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1 month ago

F(x) = -4x(2)+ 12x – 9

Mathematics

2 answers:

AnnZ [12.3K]1 month ago

5 0

For this context, we examine the function:

$f (x) = - 4x ^ 2 + 12x-9$

$y = 0$ presented as:

$-4x ^ 2 + 12x-9 = 0$

The definition of the discriminant in a quadratic equation is provided by:

$a = -4\\b = 12\\c = -9$

Sentences correspond to the types of roots: Different real roots, equal real roots, or distinct complex roots

$d = b ^ 2-4 (a) (c)$

$d> 0:$ Upon substituting the provided values, we arrive at

$d = 0:$

$d$

This indicates that there are two equal real roots.

To discover the intersections along the x-axis, we apply the quadratic formula: $d = (12) ^ 2-4 (-4) (- 9)\\d = 144-144$

$d = 0$

Plugging in the values yields: $y = 0:$

$-4x ^ 2 + 12x-9 = 0$

The intersection on the x-axis is

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}$

$x = \frac {-12 \pm \sqrt {12 ^ 2-4 (-4) (- 9)}} {2 (-4)}\\x = \frac {-12 \pm \sqrt {144-144}} {- 8}\\x = \frac {-12 \pm0} {- 8}\\x = \frac {-12} {- 8}\\x = \frac {3} {2}$

$(\frac {3} {2}, 0)$

Zina [12.3K]1 month ago

3 0

Answer:

Part A) The discriminant value of f is zero

Part B) The quadratic equation yields a single x-intercept

Step-by-step explanation:

Part A) What discriminant value does f possess?It is known that

In the standard form of a quadratic equation

the discriminant is equal to $ax^{2} +bx+c=0$

For this instance, we have

$D=b^2-4ac$

Consequently,

$f(x)=-4x^2+12x-9$

Substituting leads to

$a=-4\\b=12\\c=-9$

$D=12^2-4(-4)(-9)$

$D=0$

Part B) How many x-intercepts exist for the graph of f?It is understood that

In a quadratic equation, if the discriminant D equals zero, the equation possesses solely one real solution

This suggests that

the quadratic equation has a single x-intercept.

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How many solutions does the equation sin(5x) = 1/2 have on the interval (0, 2PI]

lawyer [12517]

Answer:

Step-by-step explanation:

Considering the equation

Sin(5x) = ½

5x = arcSin(½)

5x = 30°

Then,

The general formula for sin is

5θ = n180 + (-1)ⁿθ

Dividing throughout by 5

θ = n•36 + (-1)ⁿ30/5

θ = 36n + (-1)ⁿ6

The solution range is

0<θ<2π which means 0<θ<360

First solution

When n = 0

θ = 36n + (-1)ⁿθ

θ = 0×36 + (-1)^0×6

θ = 6°

When n = 1

θ = 36n + (-1)ⁿ6

θ = 36-6

θ = 30°

When n = 2

θ = 36n + (-1)ⁿ6

θ = 36×2 + 6

θ = 78°

When n =3

θ = 36n + (-1)ⁿ6

θ = 36×3 - 6

θ = 102°

When n=4

θ = 36n + (-1)ⁿ6

θ = 36×4 + 6

θ = 150

When n=5

θ = 36n + (-1)ⁿ6

θ = 36×5 - 6

θ = 174°

When n = 6

θ = 36n+ (-1)ⁿ6

θ = 36×6 + 6

θ = 222°

When n = 7

θ = 36n + (-1)ⁿ6

θ = 36×7 - 6

θ = 246°

When n =8

θ = 36n + (-1)ⁿ6

θ = 36×8 + 6

θ = 294°

When n =9

θ = 36n + (-1)ⁿ6

θ = 36×9 - 6

θ = 318°

When n =10

θ = 36n + (-1)ⁿ6

θ = 36×10 + 6

θ = 366°

When n = 10 surpasses the θ range

Thus, the solutions range from n =0 to n=9

Therefore, there are 10 solutions within the interval 0<θ<2π

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2 months ago

Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the

babunello [11817]

A is confirmed as correct since -13 falls within the domain of g(x), and 20 is included in its range. For g(x), the inequality holds: -20 < -13 < 5 and -5 < 20 < 45. B is incorrect since the number 4 exists within the domain of g(x), but -11 is not within its range, represented by -20 < 4 < 5 and -11 < -5. C is likewise incorrect, as it is stated that g(0) equals -2. D is also false since 7 does not belong to the domain of g(x).

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2 months ago

Leticia invests $200 at 5% interest. If y represents the amount of money after x time periods, which describes the graph of the

Leona [12618]

Answer:

First, it's essential to define the equation that characterizes the function.

The investment is $200 with an interest rate of 5%, where y represents the money after x periods.

After one period, the amount of money grows to 200 plus 5% interest, resulting in 200 + 5%(200) = 200 (1 +5%) = 200 (1 + 0.05) = 200 (1.05)

After two periods, the total is 200(1.05)*(1.05) = 200 (1.05)^2

After three periods, it will be 200 (1.05)^3

Consequently, it can be inferred that after x periods, y = 200 (1.05)^x

Next, this function can be analyzed to project the graph's shape and significant points.

The answers derive from the initial value and the growth factor.

The initial value occurs when x = 0, giving y = 200 (1.05)^0 = 200*1 = 200

The growth factor is 1.05, indicating each subsequent value is multiplied by 1.05.

Step-by-step explanation:

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1 month ago

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