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zavuch27 [327]
3 years ago
8

What are the next two terms in the pattern 3, 6, 5, 10, 18, 17...?

Mathematics
1 answer:
Evgen [1.6K]3 years ago
3 0
20 and 19 because you just need to follow the pattern.
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Bethany needs to solve the equation -x^2 + 4x = x - 4.
notsponge [240]

Answer:

The system of equations she could write is:

   y = -x² + 4x

   y = x - 4

The solutions are (-1 , -5) and (4 , 0)

Step-by-step explanation:

-x² + 4x = x - 4

That means two equations one quadratic which is in the left hand side and the other is linear which is in the right hand side.

They represented graphically by a parabola and a line, the solution of it will be the points of intersection of the two graphs

To find the system of equations take each side and equate it by y

∵ y = -x² + 4x

∵ y = x - 4

∴ The system of equations is:

   y = -x² + 4x

   y = x - 4

Let us solve this system using -x² + 4x = x - 4

∵ -x² + 4x = x - 4

- Subtract x from both sides

∴ -x² + 3x = -4

- Add 4 to both sides

∴ -x² + 3x + 4 = 0

- Multiply both sides by -1

∴ x² - 3x - 4 = 0

Let us use the factorization to solve it

∵ x² = (x)(x)

∵ -4 = (1)(-4)

∵ (x)(1) = x

∵ (x)(-4) = -4x

∵ x + -4x = - 3x ⇒ middle term

∴ The factors of x² - 3x - 4 are (x + 1)(x - 4)

- Substitute x² - 3x - 4 by its factors

∴ (x + 1)(x - 4) = 0

Equate each factor by 0 to find the values of x

∵ x + 1 = 0

- Subtract 1 from both sides

∴ x = -1

∵ x - 4 = 0

- Add 4 to both sides

∴ x = 4

Substitute the values of x in the equation y = x - 4 to find y

∵ y = -1 - 4

∴ y = -5

∵ y = 4 - 4

∴ y = 0

The solutions are (-1 , -5) and (4 , 0)

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Answer: $24

Step-by-step explanation:

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Parallel lines have the same slope. So if a line has a slope of 2, a line parallel to it also has a slope of 2.

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80 dollars for 16 tickets written as a unit rate, what is it?
shepuryov [24]

Answer:

5 dollars a ticket. Divide 80/16 to get tour answer.

Step-by-step explanation:

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