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3 years ago

What is the root of the polynomial equation x(x-2)(x+3) = 18? Use a graphing calculator and a system of equations.

Mathematics

1 answer:

Trava [24]3 years ago

3 0

9514 1404 393

Answer:

x = 3

Step-by-step explanation:

The equation can be rewritten to make use of the graphing calculator's ability to identify function zeros:

x(x -2)(x +3) -18 = 0

The attached shows x = 3 is the only real solution.

_____

We're not sure what "system of equations" is intended. Perhaps it is ...

y = 18

y = x(x -2)(x +3)

To create the expression we graphed, we effectively subtracted the first equation from the second.

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rewona [7]

Answer:

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3 years ago

Read 2 more answers

If (x - 4) varies inversely as (y + 3) and x = 8 when y = 2, what is x when y = - 1?

denpristay [2]

Answer:

$x=14$

Step-by-step explanation:

If two values are inversely proportional, their product must be maintained. That way, if one value goes up, the other goes down by the same extent.

Therefore, if $(x-4)$ and $(y+3)$ vary inversely, their product will be the same for all values of $x-4$ and $y+3$ .

Let $x=8$ and $y=2$ as given in the problem. Substitute values:

$(8-4)(2+3)=(4)(5)=20$

Hence, the maintained product is $20$ .

Thus, we have the following equation:

$(x-4)(y+3)=20$

Substitute $y=-1$ to find the value of $x$ when $y=-1$ :

$(x-4)(-1+3)=20,\\(x-4)(2)=20,\\x-4=10,\\x=10+4=\boxed{14}$

3 0

2 years ago

Rena spent 6 days reading her book completing the same fraction of the book each day if she had a total of 8/9 of her book after

Artyom0805 [142]

Answer:

The fraction of the book that Rena read every day is $\frac{4}{27}$

Step-by-step explanation:

Rena spent 6 days reading her book completing the same fraction of the book every day and you want to know the fraction of the book she read each day. Knowing that Rena had a total of 8/9 of her book read after 6 days, then you simply divide the total amount of the book read during those days by 6, the number of days:

$\frac{8}{9}$ ÷6

To divide a fraction by a whole number, you must convert the whole number into a fraction, finding the reciprocal of that fraction, and multiply it by the first fraction. That is, you must find the reciprocal of the number that is after the division symbol; and then you multiply the first number (the one before the division symbol) by the reciprocal of the second number (the one after the division symbol). Remember that to find the reciprocal of a number, you simply have to change the numerator and denominator of the number.

Since 6 can be considered to be a fraction equal to $\frac{6}{1}$ , by inverting the number, then you get $\frac{1}{6}$