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2 years ago

The process of completing the square

Mathematics

1 answer:

iVinArrow [24]2 years ago

5 0

The method of completing the square can be used to determine the vertex of a function. he unknown value is -162

<h3>Completing the square of a function</h3>

The method of completing the square can be used to determine the vertex of a function.

Given the quadratic function

-2x² + 36x
-2(x²-18)

Complete the square

-2(x² - 18x + ( -9)²+ 9²)
-2(x-9)² + -2(81)
-2(x-9)² - 162

Compare

On comparing with the expression, you can see that the unknown value is -162

Learn more on completing the square here: brainly.com/question/13981588

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Answer:

$x = \frac{4}{9}$

Step-by-step explanation:

Given

Winning Percentage = 0.444 repeating

Required

Represent as a fraction

Represent the percentage with x

$x = 0.444$

Convert to fraction

$x = \frac{444}{1000}$

Next step, is to convert to fraction repeating

To do this, we simply subtract 1 from the denominator

$x = \frac{444}{1000 - 1}$

$x = \frac{444}{999}$

Simplify to the lowest term: Divide numerator and denominator by 37

$x = \frac{444/37}{999/37}$

$x = \frac{12}{27}$

Simplify to the lowest term: Divide numerator and denominator by 3

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There winning fraction is $\frac{4}{9}$

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Which point on the graph shows the amount of water in the bucket after 1 second? Hint: Type your answer in the form (x coordinat

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Answer:

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Step-by-step explanation:

<u>Graphs</u>

The graph shows the amount of water in gallons as a function of time in seconds.

We are required to find the amount of water in the bucked after 1 second. Since the graph does not show an exact location for t=1, we must find the equation of the line.

Two points are clear on the graph: (0,0) (12,5). This gives us the necessary information to find the equation of the line, which has the form:

$w=mt+b$

Where w is the amount of water in the bucket, t is the time, and m and b are two constants to be determined.

Using the point (0,0):

$0=m(0)+b$

It follows that b=0

The equation now takes the form:

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We find m:

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The final equation is:

$\displaystyle w=\frac{5}{12}\cdot t$

Substituting t=1:

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The bucket has 5/12 gallons of water at t=1 second. Expressing the answer as an ordered pair:

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