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3 years ago

Find the domain and range of y= -|x|-1

Mathematics

2 answers:

Debora [2.8K]3 years ago

7 0

R: (-inf, 0]
D: all real #'s

Mnenie [13.5K]3 years ago

4 0

The Domain is all real numbers, and since the graph is translated 1 down and flipped across the x-axis, the Range is all real numbers less than or equal to -1.

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Calculate the slope of the line going through A(-4,3) and B(0,6)

Whitepunk [10]

Answer:

3/4

Step-by-step explanation:

The slope of the line is given by

m= (y2-y1)/(x2-x1)

= (6-3)/(0 - -4)

= (6-3)/( 0+4)

3/4

5 0

3 years ago

Calculate the total area of the shaded region.

LUCKY_DIMON [66]

so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check

$\stackrel{f(x)}{2x^3-x^2-5x}~~ = ~~\stackrel{g(x)}{-x^2+3x}\implies 2x^3-5x=3x\implies 2x^3-8x=0 \\\\\\ 2x(x^2-4)=0\implies x^2=4\implies x=\pm\sqrt{4}\implies x= \begin{cases} 0\\ \pm 2 \end{cases}$

so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.

$\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill$

$\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}$

7 0

2 years ago

The average kinetic energy of the atoms in an object determines its _____.

Strike441 [17]

I am quite sure that it is B: Temperature

7 0

3 years ago

Read 2 more answers

ABC has coordinates of A(-8,-8) B(4,-2) C(2,2). Find the coordinates of its image after the dilation centered at the origin with

garri49 [273]

Answer:

A' ( -12 , -12 )

B' ( 6 , -3 )

C' ( 3 , 3 )

Step-by-step explanation:

To find the coordinates of a point after a dilation simply multiply the x and y values of the points by the scale factor

Points: A(-8,-8) B(4,-2) C(2,2)

Scale factor: 1.5

Coordinates after the dilation

A' = (-8,-8) --------> (-8 * 1.5 , -8 * 1.5 ) ------------> (-12 , -12)

B' = (4,-2) ---------> (4 * 1.5 , -2 * 1.5) -----------> (6 , -3 )

C' = (2 , 2) ----------> (2 * 1.5 , 2 * 1.5) -----------> (3, 3)

So inclusion the coordinates of ABC after a dilation centered at the origin with a scale factor of 1.5 are A' ( -12 , -12 ) B' ( 6 , -3 ) C' ( 3 , 3 )

4 0

3 years ago

What's the reciprocal of 2/3

jonny [76]

0.16666666666 that is correct

8 0

3 years ago