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6 days ago

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The graph of the function f(x) = (x – 4)(x + 1) is shown below. On a coordinate plane, a parabola opens up. It goes through (neg

ative 1, 0), has a vertex at (1.75, negative 6.2), and goes through (4, 0). Which statement about the function is true? The function is increasing for all real values of x where x < 0. The function is increasing for all real values of x where x < –1 and where x > 4. The function is decreasing for all real values of x where –1 < x < 4. The function is decreasing for all real values of x where x < 1.5.

2 answers:

Zina [3.9K]6 days ago

5 0

Answer:

The function decreases across all real numbers x where x < 1.5.

Step-by-step explanation:

This represents an upward-opening vertical parabola

The vertex signifies a minimum point

The vertex is located at (1.5,-6.25)

We know that

The function decreases within the interval ----> (-∞,1.5) x < 1.5

This indicates----> the function decreases for all real values of x under 1.5

The function increases within the interval ----> (1.5, ∞) x> 1.5

This signifies----> the function increases for all real values of x over 1.5

Refer to the attached figure for better comprehension

Thus

The true statement is

The function decreases across all real numbers x where x < 1.5.

tester [3.9K]6 days ago

5 0

Answer:

The function decreases across all real numbers x where x < 1.5.

Step-by-step explanation:

We have

$f(x)=(x-4)(x+1)$

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

$f(x)=x^2-3x-4$

This represents an upward-opening vertical parabola

The vertex denotes a minimum point

The vertex is located at (1.5,-6.25)

We know that

The function is decreasing within the interval ----> (-∞, 1.5) x < 1.5

This means----> the function is continuously decreasing for all real x values under 1.5

Conversely, the function is increasing within the interval ----> (1.5, ∞) x> 1.5

Thus, for all real x values greater than 1.5, the function is increasing

Check the attached figure for further clarification

Therefore

The true statement is

The function decreases across all real numbers x where x < 1.5.

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Answer:

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b. 71.11%

c. 0.564 micrometer

Step-by-step explanation:

To find the z value for each measurement, we must calculate and determine the percentage they correspond to, and the difference will give us the percentage between those two statistics.

The equation for z is:

z = (x - m) / (sd)

Here, x is the value being evaluated, m denotes the mean, and sd represents the standard deviation.

a.

For 0.62 copies, we calculate:

z = (0.62 - 0.5) / (0.05)

z = 2.4

This translates to 0.9918.

Therefore, p (x > 0.62) = 1 - 0.9918

p (x > 0.62) = 0.0082 = 0.82%

b.

For 0.47 copies, we have:

z = (0.47 - 0.5) / (0.05)

z = -0.6, which equates to 0.2742.

For 0.63 copies:

z = (0.63 - 0.5) / (0.05)

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p (0.47 > x > 0.63) = 0.7211 = 72.11 %

c.

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p = 0.9 corresponds to z = 1.28.

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From which we derive:

x = 1.28*0.05 + 0.5

x = 0.564 micrometer

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PIT_PIT [3919]

Answer: The result is $M=590-\dfrac{19}{20}V.$

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