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3 years ago

9

Identify the type of sequence shown in the table below and select the appropriate response. (5 points) n f(n) 1 540 2 500 3 460

4 420 5 380

2 answers:

dsp733 years ago

8 0

Answer:-40

Step-by-step explanation: Because 40 being subtracted from each number.

Svetradugi [14.3K]3 years ago

4 0

$\bf \begin{array}{ccll}
n&f(n)\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
1&540\\
2&\stackrel{540-40}{500}\\\\
3&\stackrel{500-40}{460}\\\\
4&\stackrel{460-40}{420}\\\\
5&\stackrel{420-40}{380}
\end{array}$

notice, the next term is obtained by subtracting 40 from the "current" one, meaning, is an arithmetic sequence, with a "common difference" of -40.

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The given ratios expresses the number of time a value is larger or smaller

than another value.

The correct responses are;

3. <u>(B) 12 and 24</u>

4. <u>(D) 6, 9, 21</u>

5. $\underline{(E) \ \displaystyle \frac{11}{2}}$

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7. (B) $\overline{EF}$ =<u> 6</u>, $\overline{AC}$ = <u>9·√5</u>

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3. Given that the perimeter of the rectangle = 72

The ratio of the lengths of the sides = 1:2

Let <em>a</em> and <em>b</em> represent the sides, we have;

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$\displaystyle \frac{a}{b} = \mathbf{\frac{1}{2}}$

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4. Extended ratio = 2:3:7

The perimeter = 36

The lengths of the sides are;

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$\displaystyle \frac{3}{2 + 3 + 7} \times 36 = \mathbf{9}$

$\displaystyle \frac{7}{2 + 3 + 7} \times 36 = \mathbf{21}$

The lengths are; <u>(D) 6, 9, 21</u>

5. The given equation is presented as follows;

$\displaystyle \frac{5}{x + 7} = \mathbf{\frac{3}{x + 2}}$

5 × (x + 2) = 3 × (x + 7)

5·x + 10 = 3·x + 21

5·x - 3·x = 21 - 10

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The correct option is; $\displaystyle \underline{(E) \ \frac{11}{2}}$

6. The width to length ratio is $\displaystyle \mathbf{\frac{2.5}{7.0}}$

The simplified ratio is therefore;

$\displaystyle \frac{2.5}{7.0} = \frac{2 \times 2.5}{2 \times 7.0} = \mathbf{\frac{5}{14}}$

The correct option is (E) $\displaystyle \underline{(E) \ \frac{5}{14}}$

7. The given ratio of the lengths is 3:1

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$\overline{BC}$ : $\overline{EF}$ = 3:1

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$\displaystyle \frac{18}{\overline{EF}} = \frac{3}{1}$

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$\overline{EF}$ = 6

By Pythagorean theorem, we have;

$\overline{DF}$ ² = $\mathbf{\overline{DE}}$ ² + $\mathbf{\overline{EF}}$ ²

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$\overline{AC}$ = 3 × $\mathbf{\overline{DF}}$

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$\overline{AC}$ = 9·√5

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$\displaystyle \mathbf{\frac{EF}{AB}} =\frac{1}{2}$

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$\displaystyle \frac{EF}{AB} =\displaystyle \mathbf{\frac{CD}{CE}}$

<u>(C) The values are equal</u>

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$\displaystyle \frac{3}{4} > \mathbf{\frac{1}{2}}$

Therefore;

Column A is greater than column B

<u>(A) The value in column A is greater</u>

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