Use the equation y − 5 = x3
to fill in the missing values in the table below. (Type in numbers for your answers, do not spell the numbers out or it will count it wrong.)
x y
blank 1
-3 4
0 blank
6 blank
blank 8
x y
blank 1
-3 4
0 -5
6 221
1 6
To fill in the missing values in the table, we will substitute the given values of x into the equation y - 5 = x^3 and solve for y.
Plugging in the values, we get:
1st row: y - 5 = (1)^3
y - 5 = 1
y = 1 + 5
y = 6
2nd row: y - 5 = (-3)^3
y - 5 = -27
y = -27 + 5
y = -22
3rd row: y - 5 = (0)^3
y - 5 = 0
y = 0 + 5
y = 5
4th row: y - 5 = (6)^3
y - 5 = 216
y = 216 + 5
y = 221
5th row: y - 5 = (8)^3
y - 5 = 512
y = 512 + 5
y = 517
Using these calculations, the completed table is:
x y
1 6
-3 4
0 5
6 221
8 517
To fill in the missing values in the table, we need to substitute the given values of x into the equation y - 5 = x^3 and solve for y.
For the first missing value, let's substitute 1 for y and solve for x:
1 - 5 = x^3
-4 = x^3
Taking the cube root of both sides, we find that x = -∛4. Therefore, the missing value in the first row is -∛4.
For the second missing value, let's substitute 4 for y and solve for x:
4 - 5 = x^3
-1 = x^3
Again, taking the cube root of both sides, we find that x = -1. Hence, the missing value in the third row is -1.
For the third missing value, let's substitute 8 for y and solve for x:
8 - 5 = x^3
3 = x^3
Taking the cube root of both sides, we find that x = ∛3. Therefore, the missing value in the fifth row is ∛3.
Thus, the completed table becomes:
x y
-∛4 1
-3 4
0 -1
6 3
∛3 8