The system has a corresponding augmented matrix
![\left[\begin{array}{ccccc|c}2&-4&3&-1&2&0\\3&-6&5&-2&4&0\\5&-10&7&-3&18&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D2%26-4%263%26-1%262%260%5C%5C3%26-6%265%26-2%264%260%5C%5C5%26-10%267%26-3%2618%260%5Cend%7Barray%7D%5Cright%5D)
Let's get this into reduced row echelon form.
Add 3(row 1) to -2(row 2), and add 5(row 1) to -2(row 3):
![\left[\begin{array}{ccccc|c}2&-4&3&-1&2&0\\0&0&-1&1&-2&0\\0&0&1&1&-26&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D2%26-4%263%26-1%262%260%5C%5C0%260%26-1%261%26-2%260%5C%5C0%260%261%261%26-26%260%5Cend%7Barray%7D%5Cright%5D)
Multiply through row 2 by -1:
![\left[\begin{array}{ccccc|c}2&-4&3&-1&2&0\\0&0&1&-1&2&0\\0&0&1&1&-26&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D2%26-4%263%26-1%262%260%5C%5C0%260%261%26-1%262%260%5C%5C0%260%261%261%26-26%260%5Cend%7Barray%7D%5Cright%5D)
Add -1(row 2) to row 3:
![\left[\begin{array}{ccccc|c}2&-4&3&-1&2&0\\0&0&1&-1&2&0\\0&0&0&2&-28&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D2%26-4%263%26-1%262%260%5C%5C0%260%261%26-1%262%260%5C%5C0%260%260%262%26-28%260%5Cend%7Barray%7D%5Cright%5D)
Multiply through row 3 by 1/2:
![\left[\begin{array}{ccccc|c}2&-4&3&-1&2&0\\0&0&1&-1&2&0\\0&0&0&1&-14&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D2%26-4%263%26-1%262%260%5C%5C0%260%261%26-1%262%260%5C%5C0%260%260%261%26-14%260%5Cend%7Barray%7D%5Cright%5D)
Add row 3 to row 2:
![\left[\begin{array}{ccccc|c}2&-4&3&-1&2&0\\0&0&1&0&-12&0\\0&0&0&1&-14&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D2%26-4%263%26-1%262%260%5C%5C0%260%261%260%26-12%260%5C%5C0%260%260%261%26-14%260%5Cend%7Barray%7D%5Cright%5D)
Add -3(row 2) and row 3 to row 1:
![\left[\begin{array}{ccccc|c}2&-4&0&0&24&0\\0&0&1&0&-12&0\\0&0&0&1&-14&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D2%26-4%260%260%2624%260%5C%5C0%260%261%260%26-12%260%5C%5C0%260%260%261%26-14%260%5Cend%7Barray%7D%5Cright%5D)
Multiply through row 1 by 1/2:
![\left[\begin{array}{ccccc|c}1&-2&0&0&12&0\\0&0&1&0&-12&0\\0&0&0&1&-14&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccccc%7Cc%7D1%26-2%260%260%2612%260%5C%5C0%260%261%260%26-12%260%5C%5C0%260%260%261%26-14%260%5Cend%7Barray%7D%5Cright%5D)
This tells us
The matrix has rank 3, so we can pick 2 free variables, say 
and 
. Then the general solution to the system is
where 
.
Answer:
0
Step-by-step explanation:
Given
a + 7(a + b) - 8(a + b) + b ← distribute both parenthesis
= a + 7a + 7b - 8a - 8b + b ← collect like terms
= a + 7a - 8a + 7b - 8b + b
= 0
From the given provided, we can form a right triangle as shown in the attached diagram. Since we have the statue's height and the angle formed between the top of the boat and the statue we can use the properties of the tangent function below.
From this, we can see that the side adjacent to the angle has a measurement of 188 m. This is actually the distance between boat and the base of the statue.
Answer: 188 m
Answer:
The maximum temperature will be -10°C, then if T represents the temperature, we can write this as:
T ≤ -10°C
And the minimum temperature will be -25°C, then we must have that:
T ≥ -25°C
if we use both conditions, we will have:
-25°C ≤ T ≤ -10°C
We can write this range:
[-25°C, -10°C]
Where the [] symbols mean that the extremes are possible temperatures.
The length of the range will be:
-10°C - 25°C = 15°C.
ANSWER
units
EXPLANATION
Let the other leg be x units.
According to the Pythagoras Theorem, the sum of the squares of the two shorter legs should add up to the square of the hypotenuse.
This implies that,
Group the constant terms,
Take square root.
