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Lelu [443]
3 years ago
14

Use technology to construct an appropriate model of the data. (0,1), (1,-2), (2,-3), (3,-2), (4,1) f(x) = – x2 + 4 f(x) = x2 - 4

f(x) = - x2 + 4x - 1 f(x) = x2 - 4x + 1
a. f(x) = – (x+2)2 + 3B. f(x) = (x+2)2 + 3C. f(x) = – (x-2)2 - 3D. f(x) = (x-2)2 - 3

Mathematics
1 answer:
Marina CMI [18]3 years ago
3 0
The answer choices tell you this is a parabola.
The given points tell you it opens upward and the vertex is (2, -3).
Your knowledge of the vertex form of the equation is the only "technology" that you need. The vertex form is
  y = a(x - h)² + k . . . . . for vertex (h, k)
The fact that the y-value is 1 more than its vertex value when |x-2| = 1 tells you the scale factor "a" is 1.

You can write the model as
  D. f(x) = (x -2)² - 3

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4.2kg of oranges are £8.76. How much does 2kg cost
seropon [69]

Answer:

x = 4.17

Step-by-step explanation:

We can use a ratio to solve

4.2 k                  2 k

---------------- = ---------------

8.76                     x

Using cross products

4.2 * x = 2 * 8.76

4.2x =17.52

Divide by 4.2

x=4.17

8 0
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The wind is blowing N 35.0 degrees W at 1.60 * 10^2 mph. A plane has an engine speed of 3.20 * 10^2 mph. Where should the pilot
andreyandreev [35.5K]

Answer: 24.2° SouthWest

<u>Step-by-step explanation:</u>

First step: DRAW A PICTURE of the vectors from head to tail <em>(see image)</em>

I created a perpendicular from the resultant vector to the vertex of the given vectors so I could use Pythagorean Theorem to find the length of the perpendicular. Then I used that value to find the angle of the plane.

<u>Perpendicular (x):</u>

 cos 35° = adjacent/hypotenuse

  cos 35° = x/160

→ x = 160 cos 35°

<u>Angle (θ):</u>

sin θ = opposite/hypotenuse

sin θ = x/320

sin θ = 160 cos 35°/320

    θ = arcsin (160 cos 35°/320)

    θ = 24.2°

Direction is down (south) and left (west)

7 0
3 years ago
X - Зу = -2<br> X - Зу = 16
Stells [14]
Answer: x - 3y = -2
x = -2 + 3y

x - 3y = 16
x = 16 + 3y

8 0
3 years ago
What is a cubic polynomial function in standard form with zeros 1,1,and -3?
Mekhanik [1.2K]

Answer:

f(x) = x³ + x² - 5x + 3

Step-by-step explanation:

The cubic polynomial has zeros at 1, 1, - 3.

Therefore, x = 1, 1, - 3 are the roots of the polynomial and hence, (x - 1), (x - 1) and (x + 3) will be factors of the cubic polynomial.

Hence, we can write the polynomial as a function of x as

f(x) = (x - 1)(x - 1)(x + 3)

⇒ f(x) = (x² - 2x + 1)(x + 3)

⇒ f(x) = x³ - 2x² + 3x² + x - 6x + 3

⇒ f(x) = x³ + x² - 5x + 3

So, this is the cubic polynomial function in standard form. (Answer)

8 0
3 years ago
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