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3 years ago

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How do you write a mixed number for each

1 answer:

Stella [2.4K]3 years ago

5 0

B is
$2 \frac{1}{2}$

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Question Help The circumference of the hub cap of a tire is 73.54 centimeters. Find the area of this hub cap. Use 3.14 for it. U

Archy [21]

See attached picture

8 0

2 years ago

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

<img src="https://tex.z-dn.net/?f=10-%5Cfrac%7B3y-1%7D%7B2%7D%20%3D%5Cfrac%7B6y%2B3%7D%7B11%7D" id="TexFormula1" title="10-\frac

Ghella [55]

$10-\frac{3x-1}{2} =\frac{6x+3}{11}$

$10 = \frac{6x+3}{11} + \frac{3x-1}{2}$

$10 = (\frac{6x+3}{11} \times \frac{2}{2} ) + (\frac{3x-1}{2} \times \frac{11}{11} )$

$10 = ( \frac{2(6x + 3)}{22} ) + ( \frac{11(3x - 1)}{22} )$

$10 = \frac{12x + 6}{22} + \frac{33x - 11}{22}$

$10 = \frac{12x + 6 + 33x - 11}{22}$

$10 = \frac{(12 x + 33x) + (6 - 11)}{22}$

$10 = \frac{45x - 5}{22}$

$10 \times 22 = 45x - 5$

$220 = 45x - 5$

$220 + 5 = 45x$

$225 = 45x$

$\frac{225}{45} = x$

$\frac{45}{9} = x$

$5 = x$

7 0

2 years ago

Complete the sentence to make it true statements 6 is 100 times

AnnyKZ [126]

Answer:

6 is 100 times 0.06

Step-by-step explanation:

0.06 times 100 = 6

8 0

3 years ago

Read 2 more answers

Which of the following represents a function that is reflected over the x-axis and shifted up 3

Travka [436]

Answer:

Option 2.

Step-by-step explanation:

f(x) = - x^2 + 3

The parent function is x^2

- the '-' before the x^2 reflects it in the x-axis, and the + 3 shifts it up 3 units.

7 0

3 years ago