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solmaris [256]
2 years ago
8

Which method do you think is easiest? Factoring, Completing the Square, or the Quadratic Formula?

Mathematics
1 answer:
stich3 [128]2 years ago
5 0
All are easy. There is no way to say thatnone way is easier than the other. Well the answer lies in every individual, it depends on which method they are comfortable with. Anyway there are more method to solve quadratic than the listed ones.
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A sine function has the following key features: Period = 4 Amplitude = 3 Midline: y=−1 y-intercept: (0,-1) The function is not a
mezya [45]

Answer:

  • See the graphs attached and the explanation below

Explanation:

The most simple sine function, considered the parent function, is:

     y=sin(x)

That function has:

  • Midline, also known as rest or equilibrium position: y = 0
  • Minimum: - 1
  • Maximum: 1
  • Amplitude: the distance between a minimum or a maximum and the midline = 1
  • period: the interval of repetition of the function = 2π

The more general sine function is:

             y=Asin(Bx+C)+D

That function has:

  • Midline: y = D (it is a vertical shift from the parent function)
  • Minimum: - A + D
  • Maximum: A + D
  • Amplitude: A
  • period: 2π/B
  • phase shift: C (it is a horizontal shift of the from the parent function)

Now, you have to draw the sine function with the given key features:

  • Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2
  • Amplitude, A = 3
  • midline y = - 1 ⇒ D = - 1
  • y-intercept = (0, -1)

Substitute the know values and use the y-intercept to find C:

       

            y=3sin(2x/\pi+C)-1

Substitute (0, -1)

             

              -1=3sin(0+C)-1\\ \\ 3sin(C)=0\\ \\ sin(C)=0\\ \\ C=0

Hence, the function to graph is:

              y=3sin(\pi x/2)-1

To draw that function use this:

  • Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
  • Minima: 3(-1) - 1 = - 3 - 1 = -4
  • y-intercept: (0, - 1)
  • x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
  • first point of the midline: (0, -1) it is the same y-intercept

With that you can understand the graphs attached.

4 0
3 years ago
HELP me.a man weighs 5/6 of his weight plus 30 pounds.what is his weight.
san4es73 [151]
X=the weight of this man
We can suggest this equation:
5x/6+30=x
least common multiple=6
5x+180=6x
5x-6x=-180
-x=-180
x=180

Answer; his weight is 180 pounds.
8 0
3 years ago
I need help figuring this question out
Marysya12 [62]
ANSWER: (4,26)
Comment below if you have any questions or want an explanation:
7 0
2 years ago
A quadrilateral is dilated by a scale factor of 2. It's original side measures are 7, 14, 21, and 28.
algol13

Answer:

14,28,42 and 56

Step-by-step explanation:

Multiply all lengths by 2 as the quadrilateral is dilated by a scale factor of 2

6 0
2 years ago
Read 2 more answers
Luke earned $36,000 during the first year of his job at Putt-Putt Kingdom. After each year he received a 10% raise. Find his tot
Lady_Fox [76]
In order to solve this problem, you need to use a geometric series:
S_{n} =  \frac{ a_{1}(1 - r^{n}) }{1 - r}
where:
a₁ = first term of the series = 36000
r = common rate = 10% raise, therefore 1.10
n = number of terms = 5

Therefore,
 <span>S_{n} =  \frac{ 36000(1 - 1.10^{5}) }{1 - 1.10}
= 219783.60 $

Luke's total earnings in five years are <span>219783.60 $.</span>

</span>
6 0
3 years ago
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