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3 years ago

13. Write a rule for each counterclockwise rotation about the origin:

Mathematics

1 answer:

ryzh [129]3 years ago

4 0

Answer:

180 degrees

(x,y) becomes (-x,-y)

270 degrees

(x,y) becomes (y,-x)

90 degrees

(x,y) becomes (-y,x)

Step-by-step explanation:

Here, we want to write a rule for each of the counterclockwise rotation

The rule are as follows;

180 degrees

(x,y) becomes (-x,-y)

270 degrees

(x,y) becomes (y,-x)

90 degrees

(x,y) becomes (-y,x)

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Step-by-step explanation:

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The potential solutions of $log_4x+log_4(x+6)=2$ are 2 and -8.

<h3>Properties of Logarithms</h3>

From the properties of logarithms, you can rewrite logarithmic expressions.

The main properties are:

Product Rule for Logarithms - $log_{b}(a*c)=log_{b}a+log_{b}c$
Quotient Rule for Logarithms - $log_{b}(\frac{a}{c} )=log_{b}a-log_{b}c$
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The exercise asks the potential solutions for $log_4x+log_4(x+6)=2$ . In this expression you can apply the Product Rule for Logarithms.

$log_4x+log_4(x+6)=2\\ \\ x*(x+6)=4^2\\ \\ x^2+6x=16\\ \\ x^2+6x-16=0$

Now you should solve the quadratic equation.

Δ= $b^2-4ac=36-4*1*(-16)=36+64=100$ . Thus, x will be $x_{1,\:2}=\frac{-6\pm \:\sqrt{100} }{2\cdot \:1}=\frac{-6\pm \:10}{2}$ . Then:

$x_1=\frac{-6+10}{2}=\frac{4}{2} =2\\ \\ \:x_2=\frac{-6-10}{2}=\frac{-16}{2} =-8$

The potential solutions are 2 and -8.

Read more about the properties of logarithms here:

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2 years ago

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Hello!

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I hope this helps you! Have a lovely day!

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