Solve the following problems by identifying the pattern. Problem 11: Top Left: 81, Bottom Left: 64, Top…

Question

Solve the following problems by identifying the pattern. Problem 11: Top Left: 81, Bottom Left: 64, Top Right: ?, Bottom Right: 370. Problem 12: Top Left: ?, Bottom Left: 36, Top Right: 169, Bottom Ri

ScanSolve AI Tutor · Accepted Answer

Here's how to solve these problems by identifying the pattern.

The pattern observed from the examples is:

The top right number is the square of the difference between the top left and bottom left numbers. $\text{Top Right} = (\text{Top Left} - \text{Bottom Left})^2$
The bottom right number is the sum of the top right number and the top left number. $\text{Bottom Right} = \text{Top Right} + \text{Top Left}$

Let's apply this rule to solve problems 11-20.

11.

Find the top right value using the first rule.
$\text{Top Right} = (81 - 64)^2 = 17^2 = 289$
Verify the bottom right value using the second rule.
$\text{Bottom Right} = 289 + 81 = 370$
This matches the given bottom right value.
The missing value is $\boxed{289}$ .

12.
Let the missing top left value be $X$ .
Use the first rule to find $X$ .
$169 = (X - 36)^2$ $\sqrt{169} = X - 36$ $13 = X - 36$ $X = 13 + 36 = 49$
Verify $X$ using the second rule.
$218 = 169 + X$ $X = 218 - 169 = 49$
Both rules give the same value for $X$ .
The missing value is $\boxed{49}$ .

13.
Find the top right value using the first rule.
$\text{Top Right} = (25 - 16)^2 = 9^2 = 81$
Verify the bottom right value using the second rule.
$\text{Bottom Right} = 81 + 25 = 106$
This matches the given bottom right value.
The missing value is $\boxed{81}$ .

14.
Find the top right value using the first rule.
$\text{Top Right} = (9 - 0)^2 = 9^2 = 81$
Find the bottom right value using the second rule.
$\text{Bottom Right} = 81 + 9 = 90$
The missing value is $\boxed{90}$ .

15.
Let the missing top left value be $X$ .
Use the first rule to find $X$ .
$121 = (X - 25)^2$ $\sqrt{121} = X - 25$ $11 = X - 25$ $X = 11 + 25 = 36$
Verify $X$ using the second rule.
$157 = 121 + X$ $X = 157 - 121 = 36$
Both rules give the same value for $X$ .
The missing value is $\boxed{36}$ .

16.
Let the missing bottom left value be $Y$ .
Use the first rule to find $Y$ .
$121 = (36 - Y)^2$ $\sqrt{121} = 36 - Y$ $11 = 36 - Y$ $Y = 36 - 11 = 25$
Verify the bottom right value using the second rule.
$157 = 121 + 36$ $157 = 157$
This matches the given bottom right value.
The missing value is $\boxed{25}$ .

17.
Let the missing top left value be $X$ .
Use the first rule to find $X$ .
$361 = (X - 81)^2$ $\sqrt{361} = X - 81$ $19 = X - 81$ $X = 19 + 81 = 100$
Verify $X$ using the second rule.
$461 = 361 + X$ $X = 461 - 361 = 100$
Both rules give the same value for $X$ .
The missing value is $\boxed{100}$ .

18.
Let the missing bottom left value be $Y$ .
Use the first rule to find $Y$ .
$225 = (64 - Y)^2$ $\sqrt{225} = 64 - Y$ $15 = 64 - Y$ $Y = 64 - 15 = 49$
Verify the bottom right value using the second rule.
$289 = 225 + 64$ $289 = 289$
This matches the given bottom right value.
The missing value is $\boxed{49}$ .

19.
Find the top right value using the first rule.
$\text{Top Right} = (9 - 9)^2 = 0^2 = 0$
Find the bottom right value using the second rule.
$\text{Bottom Right} = 0 + 9 = 9$
The missing value is $\boxed{9}$ .

20.
Find the top right value using the first rule.
$\text{Top Right} = (16 - 4)^2 = 12^2 = 144$
Verify the bottom right value using the second rule.
$\text{Bottom Right} = 144 + 16 = 160$
This matches the given bottom right value.
The missing value is $\boxed{144}$ .

Solve the following problems by identifying the pattern. Problem 11: Top Left: 81, Bottom Left: 64, Top Right: ?, Bottom Right: 370. Problem 12: Top Left: ?, Bottom Left: 36, Top Right: 169, Bottom Ri

Step-by-step solution

Find the top right value using the first rule.

Verify the bottom right value using the second rule.

Let the missing top left value be $X$ .

Verify $X$ using the second rule.

Find the top right value using the first rule.

Verify the bottom right value using the second rule.

Find the top right value using the first rule.

Find the bottom right value using the second rule.

Let the missing top left value be $X$ .

Verify $X$ using the second rule.

Let the missing bottom left value be $Y$ .

Verify the bottom right value using the second rule.

Let the missing top left value be $X$ .

Verify $X$ using the second rule.

Let the missing bottom left value be $Y$ .

Verify the bottom right value using the second rule.

Find the top right value using the first rule.

Find the bottom right value using the second rule.

Find the top right value using the first rule.

Verify the bottom right value using the second rule.

Still stuck on this one?

More Mathematics Questions

Solve the following problems by identifying the pattern. Problem 11: Top Left: 81, Bottom Left: 64, Top Right: ?, Bottom Right: 370. Problem 12: Top Left: ?, Bottom Left: 36, Top Right: 169, Bottom Ri

Step-by-step solution

Find the top right value using the first rule.

Verify the bottom right value using the second rule.

Let the missing top left value be XXX.

Verify XXX using the second rule.

Find the top right value using the first rule.

Verify the bottom right value using the second rule.

Find the top right value using the first rule.

Find the bottom right value using the second rule.

Let the missing top left value be XXX.

Verify XXX using the second rule.

Let the missing bottom left value be YYY.

Verify the bottom right value using the second rule.

Let the missing top left value be XXX.

Verify XXX using the second rule.

Let the missing bottom left value be YYY.

Verify the bottom right value using the second rule.

Find the top right value using the first rule.

Find the bottom right value using the second rule.

Find the top right value using the first rule.

Verify the bottom right value using the second rule.

Still stuck on this one?

More Mathematics Questions

Let the missing top left value be $X$ .

Verify $X$ using the second rule.

Let the missing top left value be $X$ .

Verify $X$ using the second rule.

Let the missing bottom left value be $Y$ .

Let the missing top left value be $X$ .

Verify $X$ using the second rule.

Let the missing bottom left value be $Y$ .