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MatroZZZ [7]
3 years ago
13

Which mixed number is equivalent to the improper fraction? 14/9

Mathematics
1 answer:
hodyreva [135]3 years ago
3 0

Answer: 1 5/9 (one and five-ninths)

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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
Solve the equation, Write one solution, No solution, Infinitely Many Solution
allsm [11]

Answer:

x=5.3125

One solution

6 0
3 years ago
Read 2 more answers
¿Cuál de los siguientes valores de n hace CIERTA
olga_2 [115]

Answer:

B

Step-by-step explanation:

n³-125=0

n³=125

n= ³√125

n=5

8 0
3 years ago
Mikhael wanted to rewrite the conversion factor "1 yard ≈ 0.914 meter" to create a conversion factor to convert meters to yards.
Nataly [62]

Answer:

1\ meter = 1.094\ yard

Step-by-step explanation:

Given

1\ yard = 0.914\ meter

Required

Create a convert meter to yard expression

1\ yard = 0.914\ meter

Divide both sides by 0.914

\frac{1\ yard}{0.914} = \frac{0.914\ meter}{0.914}

\frac{1\ yard}{0.914} = 1\ meter

1.09409190372\ yard = 1\ meter

1\ meter = 1.09409190372\ yard

1\ meter = 1.094\ yard --- approximated

6 0
3 years ago
There are eight dogs at the veterinarian
kotegsom [21]

Answer: Treats are an essential part of positive reinforcement, rewards-based training, but you also need to be mindful to balance your dog’s treats with their overall daily calories. Give them too many treats and you won’t just spoil their appetite for actual meals, but you could also make your dog overweight and unhealthy.

Step-by-step explanation:

6 0
3 years ago
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