Answer:
Step-by-step explanation:
Combine like terms:
Multiply both sides by -10:
Answer:
5 feet long
Step-by-step explanation:
According to the Pythagorean Theorem, a^2 + b^2 = c^2 where "a" and "b" are the two legs of the right triangle and "c" is the hypotenuse.
We are trying to find the part that is at an angle, which is "c". So if we know "a" is "3 and "b" is 4, we can plug the values into the equation.
3^2 + 4^2 = c^2 plug in the values
9 + 16 = c^2 simply the two squared values
25 = c^2 add the two values
5 = c take the square root of both sides
c = 5 switch the values
1) multiplies by 3
2)4.7
3)12
Answer:
The solution to the system is 
,
and 
Step-by-step explanation:
Cramer's rule defines the solution of a system of equations in the following way:
, 
and 
where 
, 
and 
are the determinants formed by replacing the x,y and z-column values with the answer-column values respectively. 
is the determinant of the system. Let's see how this rule applies to this system.
The system can be written in matrix form like:
![\left[\begin{array}{ccc}5&-3&1\\0&2&-3\\7&10&0\end{array}\right]\times \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}6&11&-13\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%26-3%261%5C%5C0%262%26-3%5C%5C7%2610%260%5Cend%7Barray%7D%5Cright%5D%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%26y%26z%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D6%2611%26-13%5Cend%7Barray%7D%5Cright%5D)
Then each of the previous determinants are given by:
Notice how the x-column has been substituted with the answer-column one.
Notice how the y-column has been substituted with the answer-column one.
Then, substituting the values:
Substitution: n² = t
1 ) t² - 10 t + 24 = t² - 6 t - 4 t + 24 =
= t ( t - 6 ) - 4 ( t - 6 ) = ( t - 6 ) ( t - 4 ) =
= ( n² - 6 ) ( n² - 4 )
2 ) t² - 9 t + 18 = t² - 6 t - 3 t + 18 =
= t ( t - 6 ) - 3 ( t - 6 ) = ( t - 6 ) ( t - 3 ) =
= ( n² - 6 ) ( n² - 3 )
The restrictions: n² ≠ 6, n² ≠ 3, n ≠ +/- √6, n≠ +/-√3
Simplification:
