2.06 Substitution
Evaluate:
9 k when k = 6.
- 9 z when z = 5.
q \times 5 when q = 3.
3 c + 9 when c = 6.
8 x + 4 when x = 2.
45 - 7 x when x = 6.
6 n \times 10 when n = 2.
5 + k when k = 9.
z + 2 when z = - 7.
4 - t when t = 3.
p - 8 when p = 6.
\dfrac{r}{3} when r = 12.
- \dfrac{20}{x} when x = 5.
Evaluate:
c^{2} when c = 9.
s^{3} when s = 5.
k^{2} when k = - 7.
k^{3} when k = - 9.
Evaluate:
\dfrac{5 k}{24} when k = 8.
\dfrac{15}{8 k} when k = 3.
\dfrac{4 k}{5} when k = 15.
Evaluate the expression \dfrac{45}{2 n} when:
n = 9
n = 47
Evaluate:
s t when s = 7 and t = - 8.
4 x y when x = - 6 and y = - 5.
\dfrac{a}{b} when a = 56 and b = - 8.
\dfrac{m n}{15} when m = 12 and n = 20.
\dfrac{p}{2 q} when p = - 28 and q = - 7.
\dfrac{36}{uv} when u = - 2 and v = 3.
m + n when m = 6 and n = - 4.
5 + a + b when a = - 7 and b = 4.
3 y + 5 w when y = 6 and w = 5.
6 x + 4 y + 6 when x = 3 and y = 5.
4 x - 2 y - 6 when x = 3 and y = 2.
m - n when m = 2 and n = - 9.
7 - p - q when p = 4 and q = 5.
- 5 - s + t when s = 8 and t = 15.
4 \left(p + q\right) when p = 7 and q = 8.
7 x + y when x = 6 and y = - 36.
- 4 \left(s - t\right) when s = 6 and t = 15.
m - 2 n when m = - 19 and n = - 7.
\dfrac{m v^{2}}{2} when m = 8 and v = - 15.
Evaluate:
x - y - z when x = -4, y=5 and z = 6.
3 j + 5 k + 6 l when j = 3, k = 8, and l = 7.
6 a - 3 b + 4 c when a = 8, b = 6, and c = 7.
a b c when a = 8, \, b = 9 and c = 6.
2pqr when p = 3, \,q = 4 and r = 5.
p + q + r when p = 5, \,q = 9 and r = 6.
18.6 - 3 x when x is equal to 4.1. Round your answer to one decimal place.
Evaluate \dfrac{11 s - 39}{3 r} when r = - 1.6 and s = 2.8. Round your answer to three decimal places.
Evaluate 6 x - 3 y when:
x = 5 and y = 5.
x = 7 and y = 4.
x = 8 and y = \dfrac{1}{3}.
If x = 3, evaluate:
3 x^{2}
\left( 4 x\right)^{2}
- 2 x^{2} + \left( 3 x\right)^{2}
Evaluate x^{2} + 6 x + 9 when:
x = 2
x = 5
Evaluate the expression m n when:
m = 7 and n = 9.
m = 4 and n = 3.5.
m = \dfrac{1}{8} and n = 72.
Evaluate the expression \dfrac{p q}{- 8 r} when:
p = 5, \, q = - 3 and r = - 9.
p = - 9, \, q = 21 and r = 3.
Evaluate the expression \dfrac{a b}{5 c} when:
a = 2, b = 3 and c = 4.
a = 4, b = 16 and c = 2.
Evaluate u + a t when:
u = 18, a = 2 and t = 4.
u = 37, a = 2 and t = 14.
Evaluate the expression u + v w when:
u = 59, v = 3 and w = 15.
u = 14, v = 5.5 and w = 3.6.
What is the largest whole number value that you can substitute for p so that the expression 81 - p^{2} is positive?
What is the smallest whole number value that you can substitute for p so that the expression 64 - p^{2} is negative?
The area, A, of triangle is given by the following formula:
A = \dfrac{b h}{2}
where h is the height of the triangle and b is the length of its base.
Find the area of a triangle that has a base of 7 cm and a height of 5 cm.
Find the area of a triangle that has a base of 25 cm and a height of 16 cm.
Energy can be measured in many forms. A quantity of energy is given in units of Joules (J).
The kinetic energy, E, of an object in motion is calculated using the following formula:
E = \dfrac{m v^{2}}{2}
where m is the mass of the object in kilograms and v is the speed of the object in metres per second.
Find the kinetic energy, E, of an object with a mass of 6 kg, travelling at a speed of 19 metres per second.
When the heating system in a house is on a setting of s, the temperature, T, of the house within the first 30 minutes can be estimated by using the formula T = a + \dfrac{s t}{10} where a is the initial temperature and t is the number of minutes since turning the heating system on. Calculate the temperature of the room after 18 minutes if the initial temperature is - 3 degrees Celsius and the setting on the heater is 5.
Valerie stands at the top of a cliff and launches a tennis ball across the valley. To estimate the vertical position, y, of the ball compared to herself she uses the formula: y = 14.7 t - \dfrac{9.8}{2} t^{2} where v is the initial vertical velocity and t is the number of seconds since the ball is launched.
Find the vertical position of the ball after:
2 seconds
3 seconds
8 seconds
At which of the above times as the ball above Valerie?