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3 years ago

Ethan buys a video game on sale. If the video game usually costs $49.99, and it was on sale for 30% off.

Mathematics

2 answers:

Nata [24]3 years ago

6 0

Answer:

$34.99

Step-by-step explanation:

49.99 - 14.997=

34.99

Yakvenalex [24]3 years ago

6 0

Answer:

the answer is 34.99

if you want me to explain i will ")

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Determine the domain of the function (fog)(x) where f(x)=3x-1/x-4 and g(x)=x+1/x

Katarina [22]

Answer: (-∞,-1) ∪ (0,+∞)

Step-by-step explanation: The representation fog(x) is a representation of composite function, meaning one depends on the other.

In this case, fog(x) means:

fog(x) = f(g(x))

fog(x) = $3(x+\frac{1}{x} )-\frac{1}{x+\frac{1}{x} } -4$

$fog(x)=3x+\frac{3}{x} -\frac{1}{\frac{x^{2}+x}{x} } -4$

$fog(x)=3x+\frac{3}{x} -\frac{x}{x^{2}+x} -4$

$fog(x)=\frac{3x^{2}(x^{2}+x)+3(x^{2}+x)-x-4x(x^{2}+x)}{x(x^{2}+x)}$

$fog(x)=\frac{3x^{4}+3x^{3}+3x^{2}+3x-x-4x^{3}+4x^{2}}{x(x^{2}+x)}$

$fog(x)=\frac{3x^{4}-x^{3}-x^{2}+2x}{x(x^{2}+x)}$

This is the function fog(x).

The domain of a function is all the values the independent variable can assume.

For fog(x), denominator can be zero, so:

$x(x^{2}+x) \neq 0$

If x = 0, the function doesn't exist.

$x^{2}+x \neq0$

$x(x+1) \neq0$

$x+1\neq0$

$x\neq-1$

<u>Therefore, the domain of this function is: </u><u>-∞ < -1 or x > 0</u>

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2 years ago

What is the reason that m<2 and m<3 are supplementary

katen-ka-za [31]

Answer:

see explanation

Step-by-step explanation:

∠2 and ∠3 are same- side interior angles and are supplementary.

6 0

3 years ago

Determine, to one decimal place, the length, width & height of the rectangular prism that would have the greatest volume, wi

Leya [2.2K]

Answer:

The length = The width = The height ≈ 5.8 cm

Step-by-step explanation:

The volume of a rectangular pyramid, V = l × w × h

The surface area of the pyramid = 2 × l × h + 2 × w × h + 2 × l × w = 200

∴ l × h + w × h + l × w = 200/2 = 100

We have that the maximum volume is given when the length, width, and height are equal and one length is not a fraction of the other. Therefore, we get;

At maximum volume, l = w = h

∴ l × h + w × h + l × w = 3·l² = 100

l² = 100/3

l = 10/√3

Therefore, the volume, v = l³ = (10/√3)³

The length = The width = The height = 10/√3 cm ≈ 5.8 cm

7 0

2 years ago

Which is equivalent to x^3 y^-7

PilotLPTM [1.2K]

For this case we must find an expression equivalent to:

$x ^ 3 * y ^ {- 7}$

By definition of power properties we have to meet:

$a ^ {-1} = \frac {1} {a ^ 1} = \frac {1} {a}$

Then, we can rewrite the expression as:

$x ^ 3 * \frac {1} {y ^ 7} =\\\frac {x ^ 3} {y ^ 7}$

Answer:

$\frac {x ^ 3} {y ^ 7}$

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2 years ago

Find the area and perimeter of the given rectangle.

jeka94

Answer:

The Area is 99 units², while the perimeter is 40 units

Step-by-step explanation:

Area can be found by multiplying the length of the rectangle by the width of the rectangle. Counting the boxes on the side gives you 11 horizontally and 9 vertically. Multiplying these two gives you an area of 99. The measurement is in units because there is no given unit of measurement such as inches, feet, or meters. Area is always squared which is why there is a ² after units.

Perimeter can be found by adding all 4 sides together. Counting the boxes gives you 11 + 11 + 9 + 9. This gives you a perimeter of 40. The measurement is in units because there is no given unit of measurement such as inches, feet, or meters. Perimeter is not squared like area.

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3 years ago

Ethan buys a video game on sale. If the video game usually costs $49.99, and it was on sale for 30% off.​

Ethan buys a video game on sale. If the video game usually costs $49.99, and it was on sale for 30% off.