Answer:
187/6
Step-by-step explanation:
Simplify the following:
(7 + 1/4) 2^2 + (8 + 1/2 - 2)/3
2^2 = 4:
(7 + 1/4) 4 + (8 + 1/2 - 2)/3
Put 7 + 1/4 over the common denominator 4. 7 + 1/4 = (4×7)/4 + 1/4:
(4×7)/4 + 1/4 4 + (8 + 1/2 - 2)/3
4×7 = 28:
(28/4 + 1/4) 4 + (8 + 1/2 - 2)/3
28/4 + 1/4 = (28 + 1)/4:
(28 + 1)/4×4 + (8 + 1/2 - 2)/3
28 + 1 = 29:
29/4×4 + (8 + 1/2 - 2)/3
29/4×4 = (29×4)/4:
(29×4)/4 + (8 + 1/2 - 2)/3
(29×4)/4 = 4/4×29 = 29:
29 + (8 + 1/2 - 2)/3
Put 8 + 1/2 - 2 over the common denominator 2. 8 + 1/2 - 2 = (2×8)/2 + 1/2 + (2 (-2))/2:
29 + ((2×8)/2 + 1/2 + (2 (-2))/2)/3
2×8 = 16:
29 + (16/2 + 1/2 + (2 (-2))/2)/3
2 (-2) = -4:
29 + (16/2 + 1/2 + (-4)/2)/3
16/2 + 1/2 - 4/2 = (16 + 1 - 4)/2:
29 + ((16 + 1 - 4)/2)/3
16 + 1 = 17:
29 + ((17 - 4)/2)/3
| 1 | 7
- | | 4
| 1 | 3:
29 + (13/2)/3
13/2×1/3 = 13/(2×3):
29 + 13/(2×3)
2×3 = 6:
29 + 13/6
Put 29 + 13/6 over the common denominator 6. 29 + 13/6 = (6×29)/6 + 13/6:
(6×29)/6 + 13/6
6×29 = 174:
174/6 + 13/6
174/6 + 13/6 = (174 + 13)/6:
(174 + 13)/6
| 1 | 7 | 4
+ | | 1 | 3
| 1 | 8 | 7:
Answer: 187/6
10 of the numbers are even. 4 more are odd multiples of 3. The probability of landing on even or a multiple of 3 is (10+4)/21 = 2/3.
By the fundamental theorem of calculus,
Answer:
a) Parallel when a = -2/3
b) Perpendicular when a = 6
Explanation:
a) For two parallel lines slopes are equal.
So, 6y=−2x+4 and 2y=ax−5 parallel if they are slopes equal.
Slope of 6y=−2x+4, comparing with y = mx + c
So, m = -2/6 = =-1/3
For 6y=−2x+4 and 2y=ax−5 to b parallel we have slope of 2y=ax−5 equal to -1/3
Slope of 2y=ax−5
m = a/2
We have a/2 = -1/3
a = -2/3
b) For perpendicular lines product of slope is -1.
So we have
