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3 years ago

The piecewise function f(x) has opposite expressions. f(x) = Which is the graph of f(x)?

Mathematics

2 answers:

agasfer [191]3 years ago

8 0

its the third graph or answer c

Anarel [89]3 years ago

6 0

Answer:

4) is the opposite function of 3), and vice versa. Because f(x) =2x-1 and its opposite f(x)=-2x+1. And we can see them both in pictures 3 and 4.

Step-by-step explanation:

A piecewise function is a function defined in a sequence of intervals. The most known piecewise function is the modular function. (1st picture)

An opposite function is given by f(x)=-x of f(x)=x

The following pictures describe the following functions:

1) f(x)=-|2x|+2

2) f(x)= 2.34x-2.34 and f(x)= -2.34x-2.34

Notice how the second function express the opposite line, by the opposite angular coefficient.

3) f(x) =2x-1 and f(x)=-2x+1

4) f(x) = -2x+1 and f(x)=2x-1

Different intervals but the same functions are graphed in 3 and 4. So the graph of f(x)=2x-1 and its opposite f(x)=-2x-1

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Write the equation of the line perpendicular to 2x+3y=9 that passes through (-2,5). Write your answer in slope-intercept form. S

Harman [31]

ANSWER

$y = \frac{3}{2} x + 8$

EXPLANATION

The line given to us has equation,

$2x + 3y = 9$

We need to write this equation in the slope intercept form to obtain,

$3y = - 2x + 9$

$\Rightarrow \: y = - \frac{2}{3}x + 3$

The slope of this line is

$m_1 = - \frac{2}{3}$
Let the slope of the perpendicular line be

$m_2$

Then
$m_1 \times m_2 = - 1$

$- \frac{2}{3} m_2= - 1$

This implies that,

$m_2 = - 1 \times - \frac{3}{2}$

$m_2 = \frac{3}{2}$

Let the equation of the perpendicular line be,

$y = mx + b$

We substitute the slope to get,

$y = \frac{3}{2} x + b$

Since this line passes through
$(-2,5)$
it must satisfy its equation.

This means that,

$5= \frac{3}{2} ( - 2)+ b$

$5 = - 3 + b$

$5 + 3 = b$

$b = 8$

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$y = \frac{3}{2} x + 8$

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3 years ago

What is the value of x? assume that the line is tangent to the circle

nekit [7.7K]

Answer:

70°

Step-by-step explanation:

Connect the center of the circle with endpoints of the chord. Let the center of the circle be point O and endpoints of the chord be points A (let point A lie on the tangent line too)and B.

From the figure, central angle AOB has the measure of 220°.

Consider triangle AOB. This triangle is isosceles triangle because OA and OB are both radii. In this triangle the measure of angle AOB is 360° - 220° = 140°.

Angles OAB and OBA are angles adjacent to the base AB, so they are congruent. The sum of the measures of all interior angles in triangle is always 180°, so

m∠OAB + m∠OBA + m∠AOB = 180°

m∠OAB = m∠OBA = 1/2 (180° - 140°)

m∠OAB = 20°

Since drawn line is tangent line, then OA is perpendicular to this tangent line and

x° = 90° - 20°

x° = 70°

4 0

3 years ago