Function P represents the perimeter, in inches, of a square with the side length x inches.

Mathematics

1 answer:

tatyana61 [14]3 years ago

7 0

Answer:

x =0,1,2,3,4,5,6

P(x) =0,4,8,12,16,20,24

Step-by-step explanation:

P(x)= 4x

4 x 1 = 4

4 x 2 = 8

4 x 3 =12

4 x 4 = 16

4 x 5 = 20

4 x 6 = 24

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Solve each quadratic equation by completing the square. Give exact answers--no decimals.

denis-greek [22]

Answer:

$x_1 = \frac{3}{2} + \frac{1}{2}(\sqrt{47})i\\\\x_2 = \frac{3}{2} - \frac{1}{2}(\sqrt{47})i\\\\$

Step-by-step explanation:

In this problem we have the equation of the following quadratic equation and we want to solve it using the method of square completion:

$x ^ 2 -3x +14 = 0$

The steps are shown below:

For any equation of the form: $ax ^ 2 + bx + c = 0$

1. If the coefficient a is different from 1, then take a as a common factor.

In this case $a = 1$ .

Then we go directly to step 2

2. Take the coefficient b that accompanies the variable x. In this case the coefficient is -3. Then, divide by 2 and the result squared it.

We have:

$\frac{-3}{2} = -\frac{3}{2}\\\\(-\frac{3}{2}) ^ 2 = (\frac{9}{4})$

3. Add the term obtained in the previous step on both sides of equality:

$x ^ 2 -3x + (\frac{9}{4}) = -14 + (\frac{9}{4})$

4. Factor the resulting expression, and you will get:

$(x -\frac{3}{2}) ^ 2 = -(\frac{47}{4})$

Now solve the equation:

Note that the term $(x -\frac{3}{2}) ^ 2$ is always > 0 therefore it can not be equal to $-(\frac{47}{4})$

The equation has no solution in real numbers.

In the same way we can find the complex roots:

$(x -\frac{3}{2}) ^ 2 = -(\frac{47}{4})\\\\x -\frac{3}{2} = \±\sqrt{-(\frac{47}{4})}\\\\x = \frac{3}{2} \±\frac{1}{2}\sqrt{-47}\\\\x = \frac{3}{2} \±\frac{1}{2}(\sqrt{47})i\\\\x_1 = \frac{3}{2} + \frac{1}{2}(\sqrt{47})i\\\\x_2 = \frac{3}{2} - \frac{1}{2}(\sqrt{47})i\\\\$