I noticed that this equation is in slope-intercept form (y = mx + b). M = the slope of the line, B = the y-intercept.
If the line is translated (fancy, fancy, talk for MOVED) up. The Y-intercept would change positive (because it is moved up) by four.
4 + 4 equals...well, 8.
Hope I could help you out! If my answer is incorrect, or I provided an answer you were not looking for, please let me know.
However, if my answer is explained well and correct, please consider marking my answer as Brainliest! :)
Have a good one.
God bless!
Answer:
1, 2
2, 5
3, 8
4, 11
5, 14
Step-by-step explanation:
you just plug each n value into the <em>n</em>
Answer:
![1) {n}^{2} - 81 \\ (n - 9)(n + 9)](https://tex.z-dn.net/?f=1%29%20%7Bn%7D%5E%7B2%7D%20%20-%2081%20%5C%5C%20%28n%20-%209%29%28n%20%2B%209%29)
![2) \: \: {a}^{2} - 121 \\ (a - 11)(a + 11)](https://tex.z-dn.net/?f=%202%29%20%5C%3A%20%20%5C%3A%20%7Ba%7D%5E%7B2%7D%20%20-%20121%20%5C%5C%20%28a%20-%2011%29%28a%20%2B%2011%29)
![3) \: \: {n}^{2} - 16 \\ (n - 4)(n + 4)](https://tex.z-dn.net/?f=3%29%20%5C%3A%20%20%5C%3A%20%20%7Bn%7D%5E%7B2%7D%20%20-%2016%20%5C%5C%20%28n%20-%204%29%28n%20%2B%204%29)
![4) \: \: 9 {x}^{2} - 144 \\ {3}^{2} {x}^{2} - {12}^{2} \\ (3x - 12)(3x + 12)](https://tex.z-dn.net/?f=4%29%20%20%5C%3A%20%20%5C%3A%209%20%7Bx%7D%5E%7B2%7D%20%20-%20144%20%5C%5C%20%20%7B3%7D%5E%7B2%7D%20%20%7Bx%7D%5E%7B2%7D%20%20-%20%20%7B12%7D%5E%7B2%7D%20%20%5C%5C%20%283x%20-%2012%29%283x%20%2B%2012%29)
![5) \: 2 {x}^{2} - 9 \\ (2x - 3)(x + 3)](https://tex.z-dn.net/?f=5%29%20%5C%3A%202%20%7Bx%7D%5E%7B2%7D%20%20-%209%20%5C%5C%20%282x%20-%203%29%28x%20%2B%203%29)
![6) \: \: 4 {w}^{2} - 9 \\ {2}^{2} {w}^{2} - {3}^{2} \\ (2w + 3)(2w - 3)](https://tex.z-dn.net/?f=6%29%20%5C%3A%20%20%5C%3A%204%20%7Bw%7D%5E%7B2%7D%20%20-%209%20%5C%5C%20%20%7B2%7D%5E%7B2%7D%20%20%7Bw%7D%5E%7B2%7D%20%20-%20%20%7B3%7D%5E%7B2%7D%20%20%5C%5C%20%282w%20%2B%203%29%282w%20-%203%29)
![7) \: \: 4 {n}^{2} - 1 \\ {2}^{2} {n}^{2} - {1}^{2} \\ (2n + 1)(2n - 1)](https://tex.z-dn.net/?f=7%29%20%5C%3A%20%20%5C%3A%204%20%7Bn%7D%5E%7B2%7D%20%20-%201%20%5C%5C%20%20%7B2%7D%5E%7B2%7D%20%20%7Bn%7D%5E%7B2%7D%20%20-%20%20%7B1%7D%5E%7B2%7D%20%20%5C%5C%20%282n%20%20%2B%201%29%282n%20-%201%29)
![8) \: \: 1 - 16 {x}^{2} \\ {1}^{2} - {4}^{2} {x}^{2} \\ (1 - 4x)(1 + 4x)](https://tex.z-dn.net/?f=8%29%20%5C%3A%20%20%5C%3A%201%20-%2016%20%7Bx%7D%5E%7B2%7D%20%20%5C%5C%20%20%7B1%7D%5E%7B2%7D%20%20-%20%20%7B4%7D%5E%7B2%7D%20%20%7Bx%7D%5E%7B2%7D%20%20%5C%5C%20%281%20-%204x%29%281%20%20%2B%20%204x%29)
![9) \: \: {x}^{2} - {y}^{2} \\ (x - y)(x + y)](https://tex.z-dn.net/?f=%209%29%20%5C%3A%20%20%5C%3A%20%7Bx%7D%5E%7B2%7D%20%20%20-%20%7By%7D%5E%7B2%7D%20%20%5C%5C%20%28x%20-%20y%29%28x%20%2B%20y%29)
![10) \: \: 9 - {c}^{2} \\ {3}^{2} - {c}^{2} \\ (3 - c)(3 + c)](https://tex.z-dn.net/?f=10%29%20%5C%3A%20%20%5C%3A%209%20-%20%20%7Bc%7D%5E%7B2%7D%20%20%5C%5C%20%20%7B3%7D%5E%7B2%7D%20%20-%20%20%7Bc%7D%5E%7B2%7D%20%20%5C%5C%20%283%20-%20c%29%283%20%2B%20c%29)
![11) \: \: {n}^{2} - 25 \\ {n}^{2} - {5}^{2} \\ (n + 5)(n - 5)](https://tex.z-dn.net/?f=11%29%20%5C%3A%20%20%5C%3A%20%20%7Bn%7D%5E%7B2%7D%20-%20%2025%20%5C%5C%20%20%7Bn%7D%5E%7B2%7D%20%20-%20%20%7B5%7D%5E%7B2%7D%20%20%5C%5C%20%28n%20%2B%205%29%28n%20-%205%29)
![13)49 - 4 {a}^{2} \\ {7}^{2} - {2}^{2} {a}^{2} \\ (7 - 2a)(7 + 2a)](https://tex.z-dn.net/?f=13%2949%20-%204%20%7Ba%7D%5E%7B2%7D%20%20%5C%5C%20%20%7B7%7D%5E%7B2%7D%20%20-%20%20%7B2%7D%5E%7B2%7D%20%20%7Ba%7D%5E%7B2%7D%20%20%5C%5C%20%287%20-%202a%29%287%20%2B%202a%29)
![14) {a}^{2} {b}^{2} - {c}^{4} \\ (ab - {c}^{2} )(ab + {c}^{2} )](https://tex.z-dn.net/?f=14%29%20%7Ba%7D%5E%7B2%7D%20%20%7Bb%7D%5E%7B2%7D%20%20-%20%20%7Bc%7D%5E%7B4%7D%20%20%5C%5C%20%28ab%20-%20%20%7Bc%7D%5E%7B2%7D%20%29%28ab%20%2B%20%20%7Bc%7D%5E%7B2%7D%20%29)
![15) \: \: 4 {x}^{2} {y}^{2} - 9 {z}^{2} \\ {2}^{2} {x}^{2} {y}^{2} - {3}^{2} {z}^{2} \\ (2xy - 3z)(2xy + 3z)](https://tex.z-dn.net/?f=15%29%20%5C%3A%20%20%5C%3A%204%20%20%7Bx%7D%5E%7B2%7D%20%20%7By%7D%5E%7B2%7D%20%20-%209%20%7Bz%7D%5E%7B2%7D%20%5C%5C%20%20%7B2%7D%5E%7B2%7D%20%20%20%7Bx%7D%5E%7B2%7D%20%20%7By%7D%5E%7B2%7D%20%20-%20%20%7B3%7D%5E%7B2%7D%20%20%7Bz%7D%5E%7B2%7D%20%20%5C%5C%20%282xy%20-%203z%29%282xy%20%2B%203z%29)
hope this helps
sorry, I don't know how solve the 12th one.
thanks.
Answer:
A length of 959.401 meters is needed for the zip line is needed to string it from the top of the tower to the platform.
Step-by-step explanation:
The geometrical representation of the statement is summarized in the figure below attached. The length of the line is represented by hypotenuse of the right triangle, whose value is calculated by the help of trigonometrical relations:
(1)
Where:
- Angle formed between the zip line and the tower, measured in sexagesimal degrees.
- Vertical distance between the tower and the platform, measured in meters.
- Length of the zip line, measured in meters.
If we know that
and
, then the length of the zip line is:
![r = \frac{h}{\cos \alpha}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7Bh%7D%7B%5Ccos%20%5Calpha%7D)
![r = \frac{232.1\,m}{\cos 76^{\circ}}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B232.1%5C%2Cm%7D%7B%5Ccos%2076%5E%7B%5Ccirc%7D%7D)
![r = 959.401\,m](https://tex.z-dn.net/?f=r%20%3D%20959.401%5C%2Cm)
A length of 959.401 meters is needed for the zip line is needed to string it from the top of the tower to the platform.