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kow [346]
2 years ago
7

Is 74 fl oz greater than less than or equal to 8cups

Mathematics
1 answer:
Mariana [72]2 years ago
6 0
It is greater than because 74 fl. oz. is equal to 9.25 cups.
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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
2 years ago
Jennifer pays $12.50 a month for Amazon Prime and pays extra every time she rents a movie. One month she rented 1 movie and paid
Dafna1 [17]

Answer: y=5.25x+12.50

Step-by-step explanation:

The original 12.50 is how much she pays each month regardless of rented movies, it is the 0 value and doesn't change. Each rented movie costs 5.25 (17.75-12.50=5.25) and that value would be multiplied by the amount of movies she rents that month, and then added onto the original base value.

6 0
2 years ago
Read 2 more answers
How do I divide 49 by 14
stira [4]
You can do pencil and paper or use a calculator if necessary 
Your answer is
<em>3.5</em>
4 0
3 years ago
Read 2 more answers
A carpenter is building a rectangular room with a fixed perimeter of 440 ft. what are the dimensions of the largest room that ca
olga55 [171]
The biggest it can be is 110 by 110, and the area would be 2,100 ft.

Hope this helps!
4 0
3 years ago
Peter bought p shirts at $(p-4) each. He spent $60 on the shirts. Determine the number of shirts bought.​
DochEvi [55]

Answer:

He bought fifteen shirts.

Step-by-step explanation:

Divide the price of the shirts to mow much they each cost.

4 0
2 years ago
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