Answer:
Step-by-step explanation:
Step1:-
Given 4 b+5=t
subtracting on both sides with 5 we get
After simplification 
Dividing '4' on both sides , we get and simplification
now Final answer 
1.
<span>{a, e, i, o}
</span>{a} , {e} , {i} , {o} , {a,e} , {a,i} , {a,o} , {e,i} , {e,o} , {i,o} , {a,e,i} , {a,e,o} , {a,i,o}
2.
<span>{0, 1, 2}
</span>{0} , {1} , {2} , {0,1} , {0,2} , {1,2}
3.
<span>Suppose U = {1, 2, 3, 4, 5} is the universal set and A = {2, 3}. What is A ?
Well "A" is {2, 3}, but I'm guessing you meant A'.
A' is all the numbers you don't see, which is
{1, 4, 5}
4.
</span><span>Suppose U={1, 2, 3, 4, 5, 6, 7, 8} is the universal set and P={2,4, 6, 8}. What is P?
Again, "P" is just {2,4, 6, 8}, but P' is all the numbers you don't see, which are all prime numbers in this sequence:
{1, 3, 5, 7}
5.
</span><span>-4 < k + 3 < 8
subtract 3 from all sides
-7 < k < 5
6.
</span><span> 5 <= y + 2 <= 11
subtract 2 from all sides
3 <= y <= 9
7.
</span><span>6b - 1 < -7 or 2b + 1 > 5
solve both
</span>6b - 1 < -7
add both sides by 1
6b < -6
divide both sides by 6
b < -1
now do the other problem
2b + 1 > 5
subtract both sides by 1
2b > 4
divide both sides by 2
b > 2
answer: b < -1 or b > 2
<span>8.
5 + m > 4 or 7m < -35
subtract both sides by 5 |or| divide both sides by 7
m > -5 or m < -5
m = -5</span>
Answer:
1. b. 2. a. 3. a.
Step-by-step explanation:
1. (f + g)x = f(x) + g(x)
= x^2 + 2x + 4
(f + g)(-1) = (f + g)(x) where x = 1 so it is
(-1)^2 + 2(-1) + 4
= 1 - 2 + 4
= 3.
2. We find (f o g)(x) by replacing the x in f(x) by g(x):
= √(x + 1) and
(f o g)(3) = √(3 + 1)
= √4
= 2.
3. (f/g) c = f(x) / g(x)
= (x - 3)/(x + 1)
The domain is the values of x which give real values of (f/g).
x cannot be - 1 because the denominator x + 1 = -1+1 = 0 and dividing by zero is undefined. So x can be all real values of x except x = -1.
The domain is (-∞, -1) U (-1, ∞)
Yes, the inverse of a symmetric matrix is also symmetric.
Take the symmetric matrix A, we have:
and
This gives:
Using the properties:
and
We get:
Since
, we can perform the substitution to get:
Multiplying by
on both sides:
Proving that the inverse of a symmetric matrix is also symmetric.
