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Sagot :
Sure, let's solve each of these algebraic expressions step-by-step using the given values:
1. Evaluate [tex]\(70a\)[/tex] when [tex]\(a = 5\)[/tex]:
[tex]\[ 70a = 70 \cdot 5 \][/tex]
[tex]\[ 70 \cdot 5 = 350 \][/tex]
So, the value of [tex]\(70a\)[/tex] when [tex]\(a = 5\)[/tex] is [tex]\(350\)[/tex].
2. Evaluate [tex]\(x-9\)[/tex] when [tex]\(x = 10.5\)[/tex]:
[tex]\[ x - 9 = 10.5 - 9 \][/tex]
[tex]\[ 10.5 - 9 = 1.5 \][/tex]
So, the value of [tex]\(x-9\)[/tex] when [tex]\(x = 10.5\)[/tex] is [tex]\(1.5\)[/tex].
3. Evaluate [tex]\(j + \frac{2}{3}\)[/tex] when [tex]\(j = \frac{1}{4}\)[/tex]:
[tex]\[ j + \frac{2}{3} = \frac{1}{4} + \frac{2}{3} \][/tex]
To add these fractions, we need a common denominator. The common denominator for 4 and 3 is 12.
[tex]\[ \frac{1}{4} = \frac{3}{12} \quad \text{and} \quad \frac{2}{3} = \frac{8}{12} \][/tex]
[tex]\[ \frac{1}{4} + \frac{2}{3} = \frac{3}{12} + \frac{8}{12} = \frac{11}{12} \][/tex]
Converting [tex]\(\frac{11}{12}\)[/tex] to decimal form, we have approximately 0.9166666666666666.
4. Evaluate [tex]\(\frac{\pi}{7}\)[/tex] when [tex]\(n = 35\)[/tex]:
[tex]\[ \frac{\pi}{7} \][/tex]
Given approximate value of [tex]\(\pi\)[/tex] is [tex]\(3.14159\)[/tex],
[tex]\[ \frac{3.14159}{7} \approx 0.448 \][/tex]
To be precise, [tex]\(\frac{\pi}{7}\)[/tex] is approximately [tex]\(0.4487989505128276\)[/tex].
So, to match the algebraic expressions with their correct evaluated values:
- [tex]\(70a\)[/tex] evaluates to [tex]\(350\)[/tex].
- [tex]\(x-9\)[/tex] evaluates to [tex]\(1.5\)[/tex].
- [tex]\(j + \frac{2}{3}\)[/tex] evaluates to [tex]\(\frac{11}{12}\)[/tex] or approximately [tex]\(0.9166666666666666\)[/tex].
- [tex]\(\frac{\pi}{7}\)[/tex] evaluates to approximately [tex]\(0.4487989505128276\)[/tex].
Thus, the matched list is as follows:
[tex]\[ \begin{align*} 70a \quad &\text{evaluates to} \quad 350, \\ x - 9 \quad &\text{evaluates to} \quad 1.5, \\ j + \frac{2}{3} \quad &\text{evaluates to} \quad \frac{11}{12}, \\ \frac{\pi}{7} \quad &\text{evaluates to} \quad 0.4487989505128276. \end{align*} \][/tex]
1. Evaluate [tex]\(70a\)[/tex] when [tex]\(a = 5\)[/tex]:
[tex]\[ 70a = 70 \cdot 5 \][/tex]
[tex]\[ 70 \cdot 5 = 350 \][/tex]
So, the value of [tex]\(70a\)[/tex] when [tex]\(a = 5\)[/tex] is [tex]\(350\)[/tex].
2. Evaluate [tex]\(x-9\)[/tex] when [tex]\(x = 10.5\)[/tex]:
[tex]\[ x - 9 = 10.5 - 9 \][/tex]
[tex]\[ 10.5 - 9 = 1.5 \][/tex]
So, the value of [tex]\(x-9\)[/tex] when [tex]\(x = 10.5\)[/tex] is [tex]\(1.5\)[/tex].
3. Evaluate [tex]\(j + \frac{2}{3}\)[/tex] when [tex]\(j = \frac{1}{4}\)[/tex]:
[tex]\[ j + \frac{2}{3} = \frac{1}{4} + \frac{2}{3} \][/tex]
To add these fractions, we need a common denominator. The common denominator for 4 and 3 is 12.
[tex]\[ \frac{1}{4} = \frac{3}{12} \quad \text{and} \quad \frac{2}{3} = \frac{8}{12} \][/tex]
[tex]\[ \frac{1}{4} + \frac{2}{3} = \frac{3}{12} + \frac{8}{12} = \frac{11}{12} \][/tex]
Converting [tex]\(\frac{11}{12}\)[/tex] to decimal form, we have approximately 0.9166666666666666.
4. Evaluate [tex]\(\frac{\pi}{7}\)[/tex] when [tex]\(n = 35\)[/tex]:
[tex]\[ \frac{\pi}{7} \][/tex]
Given approximate value of [tex]\(\pi\)[/tex] is [tex]\(3.14159\)[/tex],
[tex]\[ \frac{3.14159}{7} \approx 0.448 \][/tex]
To be precise, [tex]\(\frac{\pi}{7}\)[/tex] is approximately [tex]\(0.4487989505128276\)[/tex].
So, to match the algebraic expressions with their correct evaluated values:
- [tex]\(70a\)[/tex] evaluates to [tex]\(350\)[/tex].
- [tex]\(x-9\)[/tex] evaluates to [tex]\(1.5\)[/tex].
- [tex]\(j + \frac{2}{3}\)[/tex] evaluates to [tex]\(\frac{11}{12}\)[/tex] or approximately [tex]\(0.9166666666666666\)[/tex].
- [tex]\(\frac{\pi}{7}\)[/tex] evaluates to approximately [tex]\(0.4487989505128276\)[/tex].
Thus, the matched list is as follows:
[tex]\[ \begin{align*} 70a \quad &\text{evaluates to} \quad 350, \\ x - 9 \quad &\text{evaluates to} \quad 1.5, \\ j + \frac{2}{3} \quad &\text{evaluates to} \quad \frac{11}{12}, \\ \frac{\pi}{7} \quad &\text{evaluates to} \quad 0.4487989505128276. \end{align*} \][/tex]
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