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irinina [24]
3 years ago
14

Calculate the average rate of change of the quadratic function y = -x2 + 4x +2

Mathematics
1 answer:
algol133 years ago
6 0

Answer:

2

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

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

Here [ a, b ] = [ 0, 2 ], thus

f(b) = f(2) = -(2)² + 4)(2) + 2 = - 4 + 8 + 2 = 6

f(a) = f(0) = 2

average rate of change = \frac{6-2}{2-0} = \frac{4}{2} = 2

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The Carson family sent 500 text messages last month. Mrs. Carson sent 15 text messages; Mr. Carson sent 1; Cathi sent 104; and B
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Answer:

76%

Step-by-step explanation:

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3 0
3 years ago
When completing the square, what value must you add to both sides of the equation to create a perfect square trinomial?
Sergeu [11.5K]
Notice that half of the coefficient of x is (1/2)(-4), or -2.

Then x^2 - 4x   becomes
         x^2 - 4x + 4 - 4 = 0, or (x -2)^2 = 4.   Then x = -2 plus or minus 2, and the two roots are 0 and -4.

Thus, add 4 to both sides to obtain x^2 - 4x + 4 = 4.
6 0
3 years ago
Is 7/12 bigger than 1/2
Varvara68 [4.7K]
Lets think of it this way:-

1/2 is one half

Whats half of 12? 6 

Now, 7 is greater than 6, which means the fraction 7/12 is greater than 1/2

Answer: 7/12 is bigger 
7 0
3 years ago
Read 2 more answers
Write a quadratic equation with the given roots. Write the equation in the form of ax^2+bx+c=0 where a b and c are integers
Bas_tet [7]

You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the x^2 coefficient is 1, i.e. the equation is written like x^2+bx+c=0, then you can say the following about the coefficients b and c:

  • b is the opposite of the sum of the roots
  • c is the multiplication of the roots.

So, for example, if we want an equation whose roots are 4 and -2, we have:

  • 4+(-2) = 4-2 = 2 \implies b = -2
  • 4 \cdot (-2) = -8 \implies c = -8

So, the equation is x^2-2x-8=0

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

  • \dfrac{3}{4}+\dfrac{1}{2} = \dfrac{3}{4}+\dfrac{2}{4} = \dfrac{5}{4} \implies b = -\dfrac{5}{4}
  • \dfrac{3}{4} \cdot \dfrac{1}{2} = \dfrac{3}{8} \implies c = \dfrac{3}{8}

And so the equation is

x^2 - \dfrac{5}{4} + \dfrac{3}{8} = 0

In order to have integer coefficients, you can multiply both sides of the equation by 8:

8x^2 - 10 + 3 = 0

5 0
3 years ago
An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before
zheka24 [161]

Answer:

68.2% of the batteries failed between 17.8 and 20.2 hours.

95.44% of the batteries failed between 16.6 and 21.4 hours.

99.97% of the batteries failed between 15.4 and 22.6 hours.

Step-by-step explanation:

The 68-95-99.7 states that, for a normally distributed sample:

68.26% of the measures are within 1 standard deviation of the sample.

95.44% of the measures are within 2 standard deviations of the sample.

99.97% of the measures are within 3 standard deviations of the sample.

In this problem, we have that:

Mean of 19 hours, standard deviation of 1.2 hours.

About 68.26% of the batteries failed between what two values?

This is within 1 standard deviation of the mean. So 68.2% of the batteries failed between 17.8 and 20.2 hours.

About 95.44% of the batteries failed between what two values?

This is within 2 standard deviations of the mean. So 95.44% of the batteries failed between 16.6 and 21.4 hours.

About 99.97% of the batteries failed between what two values?

This is within 3 standard deviations of the mean. So 99.97% of the batteries failed between 15.4 and 22.6 hours.

5 0
3 years ago
Read 2 more answers
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