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3 years ago

Where did it go wrong?

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

4 0

Answer:

Step-by-step explanation:step 3

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Given <br><img src="https://tex.z-dn.net/?f=%20log_%7B2%7D%28x%29%20%20%3D%20%20%5Cfrac%7B3%7D%7B%20log_%7Bxy%7D%282%29%20%7D%20

Naily [24]

Answer:

$\displaystyle y = x^{-\frac{2}{3}}$

Step-by-step explanation:

<u>Logarithms</u>

Some properties of logarithms will be useful to solve this problem:

1. $\log(pq)=\log p+\log q$

2. $\displaystyle \log_pq=\frac{1}{\log_qp}$

3. $\displaystyle \log p^q=q\log p$

We are given the equation:

$\displaystyle \log_{2}(x) = \frac{3}{ \log_{xy}(2) }$

Applying the second property:

$\displaystyle \log_{xy}(2)=\frac{1}{ \log_{2}(xy)}$

Substituting:

$\displaystyle \log_{2}(x) = 3\log_{2}(xy)$

Applying the first property:

$\displaystyle \log_{2}(x) = 3(\log_{2}(x)+\log_{2}(y))$

Operating:

$\displaystyle \log_{2}(x) = 3\log_{2}(x)+3\log_{2}(y)$

Rearranging:

$\displaystyle \log_{2}(x) - 3\log_{2}(x)=3\log_{2}(y)$

Simplifying:

$\displaystyle -2\log_{2}(x) =3\log_{2}(y)$

Dividing by 3:

$\displaystyle \log_{2}(y)=\frac{-2\log_{2}(x)}{3}$

Applying the third property:

$\displaystyle \log_{2}(y)=\log_{2}\left(x^{-\frac{2}{3}}\right)$

Applying inverse logs:

$\boxed{y = x^{-\frac{2}{3}}}$

7 0

3 years ago

Will someone please answer this and remind me how to solve this

Veseljchak [2.6K]

Answer:

Step-by-step explanation:

Since the two triangles are similar, you can use proportions to solve for the value of $x$

$\frac{x}{12} = \frac{4}{3}$

Now, just multiply 4 and 12.

$4 * 12 = 48$

Then divide that by 3.

$48 / 3 = 16$

Therefore, $x = 16$ .

5 0

3 years ago

Read 2 more answers

Plz help I’m getting timed

Fed [463]

id say its a rhombus. all the other shapes can have right angles

6 0

3 years ago

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Point Q' is the image of Q(-7, -6) under the translation (x, y) + (x + 12, y + 8).

Lina20 [59]

Answer:

The co-ordinates of Q' is (5,2).

Step-by-step explanation:

Given:

Pre-image point

Q(-7,-6)

To find Image point Q' after following translation.

$(x,y)\rightarrow (x+12,y+8)$

Solution:

Translation rules:

Horizontal shift:

$(x,y)\rightarrow (x+k,y)$

when $K>0$ the point is translated $k$ units to the right.

when $K$ the point is translated $k$ units to the left.

Vertical shift:

$(x,y)\rightarrow (x,y+k)$

when $K>0$ the point is translated $k$ units up.

when $K$ the point is translated $k$ units down.

Given translation $(x,y)\rightarrow (x+12,y+8)$ shows the point is shifted 12 units to the right and 8 units up.

The point Q' can be given as:

Q'= $(-7+12,-6+8)=(5,2)$

So, the co-ordinates of Q' is (5,2). (Answer)

7 0

3 years ago

Each of five friends has between $3.50 and $4.25. Which could be the total amount of money the five friends have?

sleet_krkn [62]

The answer would be around $20

7 0

3 years ago

Read 2 more answers