Draw the histogram and the frequency polygon of the given data. Age (in years) 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 Frequency 40 60 50 20 10

Given: Age (in years) 20 - 25 25 - 30 30 - 35 35 - 40 40 - 45 Frequency 40 60 50 20 10 First draw the histogram using the data and mark the mid-points of the top of the rectangles. Here, the first class interval is 20 - 25 . So, the class preceding 20 - 25 we can take it as 15 - 20 . The last class interval is 40 - 45 . So the succeeding class interval is 45 - 50 Now, the class mark of the class-interval 15 - 20 is 17 . 5 The class mark of the class-interval 20 - 25 is 22 . 5 The class mark of the class-interval 25 - 30 is 27 . 5 The class mark of the class-interval 30 - 35 is 32 . 5 The class mark of the class-interval 35 - 40 is 37 . 5 The class mark of the class-interval 40 - 45 is 42 . 5 The class mark of the class-interval 45 - 50 is 47 . 5 Mark the class mark on obtained histogram and join the midpoints Hence, the frequency polygon is obtained by joining the midpoints on histogram.

Verify that: tan 30 ° = tan 60 ° - tan 30 ° 1 + tan 60 ° tan 30 °

Given to verify: tan 30 ° = tan 60 ° - tan 30 ° 1 + tan 60 ° tan 30 ° We know, tan 30 ° = 1 3 and tan 60 ° = 3 Substituting the values, we get 1 3 = 3 - 1 3 1 + 3 × 1 3 ⇒ 1 3 = 3 - 1 3 1 + 3 × 1 3 ⇒ 1 3 = 3 - 1 3 1 + 1 ⇒ 1 3 = 3 - 1 3 2 ⇒ 1 3 = 3 - 1 2 3 ⇒ 1 3 = 2 2 3 ⇒ 1 3 = 1 3 Hence verified.

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Mathematics>Chapter 9 - Assignments>ASSIGNMENTS>Q 7

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A kite is flying at a height of $120 m$ from the level ground. It is attached to a string inclined at $60 °$ to the horizontal. Find the length of the string. Use $\sqrt{3} = 1.73$ and give answer to one decimal place.

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Mathematics>Chapter 9 - Assignments>ASSIGNMENTS>Q 7

Draw the graph of each of the equation,

2 y - x = 8, 5 y - x = 14, y - 2 x = 1,

obtain the vertices of the triangle so formed.

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Mathematics>Chapter 9 - Assignments>ASSIGNMENTS>Q 7

From the given figure, find the area of the trapezium $A B C D (in {cm}^{2})$ .

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Mathematics>Chapter 9 - Assignments>ASSIGNMENTS>Q 8

Draw the histogram and the frequency polygon of the given data.

Age (in years)	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$
Frequency	$40$	$60$	$50$	$20$	$10$

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Mathematics>Chapter 9 - Assignments>ASSIGNMENTS>Q 8

Verify that:

\tan 30 ° = (\frac{\tan 60 ° - \tan 30 °}{1 + \tan 60 ° \tan 30 °})

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Mathematics>Chapter 9 - Assignments>ASSIGNMENTS>Q 8

$ABCD$ is a quadrilateral. If $AL ⊥ BD$ and $CM ⊥ BD$ . Prove that: $ar (quad ABCD) = \frac{1}{2} \times BD \times (AL + CM)$ .
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Mathematics>Chapter 9 - Assignments>ASSIGNMENTS>Q 9

Prove that the median divides the triangle into two equal parts in area.

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Mathematics>Chapter 9 - Assignments>ASSIGNMENTS>Q 9

A chemist has $30 litres$ of solution containing $70 %$ acid. How many litres of water should be added to it so that the resultant solution contains $50 %$ acid?

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Mathematics>Chapter 9 - Assignments>ASSIGNMENTS>Q 9

In $△ ABC$ , $∠ B = 90 °$ and $D$ is the mid point of $BC$ , Prove that: ${AC}^{2} = {AD}^{2} + 3 {CD}^{2}$