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11 days ago

F(x) = -4x(2)+ 12x – 9

Mathematics

2 answers:

AnnZ [12.3K]11 days 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]11 days 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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Answer:

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Step-by-step explanation:

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Goal: To determine the cardiac output value.

Solution:

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$[\int{20te^{-0.6t}} \, dt]^{10}_0=[\frac{-20te^{-0.6t}}{0.6}+\frac{20e^{-0.6t}}{(0.6)^2}]^{10}_{0}$

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Let's convert each statement into mathematical terms.

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Answer:

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