How do you identify the opposite and the absolute value of a rational number

2 answers:

5 0

"The absolute value of an integer is its distance from zero on a number line. For example, the absolute value of -8 is +8, because -8 is 8 units from zero on the number line. Note that the absolute value of any positive or negative integer is positive." http://www.mathhelp.com/how_to/integers_and_the_number_line/opposites_and_absolute_value/

zhenek [66]3 years ago

4 0

Opposite:
Just change the sign.
If it's a positive number, make it negative.
If it's a negative number, make it positive.

Absolute value:
Even easier.
Just throw away the sign, and you have it.

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Express 2x^2+8x+3 in the form 2(x+p)^2+q

e-lub [12.9K]

Answer:

2(x + 2)² - 5

Step-by-step explanation:

Given

2x² + 8x + 3

To obtain the required form use the method of completing the square.

The coefficient of the x² term must be 1, thus factor 2 out of 2x² + 8x

= 2(x² + 4x) + 3

add/subtract ( half the coefficient of the x- term)² to x² + 4x

= 2(x² + 2(2)x + 4 - 4) + 3

= 2(x + 2)² - 8 + 3

= 2(x + 2)² - 5

with p = 2 and q = - 5

4 0

3 years ago

The proof that point (1,root 3) lies on the circle that is centered at the origin and contains the point (0,2) is found in the t

AURORKA [14]

<h2>Answer:</h2>

D. Distance formula

<h2>Step-by-step explanation:</h2>

$The \ \mathbf{distance} \ d \ between \ the \ \mathbf{points} \ (x_{1},y_{1}) \ and \ (x_{2},y_{2}) \ in \ the \ plane \ is:\\ \\ d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

As in the statement:

<em>The distance form</em> $(0,0)$ to $(0,2)$ is $\sqrt{(0-0)^2+(2-0)^2}=\sqrt{2^2}=2$ <em>whose justification is the </em><em>Distance Formula. </em>

<em />

Here in this statement the justification is also the Distance Fromula, so we take the distance from $(0,0) \ to \ (1,\sqrt{2})$ whose result is also 2 and is the radius of the circle.