Answer: 1 and 2
Step-by-step explanation: 1 and 2 because if you are graphing this the formula to find the slope / the line is y = x + some number. In the formula x is how much the line goes from the x axis and the number is how much it is from the y axis. On #2 the problem is 3y = 2x + 4 so to follow the formula you need to divide both sides by 3 to get y = 2/3x + 4. For #3 you do the same thing to get y = -3/2x -5. Finally for #1 the equation is 2x + 3y = 7 so to get the slope / line you need to put x on the other side so now it is 3y = 7-2x then you divide both sides by 3 and get y = -2/3x + 7 and on 1 and 2 there x is 2/3 (the negative doesn't matter and the random number) so they are parallel.
Answer:
Yes, parallelogram OABC is a rectangle.
Step-by-step explanation:
The vertices of a parallelogram are O(0,0), A(-4,1), B(-3,5) and C(1,4).
A parallelogram is a rectangle if its any two adjacent sides are perpendicular to each other.
product of slopes of two perpendicular lines is -1.
Formula for slope is
Using the formula we get
It means OA is perpendicular to AB.
Since two adjacent sides are perpendicular, therefore the given parallelogram OABC is a rectangle.
Answer:
Answer: log(81)
Decimal Form: 1.90848501
Step-by-step explanation:
Answer:
a) positive direction: t < 2s & t>6s ; negative direction: 2s < t < 6s
b) 7 m
c) 71 m
Step-by-step explanation:
Given:
v(t) = 3t^2 -24t +36 [0 , 7]
Find:
a) The value of time when particle is moving in positive direction:
The change in direction of the particle can be determined by v(t) > 0
Hence,
0 < 3t^2 -24t +36
0 < t^2 - 8t + 12
0 < (t - 2)*(t - 6)
t < 2s , t > 6s
The particle travels in positive direction in the interval t < 2s and t > 6s , While it travels in negative direction when 2s < t < 6s.
b) The displacement ds over the given interval [ 0 , 7 ]
ds = integral (v(t)).dt
ds = t^3 -12t^2 +36t
ds = 7^3 -12*7^2 +36*7
ds = 7 m
c) Total distance traveled in the interval:
Total distance= ds(0-2) + ds(2-6) + ds(6-7)
D = 2*(2^3 -12*2^2 +36*2) - 2*(6^3 -12*6^2 +36*6) + 7
D = 2*32 - 2*0 + 7
D = 71 m
1. The sum of b and ninety-eight
