Answer:b
=0,-17
Step-by-step explanation:
5 2/3 + 2 1/5 = 118/15
= 7 13/15
The slope of the first equation has a slope of one and a y intercept of -4. The second equation has a y intercept of -2.3333 as seen when plugging in 0 for x, so the same y-intercept and same line are out of the question. This means either they have the same slope and thus are parallel or intersect at some point. A simple way to find out? Plug in 1 for x on the second. If it isn't -1.33333, which is a slope of positive 1 such as in the first equation, they WILL INTERSECT somewhere. When plugging in 1, we get
3y - 1 = -7
3y = -6
y = -2
(1, -2) is the next point after (0, -2.3333)
That means it is most certainly not the same slope, and thus they will intersect at some point. The two slopes are 1/1 and 1/3 if you weren't aware.
Answer:
#1
<u>Since half of the numbers are even, 2, 4, 6</u>
#2
<u>Multiple of 3 are 3 and 6:</u>
- P(multiple of 3) = 2/6 = 1/3
#3
<u>The numbers ≤ 4 are: 1, 2, 3, 4</u>
#4
<u>Prime numbers are 2, 3, 5</u>
#5
<u>Numbers > 1 are 2, 3, 4, 5, 6</u>
#6
<u>A four, there is one option</u>
Answer:
<em>Answer: choice D.</em>
Step-by-step explanation:
<u>Trigonometric Functions</u>
We need to recall some properties and definitions of the trigonometric functions.
![\displaystyle \tan \theta=\frac{\sin\theta}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctan%20%5Ctheta%3D%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5Ctheta%7D)
![\displaystyle \sec \theta=\frac{1}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csec%20%5Ctheta%3D%5Cfrac%7B1%7D%7B%5Ccos%5Ctheta%7D)
We need to simplify the following expression:
![5\sin\theta\sec\theta](https://tex.z-dn.net/?f=5%5Csin%5Ctheta%5Csec%5Ctheta)
Substituting the identity for the secant:
![\displaystyle 5\sin\theta\sec\theta=5\sin\theta.\frac{1}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Csin%5Ctheta%5Csec%5Ctheta%3D5%5Csin%5Ctheta.%5Cfrac%7B1%7D%7B%5Ccos%5Ctheta%7D)
Operating:
![\displaystyle 5\sin\theta\sec\theta=5\frac{\sin\theta}{\cos\theta}](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Csin%5Ctheta%5Csec%5Ctheta%3D5%5Cfrac%7B%5Csin%5Ctheta%7D%7B%5Ccos%5Ctheta%7D)
Substituting the definition of the tangent:
![\displaystyle 5\sin\theta\sec\theta=5\tan\theta](https://tex.z-dn.net/?f=%5Cdisplaystyle%205%5Csin%5Ctheta%5Csec%5Ctheta%3D5%5Ctan%5Ctheta)
Correct choice D.