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vagabundo [1.1K]
2 years ago
14

Help please i dont get it

Mathematics
2 answers:
ale4655 [162]2 years ago
8 0

Answer:

  (c)  x = 2 and x = -8

Step-by-step explanation:

The rules of logarithms let you rewrite this as a quadratic equation. That equation will have two (2) potential solutions. We know from the domain of the log function that any negative value of x will be an extraneous solution.

__

The rules of logarithms that apply are ...

  \log(a)+\log(b)=\log(ab)\qquad\text{all logarithms to the same base}\\\\\log_b(a)=c\ \Longleftrightarrow\ b^c=a\\\\

__

<h3>take antilogs</h3>

We can rewrite the equation so that only one logarithm is involved. Then we can take antilogs.

  \log_4(x)+\log_4(x+6)=2\\\\\log_4(x(x+6))=2\qquad\text{using the first rule}\\\\4^2=x(x+6)\qquad\text{using the second rule}

__

<h3>solve the quadratic</h3>

Adding (6/2)² = 9 to both sides will "complete the square."

  16 +9 = x² +6x +9 . . . . . . . add 9

  25 = (x +3)²

  ±√25 = x +3 = ±5 . . . . . take the square root(s)

  x = -3 ±5 = {-8, +2}

The two potential solutions are x = 2 and x = -8.

Sindrei [870]2 years ago
6 0

\\ \rm\Rrightarrow log_4x+log_4(x+6)=2

\\ \rm\Rrightarrow log_4(x(x+6))=2

  • Take 4 right

\\ \rm\Rrightarrow x(x+6)=4^2

\\ \rm\Rrightarrow x^2+6x=16

\\ \rm\Rrightarrow x^2+6x-16=0

\\ \rm\Rrightarrow x^2-2x+8x-16=0

\\ \rm\Rrightarrow x(x-2)+8(x-2)=0

\\ \rm\Rrightarrow (x+8)(x-2)=0

\\ \rm\Rrightarrow x=-8\:and\:x=2

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Step-by-step explanation:

To find length we have to conver mixed fraction to improper fraction


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First we find the total length of wall remain after picture was hung to the wall.


Length of wall remain vacant =\frac{29}{2}-\frac{41}{4}


Taking LCM and solving we get


=\frac{58-41}{4} =\frac{17}{4}


Total length of wall remain vacant =\frac{17}{4}


As the picture to be centered in wall, therefore space feom one edge of wall will be half that of length remain vacant as the same length to be left vacant feom both sides.


Space from one edge =\frac{17}{4} \times \frac{1}{2}


= \frac{17}{8}

=2{\frac{1}{8}}


Length from the edge will be =2{\frac{1}{8}} feet

6 0
4 years ago
Find the value of x in the parallelogram below.
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A shop sells bag of peanuts for two dollars and a bag of walnuts for five dollars at nine bags of purchase for total cost of $36
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a point with a positive x-coordinate and a negative y- coordinate is reflected over the y-axis . what sentence will describe the
scoray [572]

Answer:

The sentence that describes the reflected point (x,-y) over the y-axis

Step-by-step explanation:

Since not sure if specific options are available lets answer this question in a general notation.

Let us consider the Co-ordinate system in two dimensions (i.e.  and ); where the horizontal line represents the  values and the vertical line representes the  values.Now we are told that we have a point with a positive x-coordinate and a negative y-coordinate, thus:

This means our point is located at the 4th Quadrant (where  values are positive and  values are negative).

Reflecting it over the y-axis means that our point is now located on the 3rd Quadrant (where both  and  values are negative).

Therefore the new reflected point will now be:

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7 0
3 years ago
The bar graph shows the numbers of reserved campsites at a campground for one week. What percent of the reservations were for Fr
Slav-nsk [51]

Answer:

66.67 %

Step-by-step explanation:

As we can see from the figure

We are given a bar graph in which bars represent the number of reserved campsites at a camp ground for one week from Monday to Sunday.

First of all

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Now

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% of reservations made on friday or saturday = 66.67 %

So in total 66.67 % reservations are on friday and saturday.

6 0
3 years ago
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