Answer:
1. 8.4 2. 15
Step-by-step explanation:
1. 4x+8y= 40
wen y= 0.8
4x+8×0.8=40
4x=40-8×0.8
4x= 40- 6.4= 33.6
....x= 33.6/4 = 8.4
2. 3a+b= 54
wen b= 9
3a+ 9= 54
3a= 54- 9
3a=45
.....a = 45/3 = 15
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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:
None of the equations are true for p = 3.4
Step-by-step explanation:
In order for the inequality to be valid we need to apply the value for p and check wether or not it is true. We gonna do for each of the following:
A. 3p < 10.2
3*3.4 < 10.2
10.2 < 10.2
Not true, since the left side is equal to the right side and not less.
B. 13.6 < 3.9p
13.6 < 3.9*3.4
13.6 < 13.26
Not true since 13.6 is greater than 13.26
C. 5p > 17.1
5*3.4 > 17.1
17 > 17.1
Not true since 17 is less than 17.1
D. 8.5 > 2.5p
8.5 > 2.5*3.4
8.5 > 8.5
Not true since the left side is equal to the right side.
1m = 100cm
1cm → 0.5m
1cm → 0.5 · 100cm = 50cm
The scale: 
length = 26.8cm · 50 = 1,340cm = 13.40m
width = 12.2cm · 50 = 610cm = 6.10m
The area of the court:
A = 13.40 · 6.10 = 81.74 m²
Answer:
The minimum width of the placemat is 10 inches.
Step-by-step explanation:
Let suppose that placemat has a square form, whose width must be at least equal to the diameter of the pizza, so that pizza does not touch the table. Hence, the following relationship is obtained:
Where:
- Width of the placemat, measured in inches.
- Diameter of pizza, measured in inches.
The area of the pizza, measured in square inches, is determined by this formula:
The diameter is cleared afterwards:
If 
and 
, then:
The minimum width of the placemat is 10 inches.
