Answer:
A and E
Step-by-step explanation:
substitute and odd number into every equation :)
By definition, we have
![|p+2| = \begin{cases} p+2 &\text{ if } p+2 \geq 0 \\-p-2 &\text{ if } p+2 < 0 \end{cases}](https://tex.z-dn.net/?f=%20%7Cp%2B2%7C%20%3D%20%5Cbegin%7Bcases%7D%20p%2B2%20%26%5Ctext%7B%20if%20%7D%20p%2B2%20%5Cgeq%200%20%5C%5C-p-2%20%26%5Ctext%7B%20if%20%7D%20p%2B2%20%3C%200%20%5Cend%7Bcases%7D%20)
So, we have to solve two different equations, depending of the possible range for the variable. We have to remember about these ranges when we decide to accept or discard the solutions:
Suppose that ![p+2\geq 0 \iff p \geq -2](https://tex.z-dn.net/?f=%20p%2B2%5Cgeq%200%20%5Ciff%20p%20%5Cgeq%20-2%20)
In this case, the absolute value doesn't do anything: the equation is
![p+2 = 10 \iff p = 10-2 = 8](https://tex.z-dn.net/?f=%20p%2B2%20%3D%2010%20%5Ciff%20p%20%3D%2010-2%20%3D%208%20)
We are supposing
, so we can accept this solution.
Now, suppose that
. Now the sign of the expression is flipped by the absolute value, and the equation becomes
![-p-2 = 10 \iff -p = 12 \iff p = -12](https://tex.z-dn.net/?f=%20-p-2%20%3D%2010%20%5Ciff%20-p%20%3D%2012%20%5Ciff%20p%20%3D%20-12%20)
Again, the solution is coherent with the assumption, so we can accept this value as well.
It's said "The value √-9 is not -3 because --------------------
So you need to prove why -3 is not the value of √-9.
As you know (-3)^2 = (-3) * (-3) = 9, ≠ -9
Answer is A.
(-3)^2 ≠ -9
Answer:
![21^{\circ}](https://tex.z-dn.net/?f=21%5E%7B%5Ccirc%7D)
Step-by-step explanation:
The Law of Sines is given by
and works for every triangle.
Substituting given values, we have the following equation:
![\frac{\sin 68^{\circ}}{18}=\frac{\sin C}{7}, \\\\\sin C=\frac{7\sin 68^{\circ}}{18},\\\\C=\sin^{-1}(0.36057149899),\\\\C\approx \boxed{21^{\circ}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%2068%5E%7B%5Ccirc%7D%7D%7B18%7D%3D%5Cfrac%7B%5Csin%20C%7D%7B7%7D%2C%20%5C%5C%5C%5C%5Csin%20C%3D%5Cfrac%7B7%5Csin%2068%5E%7B%5Ccirc%7D%7D%7B18%7D%2C%5C%5C%5C%5CC%3D%5Csin%5E%7B-1%7D%280.36057149899%29%2C%5C%5C%5C%5CC%5Capprox%20%5Cboxed%7B21%5E%7B%5Ccirc%7D%7D)
*Note that because
, when solving for an angle with the Law of Sines, there may be two answers. However, since the problem designates angle C as an acute angle, the other angle is negligible.