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vampirchik [111]
2 years ago
5

1. Simplify the expression below. -5(3x) + x A. -15x B. – 13x C. -14x D. –15 + x

Mathematics
2 answers:
Ulleksa [173]2 years ago
7 0

Answer:

i think it's D or B. i hope this helps I didn't really know what to do

elena-s [515]2 years ago
4 0
C. -14x
Just multiply 3 with -5 and get -14x. And then add a positive x to get -14x
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Which is an asymptote of the graph of the function y = cot ( x - 2pi / 3 )
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\bf y=cot\left(x-\frac{2\pi }{3}  \right)\implies y=\cfrac{cos\left(x-\frac{2\pi }{3}  \right)}{sin\left(x-\frac{2\pi }{3}  \right)}

now, if the denominator turns to 0, the fraction becomes undefined, and you get a "vertical asymptote" when that happens, so let's check when is that

\bf sin\left(x-\frac{2\pi }{3}  \right)=0\implies sin^{-1}\left[ sin\left(x-\frac{2\pi }{3}  \right) \right]=sin^{-1}(0)
\\\\\\
x-\frac{2\pi }{3}=
\begin{cases}
0\\
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now, at those angles, the function is asymptotic, check the picture below

3 0
3 years ago
Read 2 more answers
Help please
rusak2 [61]

Answer:

  • See below

Step-by-step explanation:

f(x) is quadratic function and g(x) is linear (since AP in the right column).

<u>Find the equation of the function f(x), use the points on the graph:</u>

  • f(x) = ax² + bx + c
  • c = 5 as the y-intercept is (0, 5)
  • a(-1)² + b(-1) + 5 = 0 ⇒ a + 5 = b
  • a(5²) + b(5) + 5 = 0 ⇒ 25a + 5b + 5 = 0 ⇒ 25a + 5a + 25 + 5= 0 ⇒ a = -1 ⇒ b= 4

<u>The function is:</u>

  • f(x) = -x² + 4x + 5

Find the equation of g(x)

<u>Find the slope of g(x):</u>

  • m = (1 - 7)/(-1 + 4) = -2

<u>Use (-4, 7) to find its equation:</u>

  • y - 7 = -2(x + 4)
  • y = -2x + 7 - 8
  • y = -2x - 1
<h3>See the required comparison below</h3>

<u>The y-intercepts:</u>

  • f(x) ⇒ 5,
  • g(x) ⇒ -1
  • -5 < - 1

<u>Values at x = 3:</u>

  • f(3) = -3² + 4(3) + 5 = 8
  • g(3) = -2(3) - 1 = - 7
  • 8 > 7

<u>Average rate of change in the interval [2,5]:</u>

  • f(x) ⇒ (0 - 9)/(5 - 2) = -3
  • g(x) ⇒ (-11 + 5)/ (5 - 2) = -2
  • -3 < -2

<u>Max of function in the interval [-5, 5];</u>

  • f(x) ⇒ 9, vertex of the function
  • g(x) ⇒ g(-5) = -2(-5) - 1 = 9, taken the least point of x as it is a decreasing function
  • 9 = 9
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