Not sure about the first one,
The second one is 1/9.
Answer:
The answer is <em>1</em>.
Step-by-step explanation:
Given the expression:

To find:
The expression without absolute value.
Solution:
First of all, let us learn about the absolute value function:

i.e. value is x if x is positive
value is -x if x is negative
Here the given expression contains two absolute value functions:
and 
Using the definition of absolute value function as per above definition.


Now, it is given that z < 5 that means z will also be lesser than 6 i.e. z < 6
So, given expression
will be equivalent to :

So, the expression is equivalent to <em>1</em>.
Answer:
9, 32 and 36
Step-by-step explanation:
The perimeter of a triangle is the sum of all the sides. Since you know the perimeter and the expressions for each of the sides, you can set up an equation to solve for the variable and find the values of the other sides:
one side: '4 times the shortest side' = 4s
shortest side: 's'
third side: '23 more than the shortest side' = s + 23
perimeter = 77
Equation: 4s + s + (s + 23) = 77
Combine like terms: 6s + 23 = 77
Subtract 23 from both sides: 6s + 23 - 23 = 77 - 23 or 6s = 54
Divide by 6: 6s/6 = 54/6 or s = 9
one side: 4s = 4(9) = 36
shortest side: s = 9
third side: s + 23 = 9 + 23 = 32
9514 1404 393
Answer:
12 1/2 laps
Step-by-step explanation:
To find the number of laps, divide the distance by the distance per lap.
(3 1/8) ÷ (1/4) = (3 1/8) × (4/1) = 3·4 +(1/8)·4 = 12 4/8 = 12 1/2
Quadir needs to jog 12 1/2 laps if he wants to jog 3 1/8 miles.