Answer:
lol no. They are still frogs but you probaly not do that. lol
Explanation:
A system of equation is a collection of equations
The system of equation is:
and ![\mathbf{3x + 2y = 3 }](https://tex.z-dn.net/?f=%5Cmathbf%7B3x%20%2B%202y%20%3D%203%20%7D)
The points are given as:
![\mathbf{Line\ m = (0,-8)(1,-2)}](https://tex.z-dn.net/?f=%5Cmathbf%7BLine%5C%20m%20%3D%20%280%2C-8%29%281%2C-2%29%7D)
![\mathbf{Line\ n = (1,3)(3,0)}](https://tex.z-dn.net/?f=%5Cmathbf%7BLine%5C%20n%20%3D%20%281%2C3%29%283%2C0%29%7D)
<u>For line m</u>
Calculate the slope
![\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bm%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%7D)
So, we have:
![\mathbf{m = \frac{-2 + 8}{1 - 0}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bm%20%3D%20%5Cfrac%7B-2%20%2B%208%7D%7B1%20-%200%7D%7D)
![\mathbf{m = \frac{6}{1}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bm%20%3D%20%5Cfrac%7B6%7D%7B1%7D%7D)
![\mathbf{m = 6}](https://tex.z-dn.net/?f=%5Cmathbf%7Bm%20%3D%206%7D)
The equation is then calculated as:
![\mathbf{y = m(x - x_1) + y_1}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%20m%28x%20-%20x_1%29%20%2B%20y_1%7D)
This gives
![\mathbf{y = 6(x - 0) -8}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%206%28x%20-%200%29%20-8%7D)
![\mathbf{y = 6x -8}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%206x%20-8%7D)
Rewrite as:
![\mathbf{6x -y = 8}](https://tex.z-dn.net/?f=%5Cmathbf%7B6x%20-y%20%3D%208%7D)
<u>For line n</u>
Calculate the slope
![\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bm%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%7D)
So, we have:
![\mathbf{m = \frac{0 - 3}{3 - 1}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bm%20%3D%20%5Cfrac%7B0%20-%203%7D%7B3%20-%201%7D%7D)
![\mathbf{m =- \frac{3}{2}}](https://tex.z-dn.net/?f=%5Cmathbf%7Bm%20%3D-%20%5Cfrac%7B3%7D%7B2%7D%7D)
The equation is then calculated as:
![\mathbf{y = m(x - x_1) + y_1}](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D%20m%28x%20-%20x_1%29%20%2B%20y_1%7D)
This gives
![\mathbf{y =- \frac{3}{2}(x -0) + 3 }](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D-%20%5Cfrac%7B3%7D%7B2%7D%28x%20-0%29%20%2B%203%20%7D)
![\mathbf{y =- \frac{3}{2}x + 3 }](https://tex.z-dn.net/?f=%5Cmathbf%7By%20%3D-%20%5Cfrac%7B3%7D%7B2%7Dx%20%2B%203%20%7D)
Multiply through by 2
![\mathbf{2y =- 3x + 3 }](https://tex.z-dn.net/?f=%5Cmathbf%7B2y%20%3D-%203x%20%2B%203%20%7D)
Rewrite as:
![\mathbf{3x + 2y = 3 }](https://tex.z-dn.net/?f=%5Cmathbf%7B3x%20%2B%202y%20%3D%203%20%7D)
Hence, the system of equation is:
and ![\mathbf{3x + 2y = 3 }](https://tex.z-dn.net/?f=%5Cmathbf%7B3x%20%2B%202y%20%3D%203%20%7D)
Read more about system of equations at:
brainly.com/question/13997560
Answer:
Possible economic consequences of using non-local resources include increased costs of resources, loss of jobs, increased security risks, and a trade deficit.
Explanation:
1. Diagrams can group all information that is used together thus avoiding large amounts of search for needed elements. Text only indexes to the next element in the sentence list (the adjacent piece of information) while diagrams have many adjacent elements. 2. Diagrams explicitly preserve information about geometry and topology, whereas text is only serial in nature. This feature of diagrams allows for easy indexing of information to support computation processes. However, text preserves the temporal or logical sequence of information. This is lost in diagrams. 3. Diagrams use location to group information about a single element, avoiding the need to match symbolic labels. Diagrams automatically support a large number of perceptual inferences; the information can be indexed in a variety of manners. It seems reasonable that these conclusions, made about diagrammatic representations, can be extended to all graphical representations. Based on Larkin and Simon's conclusions it is easy to see why, in the complexity of mechanical design, drawings are preferred over text.
Later in this paper we will analyze all the marks-on-paper made by a small group of engineering designers. Their drawing marks will be classified as either free hand (sketching) or drafting marks. The hypothesis above states that the sketches have a role that more formal drafting cannot fill. Dan Herbert in Study Drawings in Architectural Design: Applications for CAD Systems [7] considers the use of sketches (study drawings) in the solution of architectural design problems. He defines "study drawings" as "informal, private drawings that architectural designers use as a medium for graphic thinking in the exploratory stages of their work." Architects often make these study drawings in the borders of or adjacent to their formal drawings. In his paper Herbert conjectures about the properties of sketches that affect the design process. These properties form the basis for his theory of the use of sketches in design.
you could just use the 1st 2nd and 3rd reason stated in the beginning. :D
Complex conjugates are two complex numbers and so must occur in pairs
- That is if there is 3 + i
- There must also be 3 - i
- X=(3+i) X=(3-i)
The conjugate root theorem tell us t that when the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial.
Complex conjugates are often referred to as two complex numbers, that is they have 2 forms a + bi,
- a = real part of a complex numbers
- i = √ -1.
- bi = imaginary part of complex number
The two complex numbers are often referred to as conjugates of each other. That is they will have the same real part and their imaginary parts are negatives of each other.
Example are:
- a+ bi is a - bi.
- 5 + 3i is 5 - 3i
Conclusively we can therefore say that getting the complex conjugate of a complex number entails changing the sign of the imaginary part of the number.
- That is if there is 3 + i
- There must also be 3 - i
Learn more from
brainly.com/question/7800875