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PtichkaEL [24]
3 years ago
8

Which of the following would best represent a cosine function with an amplitude of 2, a period of pi over 3, and a midline at y

= 1?
f(x) = cos(x − pi over 3) + 2
f(x) = 2 cos(x − pi over 3) + 1
f(x) = −2 cos 6x + 1
f(x) = −cos 6x + 2
Mathematics
2 answers:
hodyreva [135]3 years ago
8 0
F(x) = −2 cos 6x + 1
OleMash [197]3 years ago
3 0
C. f(x) = – 2 cos 6x + 1

Start by determining the amplitude. Since we've deduced the amplitude is 2, the equation can include either a positive or negative 2 (since amplitude measures absolute value).

Next is the period. The equation for period P is P = (2pi)/b. If P is pi/3, then
pi/3 = (2pi)/b. Thus your b value should be 6.

Finally, the midline would be given by + 1 since adding a unit shifts the function upwards. This means that instead of the highest y value being 2 and the lowest -2, instead you'd have values of 3 and -1.
(3 – 1)/2 = 1 (midpoint theory).
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Which of the following represents the factorization of the trinomial below?
rosijanka [135]

Answer:

B. (x-3)^2

Step-by-step explanation:

x^2-6x+9 = (x-3)^2

(a-b)^2=a^2-2ab+b^2

(a+b)^2=a^2+2ab+b ^2

6 0
3 years ago
Carpet is sold in square yards. How much carpet would a person need to buy for a rectangular room that has dimensions of 10 yard
german
60 square yards is the answer.
3 0
3 years ago
Rewrite the function f(x)=3(x-1)^2+9 in the form f(x)=ax^2+bx+c
Otrada [13]

Answer:

f(x) = 3x² - 6x + 12

General Formulas and Concepts:

  • Order of Operations: BPEMDAS
  • Expand by FOIL (First Outside Inside Last)
  • Standard Form: f(x) = ax² + bx + c
  • Vertex Form: f(x) = a(bx + c)² + d

Step-by-step explanation:

<u>Step 1: Define function</u>

Vertex Form: f(x) = 3(x - 1)² + 9

<u>Step 2: Find Standard Form</u>

  1. Expand by FOILing:                         f(x) = 3(x² - 2x + 1) + 9
  2. Distribute 3:                                      f(x) = 3x² - 6x + 3 + 9
  3. Combine like terms (constants):     f(x) = 3x² - 6x + 12
7 0
3 years ago
Y'all is so nice too help me I really appreciate it help me thanks<br> plz i need help
butalik [34]
You can multiply 2/3 by 2/2 to get 4/6. This means that x=4!!!

Hope this helps :)
8 0
3 years ago
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MAVERICK [17]

Answer:

  $53.61

Step-by-step explanation:

It looks like the rate of change is supposed to be -2 2/5% = -2.4% per year. That means the "growth factor" is ...

  growth factor = 1 + growth rate

  growth factor = 1 -2.4% = 1 -0.024 = 0.976

Each year, Charisse's cactus salt and pepper shakers will have their value multiplied by this factor. After 2 years, their value will be ...

  ($56.28)(0.976)(0.976) = $56.28×0.976^2 ≈ $53.61

The value is projected to be $53.61 in 2 years.

6 0
3 years ago
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