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Black_prince [1.1K]
3 years ago
9

The ordered pairs for two points are listed in the tableWhat is the equation, in intercept form of the line that contains these

points?

Mathematics
1 answer:
Tomtit [17]3 years ago
6 0

Answer:

D, Y=2x-4

Step-by-step explanation:

The easiest way to solve this is by substitution. Plug in 3 into the X of each equation to see if you get 2 as your outcome. Double check by doing the same with 8 and seeing if 12 is the outcome. Once you do this, problems like the one should be a piece of cake.

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A garden is shaped in the form of a regular heptagon (seven-sided), MNSRQPO. A circle with center T and radius 25m circumscribes
Alenkinab [10]

The relationship between the sides MN, MS, and MQ in the given regular heptagon is \dfrac{1}{MN} = \dfrac{1}{MS} + \dfrac{1}{MQ}

The area to be planted with flowers is approximately <u>923.558 m²</u>

The reason the above value is correct is as follows;

The known parameters of the garden are;

The radius of the circle that circumscribes the heptagon, r = 25 m

The area left for the children playground = ΔMSQ

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The area of the garden planted with flowers

Solution:

The area of an heptagon, is;

A = \dfrac{7}{4} \cdot a^2 \cdot  cot \left (\dfrac{180 ^{\circ}}{7} \right )

The interior angle of an heptagon = 128.571°

The length of a side, S, is given as follows;

\dfrac{s}{sin(180 - 128.571)} = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)}

s = \dfrac{25}{sin \left(\dfrac{128.571}{2} \right)} \times sin(180 - 128.571) \approx 21.69

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A = \dfrac{7}{4} \times 22.52^2 \times cot \left (\dfrac{180 ^{\circ}}{7} \right ) \approx 1,842.94

MS = \sqrt{(21.69^2 + 21.69^2 - 2 \times  21.69 \times21.69\times cos(128.571^{\circ})) \approx 43.08

By sine rule, we have

\dfrac{21.69}{sin(\angle NSM)} = \dfrac{43.08}{sin(128.571 ^{\circ})}

sin(\angle NSM) =\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ})

\angle NSM = arcsin \left(\dfrac{21.69}{43.08} \times sin(128.571 ^{\circ}) \right) \approx 23.18^{\circ}

∠MSQ = 128.571 - 2*23.18 = 82.211

The area of triangle, MSQ, is given as follows;

Area \ of \Delta MSQ = \dfrac{1}{2}  \times  43.08^2 \times sin(82.211^{\circ}) \approx 919.382^{\circ}

The area of the of the garden plated with flowers, A_{req}, is given as follows;

A_{req} = Area of heptagon MNSRQPO - Area of triangle ΔMSQ

Therefore;

A_{req}= 1,842.94 - 919.382 ≈ 923.558

The area of the of the garden plated with flowers, A_{req} ≈ <u>923.558 m²</u>

Learn more about figures circumscribed by a circle here:

brainly.com/question/16478185

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