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djyliett [7]
2 years ago
11

Determine whether 33 divides the product of 2⋅3⋅7⋅11. If it does divide the product, find the quotient. If it does not divide th

e product, indicate the smallest factor that should be included in the product to make it divisible by 33. Please explain
Mathematics
1 answer:
swat322 years ago
5 0

Answer:

The answer would be 30

Step-by-step explanation

For positive integers: 2 ⋅ 3 ⋅ 5 ⋅ 7 ⋅ 11 = 2310 For all integers: ± ( 2 ⋅ 3 ⋅ 5 ) = ± 30 For Gaussian integers: ± 1 ± 3 i and ± 3 ± i (all combinations of signs) Explanation: A prime number is a number whose only factors are itself, units and unit multiples of itself. So in the positive integers, the first few primes are: 2 , 3 , 5 , 7 , 11 , ... So the smallest composite positive integer with the five smallest prime positive integers as factors is: 2 ⋅ 3 ⋅ 5 ⋅ 7 ⋅ 11 = 2310 If we extend our interest to include negative integers, then the smallest primes are: 2 , − 2 , 3 , − 3 , 5 , − 5 , ... So the smallest composite integers with the five smallest prime integers as factors are: ± ( 2 ⋅ 3 ⋅ 5 ) = ± 30 If we consider Gaussian integers, then the smallest primes are: 1 + i , 1 − i , − 1 + i , − 1 − i , 1 + 2 i , 1 − 2 i , − 1 + 2 i , − 1 − 2 i , 2 + i , 2 − i , − 2 + i , − 2 − i , 3 , − 3 ,... So the smallest composite Gaussian integers with the five smallest prime Gaussian integers as factor are: ( 1 + i ) ( 1 + 2 i ) = − 1 + 3 i , 1 + 3 i , − 1 − 3 i , − 1 + 3 i , 3 + i , 3 − i , − 3 + i , − 3 − i

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Lelu [443]

Answer:

-1 1/4

Step-by-step explanation:

1/4 - (1 1/2)

Get a common denominator

1/4 - 1 2/4

Take the larger number and subtract the smaller number and take the sign of the larger

1 2/4 - 1/4 = 1 1/4

The sign of the larger was negative

-1 1/4

3 0
3 years ago
Solve or check ' whether your answer is correct or not 3x -9=12​
Kruka [31]

Answer:

x = 7

Step-by-step explanation:

3x - 9 = 12

3x = 12 + 9

3x = 21

x = 21 ÷ 3

x = 7

5 0
3 years ago
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A standard form of a parabola with points through (2, 0) (3, 2) (4, 6)
LenKa [72]

The standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

is y = x² - 3x + 2 ⇒ 3rd answer

Step-by-step explanation:

The standard form of a parabola is y = ax² + bx + c, where a, b , c are constant

To find a , b , c

  • You must have 3 points lie on the parabola
  • Substitute the coordinates of each point in the equation to make system of equations of a , b and c
  • Solve the system of equation to find them

∵ The standard form of a parabola is y = ax² + bx + c

∵ The parabola passes through points (2 , 0) , (3 , 2) , (4 , 6)

- Substitute the coordinates of each point in the equation

Point (2 , 0)

∵ x = 2 and y = 0

∴ 0 = a(2)² + b(2) + c

∴ 0 = 4a + 2b + c

- Switch the two sides

∴ 4a + 2b + c = 0 ⇒ (1)

Point (3 , 2)

∵ x = 3 and 2 = 0

∴ 2 = a(3)² + b(3) + c

∴ 2 = 9a + 3b + c

- Switch the two sides

∴ 9a + 3b + c = 2 ⇒ (2)

Point (4 , 6)

∵ x = 4 and y = 6

∴ 6 = a(4)² + b(4) + c

∴ 6 = 16a + 4b + c

- Switch the two sides

∴ 16a + 4b + c = 6 ⇒ (3)

Subtract equation (1) from equations (2) and (3)

∴ 5a + b = 2 ⇒ (4)

∴ 12a + 2b = 6 ⇒ (5)

- Multiply equation (4) by -2 to eliminate b

∴ -10a - 2b = -4 ⇒ (6)

- Add equations (5) and (6)

∴ 2a = 2

- Divide both sides by 2

∴ a = 1

Substitute the value of a in equation (4) to find b

∵ 5(1) + b = 2

∴ 5 + b = 2

- Subtract 5 from both sides

∴ b = -3

Substitute the value of a and b in equation (1) to find c

∵ 4(1) + 2(-3) + c = 0

∴ 4 - 6 + c = 0

- Add like terms

∴ -2 + c = 0

- Add 2 to both sides

∴ c = 2

Substitute the values of a , b , c in the standard form above

∵ y = ax² + bx + c

∵ a = 1 , b = -3 , c = 2

∴ y = (1)x² + (-3)x + (2)

∴ y = x² - 3x + 2

The standard form of a parabola with points through (2, 0) (3, 2)

(4, 6) is y = x² - 3x + 2

There is another solution you can substitute the x-coordinate of each point in each answer to find the corresponding value of y, if the value of y gives the same value of the y-coordinate of the point for the three points then this answer is the standard form of the parabola

Learn more:

You can learn more about the parabola in brainly.com/question/8054589

#LearnwithBrainly

6 0
3 years ago
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Ayudaaa plis<br>7-4= <br>6-2=<br>-3-2=<br>-8+9=<br>-9+5=<br>1+10=​
vladimir2022 [97]

Answer:

7-4=3

6-2=4

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Step-by-step explanation:

No es tan difícil, puedes g0oglearlo

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2 years ago
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Natasha2012 [34]
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2 years ago
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