+73 Evaluate each of the expressions if a = -2, b = 5, c = -4, and d = 6.
1. 3c - 2b
2. 8b + 2c
3. -b² + b
4. 3a²
5. c² - 2d
6. 2a² + 3b²
7. 2(a + b)
8. 4(2a - d)
9. a(b + 3c)
10. 8b/5c
11. 3d + 2c/b
12. 3d - 2b/5a + d
13. d² - b²
14. (d - b)²
15. (d - b)(d + b)
16. d³ - b³
17. (d - b)³
18. (d - b)(d² + db + b²)
19. b² + a²
20. (b + a)²
21. a² + 2ad + d²
Evaluate each of the expressions if x = -2.34, y = -3.14, and z = 4.12. Round your answer to the nearest tenth.
22. y - 2z
23. x² + y²
+9519 16) a = -2, b = 5, c = -4, and d = 6; d^3 - b^3
d^3 - b^3 = (6)^3 - (5)^3 = 216 - 125 = 91.
17) a = -2, b = 5, c = -4, and d = 6; (d - b)^3
(d - b)^3 = (6 - 5)^3 = 1^3 = 1.
18) a = -2, b = 5, c = -4, and d = 6; (d - b)(d^2 + db + b^2)
Same answer as 16). ANS: 91.
19) a = -2, b = 5, c = -4, and d = 6; b^2 + a^2
b^2 + a^2 = 5^2 + (-2)^2 = 25 + 4 = 29.
20) a = -2, b = 5, c = -4, and d = 6; (b + a)^2
(b + a)^2 = (5 - 2)^2 = 3^2 = 9.
+14903 Evaluate each of the expressions if a = -2, b = 5, c = -4, and d = 6.
1. 3c - 2b etc.
I am convinced you can do that yourself.
+9519 1) a = -2, b = 5, c = -4, and d = 6; 3c - 2b.
3c - 2b = 3(-4) - 2(5) = -12 - 10 = -22.
2) a = -2, b = 5, c = -4, and d = 6; 8b + 2c.
8b + 2c = 8(5) + 2(-4) = 40 - 8 = 32.
3) a = -2, b = 5, c = -4, and d = 6; -b^2 + b
-b^2 + b = -(5)^2 + 5 = -25 + 5 = -20.
4) a = -2, b = 5, c = -4, and d = 6; 3a^2
3a^2 = 3(-2)^2 = 3(4) = 12.
5) a = -2, b = 5, c = -4, and d = 6; c^2 - 2d
(-4)^2 - 2(6) = 16 - 12 = 4.
+9519 6) a = -2, b = 5, c = -4, and d = 6; 2a^2+3b^2
2a^2 + 3b^2 = 2(-2)^2 + 3(5)^2 = 2(4) + 3(25) = 8 + 75 = 83.
7) a = -2, b = 5, c = -4, and d = 6; 2(a+b)
2(a + b) = 2(-2 + 5) = 2(3) = 6.
8) a = -2, b = 5, c = -4, and d = 6; 4(2a - d)
4(2a - d) = 4(2(-2) - 6) = 4(-4 - 6) = 4(-10) = -40.
9) a = -2, b = 5, c = -4, and d = 6; a(b + 3c)
a(b + 3c) = -2(5 + 3(-4)) = -2(5 - 12) = 2(12 - 5) = 2(7) = 14.
Note the 3rd step: -2(5 - 12) = 2(12 - 5): \(\boxed{\color{red}-(a-b)=b-a}\)
10) a = -2, b = 5, c = -4, and d = 6; (8b) / (5c)
(8b) / (5c) = (8/5)(b/c) = (8/5)(-5/4) = -2.
+9519 11) a = -2, b = 5, c = -4, and d = 6; 3d + (2c/b)
3d + (2c/b) = 3(6) + 2(-4/5) = 18 - 8/5 = 16 2/5 OR 16.4
12) a = -2, b = 5, c = -4, and d = 6; (3d - 2b)/(5a + d)
(3d - 2b)/(5a + d) = (3(6) - 2(5))/(5(-2) + 6) = (18-10)/(-10 + 6) = 8/(-4) = -2.
13) a = -2, b = 5, c = -4, and d = 6; d^2-b^2
d^2 - b^2 = (d+b)(d-b) = (6 + 5)(6 - 5) = 6 + 5 = 11.
14) a = -2, b = 5, c = -4, and d = 6; (d - b)^2
(d - b)^2 = (6 - 5)^2 = 1^2 = 1.
15) a = -2, b = 5, c = -4, and d = 6; (d - b)(d + b)
Same answer as 13). ANS: 11.
+9519 16) a = -2, b = 5, c = -4, and d = 6; d^3 - b^3
d^3 - b^3 = (6)^3 - (5)^3 = 216 - 125 = 91.
17) a = -2, b = 5, c = -4, and d = 6; (d - b)^3
(d - b)^3 = (6 - 5)^3 = 1^3 = 1.
18) a = -2, b = 5, c = -4, and d = 6; (d - b)(d^2 + db + b^2)
Same answer as 16). ANS: 91.
19) a = -2, b = 5, c = -4, and d = 6; b^2 + a^2
b^2 + a^2 = 5^2 + (-2)^2 = 25 + 4 = 29.
20) a = -2, b = 5, c = -4, and d = 6; (b + a)^2
(b + a)^2 = (5 - 2)^2 = 3^2 = 9.
+9519 21) a = -2, b = 5, c = -4, and d = 6; a^2 + 2ad + d^2
a^2 + 2ad + d^2 = (a + d)^2 = (-2 + 6)^2 = 4^2 = 16.
22) x = -2.34, y = -3.14, and z = 4.12; to the nearest tenth; y - 2z
y - 2z = -3.14 - 2(4.12) = -3.14 - 8.24 = -11.38 approx -11.4
23) x = -2.34, y = -3.14, and z = 4.12; to the nearest tenth; x^2 + y^2
x^2 + y^2 = (-2.34)^2 + (-3.14)^2 = 15.3352(using calc.) approx 15.3
