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3 years ago

Please help me find the greatest common factor for these 2 problems..

Mathematics

2 answers:

Kisachek [45]3 years ago

4 0

A greatest common factor is the largest number that goes into two or more numbers (in this case two). To find the GCF of two numbers, we have to find the prime factorization (how to express a number as a product of prime numbers) and then see which numbers are common in both of the prime factorizations.

11. The prime factorization of 12 is 3 * 2 * 2. The prime factorization of 18 is 3 * 3 * 2. Looking at the prime factorizations, we can see that both of them have 3 and 2. That means that the GCF is 3 * 2 which is 6.

12. The prime factorization of 48 is 2 * 2 * 2 * 2 * 3. The prime factorization of 80 is 2 * 2 * 2 * 2 * 5. We see that the numbers shared are 2, 2, 2, and 2. That means that the GCF is 2 * 2 * 2 * 2 or 16.

makkiz [27]3 years ago

3 0

Problem 11.

12 = 2^2 * 3

18 = 2 * 3^2

Common factors with lower exponent: 2, 3

GCF = 2 * 3 = 6

11. Answer: 6

Problem 12.

48 = 2^4 * 3

80 = 2^4 * 5

Common factors with lower exponent: 2^4

GCF = 2^4 = 16

12. Answer: 16

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Punctele O, A, B, C sunt coliniare în această ordine, iar segmentele OA, AB și BC au lungimile exprimate în cm, prin numere natu

julia-pushkina [17]

Răspuns:

a) OC = 18cm

b) MN = 6cm

Explicație pas cu pas:

Găsiți diagrama la întrebarea atașată.

a) Din diagramă se poate observa că OC = OA + AB + AC

OC = 2n + 2n + 2 + 2n + 4

OC = 6n + 6

Următorul este să obțineți valoarea lui n:

OM = OA + AM

Să obținem segmentul AM;

Deoarece M este segmentul mijlociu al AC, atunci;

AM = AC / 2

AM = AB + BC / 2

AM = 2n + 2 + 2n + 4/2

AM = 4n + 6/2

AM = 2n + 3

Din moment ce OM = OA + AM

OM = 2n + 2n + 3

OM = 4n + 3

Dat fiind OM = 11

11 = 4n + 3

4n = 11-3

4n = 8

n = 2

Următorul pas este să calculați OC;

OC = 6n + 6

OC = 6 (2) + 6

OC = 18

Prin urmare, lungimea segmentului OC este de 18 cm

b) Această întrebare ne cere să găsim segmentul de linie MN.

Din diagramă, MN = AM - AN

Deoarece AM = 2n + 3 din întrebarea 1;

AM = 2 (2) +3

AM = 4 + 3

AM = 7

Acum, să obținem AN:

Din diagramă, AN = ON-OA și ON = OB / 2

AN = OB / 2 - OA

AN = (2n + 2n + 2) / 2 - 2n

AN = 4n + 2/2 - 2n

AN = 2n + 1 - 2n

AN = 2n-2n + 1

AN = 1

De la MN = AM - AN

MN = 7 - 1

MN = 6cm

Prin urmare, distanța dintre N, mijlocul segmentului OB și punctul M este de 6cm

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3 years ago

According to the US department of labor, total employment is expected to increase from 146 million in 2000 to 168 million in 201

saveliy_v [14]

Answer:

The percent increase in the employment from the year $2000$ to year $2010$ is $15.07\%$ .

Step-by-step explanation:

Given:

Employment in the year $2000$ $=146$ million.

Employment in the year $2010$ $=168$ million.

To find: The percent increase in the employment.

Solution: We have,

Employment in the year $2000$ $=146$ million.

Employment in the year $2010$ $=168$ million.

Increase in employment $=168-146=22$ million.

Percent increase $=\frac{\textrm{Increase in employment}}{\textrm{Original employment}}\times100\%$

Percent increase $=\frac{22}{146}\times100\%=15.07\%$

Hence, the percent increase in the employment from the year $2000$ to year $2010$ is $15.07\%$ .

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3 years ago