Question

Use the equation y − 5 = x3
to fill in the missing values in the table below.

x y
Response area
blank 1
-3 4
0 Blank
6 blank
blank 8
answers
7,1,9,0,5,12,-12

Answer 1

Given the equation \( y - 5 = x^3 \), we can rearrange it to find \( y \):

\[
y = x^3 + 5
\]

Now, we can fill in the missing values in the table using the provided values of \( x \).

1. For \( x = -3 \):
\[
y = (-3)^3 + 5 = -27 + 5 = -22
\]

2. For \( x = 0 \):
\[
y = (0)^3 + 5 = 0 + 5 = 5
\]

3. For \( x = 6 \):
\[
y = (6)^3 + 5 = 216 + 5 = 221
\]

4. For \( y = 8 \):
\[
8 = x^3 + 5 \implies x^3 = 3 \implies x = \sqrt[3]{3} \approx 1.442
\]

Now, let's fill in the missing values:

| x | y |
|-----|----|
| 1 | |
| -3 | 4 |
| 0 | 5 |
| 6 | |
| | 8 |

Now we add in the calculated values and replace the blanks:

1. The first blank \( (x = 1) \):
\[
y = 1^3 + 5 = 1 + 5 = 6
\]

Thus, replacing the blanks, we have:

| x | y |
|-----|----|
| 1 | 6 |
| -3 | 4 |
| 0 | 5 |
| 6 | 221|
| 1.442| 8 |

From the provided answers, it appears that the correct values for the blanks for your listed values (7, 1, 9, 0, 5, 12, -12) and with the relationship defined do not conform strictly to integers, as \(x = 6\) results in an output of \(221\), thus this would indicate further exploration is needed.

However, the value of \(y\) corresponding directly is confirmed.

If you want matching with given number choices answers, we'd clarify each based on x-axis values instead of output dependency showing possible noted misalignment in values occurring.