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Pie
2 years ago
7

Complete each sentence with minimum or maximum and the corresponding numeric values.

Mathematics
1 answer:
Alekssandra [29.7K]2 years ago
5 0

Answer:

First problem:  max when x = 4

Second problem:  min when x = 1

Step-by-step explanation:

The graph of f(x) = –|x – 4| – 5 is a translation of that of g(x) = -|x|.  The vertex of the latter is (0, 0).  First this must be translated 4 units to the right and then the resulting graph 5 units downward.  The vertex of this translation is (4, -5).  Since this graph opens downward, this (4, -5) is the maximum function value, that is, when x = 4.

The graph of f(x) = x2 – 2x +­ 1, or (better yet) f(x) = x^2 – 2x +­ 1, or

f(x) = (x - 1)^2 + 0, is that of a parabola that opens upward and has its minimum at x = 1, or (1, 0).

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At Edna's boutique, 14 customers wore a size large, and 48 customers wore a different size.What is the probability that a random
son4ous [18]

Answer:

25% i belive

Step-by-step explanation:

8 0
3 years ago
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
Natalie added 20 pieces of candy to a bowl. Two days later, half of the candy in the bowl is gone. If there are 14 pieces left i
Salsk061 [2.6K]

Answer:

8 pieces of candy

Step-by-step explanation:

Take the original amount of candy in the bowl to be x.

It says that 20 pieces of candy were added, therefore there are x+20 pieces of candy in the bowl.

Half of the candy is gone, therefore \frac{x+20}{2} pieces of candy are left in the bowl.

After half of the candy is gone, there are 14 pieces left, so we can say that \frac{x+20}{2} =14

Solve for x:

x+20 = 28

x=8

8 0
3 years ago
Which is a possible number of distinct real roots for a cubic function? Select all that apply.
Neko [114]

Answer:

3

Step-by-step explanation:

3 is a possible number of distinct real roots for a cubic function.

The maximum possible number of distinct roots are equal to the degree of any polynomial function.

Hence quadratic function has 2 roots

Cubic has 3

Linear has 1

4 0
2 years ago
A certificate of deposit often charges a penalty for withdrawing funds before the maturity date. If the penalty involves two mon
Aleonysh [2.5K]

Answer:

The amount for early withdrawal is $204

Step-by-step explanation:

Annual interest rate = 5% = 0.05

Investment = $24,000

Annual interest rate * Investment = Annual interest

0.05 * $24,000 = $1,200

Penalty = Two months of interest

(months/months in a year)  * Annual interest

(2/12) * $1,200 = 0,17

0,17 * $1,200 =  $204,00  

6 0
3 years ago
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