Answer:
okay this question i dont know
1st - 2/3 =π√÷
and if tiu substrate that
the answer is 12358063
you can give me the brainliest if u want
final answer-
325
You forgot to give the choices so I will solve the problem in detail step-by-step explanation and then you can select the correct choice and fill in the answer boxes within your choice correctly.
Given the criteria stated in the problem, we can obtain the following linear system:
![\left \{ {{x_{1} + x_{2} + x_{3} = 28} \atop {6000x_{1} + 12000x_{2} + 24000x_{3} =564000}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx_%7B1%7D%20%2B%20x_%7B2%7D%20%2B%20x_%7B3%7D%20%20%3D%2028%7D%20%5Catop%20%7B6000x_%7B1%7D%20%2B%2012000x_%7B2%7D%20%20%2B%2024000x_%7B3%7D%20%3D564000%7D%7D%20%5Cright.)
The corresponding augmented matrix is
![\left[\begin{array}{ccc|c}1&1&1&28\\6000&12000&24000&564000\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%261%261%2628%5C%5C6000%2612000%2624000%26564000%5Cend%7Barray%7D%5Cright%5D)
→ ![R_{2}\left[\begin{array}{ccc|c}1&1&1&28\\1&2&4&94\end{array}\right] R_{2} +(-1)R_{1}](https://tex.z-dn.net/?f=R_%7B2%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%261%261%2628%5C%5C1%262%264%2694%5Cend%7Barray%7D%5Cright%5D%20R_%7B2%7D%20%2B%28-1%29R_%7B1%7D)
→
→![R_{1} \left[\begin{array}{ccc|c}1&0&-2&-38\\0&1&3&66\end{array}\right]](https://tex.z-dn.net/?f=R_%7B1%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cc%7D1%260%26-2%26-38%5C%5C0%261%263%2666%5Cend%7Barray%7D%5Cright%5D)
The linear system corresponding to the reduced form is
![\left \{ {{x_{1} -2x_{3} =-38} \atop {x_{2}+3x_{3} =66}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx_%7B1%7D%20-2x_%7B3%7D%20%3D-38%7D%20%5Catop%20%7Bx_%7B2%7D%2B3x_%7B3%7D%20%20%3D66%7D%7D%20%5Cright.)
Since
is the free variable, we let
, where
is any real number. Then the general solution can be written as follows:
![\left \{ \begin{array}{ccc}x_{1} =&-38&+2t\\x_{2} =&66&-3t\\x_{3} =&t\end{array}\right](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%5Cbegin%7Barray%7D%7Bccc%7Dx_%7B1%7D%20%3D%26-38%26%2B2t%5C%5Cx_%7B2%7D%20%3D%2666%26-3t%5C%5Cx_%7B3%7D%20%3D%26t%5Cend%7Barray%7D%5Cright)
where
is any real number.
However, the definitions of
,
and
imply that the solutions must be non-negative integers. Therefore, we need to derive the possible range of values of
such that the general solution make sense for this problem:
![\left \{ \begin{array}{ccc}-38&+2t&\geq 0\\66&-3t&\geq 0\\t&&\geq 0\end{array}\right](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%5Cbegin%7Barray%7D%7Bccc%7D-38%26%2B2t%26%5Cgeq%200%5C%5C66%26-3t%26%5Cgeq%200%5C%5Ct%26%26%5Cgeq%200%5Cend%7Barray%7D%5Cright)
Solving the inequalities, we finally obtain all the relevant solutions to the linear system:
![\left \{ \begin{array}{ccc}x_{1} =&-38&+2t\\x_{2} =&66&-3t\\x_{3} =&t\end{array}\right](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%5Cbegin%7Barray%7D%7Bccc%7Dx_%7B1%7D%20%3D%26-38%26%2B2t%5C%5Cx_%7B2%7D%20%3D%2666%26-3t%5C%5Cx_%7B3%7D%20%3D%26t%5Cend%7Barray%7D%5Cright)
where
is any integer such that 19
22.
Thus, you just need to apply the above solution to the choices given to you and fill in the answer boxes correctly.
Multiplying two fractions together corresponds to multiplying together their components, so multiplying -9/10 · -2/3 looks like:
![\frac{-9}{10} \cdot \frac{-2}{3}= \frac{(-9)(-2)}{(10)(3)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-9%7D%7B10%7D%20%5Ccdot%20%5Cfrac%7B-2%7D%7B3%7D%3D%20%5Cfrac%7B%28-9%29%28-2%29%7D%7B%2810%29%283%29%7D%20)
If we rearrange the fractions, we can perform some simplification:
![\frac{(-9)(-2)}{(3)(10)} = \frac{-9}{3} \cdot \frac{-2}{10} =-3\cdot \frac{-1}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28-9%29%28-2%29%7D%7B%283%29%2810%29%7D%20%3D%20%5Cfrac%7B-9%7D%7B3%7D%20%5Ccdot%20%5Cfrac%7B-2%7D%7B10%7D%20%3D-3%5Ccdot%20%5Cfrac%7B-1%7D%7B5%7D%20)
When gets us:
is the original fraction
let the denominator of the original fraction be n, then
is the original fraction
adding 2 to the numerator gives
=
, hence
=
( cross- multiply )
7(n - 2) = 5n
7n - 14 = 5n ( subtract 5n from both sides )
2n - 14 = 0 ( add 14 to both sides )
2n = 14 ( divide both sides by 2 )
n = 7
original fraction =
= ![\frac{3}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B7%7D)
Answer:
The answer is below
Step-by-step explanation:
A rational expression is the ratio of two polynomials. Rational expressions are fractions such that the numerator and denominator are polynomials.
Since there are two rational expressions which can each be simplified to 5 / (x + 3), hence both of the expressions are equivalent to each other. This means that in both of the expressions, each has a numerator that can be simplified to 5 and has a denominator that can be simplified to x + 3.