The map shows a straight highway between two towns. Highway planners want to build two new rest stops between the towns so that two rest stops divided the highway into three equal parts. Find the coordinates of the points at which the rest stops should be built.

Answer:

Step-by-step explanation:

1). Since, m∠2 + m∠1 = 180° [Supplementary angles]

   125° + m∠1 = 180°

   m∠1 = 180° - 125°

   m∠1 = 55°

2). Since ∠7 ≅ ∠12 [alternate interior angles]

   m∠7 = m∠12 = 37°

3). m∠3 = m∠18 = 102° [Alternate exterior angles]

4). m∠8 + m∠3 + m∠7 = 180°

    m∠8 + 102 + 37 = 180

    m∠8 = 41°

5). m∠14 = (m∠7 + m∠8) [Alternate angles]

    m∠14 = 37 + 41 = 78°

6). m∠4 = 180° - m∠3 [Linear pairs]

             = 180 - 102

             = 78°

7). m∠9 = m∠3 = 102° [Vertical angles]

8). m∠15 = m∠2 [Alternate exterior angles]

               = 125°

9). m∠5 = m∠15 [Corresponding angles]

             = 125°

10). m∠10 + m∠5 = 180° [Sum of interior angles on one side of the transversal]

     m∠10 = 180 - 125

               = 55°

10). m∠16 = m∠10 = 55° [Vertical angles]

11). m∠6 = m∠10 = 55° [Alternate interior angles]

12). m∠11 = m∠15 = 125°

13). m∠17 = m∠14 = 78° [Vertical angles]

The answers are given as follows

Given that

a║b

m∠2 = 125°

m∠12 = 37°

m∠18 = 102°

From the identity of supplementary angles

m∠1 + m∠2= 180°

So m∠1 = 180° - 125° = 55°

m∠7 =m∠12 = 37° (Interior opposite angles )

m∠3 = m∠18=102° (Alternate Exterior angles )

m∠8 = 180° - m∠3 -m∠7  = 180°- 139° = 41°

m∠14 = m∠7+ m∠8= 37° + 41° = 78° ( Alternate opposite angles)  

So m∠13 = 180° -78° = 102° (linear pair)

m∠4= 180° - m∠3  = 180° - 102° = 78°

m∠9 =180° - m∠4 = 180° - 78 = 102° (vertically opposite to m∠3)

m∠15 = m∠2 = 125° (Alternate exterior angles)

m∠5 =m∠15 = 125° (Corresponding Angles )

m∠10 =  180° -125° = 55°

m∠16 = m∠10 =55° ( Vertically Opposite Angles)

m∠6 = m∠10 =55°  (Alternate interior angles)

m∠11 = 180 ° -  m∠6° - m∠7° = 180° - 55° - 37° =  88°

m∠17 = 180° - m∠13 = 180° -102° = 78 °

For more information please refer to the link below

https://brainly.com/question/15685431

Answer:

2 x − 2 y

I hope this helps! UwU

If you can give brainliest that will be awesome

Hey there!☺

[tex]Answer:\boxed{2x-2y}[/tex]

[tex]Explanation:[/tex]

[tex](x-y)2[/tex]

(x + -y)2 Make y negative

(x)(2) + (-y)(2)    Separate with parenthesis.

2x - 2y

Hope this helps!

Let, first integer is x.

Therefore, other two are x+1 , x+2 .

Now, mathematical expression of given conditions is :

4x + 3 = 3(x+2)

4x + 3 = 3x + 6

x = 3.

So, the consecutive numbers are 3 , 4 and 5.

Therefore, the middle integer is 4.

Hence, this is the required solution.

Answer:(5-3)=42

Step-by-step explanation:

Hello There!!

Your answer is 21.

First, You should do is (5 ₋ 3) = 2.

Then, You need to divide 42/2 =21.

[tex]\sqrt[HopeThisHelps}[/tex][tex]^{HopeThisHelps}[/tex]

[tex]\frac{Loserbrazts}{}[/tex]

3x - 6x + 2 > 65

Combine like terms.

-3x + 2 > 65

Subtract 2 from both sides.

-3x > 62

Divide both sides by -3

x < -62/3

Answer:

3x - 6x + 2 > 62

→ -3x + 2 > 62

→ -3x > 62

→ x < -62/3

Answer:

Answer down below!! :))

Step-by-step explanation:

For this problem, we need to ask ourselves, 7 plus what gives us 12?

7 + 5 = 12

So, therefore, X = 5

Answer:

x=5

Step-by-step explanation:

7+x=12

Minus both sides by 7

7+x=12

-7     -7

=0     =5

drop the x

x=5

I hope i could be of help to you! You're Welcome!

Answer:

B and C

Step-by-step explanation:

Answer: B and C

Step-by-step explanation:

Answer:

Step-by-step explanation:

step one:

Given that the scale of the map is

 2cm to represent 30 miles

That is  every 1 cm is 15 miles in reality

step one:

what we are solving for is the distance in cm on the map so,

1cm rep 15miles

xcm rep 75miles

cross multiply

Xcm= 75/15

X= 5 cm

hence on the map 75miles distance between the two towns is seen as 5 cm

Answer:

A. y=2/3x-3/2

Step-by-step explanation:

Subtract 4x over then divide both side by -6

Answer:

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

50%=0.5

0.5*92=46

Answer:

100

Step-by-step explanation:

Got it right on test

Answer:

60.1

Step-by-step explanation:

Just get 72.60 and subtract 12.50

Answer:

All real numbers except 6

5 1.80, the crackers cost $1.80 per box: 20 3 1.80 5 36. So, 20 boxes cost $36.00.

Answer:

$36

Step-by-step explanation:

To find how much one box costs you divide 9÷5 = 1.8

Then you take 1.8 × 20 = 36

If you want me to go over it in depth, let me know! Have a great day!

Answer:

d

Step-by-step explanation:

Answer:

~-1.67

Step-by-step explanation:

Multiply. Note that when you multiply a negative and positive number, your answer will be negative:

5 x (-1/3) = (5 * -1)/3

Multiply, then divide:

5 * -1 = -5

-5/3 = ~-1.67 (rounded to the nearest hundredths).

~

Answer:

-5x/3

It just is, trust me.

Answer:

its math roll dont wory ill show with no math and explantion its just awnsers

Step-by-step explanation:

8 i

4 t

11 w

1 a

6 s

9 a

14 m

7 o

10 t

3 h

13 b

5 a

2 L

I couldnt get the last one but i did in the same order as it has it

To solve the question we used the criteria that the solution depends upon the sign, if negative number is greater than sign will be a minus .

if positive number is greater than sign will be a plus.

The sign while addition and subtraction depends on the larger number .

If negative number is greater than sign will be a minus .

if positive number is greater than sign will be a plus.

1.

A. -5+2=-3

B. 7+-3= 4

C. -4+-6=-10

2.

A. 1+-8=-7

B. -6+-12=-18

C. -2+9=7

3.

A. -7+6=-1

B. 5+-8=-3

C. 12+13=25

4.

A. -10+-10=-20

B. 17+-1=16

C. -11+5=-6

5.

A. 4+-9=-5

B. -7+-15=-22

C. -3+12=9

6.

A. 16+-8 = 8

B. -5+20=15

C. -6+6=0

Similarly we can do the remaining solutions.

To learn more on Number system click:

https://brainly.com/question/22046046

#SPJ2

Answer:

8

Step-by-step explanation:

Answer:

y - (-4) = (-1/2)(x - 8)

y + 4 = (-1/2)x + 4

y = (-1/2)x

orrrr...

-4 = (-1/2)(8) + b

-4 = -4 + b

b = 0

Well, we don't write "+ 0" because that's just extra work.

y = (-1/2)x

mark me as brainlist

Answer:

1/36

Step-by-step explanation:

To get a sum of 2, both dice must roll a 1.

The probability of a 1 on the first die is 1/6.

The probability of a 1 on the second die is 1/6.

Therefore, the probability of rolling both 1s is:

P = 1/6 × 1/6 = 1/36

Answer:

Gray kangaroo weighs 87 kg.

Step-by-step explanation:

Total weight of the two kangaroo = 139 kg.

Let the weight of the gray kangaroo be represented by p.

Since the red kangaroo weighs 35 kg less than the gray kangaroo = (p - 35) kg.

Thus;

weight of gray kangaroo + weight of red kangaroo = 139 kg

p + (p -35) = 139

p + p -35 = 139

2p = 139 + 35

2p = 174

p = 87

The weight of the gray kangaroo is 87 kg.

Weigth of the red kangaroo = (87 - 35)

                                               = 52 kg

The gray kangaroo weighs 87 kg.

let the weight of the gray kangaroo as G.

We have,

the red kangaroo weighs 35 kg less than the gray kangaroo.

So, the weight of the red kangaroo can be represented as G - 35.

We also know that the combined weight of the red kangaroo and the gray kangaroo is 139 kg. So we can write the equation:

G + (G - 35) = 139

Combining like terms:

2G - 35 = 139

Now, let's solve for G by isolating the variable:

2G = 139 + 35

2G = 174

Dividing both sides by 2:

G = 174 / 2

G = 87

Therefore, the gray kangaroo weighs 87 kg.

Learn more about Algebra here:

https://brainly.com/question/29131718

#SPJ6

Answer:

12-x=x+3

12-3=x+x

9=2x

9/2=x

4.5=x

Answer:

x = 3

Step-by-step explanation:

The segment parallel to the third side and intersecting 2 sides divides those sides proportionally, that is

[tex]\frac{12-x}{x+3}[/tex] = [tex]\frac{6}{4}[/tex] ( cross- multiply )

6(x + 3) = 4(12 - x) ← distribute parenthesis on both sides

6x + 18 = 48 - 4x ( add 4x to both sides )

10x + 18 = 48 ( subtract 18 from both sides )

10x = 30 ( divide both sides by 10 )

x = 3

Answer:

152.25

Step-by-s152.25tep explanation:

Answer:

Dominique has $162.25 dollars left after shopping.

Step-by-step explanation:

250 - 17.50 - 32.75 - 12.50 x 3

250 - 17.50 - 32.75 - 37.5

232.5 - 32.75 - 37.5

199.75 - 37.5

162.25

Answer:

B

Because the right side is double the number on the left

Answer:

d = 10

Step-by-step explanation:

[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d= \sqrt{(8-8)^2+(5.3-(-4.7))^2} \\d= \sqrt{(0)^2+(10)^2} \\d= \sqrt{0+100} \\d= \sqrt{100}\\ d= 10[/tex]

Answer:

16 yellow flowers

Step-by-step explanation:

[tex]Pink: yellow\\6\:\::\:2\\\\Total\:ratio = 6+2 = 8\\\\48 \:pink\: flowers[/tex]

First calculate total no of flowers

[tex]\frac{6}{8} \times x = 48\\\\\frac{6x}{8} =48\\\\Cross\:Multiply\\6x = 48\times 8\\6x = 384\\\\Divide\:both\:sides\:of\:the\:equation\:by\:6\\\frac{6x}{6} = \frac{384}{6} \\\\x = 64\\\\Total \:flowers = 64[/tex]

Calculate no of yellow flowers

[tex]Total\:flowers-Pink\:flowers = Yellow\:flowers\\\\Yellow\:flowers = 64 - 48\\Yellow\:flowers =16[/tex]