B
given f(x) in factored form, equate to zero for x-intercepts
(x - 8)(x - 4) = 0, hence
x = 4, x = 8 ← x- intercepts
The vertex lies on the axis of symmetry which is situated at the midpoint of the x- intercepts
x- coordinate of vertex = 
= 6
f(6) = (6 - 8 )(6 - 4 ) = -2 × 2 = - 4 ← y-coordinate
vertex = (6, - 4 ) → B
Given that o<span>ne Friday night,
Roman and Malou are busy studying for their Logic exam. Meanwhile,
Hadji just tweeted a picture of himself eating crispy pata and sisig.
Jeff is sound asleep in his dorm room.
Part A:
The truth value of </span>"Either Roman has a date with Malou, or Jeff is sleeping or Hadji is eating." is obtained as follows:
From the scenario, the truth value of the individual statements are as follows:
<span>Roman has a date with Malou is True
</span>
<span>Jeff is sleeping is True
</span>
<span>Hadji is eating is True
Thus, the truth value of "True" or "True" or "True" is True.
Therefore, the truth value of "</span><span>Either Roman has a date with Malou, or Jeff is sleeping or Hadji is eating." is True.
Part B:
</span>The truth value of "Either Jeff is sleeping or Hadji is not eating" is obtained as follows:
From the scenario, the truth value of the individual statements are as follows:
<span>Jeff is sleeping is True
</span>
<span>Hadji is not eating is False
Thus, the truth value of "True" or "False" is True.</span>
Therefore, the truth value of "Either Jeff is sleeping or Hadji is not eating" is True.
Part C:
The truth value of "Roman and Malou are on a date and Jeff is sleeping, or Hadji is not eating." is obtained as follows:
From the scenario, the truth value of the individual statements are as follows:
Roman and Malou are on a date is True
<span>Jeff is sleeping is True
</span>
<span>Hadji is not eating is False
The truth value of "True" and "True" is True.
The truth value of "True" or "False" is True.
Thus, the truth value of ("True" and "True") or "False" is True.
</span>
Therefore, the truth value of "Roman and Malou are on a date and Jeff is sleeping, or Hadji is not eating." is True.
Answer:
x = 16
y = -24
Step-by-step explanation:
Recall that the addition of matrices is done when matrices are of the same dimension. In this case, you are in fact adding matrices of the same dimension (dimension 1x2). Recall as well that in the addition of matrices, the elements of each matrix combine only with the element located in the exact same position in the other matrix.
So for this case the first element of the first matrix "16" combines with the first element of the second matrix "0" resulting in an element of value16 + 0 =16 in the new matrix.
Equally, the second element of the first matrix "-24" combines with the second element of the second matrix, resulting in : -24 + 0 = -24.
Therefore, the matrix resultant from this addition is: [16 -24] (same form of the first matrix, which indicates that adding a zero matrix to an existing matrix will not change the first matrix.
Answer:
7 laps
Step-by-step explanation:
If the amount of time taken to go said distance is x and the amount of time taken to go back said distance is y, then the amount of miles total is 7x+3y due to that for every hour, she adds 7 miles when going there and 3 miles for walking back. In addition, since the total amount of time is 4 hours, x+y=4 as the total time spent as well as 7x=3y due to that they're the same distance.
x+y=4
7x=3y
Dividing the second equation by 7, we get x=3y/7. Plugging that into the first equation, we get 3y/7+y=4=10y/7 (since y=7y/7). Multiplying both sides by 7 and then dividing both by 10, we get 28/10=2.8=y in hours. Since 0.1 hours is 60/10=6 minutes, and 0.8/0.1=8, 6*8=48 minutes=0.8 hours, meaning that she should plan to spend 2 hours and 48 minutes walking back
