The ratio of the same side interior angles of two parallel lines is 1:14. Find the measures of all eight angles formed by the parallel lines and transversal. Sorry! Would appreciate if you give the answer by Tuesday! Thanks

Answers

Answer 1

Answer:

At the intersection of the first parallel line with the transversal, a = 12°, c = 168°, d = 12°, e = 168°. Counting counterclockwise from a.

At the first intersection of the second parallel line with the transversal, b = 168°, f = 12°, g = 168°, h = 12°. Counting clockwise from b.

Step-by-step explanation:

Let a be the first interior angle. Since they are in 1:14, the second same side interior angle is b = 14a.

We know that the sum of interior angles equals 180°.

So, a + b = 180°

a + 14a = 180°

15a = 180°

a = 180/15

a = 12°

At alternate angle to the other interior angle, b adjacent to a is c = b = 14a = 14 × 12 = 168°

The angle vertically opposite to a is d = a = 12°

The angle vertically opposite to a is b = e = 168°

At the intersection of the second parallel line and the transversal, the angle alternate to a is f = a = 12°

the angle vertically opposite to angle b is g = b = 168°

the angle vertically opposite to f is h = 12°

Answer 2

Given that the same-side interior angles formed by two parallel lines and a transversal have an angle ratio of 1:14, the eight angles formed are:

m<1 = 12°

m<2 = 168°

m<3 = 168°

m<4 = 12°

m<5 = 12°

m<6 = 168°

m<7 = 168°

m<8 = 12°

Applying the knowledge of ratio, transversal and parallel lines, we can determine the measures of all 8 angles that are formed when a transversal intersects two parallel lines as shown in the image attached below.

Let < 1 and < 6 be the two same-side interior angles whose measures are in the ratio, 1:14.

Thus:

m<1 : m<6 = 1 : 14

Recall:

Same-side interior angles are always supplementary. That is,

m<1 + m<6 = 180 degrees.

Let's apply ratio to find the measure of <1 and <6.

m<1 = ratio of <1 / sum of ratio x 180

[tex]m \angle 1 = \frac{1}{1 + 14} \times 180\\\\m \angle 1 = \frac{1}{15} \times 180\\\\m \angle 1 = 12^{\circ}[/tex]

m<6 = ratio of <6 / sum of ratio x 180

[tex]m \angle 6 = \frac{14}{1 + 14} \times 180\\\\m \angle 6 = \frac{14}{15} \times 180\\\\m \angle 6 = 168^{\circ}[/tex]

Since we know the measure of <1 and <6, we can find the measure of others as follows:

m<2 = m<6 = 168° (corresponding angles are congruent)

m<3 = m<6 = 168° (alternate interior angles are congruent)

m<4 = m<1 = 12° (vertical angles are congruent)

m<5 = m<1 = 12° (corresponding angles are congruent)

m<7 = m<6 = 168° (vertical angles are congruent)

m<8 = m<4 = 12° (corresponding angles are congruent)

In conclusion, given that the same-side interior angles formed by two parallel lines and a transversal have an angle ratio of 1:14, the eight angles formed are:

m<1 = 12°

m<2 = 168°

m<3 = 168°

m<4 = 12°

m<5 = 12°

m<6 = 168°

m<7 = 168°

m<8 = 12°

Learn more here:

https://brainly.com/question/15937977

The Ratio Of The Same Side Interior Angles Of Two Parallel Lines Is 1:14. Find The Measures Of All Eight

Related Questions

F
D
80°
E
B
160
G
NOTE: Angles not necessarily drawn to scale.
2=

PLEASE HELPPP!!!

Answers

Answer:

[tex] \boxed{x\degree = 80\degree} [/tex]

Step-by-step explanation:

Vertically opposite angles are equal.

[tex] = > x \degree + 80\degree = 160\degree \\ \\ = > x\degree = 160\degree - 80\degree \\ \\ = > x\degree = 80\degree[/tex]

Answer:

80°

Step-by-step explanation:

Look at the picture* *

Which values are equivalent to the fraction below? 6^7/6^5

Answers

Answer:

36

Step-by-step explanation:

Because the bases are the same we can just subtract the exponents to get us 6² or 36.

Which graph shows the axis of symmetry for the function f(x) = (x – 2)2 + 1?

Answers

Answer:

B - The correct answer is graph B

Step-by-step explanation:

Answer:

the correct choice is graph B. (see attachment below)

In need of help PLEASE!!!!​

Answers

Answer:

a bc I think it's right idk really

Step-by-step explanation:

jdlaifnshfjtjtjfjdjsjdurbxusnejskshduanwufnrudjdjfkgkgjdjfjgktjvinehdovndintivnsjvolebvinebfirbxjbwhgoenchbtijbegijrgcihegcinrhd

Una escalera está apoyada sobre una pared a 4,33 m de altura y forma con el piso un ángulo de 60°. a) Calcula el largo de la escalera. b) Si el punto B correspondiera a (5,0) y el punto a correspondiera a (0,7). Halla la ecuación de la recta que pasa por los dos puntos, es decir la escalera.

Answers

Answer:

a) 5,00 m

b) y = - (7/5)x + 7

Step-by-step explanation:

The stairs and the wall forms a rectangle triangle. The wall is the opposite side respect to the angle which stairs forms with ground (I attached an image below of the situation).

a) To find the length of stairs you use the following trigonometric relation:

[tex]sin\theta=\frac{h}{l_s}[/tex]            (1)

h: height in which the stairs touch the wall = 4,33 m

ls: length of the stairs

θ: angle between ground and stairs = 60°

You solve the equation (1) for ls:

[tex]l_s=\frac{h}{sin\theta}=\frac{4,33m}{sin60\°}=4,99m\approx5,00m[/tex]

b) The line equation is given by:

[tex]y-y_o=m(x-x_o)[/tex]           (2)

Firs, you calculate the slope by using the equation (2):

[tex]m=\frac{0-7}{5-0}=-\frac{7}{5}[/tex]

Next, you use one of the point, say B, an you replace this points for yo and xo:

[tex]y-0=-\frac{7}{5}(x-5)\\\\y=-\frac{7}{5}x+7[/tex]

Find the number missing from the following equivalent fractions 20/35=4/?

Answers

since the common number of the fraction 20/35 is 5 then divide both sides by 5 which would equal to 4/6 as the equivalent fraction

The missing number is 7.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

PLZ HELP QUICK PLZ
Find the arc length of the semicircle.
Either enter an exact answer in terms of
π
πpi or use
3.14
3.143, point, 14 for
π
πpi and enter your answer as a decimal.

Answers

Answer:

hope this helps you

Answer: it’s 11n

Step-by-step explanation: so we all know this is the answer people :^

Based on an architectural drawing, a roof slopes to a drain
along the function represented in the table that defines the
edge of slope, where x is the horizontal distance in feet and
f(x) is the vertical distance in feet.
If the drain is at the minimum point, how far is it from the wall
defined by the y-axis?
0 feet
8 feet
80 feet
160 feet

Answers

Answer:

  80 feet

Step-by-step explanation:

The smallest value of f(x) in the table is f(x) = 0. It occurs where x = 80.

Since x is the horizontal distance in feet from the wall, the minimum point (drain) is 80 feet from the wall.

Answer:

c

Step-by-step explanation:

edge2020

Which of the following statements is true of the Alien and Sedition Acts?


They were designed to keep immigrants and the French in power.


They encouraged Americans to speak out against the government.


They were supported by Federalists and not by Democratic-Republicans.

Answers

Answer:

C (the last one)

Step-by-step explanation:

The Alien and Sedition Acts were a series of four laws passed by the U.S. Congress in 1798 amid widespread fear that war with France was imminent. The four laws–which remain controversial to this day–restricted the activities of foreign residents in the country and limited freedom of speech and of the press. Also, The Alien and Sedition Acts were four laws passed by the Federalist-dominated 5th United States Congress and signed into law by President John Adams in 1798. Seeing this, the last on is the only reasonable one.

Hope this helps!!!!

Answer:

They were supported by Federalists and not by Democratic-Republicans.

Step-by-step explanation:

I took the edge 2021 test

BRAILIEST?

HELP!!!! Position and label the triangle on the coordinate plane

Answers

Answer:

Option (2).

Step-by-step explanation:

It is given in the question,

ΔLMN is a right triangle with base LM = 3a units

Hypotenuse MN = 5a

By applying Pythagoras theorem in ΔLMN,

MN² = LM² + NM²

(5a)² = (3a)² + MN²

25a² - 9a² = MN²

MN = √16a²

MN = 4a

Therefore, vertices of the triangle will be L(0, 0), M(3a, 0) and N(0, 4a).

Option (2) will be the answer.

Claire is on a business trip. She’ll be traveling from Liverpool, England, to Melbourne, Australia. The latitude value of Liverpool is 53.41 degrees, and the longitude value is -2.99 degrees. The latitude value of Melbourne is -37.81 degrees, and the longitude value is 144.96 degrees. The two cities are degrees apart in latitude. The two cities are degrees apart in longitude.

Answers

Answer:

The change in latitude, Δφ, from Liverpool to Melbourne is 91.22° south

The change in longitude, Δλ, from Liverpool to Melbourne is 147.95° East

Step-by-step explanation:

The parameters given are;

The latitude of Liverpool is 53.41°

The longitude of Liverpool is -2.99°

The latitude of Melbourne is -37.81°

The longitude of Melbourne is 144.96°

The change in latitude from Liverpool to Melbourne = Δφ

Δφ = 53.41° - (-37.81°) = 53.41° + 37.81° = 91.22°

The change in latitude, Δφ, from Liverpool to Melbourne = 91.22° south

The change in longitude from Liverpool to Melbourne = Δλ

Δλ = -2.99° - 144.96°  = -147.95°

Therefore the change in longitude from Liverpool to Melbourne = 147.95° East.

Answer:

the difference in latitude is 91.22°

the difference in longitude is 147.95°

Explanation:

For Liverpool, London. The latitude is 53.41°, longitude is -2.99°

For  Melbourne, Australia. The latitude is -37.81°, longitude is 144.96°

The negative or positive magnitude of their values shows their position on either sides of the origin of the latitude (equator) and the origin of the longitude (prime meridian).

The latitude measures the relative position of a point, north or south of the equator (latitude 0°). The longitude measures the relative position, east or west of the prime meridian (longitude 0°)

the difference in latitude is 53.41° - (-37.81°) = 53.41° + 37.81° = 91.22°

the difference in longitude = 144.96° - (-2.99°) = 144.96 + 2.99 = 147.95°

The explicit formula for a particular arithmetic
sequence is an = 8 + (n - 1)3, with n > 1
What are the first three terms?
ai -
11
az
a3 =

Answers

Answer:

8, 11, 14

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given

[tex]a_{n}[/tex] = 8 + (n - 1)3 , then

a₁ = 8 and d = 3 , thus

a₂ = 8 + 3 = 11

a₃ = 11 + 3 = 14

The first 3 terms are 8, 11, 14

Answer:

8

11

14

THAT IS THE ANSWER TO THE QUESTION

A car was bought a year ago for £1875. It is now worth £1335. By what percentage has the car depreciated in value? (round to 1 decimal place)

Answers

Answer:

28.8%

Step-by-step explanation:

1875 - 1335 = 540

[tex]\frac{540}{1875}[/tex] x 100% = 28.8%

Is 6 a solution to the equation x^2 - 4 = 5x? Please tell me why or why not

Answers

Answer:

6 is not a solution to the given equation.

Step-by-step explanation:

We are given the equation [tex]x^2-4=5x[/tex]

We need to know whether or not x=6 is a solution. This means that we should substitute in 6 for each instance of x. Then, if both sides of the equation are equal, then 6 is a solution to the equation.

[tex]x^2-4=5x\\\\(6)^2-4=5(6)\\\\36-4=30\\\\32=30[/tex]

As 32 ≠ 30, 6 is not a solution to the given equation.

What is the area, in yards, of
a box thats 38 feet wide by
15 feet
long?​

Answers

Answer:

570

step-by-step explanation:

assuming you're talking about a 2-dimensional rectangle,

Area = base x height

base = 38

width = 15

Area = 38 * 15

Area = 570 ft

570ft * (1 yard/3ft) = 190 yards

Answer:

190 yards

Step-by-step explanation:

area= length*width

area= 15*38

area= 570 feet

feet/3= yards

570/3= 190 yards

hope this helps!

Why do you think you can prove congruency with SSS but not with AAA Property. Explain your answer with figures.

Answers

In AAA (Angle-Angle-Angle), triangles do not have the same size and only have 3 pairs of congruent angles.

In SSS (Side-Side-Side), if the three sides of one triangle are equal to the three sides of another triangle, the triangles are congruent.

a.
If f(x) = 25 - xand g(x) = 5 - , which is the rule of function (8 + 9)(x)?
-x2 + x+ 20
5 + x
x? - 5x2 - 25x + 125
--X2 - x + 30
b.
C.
d.
Please select the best answer from the choices provided

Answers

Answer:

The answer is D.

Step-by-step explanation:

You have to add both functions together :

[tex]f(x) = 25 - {x}^{2} [/tex]

[tex]g(x) = 5 - x[/tex]

[tex](f + g)(x) = 25 - {x}^{2} + 5 - x[/tex]

[tex](f + g)(x) = 30 - {x}^{2} - x[/tex]

[tex](f + g)(x) = - {x}^{2} - x + 30[/tex]

I NEED ANSWERS FAST. 1.Using the following image, find
FE given GF=6 and GE=13, 2.Using the following image, find
RS given ST=5and RT=11

.

Answers

Answer: FE  is  7 and RS  is  6.

Step-by-step explanation:

13 - 6 = 7  

11-5= 6

Answer:

FE = 7

RS = 6

Step-by-step explanation:

for the first line, we know that line GE is 13 units long, and segment GF is 6 units. simply subtract 6 from 13 to get the length of segment FE.

13 - 6 = 7

You can do the same thing for the second problem.

11 - 5 = 6

hope it helps!

The units of the subway map below are in miles. Suppose the routes between stations are straight, find the distance you would travel between the Jackson and Symphony stations.Write your answer to the nearest tenth of a mile.

Answers

Answer:

Distance between Jackson and Symphony stations is 2.2 miles.

Step-by-step explanation:

From the given map,

Location of two stations can be represented by the ordered pairs Jackson(2, 4) and Symphony(1, 2)

Every unit of the map represents the distance of 1 mile.

Distance between two points is measured by the formula,

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]

Therefore, distance between the given stations will be,

d = [tex]\sqrt{(2-1)^2+(4-2)^2}[/tex]

  = [tex]\sqrt{1+4}[/tex]

  = [tex]\sqrt{5}[/tex]

  = 2.236

  ≈ 2.2 miles

Distance between Jackson and Symphony stations is 2.2 miles.



Estimate the measure of ∠DBC.

Could someone please help me with this?

Answers

Answer:

Option (4). 135°

Step-by-step explanation:

From the figure attached,

Two pair of vertical angles have been given,

∠ABD and ∠CBE

∠ABE and ∠CBD

One pair of angles ∠ABD and ∠CBE are acute angles which are less than 90°.

Similarly, other pair ∠ABE and ∠DBC are obtuse angles which are more than 90°.

Therefore, out of the given options measure of one pair ∠DBC and ∠ABE should be 135°.

Option (4) will be the answer.

Me pueden ayudar en este problema de potencia antonio tiene3 cajas , en cada caja hay 3 botones que contienen 3 lapices cuantos lapices habra en total

Answers

Answer:

23 lapices

Step-by-step explanation:

Él tiene 3 cajas.

Cada caja contiene 3 botones.

Cada botón contiene 3 lápices.

La cantidad de lápices que tendrá en total es:

[tex]N = 3 * 3 * 3 = 3^3 = 27[/tex]

Tendrá 23 lápices

Find a solution for the equation y = 4x - 3.

Answers

Answer:

y=1

Step-by-step explanation

the x is like a imaginary 1 so 4*x=4-3=1

Please answer correctly !!!!!! Will mark brainliest Answer !!!!!!!!!!!

Answers

Answer:

45 meters

Step-by-step explanation:

graph the equation and find the y-intercept

Which expression is equivalent to (9x + 5y)²?
a) 9x² + 45xy + 5y²
b) 18x² + 45xy + 10y²
c) 45x² + 45xy + 45y²
d) 81x² + 90xy + 25y²
e) 0

Answers

D is the correct answer.

If you don’t understand how then plz don’t hesitate to ask me in the comments.

Can someone help me please??

Answers

Answer:

B.

Step-by-step explanation:

It's just y = 2x because if you look the y is two times the x.

1. Make sure your answers and work is SHOWN please and steps are in order.
2. List all of the possible rational roots.
3. Use synthetic division to test the possible rational roots and factor as far as possible.
4. Identify complex roots, if possible.
5. Sketch a graph of the function, please show:
a. the end behavior correctly
b. the shape of the near x-int
c. (if possible) anything you can learn by considering symmetry and transformations.

1a. p(x)- 2x^4-3x^3-6x^2+5x+6

2a. p(x)= x^4 + 4x^3 + 13x^2 + 36x + 36

3a. p(x)= 2x^5 - 9x^4 + 6x^3 + 22x^2 - 20x - 25

Answers

Been a while since I've done synthetic division.

1a. Let's assume that's supposed to be an equals sign

p(x) = 2x⁴ - 3x³ - 6x² + 5x + 6

possible rational roots have factors of 6 in the numerator and of 2 in the denominator.  We'll only worry about negative numerators.

Factors of six: 1,2,3,6, and we don't forget -1,-2,-3,-6

Factors of 2: 1,2

Possible rational roots:

(dividing by 1:) 1,-1,2,-2,3,-3,6,-6

(dividing by 2:) 1/2, -1/2  (2/2=1 is a duplicate, don't have to repeat it), 3/2, -3/2

Possible rational roots: 1,-1,2,-2,3,-3,6,-6, 1/2, -1/2, 3/2, -3/2

Synthetic division, trying x=1,

   1 | 2  -3  -6  5  6

             2  -1  -7  -2

       2    -1  -7  -2  4

Got a remainder of 4, so 1 isn't a root;

Trying x=-1  

-1 | 2  -3  -6  5  6

         -2   5  1  -6

     2  -5  -1  6  0

Zero remainder, found a root, x=-1.  This division says

(2x⁴ - 3x³ - 6x² + 5x + 6) / (x + 1) = 2x³ - 5x² - x + 6

Same set of rational roots on the cubic, we continue with x=2

2 | 2 -5 -1 6

         4 -2 -6

    2  -1 -3 0

Another zero remainder, x=2 is a root.  We're left with 2x² - x - 3 = 0, which factors as

(2x - 3)(x + 1) = 0

That's a second factor of x+1.  Our final factorization is

2x⁴ - 3x³ - 6x² + 5x + 6 = (x + 1)²(x-2)(2x - 3)

Fourth degree with a positive leading coefficient so goes to +infinity at both ends.  Double zero at x=-1, so it's tangent there, just touching the x axis, then down through x=3/2 and up through x=2.  

I'll leave the actually sketching and the other two polynomials to you -- that took some time.

A farmer has a 100 ft by 200 ft rectangular field that he wants to increase by 15.5% by cultivating a strip of uniform width around the current field. How wide of a strip should he cultivate around the edge of his field to do this? The strip around the outside is _ feet wide

Answers

Answer:

(a) The strip should be 5ft wide

(b) The strip around the outside field is 10ft wide.

Step-by-step explanation:

Given:

Length of the rectangular field, L= 200 ft

width of the rectangular field, w = 100 ft

Area of the rectangular field, A = 200ft x 100ft = 20000 ft^2

let the width of the strip = x

The strip around the outside field = 2x

If the field is increased by 15.5%

New area of the field = 1.155 x 20000 = 23,100 ft^2

The increase in area of the field = 3,100 ft

3,100 = New area of field - old area of the field

3100 = (200 + 2x)(100 + 2x) - 20000

3100 = 20000 + 400x 200x + 4x^2 - 20000

3100 = 600x + 4x^2

Divide through by 4

775 = 150x + x^2

x^2 + 150x - 775 = 0

Factorize

(x + 155)(x-5) = 0

x = 5 ft

The strip should be 5ft wide.

The strip around the outside field = 2 x 5 ft = 10 ft

Thus, the strip around the outside field is 10ft wide.

Find the
a
circle
circumference of
whose
area is 616 cm

Answers

Answer: 88 cm

Step-by-step explanation:

The area of a circle is A=πr². Since we know the area, we can use find the radius, and use the radius to find the circumference,

616=πr²

196=r²

r=14

Now that we have the radius, we can use it to find the circumference. The formula for circumference is C=2πr.

C=2π(14)

C=28π

C=88 cm

Answer: 87.96 cm

Step-by-step explanation:

Radius = √a/π

=√616 / π = 14 cm

Circumference = 2πr

= 2 x π x 14

= 87.96 cm

Is it possible to form a triangle with
side lengths 5, 3, and 5 units?


Answers

Answer:

Yes

Step-by-step explanation:

Isosceles triangle with base of 3 units and sides of 5 units

Answer:

yes

Step-by-step explanation:

use a+b > c, a+c > b, and b+c > a if two sides are bigger than one side for every combination then you can form a triangle

The cost of a hall rental for a wedding is $500. Each meal at the wedding will cost an additional $45.50
a) Write an algebraic expression equation for the total cost of the wedding.
b) Calculate how many people attended the wedding if the wedding cost totalled $3912.50.

Answers

Answer:

a) 45.50p + 500

b) 45.50p + 500 = 3912.50

p = 70

Step-by-step explanation:

p = number of people

$45.50 for a meal for each person, so:

45.50p

The constant is $500, so let's add that to the expression:

45.50p + 500

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