Answer:
Step-by-step explanation:
Solve the system of inequalities:
x + 4 < 0
OR:
6x > -12
The first inequality yields the solution:
x < -4
The second inequality gives the solution:
x > -2
The total solution is the disjunction of the individual solutions, i.e., the union of both.
It can be expressed as
Check the picture below.
thus, if one side on the square is x - x², then the area for the square is (x - x²)(x - x²), or (x - x²)²
now... what is the "x" value for the region, let's check their intersection.
![\bf \begin{cases} y=x\\ y=x^2 \end{cases}\implies x=x^2\implies 0=x^2-x\implies 0=x(x-1) \\\\\\ x= \begin{cases} 0\\ 1 \end{cases}\\\\ -------------------------------\\\\ \displaystyle \int\limits_{0}^{1}\ (x-x^2)^2\cdot dx\implies \int\limits_{0}^{1}\ (x^2-2x^3+x^4)\cdot dx \\\\\\ \cfrac{x^2}{2}-\cfrac{2x^4}{4}+\cfrac{x^5}{5}\implies \left. \cfrac{x^2}{2}-\cfrac{x^4}{2}+\cfrac{x^5}{5} \right]_{0}^{1}\implies \left[ \cfrac{1}{2}-\cfrac{1}{2}+\cfrac{1}{5} \right]-[0]\implies \cfrac{1}{5}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Ay%3Dx%5C%5C%0Ay%3Dx%5E2%0A%5Cend%7Bcases%7D%5Cimplies%20x%3Dx%5E2%5Cimplies%200%3Dx%5E2-x%5Cimplies%200%3Dx%28x-1%29%0A%5C%5C%5C%5C%5C%5C%0Ax%3D%0A%5Cbegin%7Bcases%7D%0A0%5C%5C%0A1%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%5Cdisplaystyle%20%5Cint%5Climits_%7B0%7D%5E%7B1%7D%5C%20%28x-x%5E2%29%5E2%5Ccdot%20dx%5Cimplies%20%5Cint%5Climits_%7B0%7D%5E%7B1%7D%5C%20%28x%5E2-2x%5E3%2Bx%5E4%29%5Ccdot%20dx%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bx%5E2%7D%7B2%7D-%5Ccfrac%7B2x%5E4%7D%7B4%7D%2B%5Ccfrac%7Bx%5E5%7D%7B5%7D%5Cimplies%20%5Cleft.%20%5Ccfrac%7Bx%5E2%7D%7B2%7D-%5Ccfrac%7Bx%5E4%7D%7B2%7D%2B%5Ccfrac%7Bx%5E5%7D%7B5%7D%20%5Cright%5D_%7B0%7D%5E%7B1%7D%5Cimplies%20%5Cleft%5B%20%5Ccfrac%7B1%7D%7B2%7D-%5Ccfrac%7B1%7D%7B2%7D%2B%5Ccfrac%7B1%7D%7B5%7D%20%5Cright%5D-%5B0%5D%5Cimplies%20%5Ccfrac%7B1%7D%7B5%7D)
Answer:
-1/5+(√3)/20i or -0.2+0.05√3i
Step-by-step explanation:
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<em>Comment on answer form</em>
Satisfying the input format requirements of a computer is always problematic. One never knows if fractions or decimals are preferred, whether radicals must be simplified, and so on. If no clues are offered by general instructions, other questions, or previous experience, then it might be useful to consult your instructor.
The correct statements about the associative property to create equivalent expressions to a + b + (c + d) are as follows.
The associative property allows us to change the grouping of terms that are added together.
When changing the grouping, the order of the terms stays the same; only the parentheses change position.
The expression a + (b + c) + d is an equivalent expression.
The expression (a+ b) + c + d is an equivalent expression.
Given
Use the associative property to create equivalent expressions to a + b + (c + d).
<h3>Associative property;</h3>
Associative property explains that the addition and multiplication of numbers are possible regardless of how they are grouped.
The correct statements about the associative property to create equivalent expressions to a + b + (c + d) are as follows.
- The associative property allows us to change the grouping of terms that are added together.
- When changing the grouping, the order of the terms stays the same; only the parentheses change position.
- The expression a + (b + c) + d is an equivalent expression.
- The expression (a+ b) + c + d is an equivalent expression.
To know more about associative property click the link given below.
brainly.com/question/7043734
