2009.66

Step-by-step explanation:

A = P(1 + r/n)^nt

The balance at the end of 10 years in account after the credit union drawing 7% compounded monthly is $2009.66

What is compound interest?

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\[/tex]

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.

A thousand dollars is left in a credit union drawing 7% compounded monthly. The balance at the end of 10 years has to be find out.

Here the data given are,

Principal amount $1000.The rate of interest is 7%.Time period is 10 years.The number of month in a year is 12.

Put these values in the above formula as,

[tex]A=1000\times\left(1+\dfrac{7}{12\times100}\right)^{12\times10}\\A=2009.66[/tex]

Thus, the balance at the end of 10 years in account after the credit union drawing 7% compounded monthly is $2009.66

Learn more about the compound interest here;

https://brainly.com/question/24274034

A. -3/2
B.2/3
C.-2/3
D.3/2
I need help pls

Answers

Answer:

The slope of the line is D. 3/2.

Step-by-step explanation:

D. 3/2 (go up 3 and to the right 2)

Order 0.12, 0.1, 0.02, and 0.21 in order from least to greatest.

Answers

This is the answer

0.02

0.1

0.12

0.21

Answer:

Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thnk me...

a line passes through the point (2, -9) and has a slope of -6, what is the equation for this line?

Answers

Answer:

Step-by-step explanation:

y + 9 = -6(x - 2)

y + 9 = -6x + 12

y = -6x + 3

I need help please!!!!!!!

Answers

Answer:

m = 1 and c = 3

Step-by-step explanation:

y = mx + c

so comparing with y = x + 3

m = 1 ( since there isn't any co-efficient of x)  and c = 3

Is (–5, 0) a solution to the equation y = 7x − 5?

Answers

Answer:

no

Step-by-step explanation:

to see, plug in -5 for x and find your y outcome.

y = 7(-5) -5

y = -35 - 5

y = -40

since y does not equal 0, (-5,0) is not a solution for the equation.

Answer:

no

Step-by-step explanation:

y = 7x − 5?

Substitute the point into the equation

0 = 7(-5) -5

0 = -35-5

0 = -40

This is not true so (-5,0) is not a solution

IO
80
14x + 2
The figure is a parallelogram.
Solve for x.
'S
2
7

Answers

Answer:

x = 7

Step-by-step explanation:

The consecutive angles in a parallelogram are supplementary, thus

80 + 14x + 2 = 180

14x + 82 = 180 ( subtract 82 from both sides )

14x = 98 ( divide both sides by 14 )

x = 7

In the given parallelogram QRST, x = 7°.

What are adjacent angles?

In a quadrilateral, adjacent angles are the pair of angles, that come is formed by the intersection of any common line.

How do we solve the given question?

In the question, we are shown a parallelogram QRST and are asked to find the value of x.

We know that ∠TQR and ∠QRS are adjacent, as they include a common side, QR.

∠TQR = 80°, ∠QRS = (14x + 2)°

Now, we know that adjacent angles of a parallelogram are supplementary, that is their sum = 180°

∴ ∠TQR + ∠QRS = 180°

or, 80° + (14x + 2)° = 180°

or, 14x = 180° - 80° -2° = 98°

or, x = 98°/14 = 7°

∴ In the given parallelogram QRST, x = 7°.

Learn more about Parallelograms at

https://brainly.com/question/24056495

#SPJ2

Anyone know the answer to this?

Answers

3x-5+19-x+2x
5x-x=14
4x=14

Answer:

3x-5+19-x+2x

5x-x=14

4x=14

Hope that helps

Which of the following phrases translates to 8 - m?
the difference between a number and eight
eight decreased by a number
eight subtracted from a number
a number minus eight

Answers

Answer: B) eight decreased by a number

Step-by-step explanation:

decreased = subtraction, therefore, eight decreased by a number is 8 - m.


A bacteria colony is quickly growing in a petri dish. The number of bacteria, y , is modeled by the function y=2(10)^2 where x is the number of days since the colony started. Baelsed on the equation how many more bacteria are there on day 4 than on day 2?

A. 19800

B. 9900

C. 159600

D. 40​

Answers

Answer:

C = 159600

Step-by-step explanation:

Because its Y=2 (10) square so times by its self.

Solve for x pls hurry !

Answers

Answer:

x = 7

Step-by-step explanation:

7x + 68 = 2x + 103

5x = 35

x = 7

welp lol <3 find the value of x that makes j||k

Answers

Answer: C. 42

Step-by-step explanation:

(3x + 3) is the same angle as 129.

So, you have to equal them to each other.

3x + 3 = 129

Now you solve.

Subtract 3 from each sides.

3x = 126

Divide 3 from each side.

x=42

Answer:

x = 42°

Step-by-step explanation:

J//k if the the two corresponding angles are equal

which means 3x + 3 = 129

solving 3x + 3 = 129

3x = 129 - 3

3x = 126

then

x = 126/3

 = 42°

Jesse is in a lab examining sizes of skin cells. Cell A has a diameter of 5.8 × 10 ^-9 mm. Cell B has a diameter of 4.2 × 10 ^-7 mm.

How much longer is the diamter of Cell B than Cell A?

A. 1.6 x 10 ^-2

B. 1.6 x 10 ^-16

C. 4.14 x 10 ^-7

D. 4.14 x 10 ^-9

Answers

Answer:

The diameter of Cell B is [tex]4.14 \times 10^{-7} mm[/tex] longer than Cell A

Step-by-step explanation:

Diameter of Cell A = [tex]5.8 \times 10^{-9} mm[/tex]

Diameter of Cell B = [tex]4.2 \times 10^{-7} mm[/tex]

Now we are supposed to find How much longer is the diameter of Cell B than Cell A?

So,Diameter of Cell A =[tex]5.8 \times 10^{-9} = 5.8 \times 10^{-7} \times 10^{-2}=5.8 \times 10^{-7} \times \frac{1}{10^2} = 0.058 \times 10^{-7}[/tex]

Diameter of Cell B = [tex]4.2 \times 10^{-7} mm[/tex]

So, Difference in diameters = [tex]4.2 \times 10^{-7} - (0.058 \times 10^{-7})=4.14 \times 10^{-7}[/tex]

So, Option C is true

Hence the diameter of Cell B is [tex]4.14 \times 10^{-7} mm[/tex] longer than Cell A

If the acute angle made by two intersecting lines l and m is 51° and image ABCD is reflected across the line l followed by a reflection across line m, then find the angle through which ABCD is rotated. Question 10 options: A) 25.5° B) 102° C) 26° D) 51°

Answers

Answer:

B) 102°

Step-by-step explanation:

Reflection is an example of transformation in which a given image is flipped over a reference line which changes the orientation of the figure, but not its length and shape. A rotational transformation is formed by two reflections.

In the given question, image ABCD is reflected over lines I, then m at an angle of 51° to each other. Since rotation is twice the acute angle with respect to the center of rotation, therefore ABCD rotates through an angle of 102°.

what is the difference for -22 - (-26)​

Answers

______________________________

Hey!!!

-22-(-26)

= -22+26

= 4

So the answer is 4.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

____________________________

-22 - (-26)​ = -22+26=4

So the answer is 4

If this helped mark me as brainliest plss

Hope this helps! Good luck!!

please help!

Given:
AB = BC

ADB =
a. 30
b. 37.5
c. 60

Answers

The Correct answer is B

The measure of the angle is ∠ADB=60

What is the angle sum property of a triangle?

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here: ∠A =∠B=60

By triangle sum property we must have ∠A +∠B+∠D=180

                                                                                 ∠D=60

Thus the triangle must be an equilateral triangle with all its angles equal to 60

Hence, The measure of the angle is ∠ADB=60

Learn more about triangles here:

https://brainly.com/question/29133099

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(-4ab - 5a + 3) - (-7ab + 9)

Answers

________________________________

Hey!!!

solution,

(-4ab - 5a +3)-(-7ab+9)

=-4ab -5a+3 + 7ab - 9

= -4ab+7ab-5a+3-9

= 3ab-5a-6

Hope it helps...

Good luck on your assignment

______________________________

Line d is parallel to line c in the figure below. Parallel lines d and c are intersected by lines q and p to form 2 triangles. At lines d and p, the angle is 2, at d and q, the angle is 1, and at q and p the angle is 3. At lines c and q, the angle is 4, at p and c, the angle is 5, and the third angle is 6. Which statements about the figure are true? Select three options. Vertical angles prove that Angle 2 is congruent to angle 5. In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles. Vertical angles prove that Angle 3 is congruent to angle 6. The triangles are similar because alternate interior angles are congruent. In the two similar triangles, Angle 2 and Angle 4 are corresponding angles. The triangles are similar because corresponding sides are congruent.

Answers

Answer:

Its the 2nd, 3rd, and 4th answer.

Step-by-step explanation:

i figured it out cause i did somehow

Answer:

it is 2 3 and 4 on edge 2021

Step-by-step explanation:

have a good day because i said so but mostly because you want to....ok bye love you

What is the equation of the graphed line?

a. y = 4x - 6
b. y = -4x + 6
c. y = 2/3x - 4
d. y = 3/2x - 4

Answers

Answer:

its c

Step-by-step explanation:

-4 is the y- intercept form and 2/3 is the slope

Answer:

C.

Step-by-step explanation:

Y intercept is -4 so a. and b. are out right away

the slope is up two over three so change in Y over change in X

Which statement is true about the end behavior of the
graphed function?

A: As the x-values go to positive infinity, the function's
values go to negative infinity.

B: As the x-values go to zero, the function's values go to
positive infinity

C: As the x-values go to negative infinity, the function's
values are equal to zero.

D: As the x-values go to positive infinity, the function's
values go to positive infinity.

Answers

Answer:

Option A.

Step-by-step explanation:

Let the given graph represent the function f(x).

From the given that given graph it is clear that the end behavior of the function f(x):

1. As the x-values go to positive infinity, the function's values go to negative infinity.

[tex]\lim\limits_{x\to \infty}f(x)=-\infty[/tex]

2. As the x-values go to negative infinity, the function's values go to positive infinity.

[tex]\lim\limits_{x\to -\infty}f(x)=\infty[/tex]

Therefore, the correct option is A.

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