Evaluate the following algebraic expressions. Show your complete solutions.
1. 3(v)2, where y = 5
2. 2m - r, where r= -1 and m= 6
3. xyz, where x = 2, y = 3.3 and z = 9
1. 3(v)2, where y = 5
2. 2m - r, where r= -1 and m= 6
3. xyz, where x = 2, y = 3.3 and z = 9
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Answer:
1. 3(v)², v = 5
Substitute all given terms.
3(5)²
Evaluate the power.
3(25)
Multiply.
= 75
2. 2m - r, m = 6, r = -1
Substitute all given terms.
2(6) - (-1)
Using -(-x) = +x, simplify.
2(6) + 1
Multiply.
12 + 1
Add.
= 13
3. xyz, x = 2, y = 3.3, z = 9
Substitute all given terms.
2(3.3)(9)
Multiply.
= 59.4
≈ 59 ⅖
≈ 297/5
4. 5/9(F - C), F = 212, C = 32
Substitute all given terms.
5/9(212 - 32)
Subtract.
5/9(180)
Multiply.
= 100
5. 2x(3x)² - 7x + 12x², x = 1.5
Substitute all given terms.
2(1.5)(3(1.5)²) - 7(1.5) + 12(1.5)²
Evaluate the powers.
2(1.5)(3(2.25)) - 7(1.5) + 12(2.25)
Multiply.
3(6.75) - (10.5) + 27
20.25 - 10.5 + 27
Add.
20.25 + 16.5
= 36.75
≈ 36 ¾
≈ 147/4
6. 6(g + h), g = 8, h = 7
Substitute all given terms.
6(8 + 7)
Add.
6(15)
Multiply.
= 90
7. 2xy - z, x = 4, y = 3, z = 1
Substitute all given terms.
2(4)(3) - 1
Multiply.
24 - 1
Subtract.
= 23
8. 3ab + (c / 2), a = 2, b = 5, c = 10
Substitute all given terms.
3(2)(5) + (10 / 2)
Multiply.
30 + (10/2)
Divide.
30 + 5
Add.
= 35
9. 63 - 5x, x = 7
Substitute all given terms.
63 - 5(7)
Multiply.
63 - 35
Subtract.
= 28
10. 4(t + 3 + 1), t = 8
Substitute all given terms.
4(8 + 3 + 1)
Add.
4(12)
Multiply.
= 48