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GenaCL600 [577]
3 years ago
11

%5E%7Bx%7D%20%7D%20%20-%20%20%20%5Csqrt%7B%20%7B9%7D%5E%7Bx%20%7D%20%7D%20" id="TexFormula1" title=" {2}^{x} - {3}^{x} = \sqrt{ {6}^{x} } - \sqrt{ {9}^{x } } " alt=" {2}^{x} - {3}^{x} = \sqrt{ {6}^{x} } - \sqrt{ {9}^{x } } " align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
strojnjashka [21]3 years ago
5 0

Answer:

x = 0

Step-by-step explanation:

{2}^{x} - {3}^{x} = \sqrt{ {6}^{x} } - \sqrt{ {9}^{x } } \\  \\ {2}^{x} - {3}^{x} = \sqrt{ {6}^{x} } - \sqrt{ {( {3}^{2}) }^{x } } \\  \\ {2}^{x} - {3}^{x} = \sqrt{ {6}^{x} } - \sqrt{ {({3)}^{2x}}}\\  \\ {2}^{x} -  \cancel{{3}^{x}} = \sqrt{ {6}^{x} } - \cancel{ {3}^{x} } \\  \\ {2}^{x} = \sqrt{ {6}^{x} } \\ squaring \: both \: sides \\  \\  {( {2}^{x} )}^{2}  =  {(\sqrt{ {6}^{x} })}^{2}  \\  \\  {2}^{2x}  =  {6}^{x}  \\  \\   {2}^{2x}  =  {(2 \times 3)}^{x}  \\  \\   {2}^{2x}  =  {2 ^{x}  \times 3}^{x}  \\  \\  \frac{ {2}^{2x}  }{ {2}^{x}  } =  3^{x}  \\  \\   {2}^{2x - x}  =  {3}^{x}  \\  \\  {2}^{x}  =  {3}^{x}  \\  \\   \frac{ {2}^{x} }{ {3}^{x} }  = 1 \\  \\  \bigg(  \frac{2}{3} \bigg)^{x}  = 1 \\  \\  \implies \: x = 0 \\  \\  \because \: for \: x = 0 \\  \\ \bigg(  \frac{2}{3} \bigg)^{0}  = 1

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Gears A and B turn together. Gear A turns 20 times when
Bingel [31]

Answer: Gear B turns 90 times when gear A turns 60 times

Step-by-step explanation: To solve this you just 30x3=90

7 0
3 years ago
3
julsineya [31]

Answer:

In order to ride on the ride an individual must be at least 4 feet tall.

This means that the individual must be equal to 4 ¾ feet tall.

h = 4 ⅓

and the individual could be greater than 4¾ feet tall.

h > 4 ¾

So the individual could be greater than and equal to 4¾ feet tall.

h ≥ 4¾

4 0
3 years ago
Find the value of x.<br><br> Please help
bekas [8.4K]

Answer:

86 degrees

Step-by-step explanation:

For triangle the sum of angles is equal to 180 degrees

so,

x+(x-35)+43=180

2x -35+43=180

2x = 180-43+35

2x = 172

x = 86

6 0
3 years ago
Read 2 more answers
A biologist studied how cells grow by adding liquid protein to cell samples. She reported in her study that she divided 3/5 of a
r-ruslan [8.4K]

Answer: \dfrac{1}{5}\text{ of an ounce.}

Step-by-step explanation:

Given : A biologist studied how cells grow by adding liquid protein to cell samples.

She divided \dfrac{3}{5} of an ounce of liquid protein evenly among 3 cell samples.

Here , total quantity of liquid protein = \dfrac{3}{5} of an ounce

Total cell samples = 3

Now , Quantity of liquid protein given by her to each cell = (total quantity of liquid protein ) ÷ (3)

= \dfrac{3}{5}\times\dfrac{1}{3}=\dfrac{1}{5}\text{ of an ounce} .

Hence, Quantity of liquid protein given by her to each cell =  \dfrac{1}{5}\text{ of an ounce.}

4 0
3 years ago
System of Equations <br> Need help<br> Trig
Yanka [14]

Looks like the system is

\begin{cases}-2x+y+6z=1\\3x+2y+5z=16\\7x+3y-4z=11\end{cases}

We can eliminate y by taking

(3x+2y+5z)-2(-2x+y+6z)=16-2(1)

\implies3x+2y+5z+4x-2y-12z=16-2

\implies7x-7z=14

\implies x-z=2

so that z=x-2, and

(7x+3y-4z)-3(-2x+y+6z)=11-3(1)

\implies7x+3y-4z+6x-3y-18z=11-3

\implies13x-22z=8

Substitute z=x-2 into this last equation and solve for x:

13x-22(x-2)=8

\implies13x-22x+44=8

\implies-9x=-36

\implies x=4

Then

z=x-2

\implies z=4-2

\implies z=2

Plug these values into any one of the original equation to solve for y:

-2x+y+6z=1

\implies-2(4)+y+6(2)=1

\implies-8+y+12=1

\implies y=-3

Hence the solution is x = 4, y = -3, and z = 2.

6 0
3 years ago
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