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3 years ago

3(2^x) = 6^2x How do you solve this?

1 answer:

7 0

$3(2^x)=6^{2x}$
$3(2^x)=(3\times2)^{2x}$
$3(2^x)=3^{2x}2^{2x}$
$\ln(3(2^x))=\ln(3^{2x}2^{2x})$
$\ln3+\ln2^x=\ln3^{2x}+\ln2^{2x}$
$\ln3+x\ln2=2x\ln3+2x\ln2$
$\ln3=2x\ln3+2x\ln2-x\ln2$
$\ln3=x(2\ln3+\ln2)$
$x=\dfrac{\ln3}{2\ln3+\ln2}$

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I need help with #11

Troyanec [42]

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}$

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\end{array}$

$\bf \begin{array}{llll}


\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}$

now, with that template in mind, let's take a peek at this function

$\bf \begin{array}{lllcclll}
y=&2(&1x&-2)^2&-4\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}\\\\
-----------------------------\\\\
A\cdot B=2\impliedby \textit{shrunk by a factor of 2, of half-size}\\\\
\cfrac{C}{B}= \cfrac{-2}{1}\implies -2\impliedby \textit{horizontal right shift of 2 units}\\\\
D=-4\impliedby \textit{vertical down shift of 4 units}$

so, the graph of y=2(x-2)²-4, is really the same graph of y=x², BUT, narrower, and moved about horizontally and vertically

8 0

3 years ago

Read 2 more answers

20 points!!!

Ghella [55]

Area of semi circle: you know the radius is 5. 5^2 * pi = 25pi/2 = 12.5pi
For triangle: bh/2 = (10 * 10)/2 = 50
Add them together: 12.5pi + 50
12.5pi = 39.25
39.25 + 50 = 89.25
It’s closest to D

8 0

3 years ago

Read 2 more answers

What are all the true statements

Finger [1]

Answer:

i am going to say number 1 even though they all sound right hope i helped <3

Step-by-step explanation:

3 0

4 years ago

Solve the following system of equations: 2x + 4y − 3z = −7 3x + y + 4z = −12 x + 3y + 4z = 4

lukranit [14]

2x + 4y − 3z = −7 ---> first equation

3x + y + 4z = −12 ---> second equation

x + 3y + 4z = 4 ---> third equation

We try to eliminate z and make two equations

Multiply first equation by 4 and second equation by 3. then add both equations

8x + 16y -12z = -28

9x + 3y +12z = -36

----------------------------

17x + 19y = -64 ---------------> equation 4

multiply third equation by -1 and add second and third equation

3x + y + 4z = −12

-x - 3y - 4z = -4

-------------------------------------

2x -2y = -16 ---------------> equation 5

Multiply equation 4 by 2 and equation by 19

34x + 38y = -128

38x - 38y = -304

------------------------------------

72x = -432

Divide by 72 on both sides

x = -6

use equation 2x -2y = -16 ---------------> equation 5

2(-6) - 2y = -16

-12 -2y = -16

-2y = -4

So y = 2

Now plug in 2 for y and -6 for x

Using any one of the three equations

x + 3y + 4z = 4

-6 + 3(2) +4z = 4

4z = 4 (divide by 4 on both sides)

So z=1

So x= -6, y = 2 and z= 1

4 0

3 years ago

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Nathaniel is making muffins. Each batch uses 2 cups of flour. He plans to use less than 40 cups of flour for muffins so that he

MAXImum [283]

The number of batches Nathaniel can make is 16.5 batches.

Nathaniel plans to make use of less than 40 cups of flour and he has already used 6 cups of flour. In order to determine how many batches he can make, we have to determine the number of cups of flour he can use. The cups of flour would be divided by the amount of flour that can be used to make a batch of muffins.

Maximum amount of flour Nathaniel can use = 39 - 6 = 33

Number of batches he can make = 33 / 2 = 16.5 batches

To learn more about division, please check: brainly.com/question/194007

8 0

2 years ago