Find the circumference of circle L. Write your answer as a decimal, rounded to the nearest hundredth.

Answer:

6.78 m

Step-by-step explanation:

Since the set up forms a triangle with length of ropes two sides of the triangle a = 8 m and b = 7 m respectively, the distance between them which is c = 6 m forms the third side of the triangle.

To find the height of the pole, we need to find the angle between any of the ropes and the ground. So, choosing the 8 m long rope side and using the cosine rule,

b² = a² + c² - 2accosФ where Ф is the angle opposite the 7 m long side which is also the angle between the 8 m long side and the ground.

So, making, Ф subject of the formula, we have

b² - (a² + c²) = 2accosФ

cosФ = [b² - (a² + c²)]/2ac

Ф = cos⁻¹{[b² - (a² + c²)]/2ac}

substituting the values of the variables into the equation, we have

Ф = cos⁻¹{[b² - (a² + c²)]/2ac}

Ф = cos⁻¹{[7² - (8² + 6²)]/2(8)(6)}

Ф = cos⁻¹{[49 - (64 + 36)]/96}

Ф = cos⁻¹{[49 - 100]/96}

Ф = cos⁻¹{-51/96}

Ф = cos⁻¹{-0.53125}

Ф = 122.09°

Since the height of the pole, h is a perpendicular bisector to the base of the triangle, and the 8 m long side form a triangle with it and the ground and the 8 m long side being the hypotenuse side of this triangle, we have that

sinФ = h/a where a = 8 m and Ф = 122.09° = the angle between the 8 m long side and the ground.

h = asinФ

substituting the values of the variables into the equation, we have

h = asinФ

h = (8 m)sin122.09°

h = 8 m × 0.8472

h = 6.78 m

Answer:

Option (2)

Step-by-step explanation:

To get the transformation applied in triangle ABC to map triangle DEF we will apply the following rules.

If a point A of triangle ABC maps the point D of triangle DEF,

Coordinates of point A → (-4, -5)

Coordinates of point D → (2, 6)

First point A is shifted to quadrant (4) from quadrant (3),

Rule for the translation,

A(x, y) → A'(x + 6, y - 1)

A(-4, -5) → A'(2, -6)

Followed by reflection across x-axis (y = 0)

A'(x, y) → D(x, -y)

A'(2, -6) → D(2, 6)

Therefore, Option (2) will be the answer.

Step-by-step explanation:

my answer is in the image above

Answer:

I've attached the Answer here

Answer:

The answer is A, that's the correct one

Answer:

looks like 154 degrees to me

Step-by-step explanation:

Answer:

Set y = 0, evaluate the quadratic at h=−b2a and solve for k.

k=9 I think..... I'm not completely sure but I think that's how it is

Answer:

[tex]\displaystyle \text{Vertex} = \left(k, 3-k^2\right)[/tex]

Step-by-step explanation:

We are given the quadratic equation:

[tex]y=x^2-2kx+3[/tex]

Where k is a non-zero constant.

And we want to determine the vertex of the parabola in terms of k.

The vertex of a parabola is given by the formulas:

[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = 1, b = -2k, and c = 3.

Find the x-coorinate of the vertex:

[tex]\displaystyle x=-\frac{(-2k)}{2(1)}=\frac{2k}{2}=k[/tex]

To find the y-coordinate, we substitute the value we acquired back into the equation. So:

[tex]\displaystyle \begin{aligned} y(k)&=(k)^2-2k(k)+3\\&=k^2-2k^2+3\\&=3-k^2\end{aligned}[/tex]

Therefore, our vertex in terms of k is:

[tex]\displaystyle \text{Vertex} = \left(k,3-k^2\right)[/tex]

Answer:

The fourth angles is 105

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360

3*85 = 225

Let the fourth angle be x

225 +x = 360

x = 360 -225

x =105

Answer:

[tex]a = 2 \\ b = 11[/tex]

Step-by-step explanation:

[tex] {x}^{2} + 4x + 4 - 4 - 7 = {(x + 2)}^{2} - 11[/tex]

Answer:

[tex]P(Cheese) = 0.30[/tex]

Step-by-step explanation:

Given

[tex]Cheese = 36[/tex]

[tex]Pepperoni = 64[/tex]

[tex]Veggie = 20[/tex]

Required

[tex]P(Cheese)[/tex]

This is calculated as:

[tex]P(Cheese) = \frac{Cheese}{Total}[/tex]

[tex]P(Cheese) = \frac{36}{36+64+20}[/tex]

[tex]P(Cheese) = \frac{36}{120}\\[/tex]

[tex]P(Cheese) = 0.30[/tex]

Answer:

guessing that the area of the inner rectangle is 10m²

and the other rectangle is 16m*10m= 160m²

we can say that

(16-x) * (10-x) = 10

for the area of the inner rectangle

let's calculate the lefthand side of the equation

160 - 16x -10x + x² = 10

160 -26x +x² = 10

subtract 10 on both sides

150 -26x +x² = 0

rearrange

x² -26x + 150 = 0

looks like something we can throw the pq formula on to solve for x

with p = -26 and q = 150

[tex]x = - \frac{ - 26}{2} \frac{ + }{ - } \sqrt{( \frac{ - 26}{2})^{2} - 150 } [/tex]

[tex]x = 13 \frac{ + }{ - } \sqrt{169 - 150 } [/tex]

[tex]x = 13 \frac{ + }{ - } \sqrt{19 } [/tex]

[tex]x1 = 8.64[/tex]

[tex]x2 =17.36 [/tex]

we need to interpret this solutions

but to be sure on this, I need the unreadable text of the photographed problem

Answer:

31/24 menos 5/8 cuanto es 2/3

Step-by-step explanation:

=31/24- 5/8

=31-15/24

= 16/24

=2/3

Hence the final answer is 2/3

Answer:

x = 15

Step-by-step explanation:

Given that,

The length of the base of an isosceles triangle is x.

The length of a leg is 3x-4.

Perimeter, P = 97

An isosceles triangle has one base. The perimeter of a triangle is given by :

97=x+3x-4+3x-4

97 = 7x-8

97+8=7x

105 = 7x

x = 15

So, the value of x is 15.

Two consecutive odd integers with a sum of 36 are 17 and 19.

Hope it helps you I'm from ph❤️

Answer:

Two consecutive odd integers with a sum of 36 are 17 and 19.

Step-by-step explanation:

hope i helped

Answer:

Determine AC with the pythagorean theorem, then you can find CD by subtracting AD.

with DC and BC, you can find BD. again, with the pythagorean theorem

Answer:

20

Step-by-step explanation:

Find AC

[tex]\sqrt{65^{2} -16^{2} } = 63[/tex]

Substract

63 - AD = 12

Find "?"

[tex]\sqrt{12^{2} +16^{2} } = 20[/tex]

Answer:

y = (x + 3)² - 6

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

f(x) = x² + 6x + 3

Using the method of completing the square

add/subtract ( half the coefficient of the x- term)² to x² + 6x

f(x) = x² + 2(3)x + 9 - 9 + 3

     = (x + 3)² - 6 ← in vertex form

Step-by-step explanation:

How to Calculate the Semi Interquartile Range / Quartile Deviation. As the SIR is half of the Interquartile Range, all you need to do is find the IQR and then divide your answer by 2. Note: You might see the formula QD = 1/2(Q3 – Q1). Algebraically they are the same.

Answer:

c

Step-by-step explanation:

all real values of x where 1 < x < 4

Answer:

c

Step-by-step explanation:

trust me

Answer:

3.14 million

Step-by-step explanation:

10.676 - 7.536 = 3.14

To check

7.536 + 3.14 = 10.676

Answer:

3.14 million is the correct answer

Answer:

option D

Step-by-step explanation:

length of a square = 21 cm

perimeter of a square = 4l

=4*21

=84 centimeters

Answer:

C

Step-by-step explanation:

The square looks like it has equivalent sides so

21 x 21 = 441 square centimeters

Answer: 87.

Step-by-step explanation:

Let x be the tens digit, then (x - 1) - unit digit.

x + x - 1 = 15

2x - 1 = 15

2x = 15 + 1

2x = 16

x = 16 ÷ 2

x = 8 - the tens digit.

8 - 1 = 7 - the units digit.

87 - the number.

Answer:

39.24 sec

How long will it take a 1500 W motor to lift a 300 kg piano to a sixth-story window 20 m above? All tutors are evaluated by Course Hero as an expert in their subject area. Answer is t = 39.24 sec

Step-by-step explanation:

It will take the motor 39.2 seconds to lift the piano to the sixth-story window.

Given the following data;

We know that acceleration due to gravity is equal to 9.8 m/s².

To find how long it will take to lift the piano to the sixth-story window;

First of all, we would have to determine the gravitational potential energy required to lift the piano up.

Mathematically, gravitational potential energy is given by the formula;

[tex]G.P.E = mgh[/tex]

where:

Substituting into the formula, we have;

[tex]G.P.E = 300*9.8*20[/tex]

G.P.E = 58,800 Joules

Next, we would determine the time using the following formula;

[tex]Time = \frac{Energy}{Power}[/tex]

Substituting the values into the formula, we have;

[tex]Time = \frac{58800}{1500}[/tex]

Time = 39.2 seconds.

Therefore, it will take the motor 39.2 seconds to lift the piano to the sixth-story window.

Find more on power, time and energy here: https://brainly.com/question/20488953

Answer:

gradient =y2-y1÷x2-x1

=10-5÷2-(-3)

1

y-y1=m(x-x1)

y-5=1(x-(-3))

y=x+2

THE CORRECT EQUATION IS..

(8X+3)°=(7X+12)°

[BEING VERTICALLY OPPOSITE ANGLES ARE ALWAYS EQUAL ]

HOPE THIS HELPS YOU...

Answer:

8x + 3 = 7x + 12

8x -7x= 12-3

x=9

Answer:

The blue dot is at 3.

Answer:

y=63x+65

Step-by-step explanation:

Answer:

correct 42 in bsae 10 is 60

Answer:

Dimensions Of The Driveway is Length=16 Feet & Width=9 Feet

Step-by-step explanation:

According To Question,We Have Given

Length of Driveway Is 7 feet longer than its Width

Let the Width be X Feet . So Length is (X+7)Feet

Area Of Driveway = 144 sq. Feet

X * (X+7) = 144

[tex]X^{2}[/tex]+7X=144

[tex]X^{2}[/tex]+16X-9X-144=0

X(X+16)-9(X+16)=0

X = -16 & +9 (Neglect -16 because Width=X, that Can Never be in Negative)

So X = +9

Now Put this value, We get Width = 9 Feet & Length =16 Feet