Evaluating algebraic expressions. Find the value of each expression when a = 4, b = 5, and c = 6.(a)    (b)    (c)   (d)   (e)

To evaluate the algebraic expressions, we'll first define the specific expressions based on the variables a = 4, b = 5, and c = 6. Since the actual expressions are not provided, I will guide you through the process assuming generic expressions. You can substitute the given values into those expressions as needed.

1. Break Down the Problem

Identify the expressions that need to be evaluated. Let's assume they are:

• (a) $x = a + b + c$
• (b) $y = a \times b - c$
• (c) $z = \frac{a^2 + b^2}{c}$
• (d) $w = a + b - 2c$
• (e) $v = a^3 + b^3 + c^3$

2. Relevant Concepts

Use the algebraic operations relevant to each expression which include addition, subtraction, multiplication, division, and exponentiation.

3. Analysis and Detail

Evaluate each expression by substituting $a = 4$, $b = 5$, and $c = 6$.

(a)

$x = a + b + c = 4 + 5 + 6 = 15$

(b)

$y = a \times b - c = 4 \times 5 - 6 = 20 - 6 = 14$

(c)

$z = \frac{a^2 + b^2}{c} = \frac{4^2 + 5^2}{6} = \frac{16 + 25}{6} = \frac{41}{6} \approx 6.83$

(d)

$w = a + b - 2c = 4 + 5 - 2 \times 6 = 9 - 12 = -3$

(e)

$v = a^3 + b^3 + c^3 = 4^3 + 5^3 + 6^3 = 64 + 125 + 216 = 405$

4. Verify and Summarize

Recheck the calculations for accuracy.

• Expression (a) results in 15.
• Expression (b) results in 14.
• Expression (c) approximately equals 6.83.
• Expression (d) results in -3.
• Expression (e) results in 405.

Final Answer

Thus, the evaluated expressions yield the following results:

• (a) $15$
• (b) $14$
• (c) $\frac{41}{6} \approx 6.83$
• (d) $-3$
• (e) $405$