Graph the system of linear equations. y = x + 5 and y = 2x + 2.

Nastasia [14]

Answer:
If m is nonnegative (ie not allowed to be negative), then the answer is m^3
If m is allowed to be negative, then the answer is either |m^3| or |m|^3

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Explanation:

There are two ways to get this answer. The quickest is to simply divide the exponent 6 by 2 to get 6/2 = 3. This value of 3 is the final exponent over the base m. Why do we divide by 2? Because the square root is the same as having an exponent of 1/2 = 0.5, so
sqrt(m^6) = (m^6)^(1/2) = m^(6*1/2) = m^(6/2) = m^3
This assumes that m is nonnegative.

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A slightly longer method is to break up the square root into factors of m^2 each and then apply the rule that sqrt(x^2) = x, where x is nonnegative

sqrt(m^6) = sqrt(m^2*m^2*m^2)
sqrt(m^6) = sqrt(m^2)*sqrt(m^2)*sqrt(m^2)
sqrt(m^6) = m*m*m
sqrt(m^6) = m^3
where m is nonnegative

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If we allow m to be negative, then the final result would be either |m^3| or |m|^3.

The reason for the absolute value is to ensure that the expression m^3 is nonnegative. Keep in mind that m^6 is always nonnegative, so sqrt(m^6) is also always nonnegative. In order for sqrt(m^6) = m^3 to be true, the right side must be nonnegative.

Example: Let's say m = -2
m^6 = (-2)^6 = 64
sqrt(m^6) = sqrt(64) = 8
m^3 = (-2)^3 = -8
Without the absolute value, sqrt(m^6) = m^3 is false when m = -2

4 0

2 years ago

1. What is the prime factorization of 402? * Your answer

docker41 [41]

Answer:

Step-by-step explanation:

Prime factorization requires dividing by primes starting with smallest prime number

402/2=201

201/3=67, 67 is prime so we cannot go further so the prime factorization of 402 is

2X3X67

3 0

2 years ago

In a programming team of 20 persons, 1/4 are women and 3/4 are men. to obtain a team with 40% women, how many women should be hi

Savatey [412]

This is the concept of algebra, to solve the question we proceed as follows;
the current number of women is:
1/4*20=5 women
the percentage of women is:
1/4*100=25%
therefore for the team to have 40% women, the number of women should be:
40/25*5
=8 women
The answer is 8 women

3 0

3 years ago

How do i make (9x-7y=-7) into slope intercept form?

ahrayia [7]

It's called "solve the equation for 'y' ". That means move things
around so that you end up with 'y' all alone on one side, and
everything else on the other side.

You started with 9x - 7y = -7

Subtract 9x from each side: - 7y = -9x - 7

Divide each side by -7 : y = 9/7 x + 1

6 0

2 years ago

F(x)

mina [271]

a) Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.

b) The function $f(x) = \frac{x}{x^{2}+ x}$ is equivalent to the function $g(x) = \frac{1}{x + 1}$ .

<h3>How to determine whether a limit exists or not</h3>

According to theory of limits, a function f(x) exists for x = a if and only if $\lim_{x\to a^{-}} f(x) = \lim_{x \to a^{+}} f(x)$ . This criterion is commonly used to prove continuity of functions.

Rational functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following lateral limits:

$\lim_{x \to -1^{-}} \frac{x}{x^{2}+x} = - \infty$

$\lim_{x \to -1^{+}} \frac{x}{x^{2}+x} = + \infty$

Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.

In addition, we can simplify the function by algebra properties:

$\frac{x}{x^{2}+ x} = \frac{x}{x\cdot (x + 1)} = \frac{1}{x + 1}$

$g(x) = \frac{1}{x + 1}$

The function $f(x) = \frac{x}{x^{2}+ x}$ is equivalent to the function $g(x) = \frac{1}{x + 1}$ .

To learn more on lateral limits: brainly.com/question/21783151

#SPJ1

7 0

1 year ago