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Schach [20]
2 years ago
15

75,15,3 find the 6th term

Mathematics
1 answer:
Karolina [17]2 years ago
8 0

Answer:

0.024

Step-by-step explanation:

75, 15, 3, ...

Now, let's take a look at thus pattern.

You'll notice how the numbers decrease.

Divide 75 by 5.

We get 15

Divide 15 by 5.

We get 3.

Then we have the pattern now.

3 ÷ 5 = 0.6 (4th term)

0.6 ÷ 5 = 0.12 (5th term)

0 12 ÷ 5 = 0.024 (6th term)

I hope it helps.

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15. Rewrite the given functions in
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15. The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26

17. The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5

Step-by-step explanation:

Any quadratic function has:

1. A vertex form form f(x) = a(x - h)² + k, where (h , k) are the

   coordinates of its vertex point

2. A standard form g(x) = ax² + bx + c, where a , b , c are constant and

   a is the coefficient of x², b is the coefficient of x and c is the

    y-intercept

3. the x-coordinate of the vertex point h = \frac{-b}{2a} and

    k = f(h)

15.

∵ f(x) = x² + 8x - 10

∴ a = 1 and b = 8

∵ h = \frac{-b}{2a}

∴ h = \frac{-8}{2(1)}=-4

∴ h = -4

∵ k = f(h)

∴ k = f(-4)

- Substitute x by -4 in f(x)

∴ k = (-4)² + 8(-4) - 10

∴ k = 16 - 32 - 10

∴ k = -26

∴ f(x) = (x - -4)² + (-26)

∴ f(x) = (x + 4)² - 26

The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26

17.

∵ g(x) = (x + 3)² - 4

- Lets solve the power 2 of the bracket:

 (1st + 2nd)² = (1st)(1st) + 2(1st)(2nd) + (2nd)(2nd)

∵ (x + 3)² = (x)(x) + 2(x)(3) + (3)(3)

∴ (x + 3)² = x² + 6x + 9

∴ (x + 3)² - 4 = (x² + 6x + 9) - 4

∵ 9 - 4 = 5

∴ (x + 3)² - 4 = x² + 6x + 5

The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5

Learn more:

You can learn more about the vertex form of quadratic function in brainly.com/question/9390381

#LearnwithBrainly

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How to solve rational equations
VashaNatasha [74]

Answer:

A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.

   Find the common denominator.

   Multiply everything by the common denominator.

   Simplify.

   Check the answer(s) to make sure there isn't an extraneous solution.

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