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3 years ago

Help me with this problem, please.

Mathematics

1 answer:

Novay_Z [31]3 years ago

7 0

Answer:

m² + 7m + 12 = 0 is equivalent to (5x - 2)² + 35x - 14 = -12 ⇒ C

Step-by-step explanation:

To solve this problem substitute m by 5x - 2 in each answer to find which one give you the equation of x

The given equation is (5x - 2)² + 35x - 14 = -12

Let us start with answer A

∵ m² - 7m + 12 = 0

∵ m = 5x - 2

- Substitute m by 5x - 2

∴ (5x - 2)² - 7(5x - 2) + 12 = 0

- Simplify the middle term

∵ - 7(5x - 2) = - 7(5x) + - 7(-2)

∴ - 7(5x - 2) = - 35x + 14

- Substitute - 35x + 14 in the equation

∴ (5x - 2)² - 35x + 14 + 12 = 0

- Subtract 12 from both sides

∴ (5x - 2)² - 35x + 14 = -12 ⇒ Not equal to the given equation

Let us check answer B

∵ m² - 7m - 2 = 0

∵ m = 5x - 2

- Substitute m by 5x - 2

∴ (5x - 2)² - 7(5x - 2) - 2 = 0

- Simplify the middle term

∴ -7(5x - 2) = - 35x + 14

- Substitute - 35x + 14 in the equation

∴ (5x - 2)² - 35x + 14 - 2 = 0

- Add 2 to both sides

∴ (5x - 2)² - 35x + 14 = 2 ⇒ Not equal to the given equation

Now let us check answer C

∵ m² + 7m + 12 = 0

∵ m = 5x - 2

- Substitute m by 5x - 2

∴ (5x - 2)² + 7(5x - 2) + 12 = 0

- Simplify the middle term

∵ 7(5x - 2) = 7(5x) + 7(-2)

∴ 7(5x - 2) = 35x - 14

- Substitute 35x - 14 in the equation

∴ (5x - 2)² + 35x - 14 + 12 = 0

- Subtract 12 from both sides

∴ (5x - 2)² + 35x - 14 = -12 ⇒ Equal to the given equation

Let us check answer D

∵ m² + 7m - 2 = 0

∵ m = 5x - 2

- Substitute m by 5x - 2

∴ (5x - 2)² + 7(5x - 2) - 2 = 0

- Simplify the middle term

∴ 7(5x - 2) = 35x - 14

- Substitute 35x - 14 in the equation

∴ (5x - 2)² + 35x - 14 - 2 = 0

- Add 2 to both sides

∴ (5x - 2)² + 35x - 14 = 2 ⇒ Not equal to the given equation

m² + 7m + 12 = 0 is equivalent to (5x - 2)² + 35x - 14 = -12

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Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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Solution to the problem

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The confidence interval would be given by this formula

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And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

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