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Ivahew [28]
3 years ago
11

Rita is hiking along a trail that is 15.8 miles long. So far she has hiked along one-tenth of the trail. How far has Rita hiked?

Mathematics
1 answer:
Phantasy [73]3 years ago
8 0
The answer is 1.58 miles
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The volume of a triangular prism is increased by a factor of 8.
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4

Step-by-step explanation:

when all the lengths are multiplied by x (length scale factor), the volumes are multiplied by x³ (volume scale factor).

∴ when volume scale factor = 8

the length scale factor = ∛8 = 2

while When all the lengths are multiplied by x (length scale factor), the areas are multiplied by x² (surface area scale factor).

∴ when the length scale factor =  2

the surface area scale factor = 2² = 4

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Find the distance between points M and N<br><br>M= (3,-2)<br>N= (5,-6)<br><br><br>​
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MN = \sqrt{(5-3)^{2}+(-6-(-2))^{2}  } = \sqrt{2^{2}+(-4)^{2}  } = \sqrt{20} = 2\sqrt{5}

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Two lines intersect creating angles with the measures shown below.
Basile [38]

Answer:

The angles are called Vertical Angles. And vertical angles are always equal. So,

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3 years ago
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
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