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2 years ago

5

Robin, Ashley, Joy, and Christina collected 156 acorns to make fall decorations. Robin collected three times as many acorns as A

shley.Christina
has 12 more acorns than Robin. Ashley and Joy collected the same number of acorns.
How many acorns did Ashley collect?

PLEASE HELP

1 answer:

elena-s [515]2 years ago

3 0

Answer:12

Step-by-step explanation:

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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

2 years ago

telo118 [61]

Answer:

Question D: what type of chips do students in this class prefer?

Step-by-step explanation:

5 0

9 months ago

Pls help With this question thank you

Lapatulllka [165]

Answer:

$CD=4 \text{ cm }$

Step-by-step explanation:

We have a similarity of triangles. Once the side BC and ED are parallel,

$\frac{BC}{AC} =\frac{ED}{AD}$

$\frac{10}{AC} =\frac{5}{4}$

Once $AC=AD+CD \Rightarrow AC=4+CD$

$\frac{10}{4+CD} =\frac{5}{4}$

$5CD+20=40$

$5CD=20$

$CD=4 \text{ cm }$

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3 years ago

wariber [46]

Answer:

b

Step-by-step explanation:

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2 years ago

Multiply. (3.5x10^-5) (3x10^-10) express your answer in scientific notation.

Len [333]

Answer:

5.69034 × 1011

Step-by-step explanation:

Decimal

1234000000

Scientific Notation

1.234 x 10^9

×10^

9

1st Number

1.234

×10^

9

Operation

2nd Number

5.678

×10^

11

3 0

3 years ago