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2 years ago

What is the value of 8 in 686,293

1 answer:

4 0

The answer is 80,000. I learned how to solve this many years ago by finding the number in the problem then simply adding zeros after it in replacement for the rest. Also know as eighty thousand

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Write the equation of a line perpendicular to 3x + 4y = 9 that passes through (8, - 4)

Arisa [49]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's find the slope of 3x + 4y = 9, by simply putting it in slope-intercept form.

$\bf 3x+4y=9\implies 4y=-3x+9\implies y=-\cfrac{3x+9}{4}\implies y=\stackrel{slope}{-\cfrac{3}{4}}x+\cfrac{9}{4} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{4}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{4}{3}}\qquad \stackrel{negative~reciprocal}{+\cfrac{4}{3}}\implies \cfrac{4}{3}}$

so we're really looking for the equation of a line whose slope is 4/3 and runs through 8, -4.

$\bf (\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})~\hspace{10em} slope = m\implies \cfrac{4}{3} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-4)=\cfrac{4}{3}(x-8) \implies y+4=\cfrac{4}{3}x-\cfrac{32}{3} \\\\\\ y=\cfrac{4}{3}x-\cfrac{32}{3}-4\implies y=\cfrac{4}{3}x-\cfrac{44}{3}$

5 0

2 years ago

If a yard is 3 feet long how many inches are in a yard

Likurg_2 [28]

there are 36 inches in a yard

8 0

3 years ago

Read 2 more answers

the school newspaper has a circulation of 500 and sells for $.035 a copy. the students decide to raise the price to increase the

Alik [6]

Let x be the number of times they raise the price on the newspaper. Then the new cost of the newspaper is

$.35+.05x$

Let y be the newspaper they sell, then the income will be

$y(.35+.05x)$

Now, we know that the circulation is of 500, assuming that they sold every newspaper at the original price now the number the will sell will be

$y=500-20x$

Plugging the value of y in the first expression we have that the income will be

$\begin{gathered} f(x)=(500-20x)(.35+\text{0}.5x)=175+25x-7x-x^2 \\ =-x^2+18x+175 \end{gathered}$

Then the income is given by the function

$f(x)=-x^2+18x+175$

To find the maximum value of this functions (thus the maximum income) we need to take the derivative of the function,

$\begin{gathered} \frac{df}{dx}=\frac{d}{dx}(-x^2+18x+175) \\ =-2x+18 \end{gathered}$

no we equate the derivative to zero and solve for x.

$\begin{gathered} \frac{df}{dx}=0 \\ -2x+18=0 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}$

This means that we have an extreme value of the function when x=9. Now we need to find out if this value is a maximum or a minimum. To do this we need to take the second derivative of the function, then

$\begin{gathered} \frac{d^2f}{dx^2}=\frac{d}{dx}(\frac{df}{dx}) \\ =\frac{d}{dx}(-2x+18) \\ =-2 \end{gathered}$

Since the second derivative is negative in the point x=9, we conclude that this value is a maximum of the function.

With this we conclude that the number of times that they should raise the price to maximize the income is 9. This means that they will raise the price of the newspaper (9)($0.05)=$0.45.

Therefore the price to maximize the income is $0.35+$0.45=$0.80.

4 0

11 months ago

For each sentence below, find the value of x that makes each sentence true.

vitfil [10]

ANSWER

1. $x=\frac{1}{2}$