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12345 [234]
2 years ago
10

Find all solutions for X and check. (different from the other question I asked earlier) thanks!

Mathematics
1 answer:
KiRa [710]2 years ago
4 0
   
\displaystyle  \\ 
17) \\ 
x(5x-10)=0 \\ 
x = 0 ~~\texttt{or}~~5x-10 = 0 \\ 
x_1 = \boxed{0} \\  \\ 
x_2 =  \frac{10}{5} =\boxed{2} \\ 
\texttt{Check: } \\ 
x_1 = 0~~\Longrightarrow ~~ 0(5\cdot 0 - 10) = 0 \cdot (-10) = 0 \\ 
x_2 = 2~~\Longrightarrow ~~ 2(5\cdot 2 - 10) = 2(10 - 10) = 2 \cdot 0 = 0


\displaystyle 18) \\ 
x^2 + 7x-18 = 42 \\ 
x^2 + 7x-18 - 42 =0 \\ 
x^2 + 7x-60 =0 \\ 
.~~~~~7x = 12x - 5x  \\ 
\underbrace{x^2 + 12x} -\underbrace{5x - 60} = 0 \\  \\ 
x(x+12) -5(x+12)=0 \\ 
(x+12)(x-5)=0 \\ 
x + 12 = 0 ~~\texttt{or}~~x-5 = 0 \\  \\ 
x_1 = \boxed{-12} \\ 
x_2 = \boxed{5} \\  \\ 
 \texttt{Check: } \\
x1 = -12 ~~\Longrightarrow~~ (-12)^2 + 7\cdot (-12)-18 = 144-84-18 = 42  \\  \\ 
x2 = 5 ~~\Longrightarrow~~ (5)^2 + 7\cdot (5)-18 = 25+35-18 = 42  \\  \\



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Write the absolute value function as a​ piecewise-defined function with linear parts.
KengaRu [80]

The piecewise-defined function with linear parts ​f(x)= |2x + 9|

f(x) = {2x + 9   x ≥ -9/2)

     {-2x - 9   x < 9/2}

<h3>How to write piecewise functions?</h3>

To write this function as a piecewise function, you have to use the definition of absolute value.

The absolute value equation is; ​f(x)= |2x + 9|

The definition says that;

|x| = {x   x ≥ 0)

     {-x   x < 0}

Applying this definition to the function you get:

|2x + 9| = {2x + 9   2x + 9 ≥ 0)

     {-2x - 9   2x + 9 < 0}

After simplifying the inequalities you get:

|2x + 9| = {2x + 9   x ≥ -9/2)

     {-2x - 9   x < 9/2}

So finally you can write the piecewise  function as:

f(x) = {2x + 9   x ≥ -9/2)

     {-2x - 9   x < 9/2}

Read more about piecewise function at; brainly.com/question/18499561

#SPJ1

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