The answer is 2.5 because the point is on -1.5, so -1.5+4=2.5
Answer and Step-by-step explanation:
You are correct in that we need to use the Law of Sines:
.
Here, when we use the Law of Sines, we have:
.
Cross multiply:
(sinB) * 28 = (sin63) * 29
28sinB ≈ 25.839
sinB ≈ 0.9228
Now, in order to solve for B, we need to use inverse sin (
):
![sin^{-1}(sinB)=sin^{-1}(0.9228)](https://tex.z-dn.net/?f=sin%5E%7B-1%7D%28sinB%29%3Dsin%5E%7B-1%7D%280.9228%29)
The sines on the left cancel out, and we're left with:
B ≈ 67.3 degrees
Now, one thing to keep in mind when doing Law of Sines is that there is potentially more than one answer possible for the degree measure. The other degree measure can be found by subtracting this one from 180:
180 - 67.3 = 112.7 degrees.
Hope this helps!
Answer:
x^2+5x-6
a = 1 b = 5 and c = -6
Using the quadratic formula:
x = [-5 +- sq root (25 -4 * 1 *-6) ] / 2 * 1
x = [-5 +- sq root (49)] / 2
x = [-5 +- 7] / 2
x1 = 1
x2 = -6
Step-by-step explanation:
Answer:
15 divided by 2 1/2
Step-by-step explanation:
$6 per yard.
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.