Given that OA = 2x + 9y, OB = 4x + 8y and CD = 4x - 2y, explain the geometrical relationships between the straight lines AB and CD.

Answers

Answer 1

Answer:

The geometrical relationships between the straight lines AB and CD is that they have the same slope

Step-by-step explanation:

Given

[tex]OA = 2x + 9y[/tex]

[tex]OB = 4x + 8y[/tex]

[tex]CD = 4x - 2y[/tex]

Required

The relationship between AB, CD

Since AB is a straight line and O is the origin, then:

[tex]AB = (c - a)x + (d - b)y[/tex]

Where:

[tex]OA = ax + by[/tex] ====> [tex]OA = 2x + 9y[/tex]

[tex]OB = cx + dy[/tex] ====> [tex]OB = 4x + 8y[/tex]

This implies that:

[tex]a =2[/tex]      [tex]b = 9[/tex]     [tex]c = 4[/tex]   [tex]d = 8[/tex]  

So:

[tex]AB = (c - a)x + (d - b)y[/tex]

[tex]AB = (4 - 2)x + (8 - 9)y[/tex]

[tex]AB = 2x -y[/tex]

So, we have:

[tex]AB = 2x -y[/tex]

[tex]CD = 4x - 2y[/tex]

Calculate the slope (m) of [tex]AB\ and\ CD[/tex]

[tex]m = \frac{Coefficient\ of\ y}{Coefficient\ of\ y}[/tex]

For AB

[tex]m_1 = \frac{-1}{2}[/tex]

[tex]m_1 = -\frac{1}{2}[/tex]

For CD

[tex]m_2 = \frac{-2}{4}[/tex]

[tex]m_2 = \frac{-1}{2}[/tex]

[tex]m_2 = -\frac{1}{2}[/tex]

By comparison:

[tex]m_1 = m_2 = -\frac{1}{2}[/tex]

This implies that both lines have the same slope


Related Questions

Help will give b if correct

Answers

Answer:

0.28

Step-by-step explanation:

28 divided by 100=0.28

Answer:0.28m

Step-by-step explanation:

Carlos is helping his grandfather paint the patio in their backyard. What is the area of the patio?

Answers

128 ft. for the square i square it so basically 8x8 and then the area for the triangle is 32 so i added them all together to get 128

Please help! 30 points!

Use the Law of Cosines to solve the problem.

A ship travels due west for 83 miles. It then travels in a northwest direction for 111 miles and ends up 165 miles from its original position. To the nearest tenth of a degree, how many degrees north of west did it turn when it changed direction? Show your work.

Answers

Answer: [tex]64.2^{\circ}[/tex]

Step-by-step explanation:

According to the cosine rule

[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}[/tex]

Here, [tex]a=83, b=111, c=165,\ C=180^{\circ}-\theta[/tex]

Putting values

[tex]\Rightarrow \cos (180^{\circ}-\theta)=\dfrac{83^2+111^2-165^2}{2\times 83\times 111}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{6889+12321-27225}{18426}\\\\\Rightarrow \cos(180^{\circ}-\theta)=\dfrac{-8015}{18426}=-0.4349\\\\\Rightarrow 180^{\circ}-\theta=\cos^{-1}(-0.4349)=115.77^{\circ}\\\Rightarrow \theta=64.23\approx 64.2^{\circ}[/tex]

So, the ship turns by [tex]64.2^{\circ}[/tex] north of west

The ship turned an at angle of 64.2 degrees north of west

Represent the angle, the ship turned due north of west with theta.

From the figure, we have the following equation

[tex]\cos(A) = \frac{b^2 + c^2 - a^2}{2bc}[/tex]

So, we have:

[tex]\cos(A) = \frac{83^2 + 111^2 - 165^2}{2 * 83 *111}[/tex]

Evaluate the expression on the right-hand side

[tex]\cos(A) = -0.4350[/tex]

Take the arc cos of both sides

[tex]A = \cos^{-1}(0.4350)[/tex]

[tex]A =115.8^o[/tex]

The value of theta is then calculated as:

[tex]\theta = 180 -A[/tex]

This gives

[tex]\theta = 180 -115.8^o[/tex]

[tex]\theta = 64.2^o[/tex]

Hence, the ship turned an at angle of 64.2 degrees north of west

Read more about bearing and elevation at

https://brainly.com/question/19594654

Cual es el valor absoluto de 6.3

Answers

Answer:

Usamos la notación para decir "el valor absoluto de -2", lo cual significa "la distancia de -2 al 0 en la recta numérica". ... 6.3: Altitud y temperatura absoluta.

Mrs smith and i went to the shop to creme eggs at 23p each & kinder eggs at 47 peach in bulk. We bought 141 eggs altogether & it came to 48.51 how many creme eggs did we buy ?

Answers

Answer:

Step-by-step explanation:

Mrs smith and i went to the shop to creme eggs at 23p each & kinder eggs at 47 peach in bulk. We bought 141 eggs altogether & it came to 48.51 how many creme eggs did we buy ?

David uses 1/4 bag of potting soil to plant 6 tomato plants. If he uses the same amount of potting soil for each plant, what fraction of the bag of potting soil will each plant get?
1/24
24
2/3
1 1/2

Answers

Answer:

Step-by-step explanation:

A

5. Jovi solved the following system of equations by
substitution. His partner Giselle checked his work
and said she found an error. What step did Giselle
find the error?

Answers

Step three: it should be 12y=-12, because -4-8=-12

Step four should be y=1, because 12/12=1, not -1

Ann and Betty shared a sum of money in the ratio 2:3. If Ann received $120,what was the amount of money shared?

Answers

Answer:

$420

Step-by-step explanation:

Given data

GIven ratio=  2:3

The total ratio= 2+5= 7

Ann's share= $120

Let us apply the part to all approach

let the total amount be x

so for Ann

2/7= 120/x

cross multiply

2x= 120*7

2x= 840

divide both sides by 2

x= 840/2

x= 420

Hence the amount shared is $420

What is the length of a side a? Round to the nearest tenth of an inch.

Answers

Answer:

Step-by-step explanation:

a = 16 inches

NEAREST TENTH: 20

Estimate the product. 3 1/3 X 4 1/8​

Answers

Answer:

55/4=13.75

Step-by-step explanation:

3+1/3=10/3

4+1/8=33/8

(10/3)(33/8)

(33x10)/(3x24)

330/24

55/4

Hope that helps :)

6v+12b=504
2v+5b=204

Answers

Answer:

Step-by-step explanation:

6v + 12b = 504       eq1

2v +  5b = 204        eq2

6v +  15b = 612       eq2  times 3    

0     -3b   = 504 - 612        subtraction of the two bolded eqs

         -3b  =  -108                solve for b

            b  =    36

    Another way to solve the problem

6v + 12b = 504        I would eliminate the v term by multiplying the bottom

2v +  5b = 204        equation by -3 on BOTH sides and then add the two eqs

   2v +  5b  = 204

-3(2v +  5b) = -3(204)

 -6v  -  15b  =  -612

   

6v  + 12b  =   504

-6v  -  15b  =  -612            add the like terms

(6v + (-6v)) + (12b + (-15b)  =  504 + (-612)

(6v -6v)) + (12b - 15b)  =  504 - 612)

    0       +         -3b     =    - 108            solve for b   divide both sides by -3

                           b   =  -108/-3

                             b =  36                  

use eq   2v +  5b = 204       to solve for v       and knowing b = 36

        2v +  5b = 204      b=36

        2v +  5(36)  = 204                 substract 5 times 36 from both sides

                 2v   =   204 - 180

                    v  =    24 / 2

                    v  =  12

NOW CHECK the values for b and v using the OTHER eq

       6v      +     12b      =    504

       6(12)   +   12(36)    =    504

         72    +     432      =    504

                        504      =    504           IT CHECKS

Jehle and Liam a bowl serving 0.5÷200 Jehle says the question will be Less than 0.5 Liam says the quotient would be more than 0.5 which student is correct

Answers

Answer:

Jehle is correct.

Step-by-step explanation:

Given - Jehle and Liam a both solving 0.5÷200.

Jehle says the quotient will be Less than 0.5.

Liam says the quotient would be more than 0.5

To find - Which student is correct ?

Proof -

Given expression is 0.5 ÷ 200

It is equivalent to

[tex]\frac{0.5}{200} = \frac{5}{2000} = \frac{1}{400}[/tex] = 0.0025 < 0.5

∴ we get

The expression is Less than 0.5

So, Jehle is correct.

Question 1 of 10
sin = 20/29
find tan 0

Answers

Step-by-step explanation:

Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!

Cutt/ly.627929

You have already found tan 0 because the answer is 0

13 (a) Write 2016 as the product of prime factors.

Answers

Answer: 2^5*3^2*7*1

Step-by-step explanation:

Solve these simultaneous equations:

2x + 4y = 38

7x - 4y =7

Answers

Answer:

Step-by-step explanation:

Answer:

x=5, y=7

Step-by-step explanation:

2x+4y= 38

+7x-4y= 7

9x= 45

9x/9= 45/9

x=5

2x+4y=38

2(5)+4y= 38

10+4y= 38

-10 -10

4y= 28

4y/4= 28/4

y=7

What is the diameter of the Orange below ? HINT : D = 2r

Answers

Answer:

umm don't know.....

Step-by-step explanation:

......

Problem PLS HELP MY GRADES GOING DOWN

Answers

Answer:

$248

Step-by-step explanation:

given:

4 deposits

$62

solve:

4 × $62= $248

Answer:

$248

Step-by-step explanation:

You can answer it two ways:

1) add 62 + 62 + 62 + 62 = 248

2) multiply 4 * 62 = 248

Answer: $248

A washer and a dryer cost $662 combined. The washer costs $88 less than the dryer. What is the cost of the dryer?

Answers

Answer:

Step-by-step explanation:First you have to subtract 662-88 and you work it on paper so its easier and when you find the answer its 574

The cost of the dryer is $574.

Tyler has 3 times as many books as Mai. How many books does Mai have if Tyler has 21 books?

Answers

Step-by-step explanation:

Say 21 divided by 3, which gives you 7

So mai has 7 books

Answer:

Mai has 7 books

Step-by-step explanation:

Tyler has 21 books and 3 times more than Mai

21/3 = 7


Which rectangular equation represents the parametric equations x = 3t ^1/2 and y = 6t?

photo has the answer choices !

Answers

Answer:

B

Step-by-step explanation:

on edge 2021

Write an equation in point-slope form of the line that passes through the point (2, -8) and has a slope of 4. The equation is y- __=__(x-__).

Answers

Answer:

The equation is [tex]y-(-8) = 4(x-2)[/tex].

Step-by-step explanation:

The point-slope form of a line is represented by the formula [tex]y-y_1 = m (x-x_1)[/tex]. In order to write an equation of a line in point-slope form, we would need to substitute real values for the [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] in the formula.

Since [tex]m[/tex] represents the slope of the line, substitute 4 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line intersects, substitute the x and y values of (2,-8) in the formula as well. Substitute 2 for [tex]x_1[/tex] and -8 for [tex]y_1[/tex]. This results in the following equation and answer:

[tex]y-(-8) = 4(x-2)[/tex]

(Usually, we would simplify the double negatives on the left side to a positive, but because you have to type the values in to answer the problem and cannot change the written negative sign already visible in the equation, that would be the answer. I believe you can just type in -8 for the first box.)      

Solve the following quadratic by factoring. x² + 3x – 40 = 0
A. X = -8, x=5

B. X= 8, x=5

C. X=8,x= -5

Answers

Answer:

That would be A!

Step-by-step explanation:

Please tell me if i made a mistake or misunderstood!

B I kno this because I worked the problem out correctly

please hurry if answer is correct i will give brainlyyyyest thx
In this task, you will calculate the area of a complicated shape by splitting it into simpler shapes. Cut out shape C. Shape C is not a regular shape, so you cannot directly apply a formula to find its area. Split shape C into simpler shapes whose areas you can find by applying formulas. List the simple shapes into which you divided shape C, and measure their sides. Write all the measurements in inches.

Answers

Answer:

i could only get part one done

Step-by-step explanation:

Perimeter is a measurement of the distance around a shape and area gives us an idea. Understanding how much space you have and learning how to fit shapes ... If the shape is a polygon, then you can add up all the lengths of the sides to find the perimeter. ... You can write “in2” for square inches and “ft2” for square feet

Choose the graph of the solution to this inequality.
–6x < 21

Answers

Answer: A

Step-by-step explanation:

c - 12 > -16

c > -4

A

The answer is A.

c - 12 > -16

c > -16 + 12

c > -4


> means the the arrow should be pointed to the right, and should be on the point -4.

6ya +7y{a
Find the sum
O 13y^2
O O 13ay
O 13y/2a
0 13ya

Answers

Since there the same variable together just add the number
13ay is your answer
Sorry for who ever that annoying person is who uploaded those disturbing pictures...
Hope this helps! Have a nice day :)

Can someone please help me with math.

Answers

Answer:

Your answer would be B.

Step-by-step explanation:

Hope this helps!

HOW MANY ELEMENTS DOES A TRIANGLE HAS
?​

Answers

Answer:

6

Step-by-step explanation:

3 sides, 3 angles.

6 HOPE THIS HELPS!!!

The speed of boat in still water is 15km/hr if needs 4 more his to travel 63 km against the current of a river than it needs to travel down the river determine the system of equation

Answers

Answer:

[tex]\frac{63}{15 - c} - \frac{63}{15 + c} = 4[/tex]

Step-by-step explanation:

The systems of equations are

Let us assume the rate of the current be c

Now actual speed against the current is (15 - c)

And, the actual speed with the current is (15 + c)

Here we applied the time formula i.e. distance by speed

Also the upstream time  - downstream time = 4

Now the equations are

[tex]\frac{63}{15 - c} - \frac{63}{15 + c} = 4[/tex]

A bag contains 90 marbles. some green and some transparent. The ratio of green
marbles to transparent ones is 3.2. How many green marbles are there?

Answers

Answer:

54 green marbles

Step-by-step explanation:

So green : transparent = 3:2

so 3+2=5 and 3*90/5 = 54 green marbles

A window shaped like a parallelogram has an area of 73 2 3 square feet. The height of the window is 8 2 3 feet. How long is the base of the window?

Answers

Answer:

8 1/2 feet

Step-by-step explanation:

Here is the complete question

A window shaped like a parallelogram has an area of 73 2/3 square feet. The height of the window is 8 2/3 feet. How long is the base of the window?

A parallelogram is  quadrilateral that has two pairs of parallel sides. The opposite sides  equal in length

Area = base x height

73 2/3 = 8 2/3 x base

divide 73 2/3  by 8 2/3

221/3 x 3/26 = 8 1/2 feet

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