Answer:
A) d=70h
B) 245 Miles
Step-by-step explanation:
If h is hours and d is distance, you are traveling 70 miles per hour and d is miles.
Since the equation is d=70h, you substitute the 3.5 for the d:
d=70(3.5)
70 times 3.5 is 245
h=245
Answer:
![\large\boxed{a_n=n^2-n+4}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Ba_n%3Dn%5E2-n%2B4%7D)
Step-by-step explanation:
![a_1=4,\ a_2=6,\ a_3=10,\ a_4=16,\ a_5=24,\ a_6=34,\ a_7=46\\\\a_n=an^2+bn+c\\\\for\ n=1\to 4=a(1^2)+b(1)+c\to a+c+b=4\\\\for\ n=2\to 6=a(2^2)+b(2)+c\to4a+2b+c=6\\\\for\ n=3\to3=a(3^2)+b(3)+c\to 9a+3b+c=10\\\\\text{We have the system of equations:}\\\\\left\{\begin{array}{ccc}a+b+c=4&(1)\\4a+2b+c=6&(2)\\9a+3b+c=10&(3)\end{array}\right\\\\a+b+c=4\qquad\text{subtract b and c from both sides}\\a=4-b-c\qquad\text{substitute to (2) and (3)}](https://tex.z-dn.net/?f=a_1%3D4%2C%5C%20a_2%3D6%2C%5C%20a_3%3D10%2C%5C%20a_4%3D16%2C%5C%20a_5%3D24%2C%5C%20a_6%3D34%2C%5C%20a_7%3D46%5C%5C%5C%5Ca_n%3Dan%5E2%2Bbn%2Bc%5C%5C%5C%5Cfor%5C%20n%3D1%5Cto%204%3Da%281%5E2%29%2Bb%281%29%2Bc%5Cto%20a%2Bc%2Bb%3D4%5C%5C%5C%5Cfor%5C%20n%3D2%5Cto%206%3Da%282%5E2%29%2Bb%282%29%2Bc%5Cto4a%2B2b%2Bc%3D6%5C%5C%5C%5Cfor%5C%20n%3D3%5Cto3%3Da%283%5E2%29%2Bb%283%29%2Bc%5Cto%209a%2B3b%2Bc%3D10%5C%5C%5C%5C%5Ctext%7BWe%20have%20the%20system%20of%20equations%3A%7D%5C%5C%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7Da%2Bb%2Bc%3D4%26%281%29%5C%5C4a%2B2b%2Bc%3D6%26%282%29%5C%5C9a%2B3b%2Bc%3D10%26%283%29%5Cend%7Barray%7D%5Cright%5C%5C%5C%5Ca%2Bb%2Bc%3D4%5Cqquad%5Ctext%7Bsubtract%20b%20and%20c%20from%20both%20sides%7D%5C%5Ca%3D4-b-c%5Cqquad%5Ctext%7Bsubstitute%20to%20%282%29%20and%20%283%29%7D)
![(2)\\4(4-b-c)+2b+c=6\qquad\text{use the distributive property}\\(4)(4)+(4)(-b)+(4)(-c)+2b+c=6\\16-4b-4c+2b+c=6\qquad\text{subtract 16 from both sides}\\(-4b+2b)+(-4c+c)=-10\\-2b-3c=-10\\\\(3)\\9(4-b-c)+3b+c=10\qquad\text{use the distributive property}\\(9)(4)+(9)(-b)+(9)(-c)+3b+c=10\\36-9b-9c+3b+c=10\qquad\text{subtract 36 from both sides}\\(-9b+3b)+(-9c+c)=-26\\-6b-8c=-26](https://tex.z-dn.net/?f=%282%29%5C%5C4%284-b-c%29%2B2b%2Bc%3D6%5Cqquad%5Ctext%7Buse%20the%20distributive%20property%7D%5C%5C%284%29%284%29%2B%284%29%28-b%29%2B%284%29%28-c%29%2B2b%2Bc%3D6%5C%5C16-4b-4c%2B2b%2Bc%3D6%5Cqquad%5Ctext%7Bsubtract%2016%20from%20both%20sides%7D%5C%5C%28-4b%2B2b%29%2B%28-4c%2Bc%29%3D-10%5C%5C-2b-3c%3D-10%5C%5C%5C%5C%283%29%5C%5C9%284-b-c%29%2B3b%2Bc%3D10%5Cqquad%5Ctext%7Buse%20the%20distributive%20property%7D%5C%5C%289%29%284%29%2B%289%29%28-b%29%2B%289%29%28-c%29%2B3b%2Bc%3D10%5C%5C36-9b-9c%2B3b%2Bc%3D10%5Cqquad%5Ctext%7Bsubtract%2036%20from%20both%20sides%7D%5C%5C%28-9b%2B3b%29%2B%28-9c%2Bc%29%3D-26%5C%5C-6b-8c%3D-26)
![\text{Therefore we have the system of equations:}\\\left\{\begin{array}{ccc}-2b-3c=-10&\text{multiply both sides by (-3)}\\-6b-8c=-26\end{array}\right\\\underline{+\left\{\begin{array}{ccc}6b+9c=30\\-6b-8c=-26\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad\boxed{c=4}\\\\\text{Put the value of c to the first equation:}\\\\6b+9(4)=30\\6b+36=30\qquad\text{subtract 36 from both sides}\\6b=-6\qquad\text{divide both sides by 6}\\\boxed{b=-1}\\\\\text{Put the values of b and c to (1)}](https://tex.z-dn.net/?f=%5Ctext%7BTherefore%20we%20have%20the%20system%20of%20equations%3A%7D%5C%5C%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D-2b-3c%3D-10%26%5Ctext%7Bmultiply%20both%20sides%20by%20%28-3%29%7D%5C%5C-6b-8c%3D-26%5Cend%7Barray%7D%5Cright%5C%5C%5Cunderline%7B%2B%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D6b%2B9c%3D30%5C%5C-6b-8c%3D-26%5Cend%7Barray%7D%5Cright%7D%5Cqquad%5Ctext%7Badd%20both%20sides%20of%20the%20equations%7D%5C%5C.%5Cqquad%5Cqquad%5Cboxed%7Bc%3D4%7D%5C%5C%5C%5C%5Ctext%7BPut%20the%20value%20of%20c%20to%20the%20first%20equation%3A%7D%5C%5C%5C%5C6b%2B9%284%29%3D30%5C%5C6b%2B36%3D30%5Cqquad%5Ctext%7Bsubtract%2036%20from%20both%20sides%7D%5C%5C6b%3D-6%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%206%7D%5C%5C%5Cboxed%7Bb%3D-1%7D%5C%5C%5C%5C%5Ctext%7BPut%20the%20values%20of%20b%20and%20c%20to%20%281%29%7D)
![a=4-(-1)-4\\a=4+1-4\\\boxed{a=1}\\\\\text{Therefore we have the formula of nth term:}\\\\a_n=1n^2-1n+4](https://tex.z-dn.net/?f=a%3D4-%28-1%29-4%5C%5Ca%3D4%2B1-4%5C%5C%5Cboxed%7Ba%3D1%7D%5C%5C%5C%5C%5Ctext%7BTherefore%20we%20have%20the%20formula%20of%20nth%20term%3A%7D%5C%5C%5C%5Ca_n%3D1n%5E2-1n%2B4)
Answer:
the greatest common factor is 45n^2
Step-by-step explanation:
Is there something wrong with the question?