Note: Since the symbols for greatest integer function (GIF) and least integer function (LIF) are not given, I will be using the words GIF and LIF in the solution
GIF x means largest integer less than or equal to x, and LIF x means least integer greater than or equal to x.
We need to determine which expressions are equal
Option 1: GIF 4.9 and LIF 3.1
GIF 4.9 = 3
LIF 3.1 = 4
Hence GIF 4.9 ≠ LIF 3.1
Option 2: GIF 15.2 and GIF 14.8
GIF 15.2 = 15
GIF 14.8 = 14
Hence, GIF 15.2 ≠ GIF 14.8
Option 3: GIF -6 and LIF -6
GIF -6 = -6
LIF -6 = -6
Hence, GIF -6 = LIF -6
Option 4: LIF -3.2 and LIF -2.6
LIF -3.2 = -2
LIF -2.6 = -1
Hence, LIF -3.2 ≠ LIF -2.6
Hence, only in Option C the pair of expressions are equal.
Line 1 and line 4 are parallel
Step-by-step explanation:
Two lines are said to be parallel if they have same slope.
In order to compare the lines given, we have to write them all in the same form, and then compare their slopes.
Line 1:
Applying distributive property,
Line 2:
Line 3:
Applying distributive property,
Line 4:
re-arranging,
Now we have rewritten all the lines in the form 
, where m is the slope. By comparing the values of m, we see:
Therefore, the lines which are parallel are line 1 and line 4.
Learn more about parallel and perpendicular lines:
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Answer:
B
Step-by-step explanation:
using the tangent ratio on the triangle on the right and the exact value
tan60° = 
, then letting the altitude be h
tan60° = 
= 
= ( multiply both sides by h )
11
= h × ( divide both sides by )
11
= h
using the sine ratio in the triangle on the left and the exact value
sin45° = 
, then
sin45° = 
= 
= 
= ( cross- multiply )
× x = 22 ( divide both sides by )
x = 22
Answer:
B) -4 < y
Step-by-step explanation:
The lowest point on the y axis of the graph is -4 and everything else is higher
