Ten bag of beans cost 350:00cedi find the cost of 6 bags

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

3 0

1 year ago

Find all values of the variable

labwork [276]

The values of x for which the rational expression is undefined are -6 and -8.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a rational function:

$\rm f(x) = \dfrac{3x+20}{x^2+14x+48}$

As we know in the rational function denominator cannot be zero:

The values of x for which the rational expression is undefined.

x² + 14x + 48 = 0

$\rm x_{1,\:2}=\dfrac{-14\pm \sqrt{14^2-4\cdot \:1\cdot \:48}}{2\cdot \:1}$

$\rm x_1=\dfrac{-14+2}{2\cdot \:1},\:x_2=\dfrac{-14-2}{2\cdot \:1}$

x = -6, -8

Thus, the values of x for which the rational expression is undefined are -6 and -8.

Learn more about the function here:

brainly.com/question/5245372

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6 0

1 year ago

A teacher passes cards out to students. She has 52 cards. She gives one card to each student at a time to each student until all

Zarrin [17]

The problem presents 2 variables and 2 conditions to follow to determine the approach in solving the problem. The variables are 52 cards, and 9 cards. The 2 conditions presented would be the teacher giving out one card to each student at a time to each student until all of them are gone. The second variable is more likely made as a clue and the important variable that gives away the approach to be used. The approach to be used is division. This is to ensure that there will be students receiving the 9 cards. Thus, we do it as this: 52 / 9 = ?

The answer would be 5.77778 (wherein 7 after the decimal point is infinite and 8 would just be the rounded of number). This would ensure us that there will be 5 students that can receive 9 cards but there will be 7 cards remaining which goes to the last student, which is supposed to be 8 since she gives one card to each student at a time to each student. So the correct answer would be just 4 students. The fifth student will only receive 8 cards and the last student would have 8, too.

6 0

2 years ago

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Ten bag of beans cost 350:00cedi find the cost of 6 bags​

Ten bag of beans cost 350:00cedi find the cost of 6 bags