<img src="https://tex.z-dn.net/?f=3%20%2B%20%20%5Cfrac%7Bx%20-%203%7D%7B9%20-%20%20%7Bx%7D%5E%7B2%7D%20%7D%20%5Cdiv%203%20-%20%2

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2 years ago

0%5Cfrac%7B4%7D%7Bx%20%2B%203%7D%20%20" id="TexFormula1" title="3 + \frac{x - 3}{9 - {x}^{2} } \div 3 - \frac{4}{x + 3} " alt="3 + \frac{x - 3}{9 - {x}^{2} } \div 3 - \frac{4}{x + 3} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

malfutka [58]2 years ago

7 0

$\frac{3 + \frac{x - 3}{9 - {x}^{2} } }{3 -\frac{4}{x + 3} } \\ = \frac{ \frac{3(9 - {x}^{2} ) + x - 3}{9 - {x}^{2} } }{ \frac{3(x + 3) - 4}{x + 3} } \\ = \frac{27 - 3 {x}^{2} + x - 3}{9 - {x}^{2} } \times \frac{x + 3}{3x + 12 - 4} \\ = \frac{ - 3 {x}^{2} + x + 24 }{ - (x - 3)(x + 3)} \times \frac{x + 3}{3x + 8} \\ = \frac{ - (3x + 8)(x - 3)}{ - (x - 3)} \times \frac{1}{3x + 8} \\ = \frac{ - (x - 3)}{ - (x - 3)} \\ = 1$

Hope this helps. - M

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The population of a city is modeled by the equation P(t)=232012e0.23t where t is measure in years. If the city continues to grow

Gennadij [26K]

In around 6.35 years, the population will be 1 million.

<h3> how many years will it take for the population to reach one million?</h3>

The population is modeled by the exponential equation:

$P(t) = 232,012*e^{0.23*t}$

Then we just need to solve the equation for t:

$P(t) = 232,012*e^{0.23*t} = 1,000,000$

Let's solve that:

$232,012*e^{0.23*t} = 1,000,000\\\\e^{0.23*t} = 1,000,000/232,012 = 4.31\\$

If we apply the natural logarithm to both sides:

$ln(e^{0.23*t}) = ln(4.31)\\\\0.23*t = ln(4.31)\\\\t = ln(4.31)/0.23 = 6.35$

So in around 6.35 years, the population will be 1 million.

If you want to learn more about exponential equations:

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1 year ago

I don’t understand :(

viktelen [127]

Answer:

The quotient when $x^3-4x^2-8x+8$ is divided by $x+2$ is $x^2-6x+4$ with no remainder, so x+2 is a factor of p(x).

Step-by-step explanation:

As the question suggests, there are two ways to solve this problem: long division (which can always be used to divide polynomials), and synthetic division (which can only be used when you are dividing by something of the form $(x-a)$ . In this case, we may use synthetic division, since $x+2$ is equal to $x-(-2)$ . I will use synthetic division here as it is slightly faster than long division.

The -2 on the left represents that we are dividing by x-(-2), and the rest of the numbers in the top row are the coefficients of p(x): 1, -4, -8, and 8.

The first step in synthetic division is to being down the leading coefficient of the polynomial: in this case, the 1 (as indicated in red). Now, we multiply the 1 by -2. We get -2, which we place directly below the -4.

Next, we add directly down the column, (-4 + (-2) is equal to -6), and this answer is placed in the box below. We can continue this process, getting the coefficients 1, -6, 4, and 0 in the bottom row.

This is the answer: the quotient is $x^2-6x+4$ , and the remainder is zero (which indicates that x+2 is a factor of p(x)).

Edit: long division

We may also solve this problem using long division (see the second image). The first step is to look at the leading coefficients: since $x \times x^2$ is equal to $x^3$ , the first term in the quotient will be $x^2$ . Since $x^2 \times (x+2)$ is equal to $x^3+2x^2$ , we must now subtract that from $x^3-4x^2-8x+8$ .

We repeat the same process, as shown in the image. Since we eventually get to zero, the remainder is zero, and the polynomial at the top (x^2-6x+4) is the quotient.

I know this might be difficult to follow, so please comment if you have any questions.

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2 years ago

Problem #2

marta [7]

Fractions can be converted to decimals and vice versa.

The decimal equivalent of the fraction of months with 31 days is 0.583

Given:

$Total = 12$ --- months in a year

$Months = 7$ --- months with 31 days

The fraction (n) of months with 31 days is:

$n = \frac{Months}{Total}$

So, we have:

$n = \frac{7}{12}$

The decimal equivalent is:

$n = 0.583$

Hence, (c) is correct.

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2 years ago

Explaining Factored Form The trinomial x2 + bx – c has factors of (x + m)(x – n), where m, n, and b are positive. What is the re

Sliva [168]

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2 years ago

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There are 96 female staff in an office. If the ratio of male staff to female staff is 3:4, find the number of male staff.

Alex

Answer:60 male staff

Step-by-step explanation:

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2 years ago