Let $S$ be the set of points $(a,b)$ in the coordinate plane, where each of $a$ and $b$ may be $-1$, 0, or 1. How many distinct lines pass through at least two members of $S$

Answers

Answer 1

Answer:

20 Lines

Step-by-step explanation:

According to the Question,

Given That, Let S be the set of points (a, b) in the coordinate plane, where each of a and b may be -1, 0, or 1.

Now,  the total pairs of points which can be formed is 9

And, the line passing through 2 such points 9c2 = 9! / (2! x 7!) = 9x4 ⇒ 36

Here, We have overcounted all of the lines which pass through three points.

And, each line that passes through three points will have been counted 3c2 = 3! / 2! ⇒ 3 times

Now, the sides of the square consist of 3 points. We have counted each side thrice, so 4*2 are repeated.

Therefore, the distinct lines pass through at least two members of S is 3 horizontal, 3 vertical, and 2 diagonal lines, so the answer is 36 - 2(3+3+2) = 20 Lines

Related Questions

Solve for x. I have to show my work and no decimal answers. It's not mandatory, i just don't understand how to solve the problem. Someone pls help ;) & actually explain it.

Answers

Answer:

-22.5.

Step-by-step explanation:

Lets say that you meant w as the variable.

-4/3 w = 30.

To get rid of the 3, lets multiply 3 to both sides. We get:

3(-4/3 w) = 3(30)

We get:

-4w = 90.

To solve for the w, lets get rid of the -4 by dividing it from both sides.

(-4w)/-4 = 90/-4

We get:

w = -22.5

Check it if you want to make sure.

A oil company has a large tank that holds the oil before it is distributed. If it costs $3.20 per cubic meter for oil, how much money would it cost to fill the entire tank?

A. $65,280
B. $68,000
C. $5,440
D. $67,200

Answers

Answer:

Option A, $65,280

Step-by-step explanation:

The volume of the tank is,

12×20×15+40×(50-15)×12

= 3600+16800

=20400 cubic meters

For each cubic meter, it costs $3.20, so for 20400 cubic meters it'll cost,

20400×$3.20

= $65,280

Answered by GAUTHMATH

What is the volume of the cylinder to the nearest whole number?

Answers

Answer:

[tex]{ \bf{volume = \pi {r}^{2}h }} \\ = 3.14 \times {7.5}^{2} \times 20 \\ { \tt{volume = 3534.3 \: {cm}^{2} }}[/tex]

Find the area of the rectangle whose dimensions are 5cm x 9cm.

Answers

Answer: 45

Step-by-step explanation: 9*5=45

Step-by-step explanation:

hope it helps you........

which graph is that one of the inequality shown below?

Answers

Answer:

D

Step-by-step explanation:

The graph where the inequality is shown would be Graph D

Dan was thinking of a number. Dan doubles it and gets an answer of 34.7. What was the original number?

Answers

347/2 just did it!!! Good luck
You need to do 34.7/2 (divided by 2) to figure this out. The answer would then equal to 17.35

Translate the problem into a mathematical sentence, using was your variable
name. Do not use spaces in your answer.
Lisa bought 15 CDs in December. Of those, 3 were jazz, the rest were world
music. How many world music discs did she buy?
HELPPP

Answers

Answer:

12

Step-by-step explanation:

Total CD's Lisa bought = 15

Jazz music = 3

World music = x

Find x

Total CD's Lisa bought = Jazz music + World music

15 = 3 + x

Subtract 3 from both sides of the equation

15 - 3 = 3 + x - 3

12 = x

x = 12

Therefore,

World music = x = 12

Use the coordinates of the labeled point to find the point- slope equation of the line

Answers

Answer:

[tex]A(0,3)(x_1,y_2)[/tex]

[tex]B(2,-5)(x_2,y_2)[/tex]

[tex]slope(m)=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\longrightarrow[/tex] [tex]\frac{-5-3}{2-0}[/tex]

[tex]\longrightarrow \frac{8}{2}[/tex]

[tex]\longrightarrow -4[/tex]

[tex]y-y_2=m(x-x_2)[/tex]

[tex]\longrightarrow y-(-5)=-4(x-2)[/tex]

[tex]\longrightarrow y+5=-4(x-2)[/tex]

[tex]ANSWER:B[/tex]

--------------------------

hope it helps...

have a great day!!

Find the slope of the line that passes through (1, 2) and (8, 8).

Answers

Answer:

slope = [tex]\frac{6}{7}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (8, 8)

m = [tex]\frac{8-2}{8-1}[/tex] = [tex]\frac{6}{7}[/tex]

72/8 divided by 8/7=

Answers

63/8.

When you divide 72/8 by 8/7, it is the same thing as doing 72/8 x 7/8 since you are just required to flip the numerator and the denominator the other way round in the 2nd fraction.

Find the area

Help me please

Answers

Answer:

143

Step-by-step explanation:

to find the area we multiply half of the sum of the bases with height

(18+8)/2*11 = 143

Sam rolls a fair dice and flips a fair coin.
What is the probability of obtaining an odd number and a head?

Answers

Answer:

1/4

Step-by-step explanation:

Given an event A and event B, the probability of both happening can be determined by multiplying the two individual probabilities.

We can start by finding the individual probabilities

The probability of rolling an odd number is 3/6 = 1/2, as there are 3 odd numbers (1,3,5) on a die and 6 possibilities total. Furthermore, there is a equal chance of rolling each number as it is a fair die

The probability of flipping a head is 1/2, as there are two equal possibilities (heads and tails), with one of them being heads

To find the probability of both happening, we can multiply them to get (1/2) * (1/2) = 1/4

find the slope of the line that contains (6,2) and (6,-3)

Answers

Answer:

slope is undefined

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, 2) and (x₂, y₂ ) = (6, - 3)

m = [tex]\frac{-3-2}{6-6}[/tex] = [tex]\frac{-5}{0}[/tex]

Division by zero is undefined , then slope is undefined

If three children equally share half loaf of bread among themselves, what fraction will each get?​

Answers

Answer:

1/6 of the bread

Step-by-step explanation:

Given data

Let the amount of the loaf of bread be 1

But they are expected to share half

hence the amount to be shared is= 1/2 bread

The number of children is 3

Hence

=1/2/3

=1/2*1/3

=1/6 bread

Hence each child will get 1/6 of the bread

5 times 6 plus 1 times 8 plus 9 times 54 times 8 times 24 times 98 divided by 200 times 800 divided by 653 times 5782470

Answers

211512945555694/653

Decimal: 323909564403.819336

I got stuck but if someone could help me with this question it’d be greatly appreciated!

Answers

Answer:

In step 1 she multiplied the numerators together and denominators together instead she should have done this

30*5 = 12*x

150=12x

150÷12=x

12.5=x

Using the approximation of 5 miles = 8 km


How many km is 22.5 miles?

Answers

Answer:

22.5÷5= 4.5

4.5×8= 36

Step-by-step explanation:

22.5÷5=4.5

4.5×8=36

Answer:

36.21024  km are in 22.5 miles you can figure this out because you multiply the length value by 1.609

Find the sum -2/3+0 Pls answer right​

Answers

Answer:

[tex] - 1[/tex]

-1 is the answer in your questions

Answer:

[tex] - \frac{2}{3} [/tex]

Step-by-step explanation:

[tex] \frac{ - 2}{3} + 0[/tex]

when adding or subtracting by 0, the value does not change.

[tex] = \frac{ - 2}{3} = - \frac{2}{3} [/tex]

which statement proves that polygon ABCD is not a rectangle

Answers

Answer:

ummm u did not add the statements to the question

Step-by-step explanation:

but a polygon ABCD might not be a rectangle if:

opposite sides of polygon ABCD are not of equal lengthsall angles of the polygon may not be right angles (90°)opposite sides may not be parallel

A regular six sided die and an eight equal segment spinner, numbered 1 to 8, are rolled/spun simultaneously. What are the odds in favor of spinning a prime number on the spinner and rolling a number less or equal to 4 on the die?

Answers

Answer:

1/3

Step-by-step explanation:

In statistics, the probability of both an event A and an event B happening is equal to the probability of A happening multiplied by the probability of event B happening.

Let's say spinning a prime number is event A and rolling a number ≤ 4 is event B.

There are 8 possibilities on an eight equal segment spinner, and there are 4 prime numbers between 1 and 8 (including 8), which are 2, 3, 5, and 7. This means that the probability of spinning a prime number is 4/8, or 1/2

There are 6 possibilities on a die, and there are 4 possibilities of rolling a 4 or less (1, 2, 3, 4). Therefore, the probability of rolling 4 or less on a die is 4/6, or 2/3

The probability of both of these happening can be calculated by multiplying these together, so 1/2 * 2/3 = 2/6 = 1/3

m-2n = 8
n = m - 2
The value of m in the system of equations is:

Answers

Answer: m= -4


Step 1: Substitute information

To solve this we will use the substitution method. This means that we will use the information provided to us in the second equation, and substitute it into the first equation. We are told what n equals, so let’s substitute this now.

m-2n=8
m-2(m-2)=8

Step 2: Distribute

Now that we have substituted the information, let’s distribute. This means that we will multiply the numbers on the outside of the parentheses with the numbers on the inside of the parentheses. Let’s do this now.

m-2(m-2)=8
m-2m+4=8

Step 3: Combine like terms

Now that we have distributed, we can continue solving the problem. The next step is to combine like terms. This means to combine terms with the same variable, or lack of. In this case, that is m and -2m.

m-2m+4=8
-m+4=8

Step 4: Get variable alone on the left side

We can now work to get the variable alone on the left side. We can do this by moving the number on the right side, in this case by adding 4 on both sides.

-m+4=8
-m=4

Step 5: Make m positive

In this final step, we must work to make m positive. We can do this by multiplying each term by -1. This will make m positive, and 4 negative. Let’s do this now.

-m=4
-1(-m)= -1(4)
m= -4

This is your answer! M is equal to -4. Hope this helps! Comment below for more questions.

is it possible for a triangle to have an 80 degree angle and 105 degree angle? How do you know? ​

Answers

Answer:

Not possible.

Step-by-step explanation:

The sum of all 3 angles in a triangle is 180°. With the 80° and 105°, those add up to a total of 185°. This is bigger than can be with a given triangle. Therefore, a triangle with an 80° angle and a 105° angle is not possible.

Answer:

No it isn't possible

Step-by-step explanation:

sum of three angles of any triangle is 180 degrees.

so, as per Given question sum of only two angles exceeds 180 degrees which is " 80+105= 185" so it's not possible.. Hope this answer helps you

if 2 is added to denominator and nemerator it becomes 9/10 and 3 is substracted from nemerator and denominator it becomes 4/5 find the fraction​

Answers

Answer:

9-2 /10-2

7/8

4+3/5+3

7/8

fraction is 7/8

An angle measures 42.2° less than the measure of its complementary angle. What is the measure of each angle?

Answers

Answer:

x + (x-42.2) = 90

2x - 42.2 = 90

add 42.2 to both sides

2x = 132.2

divide each side by 2

x = 66.1

find the measure of the other angle

66.1 - 42.2 = 23.9

Step-by-step explanation:

Answer:

66.1° and 23.9°

Step-by-step explanation:

Complementary angles are angles that sum up to 90°

So equation : x + x - 42.2 = 90

2x - 42.2 = 90

2x = 132.2

x = 66.1

66.1° is the "other complementary angle"

This angle is 66.1 - 42.2 = 23.9°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

HELLPPPPPPPPPPPP i will give brainliest

Answers

Answer:

3[tex]\sqrt{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{18}[/tex]

[tex]\sqrt{9}[/tex] [tex]\sqrt{2}[/tex]

3[tex]\sqrt{2}[/tex]

39. Boat ride
A boat travels 50 miles
due west before adjusting
its course 25 degrees north of west and traveling an
additional 35 miles. How far is the boat from its point of departure?
How far as the boat from
its point of departure?

Answers

Answer:

64.0655322 miles is maybe the answer

Helppp and explain too

Answers

Answer:

the first option

Step-by-step explanation:

I have attached the explanation. hope this help

HELP PLS ITS ALGEBRA 1

Answers

Answer:

[tex] - \frac{2}{6} [/tex]

Step-by-step explanation:

Use distributive property to simplify both sides.

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

Use the Golden Rule of Algebra: (What we do to one side, we must do to the other).

[tex] \frac{1}{6 } - x = - 2x - \frac{1}{6} [/tex]

[tex] \frac{1}{6} = - x - \frac{1}{6} [/tex]

[tex] \frac{2}{6 } = - x[/tex]

[tex]x = - \frac{2}{6} [/tex]

Answer:

Step-by-step explanation:

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

distribute in the fractions

[tex]\frac{1}{6}[/tex] - 1x = -2x - [tex]\frac{1}{6}[/tex]

subtract [tex]\frac{1}{6}[/tex]  from both sides

-[tex]\frac{1}{6}[/tex]+[tex]\frac{1}{6}[/tex]-1x = -2x -[tex]\frac{1}{6}[/tex]-[tex]\frac{1}{6}[/tex]

-1x = -2x -[tex]\frac{2}{6}[/tex]

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

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

[tex]\frac{1}{3}[/tex] = -x

- [tex]\frac{1}{3}[/tex] = x

x = - [tex]\frac{1}{3}[/tex]

see?  :/  

will make brainliest, please help​

Answers

-5x+4y=2
9x-4y=6

eliminate the 4y as a positive 4 + negative 4 =0
this will leave you with
-5x=2
9x=6
add them
4x=8
divide both sides by 4

x=2


to find y, plug in x=2 for any one of the original equations

-5(2)+4y=2
-10+4y=2

add 10 to both sides

4y=12

divide both sides by 4

y=3

the final answer is (2,3)

PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

Answers

c.

more styrofoam is discarded than paper and plastic combined

B

7000 / 20000 is about 1/3
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