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Helen [10]
3 years ago
9

Write a division problem whose quotient has its first digit in the hundreds place

Mathematics
1 answer:
Katen [24]3 years ago
6 0
<span>Here's one --> 1000÷100=10</span>
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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
Click on the number line below to show the approximate location of 19 on the number line.
dsp73

Answer:

Between 4 and 5

Step-by-step explanation:

The closest square numbers are 16 and 25, so it’s in between 4 and 5

8 0
2 years ago
How many times larger is “8 x 10 to the power of 4” then “8 x 10 to the power of 1”
Pachacha [2.7K]
The Answer would be D
3 0
3 years ago
Read 2 more answers
Number 27.
atroni [7]
<h3>Answer:</h3>

none of these has "no solution"

<h3>Explanation:</h3>

A. The solution is (8/3, 3)

B. The second equation is -1/2 times the first, so these describe the same line. The system has an <em>infinite number of solutions</em>.

C. The solution is (-4, -2)

D. The solution is (4, -2)

E. The second equation is 2 times the first, so these describe the same line. The system has an <em>infinite number of solutions</em>.

_____

A system of equations will have "no solution" when it describes parallel lines—lines that do not intersect. In standard form, such equations are recognizable by their different constants. For example,

  • 3x -4y = -4
  • 3x -4y = 20 . . . . . . 20 is different from -4

have different constants, so the equations describe parallel lines.

We could multiply one of these by -2 and the system would still be "inconsistent"—having no solution.

  • 3x -4y = -4
  • -6x +8y = -40
5 0
3 years ago
Can someone help fast?
guajiro [1.7K]

Answer:

what is it?

Step-by-step explanation:

what's your question

7 0
3 years ago
Read 2 more answers
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