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3 years ago

Is it possible for a piece wise function to have more than one y intercept

Mathematics

1 answer:

Kaylis [27]3 years ago

3 0

If its circular, hyperbolic or ellipsoid

otherwise it will violate the rule of the verticle line test

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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 non extraneous solutions, or solutions that are found in the equation and 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:

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

Since both solutions hold true when x = 2 and x = 3, your answer is C. x = 2 or x = 3.

8 0

3 years ago

Last one for the class...

tigry1 [53]

Hope this helps!

Sorry the writing is really bad looking its hard to write on a laptop.

5 0

3 years ago

What is the least common multiple of 1/3 5/8 1/2?

joja [24]

Answer: The answer is 16.

Step-by-step explanation:

The least common denominator means the same as least common multiple.

3, 6, 9, 12, 16

8, 16

2, 4, 6, 8, 10, 12, 14, 16y-step explanation:

7 0

3 years ago

What is the area of a sector of a circle with a radius of 2.0 ft and a central angle of 2<img src="https://tex.z-dn.net/?f=%20%5

Zigmanuir [339]

$\bf \qquad \textit{area of a sector of a circle}
\\\\
A=\cfrac{\theta r^2}{2}\qquad 
\begin{cases}
\theta=\textit{angle in radians}\\
r=radius
\end{cases}$

plug in the provided radius and angle

6 0

3 years ago

13 POINTS IF YOU ANSWER!!!

Whitepunk [10]

H: 5 square yards is the correct answer, break the figure into squares and then multiply length by width to get area

6 0

3 years ago