Answer:
Step-by-step explanation:
Find A cup(B cap C) . A = \{1, 4, 6, 7\}; B = \{3, 4, 5\}; C = \{2, 4, 8\}; \{1, 4, 6, 7\} 4 } \{1, 2, 3, 4, 5, 6, 7, 8\}
Inessa05 [86]
The only common element between B and C is 4, so B ∩ C = {4}.
4 is also already contained in A, so B ∩ C is a subset of A, and thus
A U (B ∩ C) = A = {1, 4, 6, 7}
1)
2(a + 3) = -12
Divide by 2
a + 3 = -6
Subtract 3
a = -9
2)
3(p + 2) = 18
Divide by 3
p + 2 = 6
Subtract 2
p = 4
3)
4(2r + 8) = 88
Dive by 4
2r + 8 = 22
Subtract 8
2r = 14
Divide by 2
r = 7
4)
2(3a + 2) = -8
Divide by 2
3a + 2 = -4
Subtract 2
3a = -6
Divide by 3
a = -2
5)
4(k + 3) = 4
Divide by 4
k + 3 = 1
Subtract 3
k = -2
At heart we're being asked for a line through two points,
![(40^\circ \textrm{ C}, 355 \textrm { m/s}) \quad \textrm{and} \quad (49^\circ \textrm{ C}, 360 \textrm { m/s})](https://tex.z-dn.net/?f=%2840%5E%5Ccirc%20%5Ctextrm%7B%20C%7D%2C%20355%20%5Ctextrm%20%7B%20m%2Fs%7D%29%20%5Cquad%20%5Ctextrm%7Band%7D%20%5Cquad%20%2849%5E%5Ccirc%20%5Ctextrm%7B%20C%7D%2C%20360%20%5Ctextrm%20%7B%20m%2Fs%7D%29%20)
In general the line through (a,b) and (c,d) is
![(y-b)(c-a)=(x-a)(d-b)](https://tex.z-dn.net/?f=%28y-b%29%28c-a%29%3D%28x-a%29%28d-b%29)
Check that you understand why both (a,b) and (c,d) are on this line.
Here our indepedent variable, instead of x, is T, temperature. Our dependent variable is v, velocity. Substituting,
![(v - 355)(49 - 40) = (T - 40)(360 - 355)](https://tex.z-dn.net/?f=%28v%20-%20355%29%2849%20-%2040%29%20%3D%20%28T%20-%2040%29%28360%20-%20355%29)
![9(v - 355) = 5(T - 40)](https://tex.z-dn.net/?f=9%28v%20-%20355%29%20%3D%205%28T%20-%2040%29)
![v-355 = \frac 5 9 T - \frac{200}{9}](https://tex.z-dn.net/?f=v-355%20%3D%20%5Cfrac%205%209%20T%20-%20%5Cfrac%7B200%7D%7B9%7D)
![v= \frac 5 9 T - \frac{200}{9} + 355](https://tex.z-dn.net/?f=v%3D%20%5Cfrac%205%209%20T%20-%20%5Cfrac%7B200%7D%7B9%7D%20%2B%20355)
![v= \frac 5 9 T + \frac{2995}{9}](https://tex.z-dn.net/?f=v%3D%20%5Cfrac%205%209%20T%20%2B%20%5Cfrac%7B2995%7D%7B9%7D)
That's our answer; let's check it.
When T=40, v = (5/9)40 + (2995/9) = 355 good
When T=49, v= (5/9)49 + (2995/9) = 360 good
Answer:
232
Step-by-step explanation: