All categories

3 years ago

Prove that: (1213–1212+1211)(119–118+117) is divisible by 3, 7, 19, and 37.

Mathematics

1 answer:

crimeas [40]3 years ago

3 0

Answer:

It is only divisible by 3 but not divisible by 7, 19, and 37.

Step-by-step explanation:

The given expression is (1213 - 1212 + 1211)(119 - 118 + 117) and we have to prove whether this expression is divisible by 3, 7, 19 and 37 or not.

Now, the expression is (1213 - 1212 + 1211)(119 - 118 + 117)

= 1212 × 118

= 3 × 2 × 2 × 101 × 2 × 59 {Those are the prime factors of the expression}

Now, it is clear that the expression 1212 × 118 is only divisible by 3 but not divisible by 7, 19, and 37. (Answer)

You might be interested in

Elena received a $30 gift for her birthday. She plans to use it to buy one or more books. Elena will have to pay 8% sales tax on

11111nata11111 [884]

The cost of book has to be less than or equal to 26.39.

The amount of money Elena can buy has to be less than or equal to $30. Thus, the inequality sign to be used is the less than or equal to sign.

(1 + tax)cost of books + cost of bus fare ≤ value of the gift

1.08c + 1.5 ≤ 30

In order to determine the maximum cost of books, take the following steps:

Combine similar terms

1.08c ≤ 30 - 1.5

Add similar terms together

1.08c ≤ 28.50

Divide both sides of the equation by 1.08

c ≤ 28.50 / 1.08

c ≤ 26.39

To learn more about taxes, please check: brainly.com/question/25311567

3 0

3 years ago

Which statement is true regarding the graphed functions?

Vladimir79 [104]

let's analyze each case to determine the solution

case 1) f(0) = 2 and g(–2) = 0

For x=0-----> find the value of f(0) in the graph-----> f(0)=4

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 1) is false

case 2) f(0) = 4 and g(–2) = 4

For x=0-----> find the value of f(0) in the graph-----> f(0)=4

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 2) is false

case 3) f(2) = 0 and g(–2) = 0

For x=2-----> find the value of f(2) in the graph-----> f(2)=0

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 3) is true

case 4) f(–2) = 0 and g(–2) = 0

For x=-2-----> find the value of f(-2) in the graph-----> f(-2) is greater than 12

For x=-2-----> find the value of g(-2) in the graph-----> g(-2)=0

therefore

the statement of the case 4) is false

therefore

the answer is

f(2) = 0 and g(–2) = 0-------> this statement is true

6 0

4 years ago

Read 2 more answers

A regular assignment has 15 sides.Calculate the size of each interior angle

MariettaO [177]

Answer:

The measure of an interior angle of a regular 15-gon is 120°.

Step-by-step explanation:

We need to determine the measure of the size of an interior angle of a regular 15-gon having 15 sides.

Thus,

The number of sides n = 15

Hence,

Using the formula to determine the measure of an interior angle of a regular 15-gon is given by

(n - 2) × 180° = n × interior angle

substitute n = 15

(15 - 2) × 180 = 15 × interior angle

13 × 180 = 15 × interior angle

Interior angle = (10 × 180) / 15

= 1800 / 15

= 120°

Therefore, the measure of an interior angle of a regular 15-gon is 120°.

6 0

3 years ago

Millie borrowed $20 from her dad. Explain why this situation indicates a negative number for Millie even though $20 is a positiv

Nata [24]

Millie will have to pay the $20 back, and as she already has no money, she's now $20 in debt

7 0

3 years ago

Read 2 more answers

Choosing a number divisible by 3

sergejj [24]

Answer:

9 or 6 owo

Step-by-step explanation:

uwu

4 0

3 years ago