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8 months ago

Find the indicated length. Assume lines that appear to be tangent are tangent. Round tothe nearest tenth if necessary.6?6.4

Mathematics

1 answer:

andreev551 [17]8 months ago

8 0

Given

Find

Length of AC

Explanation

as we have given right angle triangle

by pythagoras theorem ,

$AC^2=AB^2+BC^2$

AB = 6 + 6 = 12

so ,

$\begin{gathered} AC^2=12^2+(6.4)^2 \\ AC^2=144+40.96 \\ AC^2=184.96 \\ AC=\sqrt{184.96} \\ AC=13.6 \end{gathered}$

Final Answer

Hence , the length of AC is 13.6 . So , the correct option is 4

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Are the ratios 2:1 and 18:9 equivalent

MrRa [10]

Answer:

Step-by-step explanation:

hello :

the ratios 2:1 and 18:9 are equivalent because :

2/1 = (2×9)/(1×9)= 18/9

6 0

3 years ago

Match each polynomial expression to its additive inverse.

fomenos

Answer:

Step-by-step explanation:

To find the additive inverse of polynomial expression, flip the sign of each term.

6x² ----> -6x²

-x -----> +x

-2 -----> +2

Additive inverse:

-6x² + x + 2

6 0

3 years ago

Part 4. Find the missing sides for the 30 60 90 triangles. Please show work for each

inna [77]

10. tan(30) = l / 6√3

l = tan(30) x 6√3

l = 6

cos(30) = 6√3 / y

y = 6√3/cos(30)

y = 12

11. tan(30) = c/30

c = 30 x tan(30)

c = 10√3

cos(30) = 27/w

w = 27/cos(30)

w = 18√3

12.

sin(60) = 36/y

y = 36/sin(60)

y = 24√3

tan(60) = 36/x

x = 36/tan(60)

x = 12√3

7 0

3 years ago

Read 2 more answers

(I need help ASAP please

Goryan [66]

Answer:

C) 24

Step-by-step explanation:

Alternate interior angles are equal

so angle 1 equals angle 6

3x+10=x+58

subtract 10 from both sides

3x=x+48

then subtract x from both sides

2x=48

dived each side by two

x=24

7 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