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AlladinOne [14]

2 years ago

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I have to do a discussion pls help

2 answers:

nekit [7.7K]2 years ago

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Hey give me you intro.

I am new in brainly.

Pachacha [2.7K]2 years ago

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not clear picture

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Help find zeros for 9 and 10

Bingel [31]

<span><span> x4-10x2+9=0</span> </span>Four solutions were found :<span> x = 3 x = -3 x = 1 x = -1</span>

Step by step solution :<span>Step 1 :</span>Skip Ad
<span>Equation at the end of step 1 :</span><span> ((x4) - (2•5x2)) + 9 = 0 </span><span>Step 2 :</span>Trying to factor by splitting the middle term

<span> 2.1 </span>    Factoring <span> x4-10x2+9</span>

The first term is, <span> <span>x4</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> <span>-10x2</span> </span> its coefficient is <span> -10 </span>.
The last term, "the constant", is  <span> +9 </span>

Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 1</span> • 9 = 9</span>

Step-2 : Find two factors of   9  whose sum equals the coefficient of the middle term, which is <span> -10 </span>.

<span> -9 + -1 = -10 That's it</span>

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -1
                     <span>x4 - 9x2</span> - <span>1x2 - 9</span>

Step-4 : Add up the first 2 terms, pulling out like factors :
                    <span>x2 • (x2-9)</span>
              Add up the last 2 terms, pulling out common factors :
                     1 • <span>(x2-9)</span>
Step-5 : Add up the four terms of step 4 :
                    <span>(x2-1)  •  (x2-9)</span>
             Which is the desired factorization

<span>Trying to factor as a Difference of Squares : </span>

<span> 2.2 </span>     Factoring: <span> x2-1</span>

Theory : A difference of two perfect squares, <span> A2 - B2  </span>can be factored into <span> (A+B) • (A-B)

</span>Proof :<span>  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 <span>- AB + AB </span>- B2 =
        <span> A2 - B2</span>

</span>Note : <span> <span>AB = BA </span></span>is the commutative property of multiplication.

Note : <span> <span>- AB + AB </span></span>equals zero and is therefore eliminated from the expression.

Check : 1 is the square of 1
Check : <span> x2  </span>is the square of  <span> x1 </span>

Factorization is :       (x + 1)  •  (x - 1)

<span>Trying to factor as a Difference of Squares : </span>

<span> 2.3 </span>     Factoring: <span> x2 - 9</span>

Check : 9 is the square of 3
Check : <span> x2  </span>is the square of  <span> x1 </span>

Factorization is :       (x + 3)  •  (x - 3)

<span>Equation at the end of step 2 :</span> (x + 1) • (x - 1) • (x + 3) • (x - 3) = 0 <span>Step 3 :</span>Theory - Roots of a product :

<span> 3.1 </span> A product of several terms equals zero.<span>

</span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span>

</span>We shall now solve each term = 0 separately<span>

</span>In other words, we are going to solve as many equations as there are terms in the product<span>

</span>Any solution of term = 0 solves product = 0 as well.

<span>Solving a Single Variable Equation : </span>

<span> 3.2 </span>     Solve  :    x+1 = 0<span>

</span>Subtract  1 from both sides of the equation :<span>
</span>                     x = -1

<span>Solving a Single Variable Equation : </span>

<span> 3.3 </span>     Solve  :    x-1 = 0<span>

</span>Add  1 to both sides of the equation :<span>
</span>                     x = 1

<span>Solving a Single Variable Equation : </span>

<span> 3.4 </span>     Solve  :    x+3 = 0<span>

</span>Subtract  3 from both sides of the equation :<span>
</span>                     x = -3

<span>Solving a Single Variable Equation : </span>

<span> 3.5 </span>     Solve  :    x-3 = 0<span>

</span>Add  3 to both sides of the equation :<span>
</span>                     x = 3

Supplement : Solving Quadratic Equation Directly<span>Solving <span> x4-10x2+9</span> = 0 directly </span>

Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula

<span>Solving a Single Variable Equation : </span>

Equations which are reducible to quadratic :

<span> 4.1 </span>    Solve  <span> x4-10x2+9 = 0</span>

This equation is reducible to quadratic. What this means is that using a new variable, we can rewrite this equation as a quadratic equation Using  w , such that <span> w = x2</span> transforms the equation into :
<span> w2-10w+9 = 0</span>

Solving this new equation using the quadratic formula we get two real solutions :
   9.0000  or   1.0000

Now that we know the value(s) of <span> w</span> , we can calculate <span> x</span> since <span> x</span> <span> is  </span><span> √<span> w </span></span>

Doing just this we discover that the solutions of
  <span> x4-10x2+9 = 0</span>
  are either :
  x =√<span> 9.000 </span>= 3.00000 or :
  x =√<span> 9.000 </span>= -3.00000 or :
  x =√<span> 1.000 </span>= 1.00000 or :
  x =√<span> 1.000 </span>= -1.00000

Four solutions were found :<span> x = 3 x = -3 x = 1 x = -1</span>

<span>
Processing ends successfully</span>

5 0

3 years ago

What is the approximate solution of the linear system represented by the graph below

VashaNatasha [74]

ANSWER

The approximate solution is

$(4, - 1)$

EXPLANATION

The point of intersection of the two lines is the solution of the linear systems represented by the graph.

From the graph we can determine that each box is 2 units.

From the graph, when we start at O and count two boxes to the right and half box down, we obtain the point of intersection of the two lines to be
$(4, - 1)$

Note that since each box is two units, half way between the boxes gives one unit.

5 0

3 years ago

Five more than three times a number is three hundred five.Find the number

Sholpan [36]

Answer:

15

Step-by-step explanation: trust me i have had the before

7 0

3 years ago

What two numbers if multiplied equal 144.585?

sergij07 [2.7K]

48.195*3
idk if u wanted any numbers that work but ya hope that helped :)

6 0

3 years ago

Which of these statements is true for f(x)=(1/10)^x

lana66690 [7]

Step-by-step explanation:

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

Analyzing option A)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

Putting $x = 1$ in the function

$f\left(1\right)=\:\left(\frac{1}{10}\right)^1$

$f\left(1\right)=\:\left\frac{1}{10}\right$

So, it is TRUE that when $x = 1$ then the out put will be $f\left(1\right)=\:\left\frac{1}{10}\right$

Therefore, the statement that '' The graph contains $\left(1,\:\frac{1}{10}\right)$ '' is TRUE.

Analyzing option B)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

The range of the function is the set of values of the dependent variable for which a function is defined.

$\mathrm{The\:range\:of\:an\:exponential\:function\:of\:the\:form}\:c\cdot \:n^{ax+b}+k\:\mathrm{is}\:\:f\left(x\right)>k$

$k=0$

$f\left(x\right)>0$

Thus,

$\mathrm{Range\:of\:}\left(\frac{1}{10}\right)^x:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:f\left(x\right)>0\:\\ \:\mathrm{Interval\:Notation:}&\:\left(0,\:\infty \:\right)\end{bmatrix}$

Therefore, the statement that ''The range of $f(x)$ is $y > \frac{1}{10}$ " is FALSE

Analyzing option C)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

The domain of the function is the set of input values which the function is real and defined.

As the function has no undefined points nor domain constraints.

So, the domain is $-\infty \:$

Thus,

$\mathrm{Domain\:of\:}\:\left(\frac{1}{10}\right)^x\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:$

Therefore, the statement that ''The domain of $f(x)$ is $x>0$ '' is FALSE.

Analyzing option D)

Considering the function

$f\left(x\right)=\:\left(\frac{1}{10}\right)^x$

As the base of the exponential function is less then 1.

i.e. 0 < b < 1

Thus, the function is decreasing

Also check the graph of the function below, which shows that the function is decreasing.

Therefore, the statement '' It is always increasing '' is FALSE.

Keywords: function, exponential function, increasing function, decreasing function, domain, range

Learn more about exponential function from brainly.com/question/13657083

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3 0

3 years ago

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