Complete the following tables using given formula: a. b = a^3 a: 2, 4, 5, 6 b. z = 10x - 3 x: 0, 3, 2, 1 If a = 2 and b = 3, find the value of: a. a + b b. a^2 + ab e. b^3 -... Complete the following tables using given formula: a. b = a^3 a: 2, 4, 5, 6 b. z = 10x - 3 x: 0, 3, 2, 1 If a = 2 and b = 3, find the value of: a. a + b b. a^2 + ab e. b^3 - a^3 f. 5b^2 - 2ab
Understand the Problem
The question asks us to complete the tables using the given formulas by plugging in the values of 'a' and 'x'. Also, we need to find the values of algebraic expressions given a=2 and b=3, such as a+b, a^2+ab, b^3-a^3, and 5b^2-2ab.
Answer
a. Table for $b = a^3$: a: 2, 4, 5, 6 b: 8, 64, 125, 216 b. Table for $z = 10x - 3$: x: 0, 3, 2, 1 z: -3, 27, 17, 7 If a = 2 and b = 3, then: a. $a + b = 5$ b. $a^2 + ab = 10$ c. $b^3 - a^3 = 19$ d. $5b^2 - 2ab = 33$
Answer for screen readers
a. Table for $b = a^3$: a: 2, 4, 5, 6 b: 8, 64, 125, 216 b. Table for $z = 10x - 3$: x: 0, 3, 2, 1 z: -3, 27, 17, 7 If a = 2 and b = 3, then: a. $a + b = 5$ b. $a^2 + ab = 10$ c. $b^3 - a^3 = 19$ d. $5b^2 - 2ab = 33$
Steps to Solve
- Complete the first table using the formula $b = a^3$
Substitute the given values of $a$ (2, 4, 5, 6) into the formula $b = a^3$ to find the corresponding values of $b$.
When $a = 2$, $b = 2^3 = 8$. When $a = 4$, $b = 4^3 = 64$. When $a = 5$, $b = 5^3 = 125$. When $a = 6$, $b = 6^3 = 216$.
- Complete the second table using the formula $z = 10x - 3$
Substitute the given values of $x$ (0, 3, 2, 1) into the formula $z = 10x - 3$ to find the corresponding values of $z$.
When $x = 0$, $z = 10(0) - 3 = -3$. When $x = 3$, $z = 10(3) - 3 = 30 - 3 = 27$. When $x = 2$, $z = 10(2) - 3 = 20 - 3 = 17$. When $x = 1$, $z = 10(1) - 3 = 10 - 3 = 7$.
- Evaluate $a + b$ given $a = 2$ and $b = 3$
Substitute $a = 2$ and $b = 3$ into the expression $a + b$. $a + b = 2 + 3 = 5$.
- Evaluate $a^2 + ab$ given $a = 2$ and $b = 3$
Substitute $a = 2$ and $b = 3$ into the expression $a^2 + ab$. $a^2 + ab = (2)^2 + (2)(3) = 4 + 6 = 10$.
- Evaluate $b^3 - a^3$ given $a = 2$ and $b = 3$
Substitute $a = 2$ and $b = 3$ into the expression $b^3 - a^3$. $b^3 - a^3 = (3)^3 - (2)^3 = 27 - 8 = 19$.
- Evaluate $5b^2 - 2ab$ given $a = 2$ and $b = 3$
Substitute $a = 2$ and $b = 3$ into the expression $5b^2 - 2ab$. $5b^2 - 2ab = 5(3)^2 - 2(2)(3) = 5(9) - 12 = 45 - 12 = 33$.
a. Table for $b = a^3$: a: 2, 4, 5, 6 b: 8, 64, 125, 216 b. Table for $z = 10x - 3$: x: 0, 3, 2, 1 z: -3, 27, 17, 7 If a = 2 and b = 3, then: a. $a + b = 5$ b. $a^2 + ab = 10$ c. $b^3 - a^3 = 19$ d. $5b^2 - 2ab = 33$
More Information
The question involved evaluating expressions by substituting given values into formulas. This is a fundamental concept in algebra and is used extensively in various mathematical and scientific applications.
Tips
A common mistake is to make errors in the arithmetic calculations, especially when dealing with exponents or multiple operations. Ensuring careful and methodical calculation at each step is vital to avoid mistakes. Another common mistake is to substitute the values incorrectly.
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