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alukav5142 [94]

3 years ago

10

The Taieri Plain in New Zealand is 6 feet below sea level (or –6 feet). If you are standing 3 feet above sea level, is your elev

ation the opposite of the elevation of the plain? Describe the steps you would follow with a vertical number line to find the answer.

2 answers:

TiliK225 [7]3 years ago

8 0

Answer:

no

Step-by-step explanation:

Opposite numbers are the same distance from 0 on the number line, but in opposite directions. Steps I would follow:

first, check the directions to make sure they are opposite,
then read the digits, or count the tick marks or compare lengths with dividers or ruler or marks on a piece of paper to see if the distances are the same.

3 is not the opposite of -6

__

6 is the opposite of -6

Iteru [2.4K]3 years ago

7 0

Answer: Sample Response: Although 6 and 3 are on opposite sides of sea level, or 0, they are not opposites because they are unequal distances from 0.

Step-by-step explanation:

3 is 3 units above 0 on a vertical number line.

–6 is 6 units below 0 on a vertical number line.

3 is not the opposite of –6.

Opposites are equal distances from 0.

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Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x3 − 6x2 − 15x + 2 (a) Find the interval on which

Burka [1]

Answer:

a) $(-\infty, -1) \cup (5, \infty)$

b) $(-1,5)$

Step-by-step explanation:

The first step to solve this question is finding the roots of the derivative of x.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$f(x) = x^{3} - 6x^{2} - 15x + 2$

So

$f'(x) = 3x^{2} - 12x - 15$

Finding the roots:

$3x^{2} - 12x - 15 = 0$

Simplifying by -3

$x^{2} - 4x - 5 = 0$

So $a = 1, b = -4, c = -5$

Then

$\bigtriangleup = (-4)^{2} - 4*1*(-5) = 36$

$x_{1} = \frac{-(-4) + \sqrt{36}}{2} = 5$

$x_{2} = \frac{-(-4) - \sqrt{36}}{2} = -1$

So the function can be divided in three intervals.

They are:

Less than -1

Between -1 and 5

Higher than 5

In which it increases and which it decreases?

Less than -1

Lets find the derivative in a point in this interval, for example, -2

$f'(x) = 3x^{2} - 12x - 15$

$f'(-2) = 3*(-2)^{2} - 12*(-2) - 15 = 21$

Positive.

So in the interval of $(-\infty, -1)$ , the function increases.

Between -1 and 5

Will choose 0.

$f'(x) = 3x^{2} - 12x - 15$

$f'(0) = 3*(0)^{2} - 12*(0) - 15 = -15$

Negative.

So in the interval of $(-1,5)$ , the function decreases.

Higher than 5

Will choose 6.

$f'(x) = 3x^{2} - 12x - 15$

$f'(6) = 3*(6)^{2} - 12*(6) - 15 = 21$

Positive

So in the interval of $(5, \infty)$ , the function increases.

(a) Find the interval on which f is increasing.

Using interval notation

$(-\infty, -1) \cup (5, \infty)$

b) Find the interval on which f is decreasing.

$(-1,5)$

5 0

3 years ago

Which statements could he include in his explanation? Select two options.

lions [1.4K]

Answer:

The domain of fx is x>5

The domain of gx is x>5

8 0

4 years ago

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Find the coordinates of the midpoint of the segment whose endpoints are given . e(4,-4) , f (1,7)

laila [671]

Let g(x,y) be the midpoint of the segment ef;
So, x = (4+1)/2; then x = 5/2;
y = (-4+7)/2; then y = 3/2;
Finally, g(5/2,3/2).

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3 years ago

A shirt boutique purchased 100 new shirts for $1072. The short-sleeved shirts cost $10 each and the long-sleeved shirts cost $12

Scilla [17]

Answer:

one equation would be S+ L=36for the number of shirts sold.

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rusak2 [61]

Step-by-step explanation:

hold up bro. this doesn't even say what u actualy have to do . or is just so blurry

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3 years ago