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goldenfox [79]
3 years ago
5

Apply the laws of exponents, calculate the result and express the result in scientific notation, and as a decimal: (8.1*10^-4)^2

Mathematics
1 answer:
AfilCa [17]3 years ago
4 0
<h3>Answer:</h3>
  • the result in scientific notation is 6.561×10⁻⁷
  • the result as a decimal is 0.000 000 656 1
<h3>Explanation:</h3>

The rules of exponents say the exponent outside parentheses applies to each factor inside parentheses.

... (8.1*10^-4)^2 = 8.1^2 × (10^-4)^2

... = 65.61 × 10^-8

... = 6.561 × 10^-7 . . . . adjust to scientific notation with one digit left of the decimal point

The exponent of -7 means the decimal point in the decimal number is 7 places to the left of where it is in scientific notation. That is ...

... 6.561 × 10^-7 = 0.0000006561

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2 years ago
Which values for h and k are used to write the function f of x = x squared 12 x 6 in vertex form?
Nesterboy [21]

The values of h and k when f(x) = x^2 + 12x + 6 is in vertex form is -6 and -30

<h3>How to rewrite in vertex form?</h3>

The equation is given as:

f(x) = x^2 + 12x + 6

Rewrite as:

x^2 + 12x + 6 = 0

Subtract 6 from both sides

x^2 + 12x = -6

Take the coefficient of x

k = 12

Divide by 2

k/2 = 6

Square both sides

(k/2)^2 = 36

Add 36 to both sides of x^2 + 12x = -6

x^2 + 12x + 36= -6 + 36

Evaluate the sum

x^2 + 12x + 36= 30

Express as perfect square

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Subtract 30 from both sides

(x + 6)^2 -30 = 0

So, the equation f(x) = x^2 + 12x + 6 becomes

f(x) = (x + 6)^2 -30

A quadratic equation in vertex form is represented as:

f(x) = a(x - h)^2 + k

Where:

Vertex = (h,k)

By comparison, we have:

(h,k) = (-6,-30)

Hence, the values of h and k when f(x) = x^2 + 12x + 6 is in vertex form is -6 and -30

Read more about quadratic functions at:

brainly.com/question/1214333

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