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Gemiola [76]
4 years ago
14

I NEED HELP SAVE ME PLEASE!!

Mathematics
1 answer:
sweet-ann [11.9K]4 years ago
3 0

Answer:

Option D x=4

Step-by-step explanation:

we have

f(x)=\frac{1}{x-3}+1

g(x)=2\sqrt{x-3}

Solve the system by graphing

Remember that the solution of the system of equations (f(x)=g(x)) is the x-coordinate of the intersection point both graphs

The intersection point is (4,2)

therefore

x=4

see the attached figure

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Write a system of linear inequalities so the points (1, 2) and (4, -3) are solutions of the system, but the point (-2, 8) is not
Verizon [17]

Answer: \left \{ {{y\leq -\frac{5}{3}x + \frac{11}{3}} \atop {y < 8}} \right

<u>Step-by-step explanation:</u>

(1, 2) and (4, -3)

First, find the slope (m): \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

m = \frac{-3-2}{4-1}

   = -\frac{5}{3}

Next, choose ONE of the points and input the point and slope into the Point-Slope formula: y - y₁ = m(x - x₁)

y - 2 = -\frac{5}{3}(x - 1)

y - 2 = -\frac{5}{3}x + \frac{5}{3}

y      = -\frac{5}{3}x + \frac{11}{3}

Then, determine which inequality symbol will result in (-2, 8) being False (since it is not a solution):

y ___ -\frac{5}{3}x + \frac{11}{3}

8 ___ -\frac{5}{3}(-2) + \frac{11}{3}

8 ___ \frac{1}{3}

8 > \frac{1}{3}

so ≤ makes the statement False

⇒ y ≤ -\frac{5}{3}x + \frac{11}{3}

****************************************************************

If you need a "system" of inequalities, then you need another equation.

There are infinite possibilities. Graph the points to see what works.  

y < 8   or  x > -2 are two examples.


---> I just realized that the system can be simpler than what I did above:

\left \{ {{x>-2} \atop {y < 8}} \right



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The length of the side joining points (1, 3) and (3, 1) is given by

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