Answer:
n = 24
p(a) = 10/24
p(b) = 15/24
[ p(a) + p(b) - [p(a) ×p(b)] ] -1 = answer
[ 35/24 - 6/24 ] -1 = 39/24 - 24/24 = 5/24
5(-11)+4(3)^2 = -19
The answer is -19
Answer:
A. y=1/3x+1
Step-by-step explanation:
When finding a line that is perpendicular to another line, all you have to do is find the "opposite reciprocal" of the slope. In this case that means writing the slope as the fraction -3/1, and then flipping the fraction over (1/-3) and taking away the negative sign which gets you 1/3 for the slope of your new line. Now, all you have of your new equation is the slope. You need to take your new equation (y=1/3x+b) and plug in the x and y coordinates to that equation, and then solve for the last variable which is b. That solving process goes as follows:
3=1/3*6+b
3=2+b
1=b
now you can replace the b with 1 in your equation to get your final answer of y=1/3x+1
The system is:
i) <span>2x – 3y – 2z = 4
ii) </span><span>x + 3y + 2z = –7
</span>iii) <span>–4x – 4y – 2z = 10
the last equation can be simplified, by dividing by -2,
thus we have:
</span>i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) 2x +2y +z = -5
The procedure to solve the system is as follows:
first use any pairs of 2 equations (for example i and ii, i and iii) and equalize them by using one of the variables:
i) 2x – 3y – 2z = 4
iii) 2x +2y +z = -5
2x can be written as 3y+2z+4 from the first equation, and -2y-z-5 from the third equation.
Equalize:
3y+2z+4=-2y-z-5, group common terms:
5y+3z=-9
similarly, using i and ii, eliminate x:
i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
multiply the second equation by 2:
i) 2x – 3y – 2z = 4
ii) 2x + 6y + 4z = –14
thus 2x=3y+2z+4 from i and 2x=-6y-4z-14 from ii:
3y+2z+4=-6y-4z-14
9y+6z=-18
So we get 2 equations with variables y and z:
a) 5y+3z=-9
b) 9y+6z=-18
now the aim of the method is clear: We eliminate one of the variables, creating a system of 2 linear equations with 2 variables, which we can solve by any of the standard methods.
Let's use elimination method, multiply the equation a by -2:
a) -10y-6z=18
b) 9y+6z=-18
------------------------ add the equations:
-10y+9y-6z+6z=18-18
-y=0
y=0,
thus :
9y+6z=-18
0+6z=-18
z=-3
Finally to find x, use any of the equations i, ii or iii:
<span>2x – 3y – 2z = 4
</span>
<span>2x – 3*0 – 2(-3) = 4
2x+6=4
2x=-2
x=-1
Solution: (x, y, z) = (-1, 0, -3 )
Remark: it is always a good attitude to check the answer, because often calculations mistakes can be made:
check by substituting x=-1, y=0, z=-3 in each of the 3 equations and see that for these numbers the equalities hold.</span>
I hope this helps you
distance=speed×time
first cars time t
second cars time t+3
same distance
distance=55.t
distance=40. (t+3)
55t=40 (t+3)
55t-40t=120
15t=120
t=8
t+3=11
