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
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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.
The 5-pound bag is better value.
The easiest way to compare and find out which is a better buy is to find out how much is being charged for 1-pound of food in each bag.
$12 is divided by 3 beacuse it's a 3-pound bag and we are aiming to find what 1-pound is equal to.
$12 ÷ 3 = $4
So the first bag charges $4 per pound of food.
Then use the same method for the 5-pound bag.
$14.25 ÷ 5 = $2.85
So the second charges $2.85 per pound of food.
So as we can see, the 5-pound bag is clearly better value. For each pound of food you are saving $1.15 in comparison to what you would be spending if you opted for the first bag.
Hope this helps!
Answer:
∠x = 13.43°
Step-by-step explanation:
area ΔABC = 1/2 ( BD x AC) = 1/2 (22 x AC) = 42
22 x AC = 84 AC = 84/22 = 42/11 = 3.82
CD = BD - BC = 22 - 6 = 16
AD² = AC² + CD² = (3.82)² + 16² = 270.59
AD = 16.45
sin ∠x = AC / AD = 3.82 / 16.45 = 0.2322
∠x = 13.43°
Answer:
-11
Step-by-step explanation:
Firstly simplify your expression...by dealing with the brackets
; -k - 7k + 6n + 3n
;then substitute with the given values into your expression,
;-(-2) -7(-2) + 6(-3) + 3(-3)
; 2 + 14 - 18 - 9
; 16 - 27
;Hence the answer is -11
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