Question

question 4: if \\(a = 1.5\\) \\(b = 4\\) \\(c = 6\\) \\(d = 0.5\\) and \\(e = -3\\)
find the value of each expression.
(a) \\(4(a + d)\\)
(b) \\(5(c + b)\\)
(c) \\(3(10 - e)\\)
(d) \\(abc\\)
(e) \\(e^3\\)
(f) \\(d^2\\)
(g) \\(5b^2\\)
(h) \\(8e^2 + 3\\)
(i) \\(\frac{b + 2}{3}\\)
(j) \\(\frac{2c - e}{4}\\)
(k) \\(\frac{10d + 4b}{7}\\)

question 5: \\(p = 2l + 2w\\), work out \\(p\\) if \\(l = 8\\) and \\(w = 3\\).

question 6: \\(c = 15h + 30\\), work out \\(c\\) if \\(h = 6\\).

Explanation:

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<reasoning>

Substitute values into expressions for Question 4

\[

$$\begin{aligned} &\text{(a) } 4(a + d) = 4(1.5 + 0.5) = 4(2) = 8\\ &\text{(b) } 5(c + b) = 5(6 + 4) = 5(10) = 50\\ &\text{(c) } 3(10 - e) = 3(10 - (-3)) = 3(13) = 39\\ &\text{(d) } abc = (1.5)(4)(6) = 6(6) = 36\\ &\text{(e) } e^3 = (-3)^3 = -27\\ &\text{(f) } d^2 = (0.5)^2 = 0.25\\ &\text{(g) } 5b^2 = 5(4^2) = 5(16) = 80\\ &\text{(h) } 8e^2 + 3 = 8(-3)^2 + 3 = 8(9) + 3 = 75\\ &\text{(i) } \frac{b + 2}{3} = \frac{4 + 2}{3} = \frac{6}{3} = 2\\ &\text{(j) } \frac{2c - e}{4} = \frac{2(6) - (-3)}{4} = \frac{12 + 3}{4} = \frac{15}{4} = 3.75\\ &\text{(k) } \frac{10d + 4b}{7} = \frac{10(0.5) + 4(4)}{7} = \frac{5 + 16}{7} = \frac{21}{7} = 3 \end{aligned}$$

\]

Evaluate perimeter formula for Question 5

\[

$$\begin{aligned} &P = 2L + 2W\\ &P = 2(8) + 2(3)\\ &P = 16 + 6 = 22 \end{aligned}$$

\]

Evaluate cost formula for Question 6

\[

$$\begin{aligned} &C = 15h + 30\\ &C = 15(6) + 30\\ &C = 90 + 30 = 120 \end{aligned}$$

\]
</reasoning>

<answer>

Question 4

(a) \(8\)
(b) \(50\)
(c) \(39\)
(d) \(36\)
(e) \(-27\)
(f) \(0.25\)
(g) \(80\)
(h) \(75\)
(i) \(2\)
(j) \(3.75\)
(k) \(3\)

Question 5

\(P = 22\)

Question 6

\(C = 120\)
</answer>

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Answer:

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<reasoning>

Substitute values into expressions for Question 4

\[

$$\begin{aligned} &\text{(a) } 4(a + d) = 4(1.5 + 0.5) = 4(2) = 8\\ &\text{(b) } 5(c + b) = 5(6 + 4) = 5(10) = 50\\ &\text{(c) } 3(10 - e) = 3(10 - (-3)) = 3(13) = 39\\ &\text{(d) } abc = (1.5)(4)(6) = 6(6) = 36\\ &\text{(e) } e^3 = (-3)^3 = -27\\ &\text{(f) } d^2 = (0.5)^2 = 0.25\\ &\text{(g) } 5b^2 = 5(4^2) = 5(16) = 80\\ &\text{(h) } 8e^2 + 3 = 8(-3)^2 + 3 = 8(9) + 3 = 75\\ &\text{(i) } \frac{b + 2}{3} = \frac{4 + 2}{3} = \frac{6}{3} = 2\\ &\text{(j) } \frac{2c - e}{4} = \frac{2(6) - (-3)}{4} = \frac{12 + 3}{4} = \frac{15}{4} = 3.75\\ &\text{(k) } \frac{10d + 4b}{7} = \frac{10(0.5) + 4(4)}{7} = \frac{5 + 16}{7} = \frac{21}{7} = 3 \end{aligned}$$

\]

Evaluate perimeter formula for Question 5

\[

$$\begin{aligned} &P = 2L + 2W\\ &P = 2(8) + 2(3)\\ &P = 16 + 6 = 22 \end{aligned}$$

\]

Evaluate cost formula for Question 6

\[

$$\begin{aligned} &C = 15h + 30\\ &C = 15(6) + 30\\ &C = 90 + 30 = 120 \end{aligned}$$

\]
</reasoning>

<answer>

Question 4

(a) \(8\)
(b) \(50\)
(c) \(39\)
(d) \(36\)
(e) \(-27\)
(f) \(0.25\)
(g) \(80\)
(h) \(75\)
(i) \(2\)
(j) \(3.75\)
(k) \(3\)

Question 5

\(P = 22\)

Question 6

\(C = 120\)
</answer>

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