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3 years ago

Which exponential equation correctly rewrites this logarithmic equation? log6 18=x

Mathematics

1 answer:

Zanzabum3 years ago

3 0

Given:

The logarithmic equation is:

$\log_618=x$

To find:

The exponential equation of this logarithmic equation.

Solution:

According to the properties of logarithm:

$\log_bm=x\Leftrightarrow m=b^x$

We have,

$\log_618=x$

Here, $b=6, m=18$ . Using the above property of logarithm, we get

$18=6^x$

Therefore, the required exponential equation is $18=6^x$ .

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Is $1.45 a natural number ,integer, irrational number, or a real number

Rainbow [258]

Answer:

Real Number

Step-by-step explanation:

These are numbers which include both rational AND irrational!!!

Doesn't go on forever.

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3 years ago

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Write the cubic polynomial function f(x)in expanded form with zeros −6,−5,and −1, given that f(0)=60

RSB [31]

Answer:

$f(x)=2x^{3}+24x^{2}+82x+60$

Step-by-step explanation:

we know that

The roots of the polynomial are the values of x when the value of the polynomial f(x) is equal to zero

The roots of the polynomial function are

x=-6 -----> (x+6)=0

x=-5 -----> (x+5)=0

x=-1 -----> (x+1)=0

The equation of the cubic polynomial is

$f(x)=a(x+6)(x+5)(x+1)$

where

a is the leading coefficient

Remember that

f(0)=60

That means ------> For x=0 the value of f(x) is equal to 60

substitute the value of x and the value of y in the function and solve for a

$60=a(0+6)(0+5)(0+1)$

$60=a(6)(5)(1)$

$60=30a$

$a=2$

$f(x)=2(x+6)(x+5)(x+1)$

Applying the distributive property

Convert to expanded form

$f(x)=2(x+6)(x+5)(x+1)\\\\f(x)=2(x+6)(x^{2}+x+5x+5)\\\\f(x)=2(x+6)(x^{2}+6x+5)\\\\f(x)=2(x^{3}+6x^{2}+5x+6x^{2}+36x+30)\\\\f(x)=2x^{3}+24x^{2}+82x+60$

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3 years ago

Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x?

jeka94

by Quadratic formula , $x^2 + 20 = 2x$ , values of x are $x = 1 \pm (1)i\sqrt{19}}$ . None of mentioned options are correct according to question!

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

Here we have , expression x2 + 20 = 2x or , $x^2 + 20 = 2x$ .

We know that Quadratic formula is :

$x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$

$x^2 + 20 = 2x$

⇒ $x^2-2x+20=0$

$a=1\\b=-2\\c=20$

Putting this value in equation $x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$ :

⇒ $x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$

⇒ $x = \frac{-(-2) \pm \sqrt{(-2)^{2}-4(1)(20)}}{2(1)}$

⇒ $x = \frac{2 \pm \sqrt{4-80}}{2}$

⇒ $x = (\frac{2 \pm 2i\sqrt{19}}{2})$

⇒ $x = 1 \pm (1)i\sqrt{19}}$

Therefore , by Quadratic formula , $x^2 + 20 = 2x$ , values of x are $x = 1 \pm (1)i\sqrt{19}}$ . None of mentioned options are correct according to question!

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3 years ago

Explain what is meant by confounding. what is a lurking variable? what is a confounding variable?

miss Akunina [59]

Explain what is meant by confounding. what is a lurking variable? what is a confounding variable?

Answer:

A Confounding is the variable that is considered in a research study, and could overall influence the relations between the variables in the study. For example, students wanting to join AP English next semester were told to write a six page essay. When the students turned in their papers and teachers say the difference and grades they believed that the variable was the time that the students handed in the paper. They thought that if the student handed in their paper later than another student that they would receive a lower score, but this was not the case. When asking the students how they prepared for the paper, students replied with different answers. Those who outlined and used other literature for reference scored much higher than those who only used prior knowledge to write their essays. In this study, the lurking variable would be the presence of an outline.

Lurking variable: A variable that is not considered in a research study that could influence the relations between the variables in the study

Confounding variable: A variable that is considered in a research study that could influence the relations between the variables in the study

To Know more about Confounding Variable

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Answer:

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