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3 years ago

14

I need help answering all of these. My teacher thinks that we should know this even though he hasn´t taught us any of this. plea

se help?! thank you!

1 answer:

bearhunter [10]3 years ago

3 0

Answer:

Step-by-step explanation:

x/2=3.5

x=3.5*2

x=7

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What is the solution of x=2+ square root x-2?

alex41 [277]

So I'm going to assume that this question is asking for <u>non extraneous solutions</u>, or solutions that are found in the equation <em>and</em> are valid solutions when plugged back into the equation. So firstly, subtract 2 on both sides of the equation:

$x-2=\sqrt{x-2}$

Next, square both sides:

$(x-2)^2=x-2\\(x-2)(x-2)=x-2\\x^2-4x+4=x-2$

Next, subtract x and add 2 to both sides of the equation:

$x^2-5x+6=0$

Now we are going to be factoring by grouping to find the solution(s). Firstly, what two terms have a product of 6x^2 and a sum of -5x? That would be -3x and -2x. Replace -5x with -2x - 3x:

$x^2-2x-3x+6=0$

Next, factor x^2 - 2x and -3x + 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

$x(x-2)-3(x-2)=0$

Now you can rewrite the equation as $(x-3)(x-2)=0$

Now, apply the Zero Product Property and solve for x as such:

$x-3=0\\x=3\\\\x-2=0\\x=2$

Now, it may appear that the answer is C, however we need to plug the numbers back into the original equation to see if they are true as such:

$2=2+\sqrt{2-2}\\2=2+\sqrt{0}\\2=2+0\\2=2\ \textsf{true}\\\\3=2+\sqrt{3-2}\\3=2+\sqrt{1}\\3=2+1\\3=3\ \textsf{true}$

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3 years ago

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3 years ago

Function to inverse function f(x) =2x/3-17

ZanzabumX [31]

Answer:

Inverse function is $f^{-1}(x)=\frac{3}{2}x+\frac{51}{2}$ .

Step-by-step explanation:

Given function is $f\left(x\right)=\frac{2}{3}x-17$ .

Now we need to find the inverse of the given function.

Step 1: replace f(x) with y

$y=\frac{2}{3}x-17$

Step 2: switch x and y

$x=\frac{2}{3}y-17$

Step 3: solve for y

$x=\frac{2}{3}y-17$

$x+17=\frac{2}{3}y$

$\frac{3}{2}(x+17)=y$

$\frac{3}{2}x+\frac{51}{2}=y$

Hence required inverse function is $f^{-1}(x)=\frac{3}{2}x+\frac{51}{2}$ .

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3 years ago