Mathematics: Which of the following constants can be added to x^2 + 2/3x to form a perfect square trinomial?

Which of the following constants can be added - id1960694, michaelchavez6959127

Ответ:

corianrigby97

31.12.2021

Take 1/2 of the linear coefient and square it

2/3 times 1/2=1/3
square 1/3 to get 1/9

the constnat is 1/9
it would factor to (x+1/3)^2

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Ответ:

lgary9462

31.12.2021

Mathematics

$\frac{1}{9}$ is to be added to make $x^2+\frac{2}{3}x$ a perfect square trinomial as $(x+\frac{1}{3})^{2}$

Step-by-step explanation:

Given : $x^2+\frac{2}{3}x$

We have to find what can be added to $x^2+\frac{2}{3}x$ to form a perfect square trinomial.

Perfect square trinomial is of the form (a+b)^2

Consider the given expression $x^2+\frac{2}{3}x$

Using algebraic identity (a+b)^2=a^2+b^2+2ab ,

Comparing , we get, a = x ......(1)

$2ab=\frac{2}{3}x$

Uisng (1) , we get,

$2b=\frac{2}{3} \\\\ \Rightarrow b=\frac{1}{3}$

To make it a perfect square trinomial we need to add b^2 term

$b^2=\frac{1}{9}$

Thus, $\frac{1}{9}$ is to be added to make $x^2+\frac{2}{3}x$ a perfect square trinomial as $(x+\frac{1}{3})^{2}$

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Ответ:

machucagm01

25.07.2022

Mathematics

The nearest distance between the two points (-6,5) and (-1,-7) is 13 units, which obtained by graphical and formula method.

Step-by-step explanation:

The given is,

Two points are (-6,5) and (-1.-7)

Step:1

By graphical method,

Locate the points (-6,5) and (-1,-7) in the graph.

First point (-6,5)

The values x=-6 and y=5 noted in the graph

Second point (-1, -7)

The values x=-1 and y=-7 noted in the graph

Now join the two points, measure the distance between two points,

Distance between two points are 13 units, some times it becomes 12,99 or 13.1 we need to convert the answer in nearest whole number.

( OR )

Step:1

By formula method,

Distance = $\sqrt{(x_{2}-x_{1} ) ^{2} +(y_{2}-y_{1} ) ^{2} }$

Where,

(-6, 5) are ( $x_{1} ,y_{1}$ )

(-1,-7) are ( $x_{2} ,y_{2}$ )

From equation,

= $\sqrt{(-1+6 ) ^{2} +(-7-5 ) ^{2} }$

= $\sqrt{(5 ) ^{2} +(-12 ) ^{2} }$

= $\sqrt{25+144}$

= $\sqrt{169}$

Distance = 13

Result:

The nearest distance between the two points (-6,5) and (-1,-7) is 13 units, which obtained by graphical and formula method.

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Which of the following constants can be added to x^2 + 2/3x to form a perfect square trinomial?

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