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Nata [24]
3 years ago
7

The fundamental theorem of Arithmetic

Mathematics
1 answer:
asambeis [7]3 years ago
7 0

Answer:

1. {2, 3, 5, 7, 11, 13, 17, 19}

2. {23, 29, 31, 37}

3. {7, 13, 19}

4. {37, 43}

Step-by-step explanation:

By extension, the set E, is given by:

E={2, 3, 5, 7, 11, ...}

In the same way, the set T, is given by:

T={4, 7, 10, 13, ...} = {t/ t is integer and (z-1) it is divisible by 3}

Let's call E1 the set of primes in E between 1 and 20.

Let's call E2 the set of primes in E between 21 and 40.

Let's call T1 the set of primes in T between 1 and 30.

Let's call T2 the set of primes in T between 31 and 60. Thus,

E1={2, 3, 5, 7, 11, 13, 17, 19}

E2={23, 29, 31, 37}

T1={7, 13, 19}

T2={37, 43}

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The median of 10,31,36,36,38,42,47,48,49,52
olga2289 [7]
So,

To find the median, arrange all the numbers from least to greatest.

10, 31, 36, 36, 38, 42, 47, 48, 49, 52

The middle two numbers are 38 and 42.  Take their average.
40

40 is the median of 10, 31, 36, 36, 38, 42, 47, 48, 49, and 52.
7 0
3 years ago
What is the volume of one cube
snow_tiger [21]
The answer would just be 64 cubic inches. The volume of a cube is 64 cubic inches.Hope this helps.
3 0
3 years ago
Which value of b would make 16x²-bx + 25 a perfect square trinomial?
blondinia [14]

Answer:

b = 40 and -40

Step-by-step explanation:

General form of Perfect square trinomial is a 2 + 2 a b + b 2

Therefore from 16 x 2 − b x + 25 a 2 = √ 16 x 2 , b 2 = 25 , then a = ± 4 x , b = ± 5 take consideration a=4x and b=-5 (different sign), then − b x = 2 ( 4 x ) ( − 5 ) − b x = − 40 x b = 40

The perfect square is ( 4 x − 5 ) 2 = 16 x 2 − 40 x + 25 .

if we consider a=4x and b=5 (same sign), then − b x = 2 ( 4 x ) ( 5 ) − b x = 40 x b = − 40

The perfect square is ( 4 x + 5 ) 2 = 16 x 2 + 40 x + 25 .

The first solution ( 4 x − 5 ) 2 is the best solution after comparing the expression given.  I hope this helps, xx .

8 0
3 years ago
find the smallest number by which 339 must be multiplied so that the product is a perfect cube. also find the cube root of the p
Murljashka [212]

Answer:

<em>The smallest number is 114921 and the cube root of the result is 339</em>

Step-by-step explanation:

The number 339 can be factored as:

339 = 3 * 113

Both factors are prime, thus to produce a perfect cube, we must multiply by each factor to the power of 2, that is:

3^2*113^2=114921

When we multiply 339 by 114921 we get 38958219, a perfect cube which cube root is 339.

Thus, the smallest number is 114921 and the cube root of the result is 339

4 0
3 years ago
What is the area of the polygon (-3,3) (-3,-1) (4,-1) (4,3) with the given verticies
Monica [59]

The area of the polygon with the given vertices: (-3,3) (-3,-1) (4,-1) (4,3) is 28 square units

<h3>What is rectangle ?</h3>

A rectangle is a polygon with four sides. The opposite sides of a rectangle are equal while the angles at the vertex is orthogonal

<h3>How to solve for area of the rectangle</h3>

The following are the data given in the question

polygon with the given vertices' as:

(-3,3)

(-3,-1)

(4,-1)

(4,3)

plotting the given polygon shows it is a rectangle with sides

Length, L =  7 units

Width, w = 4 units

Area if a rectangle is given by

= L * w

= 7 * 4

= 28 square units

The area of the polygon is 28 square units

Learn more in area of rectangle: brainly.com/question/16239445

#SPJ1

5 0
1 year ago
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