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3 years ago

358. Now consider the family of lines ax + by = c such that a, b and c are consecutive multiples

1 answer:

4 0

Any subsequence of consecutive integers of length 9 that has a term ... Assume now that we have found an n-digit number m divisible by 2n made out of ... the set of ordered triples of people (a, b, c) such that c is either a ... again we have two families of lines, but such that M1j are all of the same color; ... a1(x)x2 − ax(x)x = 0.

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Sin( X+Y ) = cos( X−Y ) = 1,<br> find the value of X and Y.

iris [78.8K]

answer x = 225 and y = -135

Step-by-step explanation:

x+y = 90 and x= 90-y and x -y = 360 so 90-y -y = 360

7 0

3 years ago

When reading a book, Charlie made a list by writing down the page number of the last page he finished reading at the end of each

Assoli18 [71]

Answer:

No. of pages he read by the end of the 8th day = 425

Step-by-step explanation:

Charlie started from page 1 and read the same number of pages each day. Suppose x is the number of pages he read each day, the last page he read on the first day would be:

This would be the first number he noted on the list.

The second page number can be determined by adding the number of pages he read to the last page for day 1.

Last page for day 2 = 1 + x + x

= 1 + 2x

Similarly, the last page he read on the third day is:

Last page for day 3 = 1 + 3x. Similarly,

Last page for day 4 = 1 + 4x

Last page for day 5 = 1 + 5x

Last page for day 6 = 1 + 6x

Last page for day 7 = 1 + 7x

Last page for day 8 = 1 + 8x

His Mom added all of the page numbers and got a total of 432. So,

432 = 1+x + 1+2x + 1+3x + 1+4x + 1+5x + 1+6x + 1+7x + 1+8x

432 = 8 + 8x

8x = 432-8

8x = 424

x = 424/8

x = 53

By the end of the 8th day he actually read 1 + 8x pages. Substituting the value of x in this expression, we get:

No. of pages he read by the end of the 8th day = 1 + 8(53)

= 1 + 424

No. of pages he read by the end of the 8th day = 425

4 0

3 years ago

What is the sum of the prime factors of 1260? For example, the sum of the prime factors of 20

Genrish500 [490]

Answer:

The answer is 22

Step-by-step explanation:

Do Prime Factorization of 1260

(as shown in the picture I attached)

Prime factors of 1260 = 2, 2, 3, 3, 5, 7

Now to get the sum of the prime factors of 1260, you just have to add all the factors

2 + 2 + 3 + 3 + 5 + 7 = 22

Hope this helps!

3 0

2 years ago

10) Show that in a group of 10 people (where any two people are either friends or enemies), there are either three mutual friend

ddd [48]

Answer with explanation:

Number of People in the group =10 People

The combination between two people is that, they can be either friends or enemies.

Total number of Possible Relation

=18 +16+14+12+10+8+6+4+2

= 90 Relations in all.

Out of 90 relations , 45 will be friends and 45 will be enemies.

⇒Now, we have to prove that, between 10 people, there are either three mutual friends or four mutual enemies, and there are either three mutual enemies or four mutual friends.

→→If there are three mutual friends, total number of people in the group =3 ×2=6 people in the group

And, four mutual enemies in a group means there are 2 people in each group.

So, total number of people if we combine the two groups in which there are either three mutual friends or four mutual enemies

=6 +4

=10

Hence proved.

→→→→Second part is ,in this group there can be either three mutual enemies or four mutual friends.

⇒If there are three mutual enemies, total number of people in the group =3 ×2=6 people in the group

And, four mutual friends in a group means there are 2 people in each group.

So, total number of people if we combine the two groups in which there are either three mutual enemies or four mutual enemies

=6 +4

=10

Hence proved.

3 0

3 years ago

Merry has twice as many pencils as sue. If X represents the number of pencils Merry has. Write an expression to represent the nu

Rus_ich [418]

Merry has twice as many pencils, so Sue will have half as many. Thus, S=X/2, where S is the amount of Sue's pencils.

6 0

3 years ago

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