4.02 Substituting into algebraic expressions
Evaluate y + 5 when:
Evaluate \dfrac{45}{2 n} when:
n = 9
n = 47
n = -10
n = -3
Evaluate:
9 + m when m = 3
x - 2 when x = 8
8 - c when c = 1
3 k when k = 4
5 v when v = 6
9 p when p = 2
\dfrac{n}{9} when n = 8
\dfrac{6}{w} when w = 3
6 n \times 10 when n = 2
3 c + 9 when c = 6
8 x + 4 when x = 2
45 - 7 x when x = 6
18.6 - 3 x when x=4.1
\dfrac{5 k}{24} when k = 8
\dfrac{15}{8 k} when k = 3
\dfrac{4 k}{5} when k = 15
Evaluate:
y^{2} when y = 4
7 y^{2} when y = 5
3 x^{2} + 5 when x = 2
\dfrac{b^{2}}{4} when b = 3
If x = 3, evaluate:
3 x^{2}
\left( 4 x\right)^{2}
x^{3} - 2x^{2}
- 2 x^{2} + \left( 3 x\right)^{2}
Evaluate x^{2} + 6 x + 9 when:
x = 2
x = 5
x = 8
x = \dfrac{1}{2}
Evaluate u + v when:
u = 7 and v = 3
u = 3 and v = 16
u = -2 and v = -8
u = -15 and v = 35
Evaluate 6 x - 3 y when:
x = 5 and y = 5
x = 7 and y = 4
x = 1.5 and y = 3.5
x = 8 and y = \dfrac{1}{3}
Evaluate m n when:
m = 7 and n = 9
m = 4 and n = 3.5
m = 1.5 and n = 4.2
m = \dfrac{1}{8} and n = 72
Evaluate:
a - b when a = 9 and b = 5
a + b when a = 5 and b = 1.1
u + v + 25 when u = 32 and v = 48
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
4 x y when x = - 6 and y = - 5
- 4 \left(s - t\right) when s = 6 and t = 15
\dfrac{a}{b} when a = 56 and b = - 8
\dfrac{m n}{15} when m = 12 and n = 20
Evaluate:
k r when k = 5 and r = 6
3 r s when r = 4 and s = 5.6
5 a \times 6 b when a = \dfrac{1}{5} and b = 4
a b - 10 when a = 7 and b = 6
2 m \times 3 n + 37 when m = 4 and n = 5
3 y \times 5 w - 209 when y = 4 and w = 5
\dfrac{4 a \times 5}{9 b} when a = 7 and b = 21
2 y \times 5 w \times 3 when y = 4 and w = 3
\left( r h\right)^{2} when r = 2 and h = 3
4 y w + 9 w when y = 9 and w = 4
Evaluate \dfrac{a b}{5 c} when:
a = 2, \, b = 3, and c = 4
a = 4, \, b = 16, and c = 2
a = 2.5, \, b = 8, and c = 4
a = 1.4, \, b = 10, and c = 3.5
Evaluate u + a t when:
u = 18, \, a = 2, and t = 4
u = 37, \, a = 2, and t = 14
u = 50, \, a = 11.5, and t = 4
u = 10, a = \dfrac{9}{4}, and t = \dfrac{4}{3}
Evaluate u + v w when:
u = 59, \, v = 3, and w = 15
u = 14, \, v = 18, and w = 22
u = 14, \, v = 5.5, and w = 3.6
u = 4.2, \, v = 1.5, and w = 8
Evaluate:
a + b + c when a = 10, b = 15, and c = 11
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
5 j k l when j = 4, k = 3 and l = 5
The perimeter of a triangle is defined by the formula P = p + q + r.
Find P if the length of each of its three sides are p = 17\text{ in},\,q = 16\text{ in} and r = 14 \text{ in}.
For many three dimensional shapes, we can find the number of edges, E, on the shape by using the formula E = V + F - 2 where V is the number of vertices and F is the number of faces.
Find the number of edges of a three dimensional shape which has:
4 vertices and 4 faces
7 vertices and 7 faces
8 vertices and 6 faces
12 vertices and 20 faces
The area, A, of triangle is given by the formula:
A = \dfrac{1}{2}bh
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 \text{ ft} and a height of 5 \text{ ft}.
Find the area of a triangle that has a base of 25 \text{ cm} and a height of 16 \text{ cm}.
Find the area of a triangle that has a base of 48 \text{ in} and a height of 28 \text{ in}.
Find the area of a triangle that has a base of 16.5 \text{ in} and a height of 24 \text{ in}.
Energy can be measured in many forms. A quantity of energy is given in units of Joules (\text{J}). The kinetic energy, E, of an object in motion is calculated using the 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 meters per second.
Find the kinetic energy, E, of an object with a mass of 6 \text{ kg}, traveling at a speed of 19 \text{ m/s}.
What is the largest whole number value that you can substitute for p so that the expression 81 - p^{2} is positive?