Determine whether the lines given in each box are parallel, perpendicular, or neither

A company's profit C (in thousands of dollars) can be modeled by the polynomial function C = - 5x ^ 3 + 6x ^ 2 + 15x , where x i

steposvetlana [31]

Answer:

849 items.

Step-by-step explanation:

Given that the profit C (in thousands of dollars) for x thousands of items related as

$C = - 5x ^ 3 + 6x ^ 2 + 15x \\\\\Rightarrow -5x^3+6x^2+15x -C=0\cdots(i)$

As the profit is $14,000 for producing 2000 items, so

C= 14 thousand dollars and

x= 2 thousand items.

Putting C= 14 in the equation ( we have),

$-5x^3+6x^2+15x -14=0\cdots(ii)$

Now, x=2 is one of the solutions to the equation (ii), so (x-2) is a factor of the equation (ii), we have

$(x-2)(-5x^2-4x+7)=0 \\\\\Rightarrow x-2=2 \; or \; -5x^2-4x+7=0$

We have the given solution for x-2=0, so sloving -5x^2-4x+7=0 for other solutions.

$-5x^2-4x+7=0 \\\\\Rightarrow x= \frac {-(-4)\pm \sqrt {(-4)^2-4\times (-5)7}}{2\times (-5)} \\\\\Rightarrow x= \frac {4\pm \sqrt {156}}{2\times (-5)} \\\\\Rightarrow x= \frac {4\pm 12.49}{2\times (-5)} \\\\\Rightarrow x = \frac {4+ 12.49}{2\times (-5)}, \frac {4- 12.49}{2\times (-5)} \\\\\Rightarrow x = -1.649, 0.849$

As the number of items cant be negative, so x= 0.849 thousand is the other number of items.

Hence, the other number of items for the same profit is 849 items.

4 0

3 years ago

A kid spent $100.00 to get 100 toy animals. The child bought at least one cat, one fish, and one bird, and did not buy any other

Rama09 [41]

Answer:

5 cats, 1 fish and 94 birds

Step-by-step explanation:

Let

c be the number of cats;
b be the number of birds;
f be the number of fish.

A kid bought 100 toy animals, then

$c+b+f=100$

If a cat costs $10.00, then c cats cost $10c.

If a fish costs $3.00, then f fish cost $3f.

If a bird costs $0.50, then b birds cost $0.5b.

In total,

$10c+3f+0.5b=100$

We get the system of two equations:

$\left\{\begin{array}{l}c+b+f=100\\10c+3f+0.5b=100\end{array}\right.$

From the first equation:

$b=100-c-f$

Substitute it into the second equation:

$10c+3f+0.5(100-c-f)=100\\ \\10c+3f+50-0.5c-0.5f=100\\ \\9.5c+2.5f=50\\ \\95c+25f=500\\ \\19c+5f=100\\ \\f=20-\dfrac{19}{5}c$

Number f must be a whole number greater than 0, so

$20-\dfrac{19}{5}c>0\\ \\c$

Number c must be a multiple of 5, thus the only possible value for c is 5.

When c = 5, then

$f=20-5\cdot \dfrac{19}{5}=20-19=1\\ \\b=100-5-1=94$

8 0

3 years ago

Write 9 and 250 thousandths as a mixed number

Naddik [55]

9 and 250 thousandths written as a mixed number is as much as 9 250/1000. We can simplify it, so we'll get:

9 25/100

Or even:

<u>9 1/4
</u>
I hope it will help you :)

4 0

4 years ago

Ava is 4 years younger than Eli. The sum of their ages is 30. How old is Eli?

Damm [24]

Eli is 17 years old because 17-4=13
and 17+13=30

5 0

3 years ago

How do I solve this question?

zubka84 [21]

Answer:

$f(x) = \frac{108}{7} (\frac{7}{6})^x$ or $f(x) = 15.429(1.167)^x$

Step-by-step explanation:

No need for a calculator.

Assuming that the equation is in the form $y = ab^x$ , we can plug in points to get our equation. For ease, let's use (1,18) and (2,21). When plugging these points in, we get $18 = ab^1, 21 = ab^2$ . Now let's divide the equations to get rid of $a$ : $\frac{21 = ab^2}{18 = ab^1} = \frac{21}{18} = \frac{7}{6} = b$ . Now that we have $b$ , we can plug in the value we just calculated to solve for $a$ : $18 = a(\frac{7}{6} )^1$ , and solving for $a$ , we get $a = \frac{108}{7}$ .

So the $f(x) = (\frac{108}{7})(\frac{7}{6} )^x$

This equation in decimal form (rounded to the nearest thousandth) is $f(x) = 15.429(1.167)^x$ .

hope this helped! :)

4 0

2 years ago