6.04 Substitution
Find the value of:
9 + m when m = 8
14 + v when v = 15
n - 2 when n = 5
n - 8 when n = 44
\dfrac{n}{7} when n = 14
\dfrac{u}{9} when u = 54
u \times 5 when u = 6
n \times 9 when n = 8
2x + 9 when x = 4
y^2 when y = -2
x^2 - 4x when x = 3
\dfrac{x+10}{4} when x = 2
\dfrac{3x}{4} when x = 8
2 \left( x+7 \right) when x = 4
\left( x+2 \right) \left( x - 1 \right) when x = -3
4y^2 + 9 when y = 2
Find the value of:
m + n when m = 7 and n = 12
4 x + 2 y + 3 when x = 5 and y = 4
x^2 - 4y when x = -2 and y = 5
8a + 4b - 9 when a = 2 and b = 5
\dfrac{5xy}{9} when x = 3 and y = 6
abc when a = 3, b = -2 and c = -1
For each formula find the value of y for the given value of x:
y = 6 x - 9, when x = 12.
y = \dfrac{x}{9} + 6, when x = 63.
y = 4-3x, when x = 7.
y = 14x+\dfrac{18}{5}, when x = \dfrac{1}{10}.
Consider the following formulae:
q = p + 7
Complete the table:
| p | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| q | 8 | 9 | 10 |
Find the value of q when p = 30.
q = 3 p
Complete the table:
| p | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| q | 3 | 6 | 9 |
Find the value of q when p = 20.
q = 6 p + 4
Complete the table:
| p | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| q | 10 | 16 | 22 |
Find the value of q when p = 40.
n = m - 7
Complete the table:
| m | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|
| n | 3 | 4 | 5 |
Find the value of n when m = 20.
q = 5 p - 3.
Complete the table:
| p | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| q | 2 | 7 | 12 |
Find the value of q when p = 20.
q = p^{2} + 5.
Complete the table:
| p | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| q | 6 | 9 | 14 |
Find the value of q when p = 20.
Vanessa is making the sequence to the right out of tiles. She creates a table comparing the sequence number of a shape to the number of tiles needed to make it:
| \text{Sequence}\\ \text{number } (S) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| \text{No. tiles } (T) | 3 | 5 | 7 |
Write an algebraic rule for the number of tiles, T, in terms of the sequence number, S.
Use your rule to complete the table of values.
James is making snowflakes out of hexagonal tiles:
James creates a table comparing the width of a snowflake to the number of tiles needed to make it:
| \text{Width } (W) | 1 | 3 | 5 | 7 | 9 | 11 | 13 |
|---|---|---|---|---|---|---|---|
| \text{No. tiles } (T) | 1 | 7 | 13 | 19 |
Write an algebraic rule for the number of tiles, T, in terms of the snowflake's width, W.
Use your rule to complete the table of values.