Greatest common factors
1. 12 & 18
2. 9 & 35
3. 15 & 25

1. 6

2. 1

3. 5

Step-by-step explanation:

You can find the GCF by finding the prime factorization of the numbers.

1. 12 and 18

12= 2*2*3

18=2*3*3

They both have 2 and 3 in common, so their GCF is 2*3 or 6.

2. 9 and 35

9= 3*3

35= 5*7

Although they don't have any prime numbers in common, all numbers have the factor one in common, so they're relatively prime but their GCF is 1.

3. 15 and 25

15 = 3*5

25= 5*5

They have one 5 in common so their GCF is 5.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐