Question

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Answer 1

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Answers

3.

Construction: Draw Two chords such that they are on the same segments meeting in the same point as shown in figure

Soln:

We have,

120°+Angle BAC=180°(Sum of the opposite angles of a cyclic quadrilateral is 180°)

Angle BAC=60°

Therefore,

Angle BOC = 2Angle BAC

Angle BOC = 120°

Therefore,

Required Reflex Angle BOC= 360°-120°=240°

4.

${y}^{2} - 7y + 12 \\ = {y}^{2} - 4y - 3y + 12 \\ = y(y - 4) - 3(y - 4) \\ = (y - 3)(y - 4)$

Therefore, required factors are (y-3) and (y-4)

5.

Given,

Circumference=24 cm

Therefore,

$r = \frac{24}{2} \times \frac{7}{22} \\ = > r = \frac{42}{11} cm$

Hence,

Required area,

$= \frac{22}{7} \times \frac{42}{11} \times \frac{42}{11} \\ = \frac{12 \times 42}{11} \\ = 4.82cm {}^{2}$

6.

To find rational numbers between -5/6 and -5/8

$\frac{ - 5 \times 8}{6 \times 8} = \frac{ -40 }{48} \\ \frac{ - 5 \times 6}{8 \times 6} = \frac{ - 30}{48 }$

So required rational number are,

$\frac{ - 39}{48} and \: \frac{ - 38}{48}$

7.

Given,

One angle of parallelogram is 70°

The other angles are ,

$2 \times 70 + 2 \times x = 360 \\ = > 2x = 360 - 140 \\ = > x = 110$

The other angles are 70°,110°,70°,110°.

8.

Given,

S.P.= Rs. 225

Profit =25%

So,

C.P.,

$225 - 2 25\times \frac{25}{100} \\ = 225 - 56.25 \\ = rs.168.75$