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 me with this please!!!!

Answers

Answer:

yes

Step-by-step explanation:

it said it is a perpendicular BISECTOR, H is the mid point of KI, HK = 7

[tex]\huge{\underline{\underline{\boxed{\sf{\red{Answer࿐}}}}}}[/tex]

Yes!

Find the modes of this data set.

Answers

Answer:

1, 2

Step-by-step explanation:

the mode is the ones that appear the most in a data set, so since 1 and 2 appear 4 times each, they are the two modes.

PLEASE SOMEONE!!HELP!! I need the answer right now

Answers

Answer:

m = -1, b = 5.

Step-by-step explanation:

We can find the slope, m, by plugging in our coordinates into the slope formula: [tex]\frac{y2-y1}{x2-x1} =\frac{2-7}{3-(-2)}=\frac{-5}{5}=-\frac{5}{5}=-\frac{1}{1}=-1[/tex]. That gives us the slope. Now we can fill that in the slope intercept formula: [tex]y=-1x+b[/tex]. We know one of the coordinates and the slope, which allows to find the y-intercept. We know that for every 1 unit down on the line, we move 1 unit right, and vice versa. Meaning we can just count down (or up in this case), so, (-2, 7), (-1, 6), (0, 5). Therefore, our y intercept is 5.

LOOK I really new help on this I will give u cash for it just give me your cash app or Venmo please help this is so many points
question
(60-5.8) ÷ 5 - 3^2
can you please explain it in an essay type like words and not just show me the answer I need it to show me how you got the answer don't give me just the answer

Answers

Answer:

1.84

Step-by-step explanation:

First you solve what is in the parenthesis.

60 - 5.8 = 54.2

The equation is now 54.2 ÷ 5 - 3^2

Now, you do the exponents. 3^2 = 9 since 3 to the second power is just another way to write 3 x 3.

Your equation is now 54.2 ÷ 5 - 9

You then divide 54.2 ÷ 5

54.2 ÷ 5 = 10.84

The last equation is 10.84 - 9

10.84 - 9 = 1.84

Answer:

Answer 1.84.

Step-by-step explanation:

The first person's answer and explanation is correct.

Write the equation of a circle with center (0,−6) and radius 4 in general form.


Answers

Answer:

x^2 + (y + 6)^2 = 4^2

Step-by-step explanation:

The general form we need here is (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

If the center is at (0, -6) and the radius is 4, then the desired equation is

(x - 0)^2 + (y + 6)^2 = 4^2, or just

x^2 + (y + 6)^2 = 4^2

PLEASE Can someone plz help me

Answers

9514 1404 393

Answer:

  $11,988

Step-by-step explanation:

A graphing calculator gives you the answer easily.

The minimum unit cost is $11,988.

__

The equation for unit cost can be put into vertex form to find the minimum.

  C(x) = 0.7x^2 -210x +27738

  C(x) = 0.7(x^2 -300x +150^2) +27738 -0.7(150^2)

  C(x) = 0.7(x -150)^2 -11,988

This is vertex form:

  C(x) = a(x -h)^2 +k . . . . . . . where (h, k) is the vertex.

The vertex of this cost function is (150, 11,988).

The minimum unit cost occurs when 150 engines are produced. That unit cost is $11,988.

Answer:

the answer is $11,988

Step-by-step explanation:

:)

There are _______ kilometers in 5,000 centimeters.

Answers

There are 0.05 kilometers in 5000 centimeters

What is the area of the given circle use 3.14 for pie diameter =18cm

Answers

Answer:

254.47

Step-by-step explanation:

1/4[tex]\pi[/tex]d^2

what is 2(3x+2)=2x+28

Answers

Answer:

x=6

Step-by-step explanation:

6x+4=2x+28

4x=24

x=6

x= 6..... i don’t have much time to explain and show why it’s the answer but i hope i’m right

About how many more website hits were there on Saturday than on Friday?

Answers

Answer:

1,000 hits

Step-by-step explanation:

Saturday: 2,000 hits

Friday: 1,000 hits

2,000 - 1,000 = 1,000

Answer: 1,000 hits

Step-by-step explanation:

I just took the test, it's right.

Question 2 of 10
If data set A has a larger standard deviation than data set B, data set A is
more spread out than data set B.
A. True
B. False
SUB

Answers

It is true that if data set A has a larger standard deviation than data set B, data set A is more spread out than data set B.

How to determine the true statement?

The standard deviation is a measure of spread.

And the more the standard deviation, the more the spread

This means that if the dataset A has a larger standard deviation than the dataset B, then the dataset A is more spread out than B

Hence, the given statement is true

Read more about standard deviation at:

https://brainly.com/question/15858152

#SPJ1

consider the system of equations
y = 2/3 x + 1
y = x
what is the solution to the system?
A. (0,0)
B. (0,1)
C. (1,1)
D (3,3)

Answers

Answer:

Use your resources wisely

Step-by-step explanation:

Answer:

[tex] \frac{2}{3} x + 1 = x \\ \frac{1}{3} x = 1 \\ x = 3 \\ y = 3[/tex]

X=3,y=3

AABC is dilated by a factor of 4 to produce AA'B'C'.

What is A'C, the length of AC after the dilation? What is the measure of ZA?

Answers

Answer:

A

Step-by-step explanation:

because the sky is blue

The length of AC after dilation will be 20. Then the measure of the angle ∠A' will be 37°.

We have given that,

AABC is dilated by a factor of 4 to produce AA'B'C'.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The triangle ΔABC is dilated by a factor of 4 to produce the triangle ΔA'B'C'.

Then the length of AC after dilation. We have

A'C' = scale factor x AC

A'C' = 4 x 5

A'C' = 20

Then the measure of the angle ∠A' will be

There is no effect of dilation on the angle.

∠A = ∠A' = 37°

Thus, the correct option is A.

More about the dilation link is given below.

brainly.com/question/2856466

#SPJ5

What is the total surface area and volume?? PLEASE HELP ME ASAP

Answers

Answer:

228

Step-by-step explanation:

ANOTHER QUESTOIn?

hii please help i’ll give brainliest!!

Answers

Answer:

direction

Step-by-step explanation:

Find the value of x and the measure of the angle labeled 3x
3x
27
A. x= 15; angle measure is 27°,
OB. X = 9; angle measure is 27".
C. x= 9; angle measure is 45°
O.D. x= 15; angle measure is 45°

Answers

Answer:

The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.

The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.

The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.

The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.

The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.

The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.

The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115The angles of A and B are 45 degrees. This is true because the other angle is a right angle (90 degrees) and if you are making a triangle the degrees of the sides have to = 180 to be a complete triangle. The triangle is complete, so I took 180 – 90 = 90 ÷ 2 = 45.

The angle of C is 115 because it is a supplementary angle. A supplementary angle is an angle that has two angles with a sum of 180 degrees and 180 – 65 = 115

Step-by-step explanation:

Factorise the exprssions
x^2-ax-bx+ab

Answers

Answer:

[tex](x - a)(x - b)[/tex]

Step-By-Step Explanations:

1) Factor out the common term in the first two terms, then in the last two terms.

[tex]x(x - a) - b(x - a)[/tex]

2) Factor out the common term x - a.

[tex](x - a)(x - b)[/tex]

Therefor, the answer is ( x - a ) ( x - b ).

Dorian is making an ice cream sundae. He has three flavors of ice cream, two flavors of syrup, and three types of toppings. If he chooses one flavor, one syrup, and one topping, how many different combinations can he make?

Answers

Convince yourself that there are 3 similar triangles in the diagram. Choose the
similarity statement that represents the relationship among the 3 triangles.

Leonard plans to build a garage on a square plot of land. If one side of the plot is 6g3h5 feet long, express the area of his plot as a monomial

Answers

Answer:

[tex]Area= 36g^6h^{10}[/tex]

Step-by-step explanation:

Given

[tex]Length = 6g^3h^5[/tex]

Required

Determine the area as a monomial

This is calculated as:

[tex]Area = Length * Length[/tex]

[tex]Area= 6g^3h^5*6g^3h^5[/tex]

This can be rewritten as:

[tex]Area= 6*6*g^3*g^3*h^5*h^5[/tex]

Apply law of indices

[tex]Area= 36*g^6*h^{10}[/tex]

[tex]Area= 36g^6h^{10}[/tex]

A bakery used 37% more chocolate chips this month than last month. If the bakery used 320 pounds of chocolate chips last month, how much did it use this month?

Answers

Answer: 438.4

Explanation: 320 x 37% = 320 x 0.37 = 118.4 so 320 + 118.4 = 438.4

Answer:

438.4

Step-by-step explanation:

100% + 37% = 137% = 1.37

320 x 1.37 = 438.4

so the answer that I got is 438.4

I really hope this helps

Which value for p makes the expressions 9p−5 and (3+p)5 equivalent?

a.7
b.6
C.5
D.4

Answers

Answer:

5

Step-by-step explanation:

9p-5

9(5)-5

45-5

40

(3+p)5

(3+5)5

(8)5

40

find the length . IF necessary round to the tenth

Answers

Answer:

24

Step-by-step explanation:

Finding the lengths of a Triangle is [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

Your triangle is [tex]7^{2}[/tex] + [tex]b^{2}[/tex] = [tex]25^{2}[/tex]

Which is 49 + b = 625

Subtract the difference 625 - 49. then you get the following

b = 576

Finally find the square root of this number and that's your answer: 24

Answer:

by using Pythagoras law

third side =√(25²-7²)=24

Joshua made a quilt for his cousin's doll. The quilt had an 8 × 8 array of different color square patches. If each patch is 2 2 3 in long, what is the area of the whole quilt?

Answers

Answer:

[tex]Area = 455.11\ in^2[/tex]

Step-by-step explanation:

Given

[tex]Patches = 8\ by\ 8[/tex]

[tex]Length = 2\frac{2}{3}\ in[/tex] each

Required

The area of the quilt

First, calculate the length of the quilt.

[tex]Length = 8 * 2\frac{2}{3}[/tex]

[tex]Length = 8 * \frac{8}{3}[/tex]

[tex]Length = \frac{64}{3}[/tex]

Next, the width

[tex]Width= 8 * 2\frac{2}{3}[/tex]

[tex]Width= 8 * \frac{8}{3}[/tex]

[tex]Width = \frac{64}{3}[/tex]

The area is then calculated using:

[tex]Area = \frac{64}{3} * \frac{64}{3}[/tex] i.e. Length * Width

[tex]Area = \frac{4096}{9}in^2[/tex]

[tex]Area = 455.11\ in^2[/tex] --- approximated

w² + 2w – 24/ + 8/
w² + w – 30 w-5​

Answers

Use photomath it’s faster and you get correct Answers!<3 have a good day

write the equation (3,5) in standard form

Answers

Answer:

We can write out 3! (three factorial) as 3x2x1, and we can write out 5! as 5x4x3x2x1. This means that, since 3x2x1 is on the top and the bottom of the fraction, it cancels out. This leaves us with 1 on top, and 4x5=20 on the bottom.

Step-by-step explanation:

can you please help me with my question

trigonometry please help! work need to be shown

Answers

Answer:

x = 5.56

Step-by-step explanation:

Apply trigonometric function to find x

Reference angle = 46°

Hypotenuse = 8

Adjacent length = x

Apply CAH:

Cos 46 = Adj/Hyp

Cos 46 = x/8

8 × Cos 46 = x

5.55726696 = x

x = 5.56 (nearest hundredth)

Mehvish buys 1/2 kg carrots, 3 kg potatoes, 2 kg onions and 1 1/2kg of chicken.

PRICE LIST
carrots: 50p per kg
potatoes: 64 per kg
onions: 42p per kg
Chicken: £6 per kg

She pays with a £20 note.

Work out the change that Mehvish should get.

Answers

Answer:

The amount of change will be £7.99

Step-by-step explanation:

Here, we want to calculate the amount of change that Mehvish should get

1/2 kg carrots at 50 p per kg will be;

1/2 * 50 = 25 p

3 kg potatoes at 64 p per kg will be

3 * 64 = p 192

2 kg onions at 42 p per kg

2 * 42 p = 84 p

1 1/2 kg chicken at £6 per kg will be:

since £1 is 100 p

1.5 * 6 = £9 (9 * 100 p = 900p)

since £1 is 100 p

£20 will be;

20 * 100 = 2,000 p

So let us make the subtraction as follows;

2,000- 900 - 84-192 - 25 = 799 p

In pounds, this is divided by 100

we have this as 799/100 = £7.99

The school band will sell pizzas to raise money for new uniforms. The supplier charges $97.00 plus $6.00 per pizza. The band members sell the pizza for $8.00 each. Enter and solve an inequality to find how many pizzas the band members will have to sell to make a profit. Let p be the numbers of pizzas sold. The inequality is ? The band members will need to sell at least __. pizzas.

Answers

Answer:

49 pizzas

Step-by-step explanation:

Start by writing it as a equation,

P stands for Pizza

6p +97 = 8p

Minus 6p from both sides

97=2p

Divide by 2

P= 48.5

You would need to round up, so it would be 49 pizza

PLEAS HELP ASAP 30 POINTS!!!
An incomplete proof of cosθsinθ/1+sinθ=tanθ(1-sinθ) is shown.
Which of the following expressions could be used to complete the third step pf the proof?

Answers

Answer:

C

Step-by-step explanation:

Take a look at the RHS of the 2nd step, the denominator -- 1-sin²∅ = cos²∅

We come up to the conclusion of C

A total of 50,000 contestants are chosen for a survey. A
computer randomly eliminates 20% of the participants
each day.
Which function models the survey?

Answers

Answer:

you are correct do not say any other answer

Answer:

The answer is either

y=50000 x 0.8^x

or

y=50000(20%)^x but this just seems wrong

Step-by-step explanation:

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