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3 years ago

Which is a difference of cubes? x6 – 27 x15 – 36 x16 – 64 x5 – 125

Mathematics

2 answers:

shutvik [7]3 years ago

6 0

Answer:

The correct option is 1.

Step-by-step explanation:

The difference of cubes is defined as

$a^3-b^3=(a-b)(a^2+ab+b^2)$

The given expression is

$x^6-27$

It can be written as

$x^6-3^3$

Using the property of exponent, the above expression can be written as

$(x^2)^3-3^3$ $[\because (x^m)^n=x^{mn}]$

This is a difference of cubes.

Therefore the correct option is 1.

prohojiy [21]3 years ago

3 0

Answer:

X6-27 is the answer

Step-by-step explanation:

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Victoria recently switched to a new electric company. If she uses between 0 and 400 kilowatt-hours (kWh) of electricity per mont

Gekata [30.6K]

Answer:

see the explanation

Step-by-step explanation:

The question is

Identify the domain and the range, using words and inequalities

Let

x -----> the number of kilowatt-hours (kWh) of electricity per month

y ----> the price per month

we know that

Part 1) For the value of x between 0 kWh and 400 kWh

$0\ kWh \leq x < 400\ kWh$

The price is equal to

$y=\$30$

therefore

The domain is the interval ------> [0,400)

The domain is all real numbers greater than or equal to 0 kWh and less than 400 kWh

The range is ($30)

The range is equal to $30

Part 2) For the value of x equal to 400 kWh or more per month

$x\geq 400\ kWh$

The domain is the interval -----> [400, infinite)

The domain is all real numbers greater than or equal to 400 kWh

The price is

$y=0.097x$

Find the range

For x=400 kWh

$y=0.097(400)=\$38.8$

$y\geq \$38.8$

The range is the interval -----> [38.8, infinite)

7 0

3 years ago

Which piecewise function is shown in the graph?

mash [69]

Based on the characteristics of linear and piecewise functions, the piecewise function $f(x) = \left \{ {{-0.5\cdot x +1, \,x < 0} \atop {2\cdot x - 2, \,x \ge 0}} \right.$ is shown in the graph attached herein. (Correct choice: A)

<h3>How to determine a piecewise function</h3>

In this question we have a graph formed by two different linear functions. Linear functions are polynomials with grade 1 and which are described by the following formula:

y = m · x + b (1)

Where:

x - Independent variable.
y - Dependent variable.
m - Slope
b - Intercept

By direct observation and by applying (1) we have the following piecewise function:

$f(x) = \left \{ {{-0.5\cdot x +1, \,x < 0} \atop {2\cdot x - 2, \,x \ge 0}} \right.$

To learn more on piecewise functions: brainly.com/question/12561612

#SPJ1

3 0

2 years ago

The burning time of a very large candle is normally distributed with mean of 2500 hours and standard deviation of 20 hours. Find

dezoksy [38]

Answer: C.-1.5

Step-by-step explanation:

Given: The burning time of a very large candle is normally distributed with mean $(\mu)$ of 2500 hours and standard deviation $(\sigma)$ of 20 hours.