is a valid argument
is not a valid argument
For the first argument:
From the definition of absolute value function
if 
That is every positive number is its own absolute value. Since
,
we can argue that
so the first argument is valid
For the second argument:
From the definition of absolute value function
This means that
or
no part of the definition allow for the option 
. So the second argument is not valid.
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Answer:
C. 7 : 18.
Step-by-step explanation:
To solve this, we need to convert each of the measurements given to inches:
2 ft 4 in = 28 inches.
2 yard = 6 feet = 72 inches.
Therefore, expressing this as a ratio would give us:
28 : 72
Simplify by reducing by a factor of 4:
7 : 18. This is the ratio in simplest form.
Answer:
54 cm
Step-by-step explanation:
The area (A) of an equilateral triangle is
A = 
( s is the side length ) then
= 81
( multiply both sides by 4 to clear the fraction )
s² = 324 ( divide both sides by )
s² = 324 ( take the square root of both sides )
s = 
= 18
Thus
perimeter = 3 × 18 = 54 cm
Answer:
Explanation:
12x = 48 - 8y
10x + 8y = 38
———————
12x + 8y = 48
10x + 8y = 38
———————
12x + 8y = 48
-1(10x + 8y = 38)
————————
12x + 8y = 48
-10x - 8y = -38
————————
2x = 10
x = 10/2 = 5
If x = 5 then:
10x + 8y = 38
10(5) + 8y = 38
50 + 8y = 38
8y = 38 - 50
8y = -12
y = -12/8
y = -3/2
Therefore, x = 5 and y = -3/2
Answer:
5575 cm³
Step-by-step explanation:
The volume of a sphere is V = (4/3)πr³. If we substitute r = (d/2 where r is the radius and d the diameter), this formula becomes:
πd³
V = (4/3)π·d³/8, or V = -------------
6
and so, if d = 22 cm, the volume is:
π(22 cm)³
V = ------------------- = 5575 cm³
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