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sertanlavr [38]
3 years ago
13

Find the missing values of the variables. The diagram is not to scale.

Mathematics
1 answer:
RideAnS [48]3 years ago
3 0

Answer:

B

Step-by-step explanation:

107 and y form a straight angle and are supplementary, thus

107 + y = 180 ( subtract 107 from both sides )

y = 73

The sum of the interior angles of a quadrilateral = 360°

Sum the given angles and equate to 360

117 + 79 + 73 + x = 360, that is

269 + x = 360 ( subtract 269 from both sides )

x = 91

Thus x = 91, y = 73 → B

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required \: scale  \\ =  \frac{12 \frac{1}{2} }{1 \frac{9}{16} }  \\  \\  =  \frac{ \frac{25}{2} }{ \frac{25}{16} }  =  \frac{25}{2}  \times  \frac{16}{25}  =  \frac{1}{2}  \times  \frac{16}{1}   \\  \\ = 8 \:  :  \: 1

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\large\boxed{a(x+4)(x-5)=0,\ a\in\mathbb{R}-\{0\}}\\\\\text{for}\ a=1\to\boxed{x^2-x-20=0}

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\text{If}\ x_1\ \text{and}\ x_2\ \text{are the roots of the quadratic equation}\ ax^2+bx+c=0,\\\text{then}\ ax^2+bx+c=a(x-x_1)(x-x_2).\\\\\text{If}\ x_1\ \text{and}\ x_2\ \text{, then they are the roots of the quadratic equation.}\\\\\text{We have}\ x_1=-4\ \text{and}\ x_2=5.\ \text{Therefore we have the equation:}\\\\a(x-(-4))(x-5)=0\\\\a(x+4)(x-5)=0\qquad\text{for any value of}\ a\ \text{except 0}.

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