1. Which number is a solution of the inequality?
10.6<b
A)-18
B)-9
C)7
D)14***
2. Which number is a solution of the inequality?
y+2>8
A)-5
B)-6
C)6
D)7***
3. Which number is a solution of the inequality?
6>z(10-z)
A)0
B)1
C)2
D)3***
4. What are all the subsets of the set?
{-1,9}
A) 0, {-1}, {9}***
B) {-1}, {9}, {-1, 9}
C) 0, {-1}, {9}, {-1, 9}
D) {-1}, {0}
1. To find the solution to the inequality 10.6 < b, we need to identify a number that satisfies the inequality. In this case, we are looking for a number that is greater than 10.6.
The answer choices are -18, -9, 7, and 14.
Comparing these numbers to 10.6, we can see that only 14 is greater than 10.6. Therefore, the correct answer is D) 14.
2. For the inequality y + 2 > 8, we need to find a number that satisfies the inequality. In this case, we are looking for a number that is greater than 8 when 2 is added to it.
The answer choices are -5, -6, 6, and 7.
To solve this, subtract 2 from each of the answer choices: -5 - 2 = -7, -6 - 2 = -8, 6 - 2 = 4, and 7 - 2 = 5.
We can see that only 7 - 2 = 5 is greater than 8. Therefore, the correct answer is D) 7.
3. For the inequality 6 > z(10 - z), we need to find a number that satisfies the inequality. In this case, we are looking for a value of z that makes the inequality true.
The answer choices are 0, 1, 2, and 3.
To solve this, we can simplify the inequality to 6 > 10z - z^2.
We can rewrite it as z^2 - 10z + 6 < 0 and solve for z using factoring or quadratic formula.
Factoring:
(z - 3)(z - 2) < 0
From this equation, we can see that the values of z that satisfy the inequality are when z is greater than 2 and less than 3. This means that the only answer choice that falls within this range is D) 3.
4. To find all the subsets of the set {-1, 9}, we need to list out all the possible combinations of elements from the set.
The answer choices are 0, {-1}, {9}, and {-1, 9}.
To find the subsets, we can use the concept of combination. For a set with n elements, there are 2^n possible subsets. In our case, we have 2 elements {-1, 9}, so there are 2^2 = 4 possible subsets.
The subsets are:
- Subset 1: 0 (This represents the empty set)
- Subset 2: {-1}
- Subset 3: {9}
- Subset 4: {-1, 9}
Therefore, the correct answer is A) 0, {-1}, {9}.
1. The number 14 is a solution of the inequality 10.6<b.
2. The number 7 is a solution of the inequality y+2>8.
3. The number 3 is a solution of the inequality 6>z(10-z).
4. The subsets of the set {-1,9} are:
- Subset 1: {}, the empty set or null set.
- Subset 2: {-1}.
- Subset 3: {9}.
- Subset 4: {-1,9}.
1 correct
2 C
4 C
3 is there a typo?