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3 years ago

Fill in the missing number to complete the linear equation that gives the rule for this table.

Mathematics

2 answers:

allsm [11]3 years ago

6 0

Answer:

y=x-5

Step-by-step explanation:

6-5=1

7-5=2

8-5=3

The rule is subtract 5

kogti [31]3 years ago

5 0

Answer:

Y=x-5

Step-by-step explanation:

In the table the rule is -5

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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

Required;

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;

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

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

$The \ apothem \ a = 25 \times sin \left ( \dfrac{128.571}{2} \right) \approx 22.52$

The area of the heptagon MNSRQPO is therefore;

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

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

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

6 0

3 years ago

Dovator [93]

12^2=144

144 is divided by b which also is an odd interger, there only 2 numbers : 1 and 3

if b=3, a^2=48, then there will be no a available

if b=1 , a^2=144, then a is 12 and 12 can not be divided by 9

The answer is D

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3 years ago

Pls help me guys! This is super hard

Mashcka [7]

I count 4 green stars and 6 red stars

ratio of green to red would be
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4:6

if you divide both numbers by 2, cause theyre both even

2:3

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3 years ago

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There are 5 green balls, 2 orange balls, 4 purple balls, and 1 pink ball in a bucket. You pick 1 ball from

bagirrra123 [75]

B
The purple balls constitute 1/3 of the amount of balls there, so you’re that likely to pluck one out.

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3 years ago

Wich is the missing number in the prime factorization will rate branleist

gogolik [260]

The answer is a. 5. Good luck

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2 years ago