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3 years ago

Can someone help me answer this?

Mathematics

1 answer:

grin007 [14]3 years ago

8 0

Answer:

The function f(x) has a hole at point x = - 5.

Step-by-step explanation:

We are given a function as

$f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}$

Now, we have to describe where the function has a hole.

Now, $f(x) = \frac{x^{2} + 7x + 10}{x^{2} + 9x + 20}$

⇒ $f(x) = \frac{(x + 5)(x + 2)}{(x + 4)(x + 5)}$

Therefore, the common factor of the numerator and denominator is (x + 5).

Now, (x + 5) = 0

⇒ x = - 5

Therefore, the function f(x) has a hole at point x = - 5. (Answer)

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2 years ago

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2 years ago

Sammy has x flavors of candies with which to make goody bags for Frank's birthday party. Sammy tosses out y flavors, because he

harkovskaia [24]

Answer:

$^{(x-y)}C_{10}=\frac{(x-y)!}{10! \times (x-y-10)!}$

Step-by-step explanation:

Total flavors Sammy initially had = x

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After throwing away y flavors, the number of flavors Sammy will be left with = x - y

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So we need to make combinations of 10 flavors from a total of (x - y) flavors. This can be represented as $^{(x-y)}C_{10}$

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3 years ago

Please explain how you came to your answer, need help ASAP. Will give brainliest

shusha [124]

The vertex is the high point of the curve, (2, 1). The vertex form of the equation for a parabola is
.. y = a*(x -h)^2 +k . . . . . . . for vertex = (h, k)

Using the vertex coordinates we read from the graph, the equation is
.. y = a*(x -2)^2 +1

We need to find the value of "a". We can do that by using any (x, y) value that we know (other than the vertex), for example (1, 0).
.. 0 = a*(1 -2)^2 +1
.. 0 = a*1 +1
.. -1 = a

Now we know the equation is
.. y = -(x -2)^2 +1

_____
If we like, we can expand it to
.. y = -(x^2 -4x +4) +1
.. y = -x^2 +4x -3

=========
An alternative approach would be to make use of the zeros. You can read the x-intercepts from the graph as x=1 and x=3. Then you can write the equation as
.. y = a*(x -1)*(x -3)
Once again, you need to find the value of "a" using some other point on the graph. The vertex (x, y) = (2, 1) is one such point. Subsituting those values, we get
.. 1 = a*(2 -1)*(2 -3) = a*1*-1 = -a
.. -1 = a
Then the equation of the graph can be written as
.. y = -(x -1)(x -3)
In expanded form, this is
.. y = -(x^2 -4x +3)
.. y = -x^2 +4x -3 . . . . . . same as above

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3 years ago