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3 years ago

The functions f(x) and g(x) are defined below.

Mathematics

2 answers:

Georgia [21]3 years ago

5 0

<h3>Answer:</h3>

none of the above

<h3>Step-by-step explanation:</h3>

This question wants you to see that the radical can be simplified because it is ...

$f(x)=\sqrt{(x+6)^2}$

The answer choices show you are expected to simplify this to ...

... f(x) = x +6

Then

... f(x)·g(x) = (x+6)(x³ -12) = x⁴ +6x³ -12x -72 . . . . . matches choice C

_____

However,

... f(x) = |x+6| . . . . . . . √(x^2) = |x|, the positive root regardless of sign of x

so the product f(x)·g(x) only matches selection C for x≥ -6. It matches the opposite of selection C for x ≤ -6.

The attached graph shows this. It graphs f(x), g(x), f(x)·g(x) (as a purple curve), and selection C (as orange dots).

SCORPION-xisa [38]3 years ago

4 0

Answer:

The answer is C. $x^{4}+6x^{3} -12x-72$

Step-by-step explanation:

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Write an equation in standard form for the line, where the points (-2, -1) and (0, 4) are on the line

DedPeter [7]

Answer:

An equation in standard form for the line is:

$\frac{5}{2}x-y=-4$

Step-by-step explanation:

Given the points

(-2, -1) and (0, 4)

The slope between two points

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:4\right)$

$m=\frac{4-\left(-1\right)}{0-\left(-2\right)}$

$m=\frac{5}{2}$

Writing the equation in point-slope form

As the point-slope form of the line equation is defined by

$y-y_1=m\left(x-x_1\right)$

Putting the point (-2, -1) and the slope m=1 in the line equation

$y-\left(-1\right)=\frac{5}{2}\left(x-\left(-2\right)\right)$

$y+1=\frac{5}{2}\left(x+2\right)$

$y=\frac{5}{2}x+4$

Writing the equation in the standard form form

As we know that the equation in the standard form is

$Ax+By=C$

where x and y are variables and A, B and C are constants

$y=\frac{5}{2}x+4$

$\frac{5}{2}x-y=-4$

Therefore, an equation in standard form for the line is:

$\frac{5}{2}x-y=-4$

7 0

2 years ago

The area of juans garden

mario62 [17]

What shape is the garden?square, rectangle, circle or... just use the area of any these shapes that is mach to the garden.

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3 years ago

Suppose f(x)=2x−5. Find the value of f(3)<br><br> can someone please help me with this?

dmitriy555 [2]

f(3) = 1

substitute x = 3 into f(x)

f(3) = (2 × 3) - 5 = 6 - 5 = 1

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2 years ago

Harold bought 3 pounds of red apples and 4.2 pounds of green apples from a grocery store, where both kinds of apples are $1.75 a

Lelechka [254]

The answer is 11.6
add 3+4.2= 7.2 times 1.75

4 0

2 years ago

10 ft

Gnom [1K]

Answer:

105.12 feets

Step-by-step explanation:

From the figure x we can identify a rectangle and a semicircle :

Area of rectangle = Length * width

Area = 8 * 10 = 80 feet²

The Area of a semicircle = 1/2πr²

Radius, r = 8 /2 = 4 feets

A = 1/2 * 3.14 * 4²

A = 3.14 * 8

A = 25.12 feet²

Area of figure = 80 + 25.12 = 105.12 feets

4 0

2 years ago