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olya-2409 [2.1K]
3 years ago
5

Is the centroid of a triangle equidistant from the three vertices?

Mathematics
1 answer:
Xelga [282]3 years ago
4 0
The point that is equidistant<span> to all sides of a </span>triangle is <span>called the incenter.

</span>
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(x+7)/(x^2-49) find the domain. show work
harina [27]
\large\begin{array}{l} \textsf{Find the domain of}\\\\ \mathsf{f(x)=\dfrac{x+7}{x^2-49}}\\\\ \mathsf{f(x)=\dfrac{x+7}{x^2-7^2}}\\\\\\ \textsf{Factor out the denominator using special products:}\\\\ \textsf{(a difference of squares)}\\\\ \mathsf{f(x)=\dfrac{x+7}{(x+7)(x-7)}} \end{array}


\large\begin{array}{l} \textsf{Restrictions for the domain:}\\\\ \bullet~~\textsf{Denominators must not be zero:}\\\\ \mathsf{(x+7)(x-7)\ne 0}\\\\ \begin{array}{rcl} \mathsf{x+7\ne 0}&~\textsf{ and }~&\mathsf{x-7\ne 0}\\\\ \mathsf{x\ne -7}&~\textsf{ and }~&\mathsf{x\ne 7} \end{array} \end{array}


\large\begin{array}{l} \textsf{Therefore, the domain of f is}\\\\ \mathsf{D_f=\{x\in\mathbb{R}:~~x\ne -7~~and~~x\ne 7\}}\\\\\\ \textsf{or using a more compact form}\\\\ \mathsf{D_f=\mathbb{R}\setminus\{-7,\,7\}}\\\\\\ \textsf{or using the interval notation}\\\\ \mathsf{D_f=\left]-\infty,\,-7\right[\,\cup\,\left]7,\,+\infty\right[.} \end{array}


<span>If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2155752


\large\textsf{I hope it helps. :-)}



Tags: <em>function domain real rational factorizing special product interval</em>

</span>
7 0
3 years ago
Which pairs of angles are alternate exterior angles?
natka813 [3]
That Would BE A and C
8 0
2 years ago
Read 2 more answers
Write a proportion
Andrej [43]

Step-by-step explanation:

4 smoothies = 2 1/2 banana

you need to make 2 more smoothies, So half of what you did already.

(2.5)/2= 1.25 then add them (2.5)+(1.25)

6 smoothies = 3.75 or 3 3/4, same thing.

3 0
2 years ago
Read 2 more answers
Find the value of k such that x-2 is a factor of 3x³-kx²+5x+k​
Nuetrik [128]

Answer:

\displaystyle k = \frac{34}{3}

Step-by-step explanation:

We are given the polynomial:

\displaystyle P(x) = 3x^3 - kx^2 + 5x + k

And we want to determine the value of <em>k</em> such that (<em>x</em> - 2) is a factor of the polynomial.

Recall that the Factor Theorem states that a binomial (<em>x</em> - <em>a</em>) is a factor of a polynomial P(x) if and only if P(a) = 0.

Our binomial factor is (<em>x</em> - 2). Thus, <em>a</em> = 2.

Hence, by the Factor Theorem, P(2) must equal zero.

Find P(2):

\displaystyle \begin{aligned} P(2) &= 3(2)^3 - k(2)^2 + 5(2) + k \\ \\ &= 3(8) - 4k + 10 + k \\ \\ &= 34 - 3k  \end{aligned}

This must equal zero. Hence:

\displaystyle \begin{aligned} 34 - 3k &= 0 \\ \\ -3k &= -34 \\ \\ k = \frac{34}{3}  \end{aligned}

In conclusion, <em>k</em> = 34/3.

6 0
2 years ago
Help!!!! f(x)=10x+3 g(x)= -7x-4
Gelneren [198K]

Answer:

8x + 7

Step-by-step explanation:

8 0
3 years ago
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