Answer:
70x³ - 73x² - 155x + 168
Step-by-step explanation:
Given
(5x - 7)(2x + 3)(7x - 8) ← expand the first pair of factors using FOIL
= (10x² + x - 21)(7x - 8)
Each term in the second factor is multiplied by each term in the first factor, that is
10x² (7x - 8) + x(7x - 8) - 21(7x - 8) ← distribute the 3 parenthesis
= 70x³ - 80x² + 7x² - 8x - 147x + 168 ← collect like terms
= 70x³ - 73x² - 155x + 168
It's <span>Diophantine equation.
First, we need to found gcd(6,(-2)):</span>
6=2*3
(-2)=(-1)*2
So, gcd(6,-2)=2
Now, the question is. Can we dived c=24, by gcd(6,-2) and in the end get integer?
Yes we can.
![\frac{24}{2} =12](https://tex.z-dn.net/?f=%20%5Cfrac%7B24%7D%7B2%7D%20%3D12)
So, we can solve it.
Now is the formula:
![{\displaystyle {\begin{cases}x=x_{0}+n{\frac {b}{\gcd(a,\;b)}}\\y=y_{0}-n{\frac {a}{\gcd(a,\;b)}}\end{cases}}\quad n\in \mathbb {Z} .}](https://tex.z-dn.net/?f=%7B%5Cdisplaystyle%20%7B%5Cbegin%7Bcases%7Dx%3Dx_%7B0%7D%2Bn%7B%5Cfrac%20%7Bb%7D%7B%5Cgcd%28a%2C%5C%3Bb%29%7D%7D%5C%5Cy%3Dy_%7B0%7D-n%7B%5Cfrac%20%7Ba%7D%7B%5Cgcd%28a%2C%5C%3Bb%29%7D%7D%5Cend%7Bcases%7D%7D%5Cquad%20n%5Cin%20%5Cmathbb%20%7BZ%7D%20.%7D)
Second, we need the first pair (x0,y0)
if
x=0
then
![y=(-12)](https://tex.z-dn.net/?f=y%3D%28-12%29)
Third, we gonna use that formula:
![{\displaystyle {\begin{cases}x=-n}\\y=-3(4+n)}\end{case}\quad n\in \mathbb {Z} .}](https://tex.z-dn.net/?f=%7B%5Cdisplaystyle%20%7B%5Cbegin%7Bcases%7Dx%3D-n%7D%5C%5Cy%3D-3%284%2Bn%29%7D%5Cend%7Bcase%7D%5Cquad%20n%5Cin%20%5Cmathbb%20%7BZ%7D%20.%7D)
Congratulations! We solve it.
Answer:
3
Step-by-step explanation:
4 1/2 + 3 1/3 + 2 + 2 1/6
= 4 3/6 + 3 2/6 + 2 + 2 1/6
= 4 + 3 + 2 + 2 + 3/6 + 2/6 + 1/6
= 11 + 6/6
= 11 + 1
= 12
There are 4 numbers, therefore average = 12 ÷ 4 = 3
Answer:
MN = 160
Step-by-step explanation:
We know that arc MN = arc NO
17g - 10 = 14g+ 20
Subtract 14g from each side
3g -10 = 14g-14g+20
3g -10 =20
Add 10 to each side
3g = 20+10
3g = 30
Divide by 3
3g/3= 30/3
g= 10
We want the arc MN
17g - 10
17(10) - 10
170 -10
160
Second: $500,000
Third: $250,000
Fourth: $125,000
Fifth: $62,500
Sixth:$31,250
Seventh:$15,625
If you need the total just add