Borderline
Your late grandfather left you and your cousin his property in his will. Below is a map of the
property with a road that cuts through the property
North Property Border
Road
South Property Border
1. On the diagram, two angles (<1 und 2) formed by the road, and the borders are congruent.
What is the relationship
between the north and south property borders of your prandfather's
land?
Explain how you know
2. How are <3 and <1 related to each other
Explain how you know

BorderlineYour Late Grandfather Left You And Your Cousin His Property In His Will. Below Is A Map Of

Answers

Answer 1

Answer:

1. The North and South property border lines are parallel

2. ∠3  and ∠1 are supplementary angles

Step-by-step explanation:

The given parameters are;

The North and South Property Boarders are given

The road intersects (transverses) the North and South Property Boarders

∠1 and ∠2 in the given diagram are congruent

1. Given that ∠1 ≅ ∠2, and from the diagram, ∠1 and ∠2 are alternate interior angles, we have that alternate interior formed by the transversal of two parallel lines are congruent

Therefore, the North and South property border lines are parallel

2. ∠3 and ∠1 are same side interior angles

When two parallel lines have a common transversal passing through them, then the same side interior angles are supplementary

Therefore, ∠3 and ∠1 are supplementary (angles whose sum is 180°)

The proof is that ∠3  and ∠2 are supplementary, because they are the angles on a straight line

∠2 ≅ ∠1 which is given

∴ ∠2 = ∠1 by definition of congruency

∠3  and ∠1 are therefore, supplementary, by substitution property of equality


Related Questions

It costs Danny $5 to park his car at a parking meter for 2 hours. What is the
price to park for 1 hour?

Answers

Answer:

$2.50

Step-by-step explanation:

Answer:

$2.5

Step-by-step explanation:

Triangle A B C with centroid G is shown on an x and y-axis. Lines are drawn from each point through the centroid to the opposite side to form line segments A F, B D, and C E. Point A is at (0, 0), point D is at (c, 0), point C is at (2 c, 0), point B is at (2 a, 2 b), point F is at (a + c, b),and point E is at (a, b).
The equation of line Line A Gis y = (StartFraction b Over a + c EndFraction)x. The midpoint of BC is (a + c, b). Does the midpoint of BC lie on Line A G? Why or why not?

no, because (StartFraction b Over a + c EndFraction)b does not equal a + c
no, because (StartFraction b Over a + c EndFraction)(a + c) does not equal b
yes, because (StartFraction b Over a + c EndFraction)b = a + c
yes, because (StartFraction b Over a + c EndFraction)(a + c) = b

Answers

Answer:

Its D my friend

Step-by-step explanation:

Answer:

(D) yes, because (StartFraction b Over a + c EndFraction)(a + c) = b

Step-by-step explanation:

Triangle A B C with centroid G is shown on an x and y-axis. Lines are drawn from each point through the centroid to the opposite side to form line segments A F, B D, and C E. Point A is at (0, 0), point D is at (c, 0), point C is at (2 c, 0), point B is at (2 a, 2 b), point F is at (a + c, b),and point E is at (a, b).The equation of line Line A Gis y = (StartFraction b Over a + c EndFraction)x. The midpoint of BC is (a + c, b). Does the midpoint of BC lie on Line A G? Why or why not?

(A) no, because (StartFraction b Over a + c EndFraction)b does not equal a + c

(B) no, because (StartFraction b Over a + c EndFraction)(a + c) does not equal b

(C) yes, because (StartFraction b Over a + c EndFraction)b = a + c

(D) yes, because (StartFraction b Over a + c EndFraction)(a + c) = b

Can someone help me and show steps I’ll mark you brainliest

Answers

Answer:

y = 2x + 21

Explanation:

The slope is 2 so it would go for mx

The y-inter. for the graph is 21

your equation is y = 2x + 21

Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Irene​'s car had 5.5 gallons in the 14​-gallon tank on the coldest day of the year. Irene filled the tank with gas that cost ​$3.60 per gallon. How much did Irene spend on​ gas?

Answers

Answer:

ok 16.5$

Step-by-step explanation:

WILL GIVE BRAINLIEST

Answers

Answer:

x axis and y axis each end

Step-by-step explanation:

The number of people who have heard a rumor often grows exponentially. Consider a rumor that starts with 3 people and where the number of people who have heard it doubles each day. How many people would know the rumor after 20 days?

Answers

Answer:

3.9125 × 10⁵² people

Step-by-step explanation:

A rumor starts with 3 people and the number of people who heard it doubles each day.

How many people would have heard the rumor after 20 days?

To calculate exponential growth, we use the formula:

[tex]y (t) = ae^{kt}[/tex]

where;

a = value at the start =3

k = growth rate = 2×3 = 6

t = time = 20 days

y(t) = value of the population at the given time (t) =??

[tex]y(t) = 3 \times e^{6\times 20}[/tex]

y(t) = 3.9125 × 10⁵² people

Unit Test Review
Active
1
leto
A triangle has side lengths measuring 2x + 2 ft, x + 3 ft,
and n ft.
COS
Which expression represents the possible values of n,
in feet? Express your answer in simplest terms.
x-1 n = 3x + 5
O n = 1 - 1
O 3x + 5

Answers

Answer:

x - 1 < n < 3x + 5

Step-by-step explanation:

If you have two sides of a triangle, the length of the third side is at least the difference between the other two sides, and at most the sum of the other two sides.

-5(8) will give brainlyest

Answers

Answer:

-5 x 8 = -40

Step-by-step explanation:

Answer:

-14

Step-by-step explanation:

-5x8 = 14

helpppppp pllzzzzzzzzz

Answers

Answer:

The length of side of largest square is 15 inches

Step-by-step explanation:

The given suares are when joined in the way as shown in picture their sides form a right agnled triangle.

Area of square 1 and perimeter of square 2 will be used to calculate the sides of the triangle.

So,

Area of square 1: 81 square inches

[tex]s^2 = A\\s^2 = 81\\\sqrt{s^2} = \sqrt{81}\\s = 9[/tex]

Perimeter of square 2: 48 inches

[tex]4*side = P\\4* side = 48\\side = \frac{48}{4}\\side = 12\ inches[/tex]

We can see that a right angled triangle is formed.

Here

Base = 12 inches

Perpendicular = 9 inches

And the side of largest square will be hypotenuse.

Pythagoras theorem can be used to find the length.

[tex](H)^2 = (P)^2+(B)^2\\H^2 = (9)^2+(12)^2\\H^2 = 81+144\\H^2 = 225\\\sqrt{H^2} = \sqrt{225}\\H = 15[/tex]

Hence,

The length of side of largest square is 15 inches

An office space is for rent downtown. The rate is $17 per square foot per
month. The space measures 20 ft x 19 ft. How much will it cost to rent this
space for a year?
A. $6460
B. $73,644
O C. $91,200
D. $77,520

Answers

D. $77,520 to rent per year

Answer:

$77,520

Step-by-step explanation:

A redwood tree in King’s Canyon National Park, California has a circumference of 220 inches. Tanner measured the circumference of some other redwoods that had been planted over the last 5 years. His data is recorded below. Write a rule for the data in the table.

Use your rule to predict the circumference of a tree after 50 years of growth.
Use your rule to estimate the age of the tree with a circumference of 221 inches.

Answers

Answer:

A). 101 inches

B). 110 years

Step-by-step explanation:

Years since planting           Circumference          Difference

             1                                        3                               -

             2                                       5                        (5 - 3) = 2

             3                                       7                         (7 - 5) = 2

             4                                       9                        (9 - 7) = 2

             5                                       11                        (11 - 9) = 2

             6                                       13                       (13 - 11) = 2

There is a difference of 2 in every successive term of the circumference.

Therefore, the given sequence is an arithmetic sequence.

Explicit formula of an arithmetic sequence is given by,

[tex]A_n=a+(n-1)d[/tex]

Here a = first term

n = number of terms

d = common difference

From the given table,

[tex]A_n=3+(n-1)2[/tex]

[tex]A_n=2n+1[/tex]

Here [tex]A_n[/tex] = circumference after 'n' years

n = Age of the plant

By this formula,

Circumference of a tree after 50 years,

[tex]A_{50}=2(50)+1[/tex]

      = 101 inches

Age of tree with the circumference = 221 inches,

221 = 2n + 1

2n = 220

n = 110 years

Which of the following is most likely to form when one tectonic plate is pushed with great force under another tectonic plate below the ocean? (4 points)

a
Continental rift

b
Fault

c
Mid-ocean ridge

d
Tsunami

Answers

C mid-ocean ridge because it pushes it below

Answer:

D I did the test on Ed.......................................

The sum of Rayson and his brother’s age is 29. If Rayson is 4 years older than his brother 7 years ago. How old is Rayson and his brother?

Answers

Answer:

16 years, 13 years

Step-by-step explanation:

Let their ages be x, 29-x

Equation formed:-

(x - 7) + 4 = 29 - x

→ 2x = 29 + 3

→ x = 16 years

Answer: 16 years, 13 years

Elena began to solve this equation:
12x + 6(4x + 3) =2(6x + 4) – 2
----------------------
3
12x + 6(4x + 3) = 3(2(6x + 4) - 2)
12x + 6(4x + 3) = 6(6x+ 4) – 6
12x + 24x + 18 = 36x + 24 - 6

When she got to the last line she stopped and said the equation is true for all values of x. How could Elena tell?​

Answers

Answer:

They have the same slope and y intercept after combining like terms, they are the same line and have infinetely many solutions.

Step-by-step explanation:

If you combine like terms it would give you 36x + 18 = 36x +18,

nThat's infinetely many solutions since they have the same slope and y-intercepts, therefore they are the same line.

The equation has infinitely many solutions. That means equation is true for all values of x.

What is an equation?

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

We have equation;

12x + 6(4x + 3) =2(6x + 4) – 2

And Elena solved,

12x + 24x + 18 = 36x + 24 - 6

Now, we will solve further,

36x + 18 = 36x + 18

That means equations are equivalent.

And there are two equations and one unknown.

So equation has infinitely many solutions.

Therefore, the equation has infinitely many solutions. That means equation is true for all values of x.

To learn more about the equation;

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Explain how they are different AND the same

Answers

Proportional and linear functions are almost identical in form. The only difference is the addition of the “b” constant to the linear function. Indeed, a proportional relationship is just a linear relationship where b = 0, or to put it another way, where the line passes through the origin

A race follows a triangular course. The three legs of the race are, in order, 0.80 km, 2.05 km, and 2.15 km. Find the angle
between the starting leg and the last leg of the race.

Answers

Answer:

2.15 km

Step-by-step explanation:

The question is jimmy scores is in the bottom 25% of the scores, but he does not have the lowest score. What is one possible value for jimmy score

Answers

Answer:

50% duhh

Step-by-step explanation:

25% is also a equation

Janet has 17 quarters and $13 in bills. How much total money does she have? *

Answers

Answer: 17.25

Step-by-step explanation:

17 x 25= 425. Obviously we can’t leave it like that. So 100 cents is one dollor right?

That means there are four dollars. Made up just by the quarters alone. Now we have to add the 13 dollars 13+4 =17.Now add back the 25 cents to make $17.25

Janet has $17.25

=)

Charis invested
$
140
$140. She earned a simple interest of
3
%
3% per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charis received at the end of two years?

Answers

Answer:

$8.53

Step-by-step explanation:

because after 2 years she would have $148.53.

I believe the answer is $4.20

Write and evaluate the expression.Check all that apply. Write the expression as 11 +t2 -6 Write the expression as 11 +2t -6 Write the expression as 11 +StartFraction t Over 2 EndFraction -6 The value when t = 5 is 16. The value when t = 5 is 30. The value when t = 5 is 7.5.

Answers

Answer:

7.5

Step-by-step explanation:

Given the expression 11 + t/2 - 6, we are the find the output value when t = 5. To do that, we will simply substitute t = 5 into the given expression as shown;

f(t) = 11 + t/2 - 6

f(5) = 11 + 5/2 - 6

f(5) = 11 + 2.5 - 6

f(5) = 13.5 - 6

f(5) = 7.5

Hence the value of the function when t = 5 is 7.5

Answer:

A,E

Step-by-step explanation:

thx person in the comments  

got it right btw to

PLEASE HELP

1. Is the rate of change in cost constant with respect to
the number of pencils bought? Explain.
Cost of Pencils
Number of Pencils 1
Cost ($)
0.25 1
1.75

Answers

Answer:

still need it??

Step-by-step explanation:

​The heights, in inches, of five players on a basketball
​team are 68, 70, 76, 71, and 70. What is the mean
​height, in inches, of these players?
​​

Answers

6’8 is 80 inches, 7’0 is 84 inches, 7’1 is 85 inches, 7’6 is 90 inches

Translate 7 units to the right and 4 units up.
Then, rotate 180° about the origin.

Answers

Answer:

Add 7 to the first value, 4 to the second, then flip the signs.

Step-by-step explanation:

Well we kind of need the current coordinates but I'll help to the extent I can!

In an ordered pair the first value is the (x) and the second is the (y) .

(x, y)

(x) is always the horizontal line (left & right).

(y) is always the vertical line (up & down).

So if you translate 7 units to the right, you'd add 7 to the (x) [First value in the ordered pair].

If you translate 4 units up, you'd add 4 to the (y) [Second value in ordered pair].

Now, rotating about the origin only changes whether the number is positive or negative.

If you rotate 180° it will just flip both of the values signs.

So if it was positive it becomes negative, if it was negative it becomes positive

Since I don't have the ordered pair I can't give you an answer but I can tell you what to do to get the answer.

Assuming it's a shape, for each point on the shape you will take it's coordinates, add 7 to the (x) and 4 to the (y), then flip the value sign.

Ex: If the starting coordinate was (-6, -3) we would add 7 to the (x), 4 to the (y) and get (-2, 4), flip the signs and end up with (2, -4).

Hope this helps! If you have any questions on how I got my answer feel free to ask. Stay safe!

The first 3 figures in a pattern are shown. image Which of the following functions represents f(n), the number of small squares in figure n? A. f(n) = n2 – 1 B. f(n) = 2n2 + 1 C. f(n) = (n + 1)2 + 1 D. f(n) = (n + 1)2 – 1

Answers

Answer:

A

Step-by-step explanation:

A is n= n2 -1 so thats the answer

NEED HELP ASAP, WILL GIVE BRAINLIEST

Find the sum of the first 36 terms in the arithmetic series -0.2, 0.3, 0,8...
a. 318.6 b. 332.2 c. 307.8 d. 315

Answers

Answer:

b.332.2

Step-by-step explanation:

Which of the following is the quotient of the rational expressions shown below? Make sure your answer is in reduced form. ​

Answers

Answer:

The answer is B.

Step-by-step explanation:

First, you have to convert division into multiplication and cross out the common term :

[tex] \frac{3x - 6}{ {x}^{3} } \div \frac{x - 2}{2x - 1} [/tex]

[tex] \frac{3(x - 2)}{ {x}^{3} } \times \frac{2x - 1}{x - 2} [/tex]

[tex] \frac{3}{ {x}^{3} } \times (2x - 1)[/tex]

[tex] \frac{3(2x - 1)}{ {x}^{3} } [/tex]

[tex] \frac{6x - 3}{ {x}^{3} } [/tex]

The quotient of the rational expressions is [tex]\frac{6x - 3}{x^2}[/tex]

calculation:

[tex]= \frac{3x - 6}{x^3}\div \frac{x-2}{2x - 1} \\\\= \frac{3(x - 2)}{x^3} \times \frac{2x-1}{x-2}\\\\ = \frac{3}{x^3} \times (2x - 1)\\\\= \frac{3(2x - 1)}{x^2}\\\\ = \frac{6x - 3}{x^2}[/tex]

Find out more information about the  equation here:

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ANSWER CORRECTLY
-2.5 - 5.5=
MUST SHOW YOUR WORK
good luck

Answers

Answer:

the answer is -7.7  

Step-by-step explanation:

−2.2−5.5

−2.2+ −5.5

= --7.7

hope it helps :)

Answer:

The answer is -8

Step-by-step explanation:

-(2.5+5.5)

-8

Factor 5n^2 - 4n - 12 by grouping. Please show the steps.

Answers

the answer is (5n+6)(n-2)

Answer:

(n - 2)(5n + 6)

Step-by-step explanation:

Given

5n² - 4n - 12

Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term

product = 5 × - 12 = - 60 and sum = - 4

The factors are - 10 and + 6

Use these factors to split the n- term

5n² - 10n + 6n - 12 ( factor the first/second and third/fourth terms )

= 5n(n - 2) + 6(n - 2) ← factor out (n - 2) from each term

= (n - 2)(5n + 6) ← in factored form

An isosceles triangle has base angles that each measure 23 degrees. Which equation can be used to find x, the measure of third angle of this isosceles triangle in degrees?

Answers

Answer:

since a triangle measures up to 180 degrees getting the value of x will be all angles added together equals to 180.

(base angles) + x = 180°

46° + x = 180°

this is what I think good luck

The measure of third angle of this isosceles triangle is 134 degrees.

What is Angle Sum Property?

According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.

S = (n-2)*180° is the angle sum property formula for any polygon, where 'n' represents the number of sides in the polygon.

Given:

Two Base angles is 23 degree.

and third angle is x.

Using Angle Sum property

x + 23+ 23 =180

x +46 =180

x= 180- 46

x= 134

Hence, the third angle is 134 degree.

Learn more about Angle Sum Property here:

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1 last geometry problem

Answers

Line AD = 9
Angle A = 60
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