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4 years ago

Describe two methods for finding the prime factorization of a number

1 answer:

7 0

By definition, a prime number is a whole number greater than or equal to 1 that is not divisible by any number other than 1 or the number itself. There are two methods of finding the prime numbers to a composite number: by factor tree, and by factoring. The two methods actually have the same concept. They just differ in the illustration for better understanding.

Factor tree is used by finding any pair of number whose product is the given number. If one of those numbers are not prime, find another pair again whose product is that number. It is repeated until all you have left are prime numbers. For example:

64
/ \
4 16
/ \ / \
2 2 4 4
/ \ / \
2 2 2 2

Therefore, the prime factorization of 64 is 2×2×2×2×2×2. The next method is just factoring. For example:

64 = (16)(4) = (4×4)(2×2) = (2×2×2×2)(2×2)
64 = 2×2×2×2×2×2

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Which statements are always true regarding the diagram?

Gekata [30.6K]

Answer:

m∠5+m∠6=180°

m∠2+m∠3=m∠6

m∠2+m∠3+m∠5=180°

Step-by-step explanation:

Verify each option

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

therefore

Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

Their sum is always 180 degrees

therefore

This option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

therefore

This option is always true

case E) we have

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

therefore

This option is always true

7 0

3 years ago

Read 2 more answers

Suppose the circumference of a circle is \color{blue}{16\pi}16πstart color blue, 16, pi, end color blue. what is its radius?

Sauron [17]

The circumference of a circle is equal to its diameter multiplied by pi. Since the circumference here is 16*pi, the diameter of the circle is 16 units. The diameter of a circle is two times the radius, so we divide 16 in half and find our result that the radius is 8 units.

3 0

4 years ago

What is the greatest value in the range of f(x)=x^2-5 for the domain {-5, -3, 0, 1, 2}?

kati45 [8]

$f(x)=x^2-5;\ x\in\{-5;-3;\ 0;\ 1;\ 2\}\\\\f(-5)=(-5)^2-5=25-5=20\\f(-3)=(-3)^2-5=9-5=4\\f(0)=0^2-5=-5\\f(1)=1^2-5=1-5=-4\\f(2)=2^2-5=4-5=-1\\\\Answer:f(-5)=20$