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3 years ago

If x=6 is the only X-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the

Mathematics

1 answer:

makkiz [27]3 years ago

8 0

Answer:

The discriminant is 0

Step-by-step explanation:

In a quadratic equation , we use the quadratic formula to find the solutions

x = (-b ± √(b2 - 4ac)) / 2a

where a, b, and c are coefficients of the equation

ax2 + bx + c = 0

Since x=6 is the only x-intercept, the equation would be

(x - 6)(x - 6) = 0

Expanding this out, we get

x2 - 12x + 36 = 0

In this equation,

a = 1

b = -12

c = 36

Now the discriminant is the square-root part of the formula:

b2 - 4ac

Now plug in the values of a,b, and c into the discriminant.

(-12)2 - 4(1)(36) = 144 - 144 = 0

This number is under the square-root. The square-root of 0 is 0.

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Folding 6 loads

Step-by-step explanation:

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3 years ago

Simplify. −5x4(−3x2+4x−2)

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3 years ago

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The graph of the function f(x) = (x - 3)(x + 1) is shown.

pychu [463]

Answer:

Step-by-step explanation:

Option A. All the real values of x where x < -1

Procedure

Solve the inequality:

(x -3)(x+1)>0

That happens in two cases.

1) When both factors >0

x-3>0 and x+1>0

x>3 and x >-1

The intersection is x >3

2) When both factors <0

x-3<0 and x+1<0

x<3 and x<-1

the intersection is x<-1.

We have obtained that the function is positive for the intervals x < -1 and x > 3. But in one of those intervals the function is decresing and in the other is increasing.

You can recognize that the function given is a parabola and, because the coefficient of the quadratic term is positive, the parabola opens upward. Then the function is decreasing in the first interval and increasing in the second interval.

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3 years ago

The population of California was 29.76 million in 1990 and 33.87 million in 2000. Use the model found in part a (f(x) =29.76(1.0

NeTakaya

Answer:

The average rate of change from 1990 to 1991 is $0.387 \:\frac{million}{years}$

The average rate of change from 2000 to 2001 is $0.440 \:\frac{million}{years}$

Step-by-step explanation:

The average rate of change of function f(x) over the interval $a\leq x\leq b$ is given by

$\frac{f(b)-f(a)}{b-a}$

It is a measure of how much the function changed per unit, on average, over that interval.

From the information given:

The function that models the population t years after 1990 is $f(t) =29.76(1.013)^t$
The year 1990 is t = 0 and the year 2000 is t = 10.

1. The average rate of change from 1990 to 1991 is:

The interval is $0\leq x\leq 1$

$\frac{29.76(1.013)^1-29.76(1.013)^0}{1-0}\\\\\frac{1.013^1\cdot \:29.76-1\cdot \:29.76}{1-0}\\\\\frac{0.38688}{1-0}\\\\0.387 \:\frac{million}{years}$

2. The average rate of change from 2000 to 2001 is

The interval is $10\leq x\leq 11$

$\frac{29.76(1.013)^{11}-29.76(1.013)^{10}}{11-10}\\\\\frac{0.44022}{11-10}\\\\0.440 \:\frac{million}{years}$

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3 years ago

You have an ant farm with 24 ants. The population of ants in your farm will

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