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goldfiish [28.3K]
3 years ago
11

For the function F(x) = 2x^2-31x-51, where is the function increasing and positive? ( for all X values greater than what number

)
Mathematics
1 answer:
Ulleksa [173]3 years ago
7 0
ANSWER
x \: > \: 17

EXPLANATION

The given function is

f(x) = 2 {x}^{2} - 31x - 51
Let us split the middle term to get,

f(x) = 2 {x}^{2} -34x + 3x- 51

We factor to obtain,

f(x) = 2x(x - 17) -+3(x - 17)

f(x) = (2x -+3)(x -17)

Let us find the zeros of f(x),

(2x +3)(x - 17) = 0

Either

2x +3 = 0 \: or \: x - 17 = 0
x = -\frac{3}{2} \: or \: x = 17

We need to find the x-value of the vertex, which is the midpoint of the x-intercepts.

This gives us,

\frac{- \frac{3}{2} + 17}{2} = 7.75
Hence the axis of symmetry of the parabola has equation,

x = 7.75

Since the given function has minimum turning point, it will decrease and then increase.

The function will be increasing for
x \: > \: 7.75

The function will be increasing and positive for
x \: > \: 17
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The population of a small rural town in the year 2006 was 2,459. The population can be modeled by the function below, where f(x)
Zepler [3.9K]

f(x)=2,459(0.92)^t

Using the information given above, complete the following statements. The percent change is %. The percent change represents .

f(x)=2,459(0.92)^t

Given equation is an exponential function and in the form of f(x) = a(1-r)^x

Where 'a' is the initial population

'r' is the decay rate

'x' is the time

f(x) = a(1-r)^x

Given function is f(x)=2,459(0.92)^t

1 - r = 0.92

r = 1 - 0.92

r = 0.08

r= 0.08 %

Percentage change = 0.08%

Percentage change represents the decay rate.

8 0
3 years ago
Read 2 more answers
I need help on these 2 questions, please and thank you!
VikaD [51]

Answer:

1.1 : C - x^2 + x - 2

1.2 : A - 4a^2 - 6b^2 + 12

Step-by-step explanation:

When we have the expression p(x) - q(x), we can substitute those functions in:

(x^2 + 2x - 5) - (x - 3)

We can distribute:

x^2 + 2x - 5 - x + 3

and then combine like terms(2x & -x, -5 & 3)

x^2 + x - 2

This is the same as C.

We can start by distributing:

a^2 - 2b^2 + 3 - 4b^2 + 5 + 3a^2 + 4

Now, we can combine all the a^2 terms(a^2 & 3a^2):

4a^2 - 2b^2 + 3 - 4b^2 + 5 + 4

Then, we can combine the b^2 terms(-2b^2 & -4b^2):

4a^2 - 6b^2 + 3 + 4 + 5

and lastly, all the constants:

4a^2 - 6b^2 + 12

This aligns with option A

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Answer:

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Step-by-step explanation:

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90 students take a test.
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Answer:

Step-by-step explanation:

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