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6. Using a ruler and a pair of compasses only,

a. Construct a quadrilateral [tex]P Q R S[/tex] in which [tex]|P Q|=6.5 \text{ cm},|P S|=7.0 \text{ cm}, Q \widehat{P S}=105^{\circ}, R \widehat{Q} P=120^{\circ}[/tex] and [tex]\overline{P Q}[/tex] is parallel to [tex]\overline{S R}[/tex].

b. Measure:
i. [tex]|Q R|[/tex]
ii. [tex]|S R|[/tex]

7. The marks obtained by 40 students in a Mathematics test are as follows:
[tex]\[
\begin{tabular}{llllllllll}
83 & 18 & 88 & 95 & 55 & 35 & 29 & 98 & 45 & 21 \\
89 & 83 & 95 & 65 & 36 & 34 & 86 & 31 & 31 & 54 \\
40 & 55 & 28 & 53 & 14 & 21 & 76 & 20 & 96 & 25 \\
39 & 99 & 45 & 77 & 92 & 67 & 69 & 84 & 38 & 68
\end{tabular}
\][/tex]

a. Copy and complete the table for the distribution.

b.
i. Draw a histogram for the distribution.
ii. Use your histogram to estimate the modal mark.

8. a. Copy and complete the table for [tex]y=3x^2-5x+4[/tex] for [tex]-3 \leq x \leq 4[/tex].
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
$x$ & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\
\hline
$3x^2$ & & 12 & 3 & & 3 & 12 & 27 & \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
Sure, let's address the given question in detail:

### Question 8
a. Copy and complete the table for [tex]\( y = 3x^2 - 5x + 4 \)[/tex] for [tex]\(-3 \leq x \leq 4\)[/tex].

Given:
[tex]\[ y = 3x^2 - 5x + 4 \][/tex]

We will fill in the respective values for each term in the table.

Let's complete each cell in sequence:

- For [tex]\( x = -3 \)[/tex]:
[tex]\[ 3(-3)^2 = 3 \cdot 9 = 27 \][/tex]

- For [tex]\( x = -2 \)[/tex]:
[tex]\[ 3(-2)^2 = 3 \cdot 4 = 12 \][/tex]

- For [tex]\( x = -1 \)[/tex]:
[tex]\[ 3(-1)^2 = 3 \cdot 1 = 3 \][/tex]

- For [tex]\( x = 0 \)[/tex]:
[tex]\[ 3(0)^2 = 3 \cdot 0 = 0 \][/tex]

- For [tex]\( x = 1 \)[/tex]:
[tex]\[ 3(1)^2 = 3 \cdot 1 = 3 \][/tex]

- For [tex]\( x = 2 \)[/tex]:
[tex]\[ 3(2)^2 = 3 \cdot 4 = 12 \][/tex]

- For [tex]\( x = 3 \)[/tex]:
[tex]\[ 3(3)^2 = 3 \cdot 9 = 27 \][/tex]

- For [tex]\( x = 4 \)[/tex]:
[tex]\[ 3(4)^2 = 3 \cdot 16 = 48 \][/tex]

Now, let's complete the table:

[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline 3x^2 & 27 & 12 & 3 & 0 & 3 & 12 & 27 & 48 \\ \hline \end{array} \][/tex]

Therefore, the completed table for [tex]\( 3x^2 \)[/tex] is:

[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline 3x^2 & 27 & 12 & 3 & 0 & 3 & 12 & 27 & 48 \\ \hline \end{array} \][/tex]

If you have any further questions or need assistance with another part of the original problem, feel free to ask!

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