PLEASE HELP!! (Look at photo)

A sample of five words was randomly selected from a 200-page book. The average number of letters of the five words was calculate

Butoxors [25]

The answer would be A).

4 0

3 years ago

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Which statement describes the inverse of m(x) = x2 – 17x?

stealth61 [152]

Answer:

The correct option is;

$The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}$

Step-by-step explanation:

The given information is that m(x) = x² - 17·x

The above equation can be written in the form;

y = x² - 17·x

Therefore;

0 = x² - 17·x - y

From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;

$x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}$

By comparison to the equation,0 = x² - 17·x - y, we have;

a = 1, b = -17, and c = -y

Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;

$x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}$

Which can be simplified as follows;

$x = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2} \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}$

And further simplified as follows;

$x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}$

Interchanging x and y in the function of the inverse, m⁻¹(x), we have;

$m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}$

We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;

m'(x) = 2·x - 17 = 0

x = 17/2

Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;

m''(x) = 2 > 0, therefore, the point is a minimum point on the graph

Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;

$The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}$ to increase m⁻¹(x) above the minimum.

8 0

3 years ago

Question: The meaning of four consecutive even numbers is 15.

nasty-shy [4]

First, a bit of housekeeping:

The meaning of four consecutive even numbers is 15. Wouldn't that be "mean," not meaning? Very different concepts!

The greatest of these numbers is _______ a^1

"a^1" means "a to the first power. There are no powers in this problem statement. Perhaps you meant just "a" or "a_1" or a(1).

The least of these numbers is ______a^2.
No powers in this problem statement. Perhaps you meant a_2 or a(2)

In this problem you have four numbers. All are even, and there's a spacing of 2 units between each pair of numbers (consecutive even).

The mean, or arithmetic average, of these numbers is (a+b+c+d) / 4, where a, b, c and d represent the four consecutive even numbers. Here this mean is 15. The mean is most likely positioned between b anc c.

So here's what we have: a+b+c+d
------------- = 15
4

This is equivalent to a+b+c+d = 60.

Since the numbers a, b, c and d are consecutive even integers, let's try this:

a + (a+2) + (a+4) + (a+6) = 60. Then 4a+2+4+6=60, or 4a = 48, or a=12.

Then a=12, b=14, c=16 and d=18. Note how (12+14+16+18) / 4 = 15, which is the given mean.

We could also type, "a(1)=12, a(2)=14, a(3) = 16, and a(4) = 18.

8 0

3 years ago

10. Giselle invests $16,250 in an account that earns 4.25% interest, compounded continuously.

denis-greek [22]

Answer: 24 years

Step-by-step explanation:

% • total = Answer

4.25% • $40,000 = Answer

.0425 • $40,000 = Answer

Answer = $1,700 per year

40,000 ÷ 1,700 = 23.5

23.5 rounded to the nearest year is 24

3 0

3 years ago

Solve the equation 7x-c=k for x

Vlad1618 [11]

Answer:

x=k+c over 7

Step-by-step explanation:

7x-c+c=k+c

7x=k+c

divide both sides by 7

4 0

3 years ago