Given:
The table represents a proportional relationship.
To find:
The equation of the function.
Solution:
If y is directly proportional to x, then

...(i)
where, k is the constant of proportionality.
From the given table it is clear that the function passes through (2,1). So, the equation must be satisfied by the point (2,1).
Putting x=2 and y=1 in (i), we get


Putting
, we get

Therefore, the correct option is A.
Answer:
21.53 in of fabric on headbands
7.67 in of fabric on wristbands.
Step-by-step explanation:
Step one:
given data
the total amount of person players plus coaches= 27+4= 31
for each person, she uses = 667.43/31= 21.53 in of fabric on headbands
She also uses 237.87inches of fabric on wristbands for just the players
For each player, she will use= 237.87/31= 7.67 in of fabric
Hence for each player, she used
21.53 in of fabric on headbands
7.67 in of fabric on wristbands
The answer is B $37.59
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Equation: SOLVE
Solution for 10=4(x-1)-(x-8) equation:
Simplifying
10 = 4(x + -1) + -1(x + -8)
Reorder the terms:
10 = 4(-1 + x) + -1(x + -8)
10 = (-1 * 4 + x * 4) + -1(x + -8)
10 = (-4 + 4x) + -1(x + -8)
Reorder the terms:
10 = -4 + 4x + -1(-8 + x)
10 = -4 + 4x + (-8 * -1 + x * -1)
10 = -4 + 4x + (8 + -1x)
Reorder the terms:
10 = -4 + 8 + 4x + -1x
Combine like terms: -4 + 8 = 4
10 = 4 + 4x + -1x
Combine like terms: 4x + -1x = 3x
10 = 4 + 3x
Solving
10 = 4 + 3x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3x' to each side of the equation.
10 + -3x = 4 + 3x + -3x
Combine like terms: 3x + -3x = 0
10 + -3x = 4 + 0
10 + -3x = 4
Add '-10' to each side of the equation.
10 + -10 + -3x = 4 + -10
Combine like terms: 10 + -10 = 0
0 + -3x = 4 + -10
-3x = 4 + -10
Combine like terms: 4 + -10 = -6
-3x = -6
Divide each side by '-3'.
x = 2
Simplifying
x = 2
Answer:

Step-by-step explanation:
Factor the equation
using formula for difference of the cubes:

then

1. The equation
has real solution 
2. The equation
has negative discriminant
then it has two complex solutions
