Trigonometric Identities.
To solve this problem, we need to keep in mind the following:
* The tangent function is negative in the quadrant II
* The cosine (and therefore the secant) function is negative in the quadrant II
* The tangent and the secant of any angle are related by the equation:
We are given:
![\text{tan}\theta=-\frac{\sqrt[]{14}}{4}](https://tex.z-dn.net/?f=%5Ctext%7Btan%7D%5Ctheta%3D-%5Cfrac%7B%5Csqrt%5B%5D%7B14%7D%7D%7B4%7D)
And θ lies in the quadrant Ii.
Substituting in the identity:
![\begin{gathered} \sec ^2\theta=(-\frac{\sqrt[]{14}}{4})^2+1 \\ \text{Operating:} \\ \sec ^2\theta=\frac{14}{16}+1 \\ \sec ^2\theta=\frac{14+16}{16} \\ \sec ^2\theta=\frac{30}{16} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csec%20%5E2%5Ctheta%3D%28-%5Cfrac%7B%5Csqrt%5B%5D%7B14%7D%7D%7B4%7D%29%5E2%2B1%20%5C%5C%20%5Ctext%7BOperating%3A%7D%20%5C%5C%20%5Csec%20%5E2%5Ctheta%3D%5Cfrac%7B14%7D%7B16%7D%2B1%20%5C%5C%20%5Csec%20%5E2%5Ctheta%3D%5Cfrac%7B14%2B16%7D%7B16%7D%20%5C%5C%20%5Csec%20%5E2%5Ctheta%3D%5Cfrac%7B30%7D%7B16%7D%20%5Cend%7Bgathered%7D)
Taking the square root and writing the negative sign for the secant:
![\begin{gathered} \sec ^{}\theta=\sqrt{\frac{30}{16}} \\ \sec ^{}\theta=-\frac{\sqrt[]{30}}{4} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Csec%20%5E%7B%7D%5Ctheta%3D%5Csqrt%7B%5Cfrac%7B30%7D%7B16%7D%7D%20%5C%5C%20%5Csec%20%5E%7B%7D%5Ctheta%3D-%5Cfrac%7B%5Csqrt%5B%5D%7B30%7D%7D%7B4%7D%20%5Cend%7Bgathered%7D)
Answer:
Explanation:
1.
x^2 - 10x + 24
= (x - 6)(x - 4)
2.
x^2 - 12x + 27
= (x - 9)(x - 3)
3.
x^2 - 13x + 36
= (x - 9)(x - 4)
4.
x^2 - 5x - 14
= (x - 7)(x + 2)
5.
x^2 + x - 20
= (x + 5)(x - 4)
6.
x^2 - 3x - 40
= (x - 8)(x + 5)
7.
x^2 + 2x - 48
= (x - 8)(x + 6)
8.
x^2 + 10x - 24
= (x - 2)(x + 12)
9.
x^2 - 7x - 44
= (x - 11)(x + 4)
10.
x^2 + x - 2
= (x + 2)(x - 1)
11.
x^2 + 2x + 1
= (x + 1)(x + 1)
12.
x^2 - x - 6
= (x - 3)(x + 2)
Answer:
C. Miles per hour
Step-by-step explanation:
9514 1404 393
Answer:
x = 4
Step-by-step explanation:
The measures of all angles in this geometry are 90 degrees.
21x +6 = 90
21x = 84 . . . . . subtract 6
x = 4 . . . . . . . divide by 21
