Hello I did my math homework, but I need someone to check if I did it right or not.
1. A = z>=4 B = z<7
Write A or B and A and B using interval notation
Answer: A or B = (-infinity, infinity)
A and B = [4,7)
2. Write the algebraic expression for the following:
8 is less than or equal to b
Answer: 8=<b
3. Write the algebraic expresison for the following:
-3 is greater than or equal to x , and x is greater than -4
Answer: -3>=x>-4
4. |-4w + 8| = 28
Answer: -5.9
typo # 4 answer = -5,9
All correct.
To check if your answers are correct, let's go through each question one by one:
1. A = z>=4, B = z<7
To write A or B using interval notation, you need to understand that "or" means either A or B can be true. In interval notation, you can express this as the union of two intervals. A is z>=4, which includes all values greater than or equal to 4. B is z<7, which includes all values less than 7.
So, A or B would be (-infinity, 7). Notice that we used the open interval on the right because 7 is not included.
To write A and B using interval notation, you need to find the intersection of the two intervals. In this case, A and B means the common values that satisfy both conditions. A = z>=4, which includes all values greater than or equal to 4. B = z<7, which includes all values less than 7.
The intersection of A and B would be [4, 7). Notice that we used the closed interval on the left because 4 is included, but the open interval on the right because 7 is not included.
2. 8 is less than or equal to b
To write the algebraic expression for this statement, you need to express it using mathematical symbols. "8 is less than or equal to b" can be written as 8 <= b.
3. -3 is greater than or equal to x, and x is greater than -4
This statement has two conditions. To express it as an algebraic expression, you need to indicate each condition separately and combine them using logical operators. The first condition is "-3 is greater than or equal to x," which can be written as -3 >= x. The second condition is "x is greater than -4," which can be written as x > -4.
To combine these conditions, you use the logical operator "and," which means both conditions must be true. So, the algebraic expression would be -3 >= x and x > -4.
4. |-4w + 8| = 28
To find the value of w that satisfies this equation, you first need to isolate the absolute value expression. In this case, |-4w + 8| = 28, you can do this by removing the absolute value signs and creating two equations, one positive and one negative:
-4w + 8 = 28 (Positive case)
-4w + 8 = -28 (Negative case)
Now, solve each equation separately for w:
For the positive case:
-4w + 8 = 28
-4w = 28 - 8
-4w = 20
w = 20 / -4
w = -5
For the negative case:
-4w + 8 = -28
-4w = -28 - 8
-4w = -36
w = -36 / -4
w = 9
So, the solutions for w are w = -5 and w = 9.
Overall, your answers seem to be correct, except for the last one. The correct answer to |-4w + 8| = 28 is w = -5 and w = 9, not w = -5.9.