Answer:
a = -4
Step-by-step explanation:
Solve for a:
-7 (3 a - 1) = 91
Divide both sides of -7 (3 a - 1) = 91 by -7:
(-7 (3 a - 1))/(-7) = 91/(-7)
(-7)/(-7) = 1:
3 a - 1 = 91/(-7)
The gcd of 91 and -7 is 7, so 91/(-7) = (7×13)/(7 (-1)) = 7/7×13/(-1) = 13/(-1):
3 a - 1 = 13/(-1)
Multiply numerator and denominator of 13/(-1) by -1:
3 a - 1 = -13
Add 1 to both sides:
3 a + (1 - 1) = 1 - 13
1 - 1 = 0:
3 a = 1 - 13
1 - 13 = -12:
3 a = -12
Divide both sides of 3 a = -12 by 3:
(3 a)/3 = (-12)/3
3/3 = 1:
a = (-12)/3
The gcd of -12 and 3 is 3, so (-12)/3 = (3 (-4))/(3×1) = 3/3×-4 = -4:
Answer: a = -4
Answer:
4/10
Step-by-step explanation:
0.4 is said by "four-tenths." Fractions are also said the same way. Notice how there is a four and a ten. This should be easier to help you make decimals in fraction form. The four would be the numerator and the ten would be the denominator, making the final answer 4/10.
Answer:
Perimeter = 90
Step-by-step explanation:
Let c = hypotenuse, 15 = b, and a = other leg
Given: c/a = 13/12, so a = 12c/13.
c^2 = b^2+a^2
Using Pythagorean Theorem: c^2 = 225 + 144c^2/169.
169c^2 = 169(225) + 144c^2
25c^2 = 169(225)
5c = 13(15)
c = 13(3) = 39.
and a = 12*39/13 = 12*3 = 36
You now can compute all three sides, and
thus obtain perimeter = 36+39+15 = 90.
For 8 rooks
Without conflict (i.e. there is no row or column can contains 2 rooks)
then there are 8 choices for the first one in the first column, 7 choices in the second, ...1 choice in the last (eighth) column for a total of
8!=40320 ways.
Unlimited conflicts
there are 64 choices for the first, 63 for the second, .... 57 for the last, for a total of 64!/56!=178462987637760 ways
Similarly, for n rooks, with unlimited conflicts, there are
64!/(64-n)! ways
