Answer:
- addition property of equality
- integers are closed to addition
- identity element
- multiplication property of equality
- commutative property of multiplication; reals are closed to multiplication; identity element
Step-by-step explanation:
<u>Given</u>:
c/2 -5 = 7
Step 1: c/2 -5 +5 = 7 +5
Step 2: c/2 +0 = 12
Step 3: c/2 = 12
Step 4: 2(c/2) = 12(2)
Step 5: c = 24
<u>Find</u>:
The property that justifies each step of the solution.
<u>Solution</u>:
Step 1: addition property of equality (lets you add the same to both sides)
Step 2: integers are closed to addition
Step 3: identity property of addition (adding 0 changes nothing)
Step 4: multiplication property of equality
Step 5: closure of real numbers to multiplication; identity property of multiplication
_____
It is hard to say what "property" you want to claim when you simplify an arithmetic expression. Above, we have used the property that the sets of integers and real numbers are closed to addition and multiplication. That is, adding or multiplying real numbers gives a real number.
In Step 5, we can rearrange 2(c/2) to c(2/2) using the commutative property of multiplication. 2/2=1, and c×1 = c. The latter is due to the identity element for multiplication: multiplying by 1 changes nothing.
Apart from the arithmetic, the other properties used are properties of equality. Those let you perform any operation on an equation, as long as you do it to both sides of the equation. The operations we have performed in this fashion are adding 5 and multiplying by 2.
Answer:
9 hours and 20 minutes.
Step-by-step explanation:
In one hour, Amanda can proofread 17 reports.
In one hour, Sally can proofread 28 reports.
That means together, they can proofread 45 reports in one hour.
So we need to divide the total amount of reports by how much they can read in an hour:
420/45 = 28/3 = 9 1/3
The time it takes between the two of them is 9 hours and 20 minutes.
Answer:
Largest possible length is <em>21 inches</em>.
Step-by-step explanation:
Given:
Total material available = 60 inches
Length to be 3 more than twice of width.
To find:
Largest possible length = ?
Solution:
As it is rectangular shaped frame.
Let length = 
inches and
Width = 
inches
As per given condition:
..... (1)
Total frame available = 60 inches.
i.e. it will be the perimeter of the rectangle.
Formula for perimeter of rectangle is given as:
Putting the given values and conditions as per equation (1):
Putting in equation (1):
So, the answer is:
Largest possible length is <em>21 inches</em>.
To make a positive profit p(x)>0 we need to make:
Now we solve this for x:
We have:
a = -2
b = 7
c = -3
We will use formula for quadratic equation:
We got two solutions. One is fraction other is whole number. We will not consider fraction because the amount of muffins sold must be whole number. So our solution is:
x>3
Answer: $135
Step-by-step explanation: 48% of $355 would be 170 so therefore the $135 would be the cheaper penalty
