You give tours on the Great Lakes and talk about points of interest. A lighthouse typically has 2 beacons that rotate together but not necessarily facing opposite directions. In that way, it can be a shorter time between the first and second flashes than between the second flash and the third flash
(when the first beacon comes around for the second time). One way of identifying which lighthouse you are looking at is to find the ratio of the short time between flashes to the long time between flashes. If the beacons are set 120 degrees apart along the rotation, ash shown below, what is this ratio?

In the right triangle in the figure the value of x is solved to be 4.5

Using SOH CAH TOA for the right triangle

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The figures show that

hypotenuse = 6

adjacent = x

given angle = 41 degrees

The value of x will be calculated using cos, CAH let the angle be y

cos y = adjacent / hypotenuse

cos 41 = x / 6

x = 6 * cos 41

x = 4.528

x = 4.5

Hence the value of x is 4.5

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Answer:

each box contain 8 x 9 = 72

Answer:

A 1 in 4 chance or a probability of 0.25

Step-by-step explanation:

There is only 3 months that start with J and 12 months in a year so simplify 3/12 you get 1/4 or 0.25

Answer:

1 unit to the left, 3 units down

Step-by-step explanation:

Take any point: I will take D. In order to get to D', you need to travel 1 unit along the x-axis towards the left, then 3 until along the y-axis downwards. The same applies for any other point.

If cosec (tetha) = 17/15 then cos (tetha) = 8/17

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

cosec , sine, cotangent, cosine , secant and tangent are trigonometry function.

cosec( tetha) = 1/sin(tetha)

tangent (tetha) = 1/ cot ( tetha)

sec (tetha) = 1/ cos(tetha)

cosec (tetha) = 17/15

therefore 1/sin ( tetha) = 17/15

sin( tetha ) = 15/17 = opp/ hyp

therefore using Pythagoras theorem adj² = 17²-15²

adj² = 289-225

adj² = 64

adj = √64 = 8

cos ( tetha) = adj/hyp

therefore cos ( tetha) = 8/17

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Answer:

Elliot = 16 years old

Miya = 10 years old

Cara = 25 years old

Step-by-step explanation:

Define the variables:

The average age of Elliot, Miya and Cara is 4 years more than the average age of Elliot and Miya:

[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y}{2}+4[/tex]

[tex]\implies \dfrac{x+y+z}{3}=\dfrac{x+y+8}{2}[/tex]

[tex]\implies 2(x+y+z)=3(x+y+8)[/tex]

[tex]\implies 2x+2y+2z=3x+3y+24[/tex]

[tex]\implies 2z=x+y+24[/tex]

[tex]\implies x=2z-y-24[/tex]

Cara is 9 years older than Elliot:

[tex]\implies z = x + 9[/tex]

Four years ago, Elliot was double the age of Miya:

[tex]\implies (x - 4) = 2(y - 4)[/tex]

[tex]\implies x - 4 = 2y-8[/tex]

[tex]\implies x +4 = 2y[/tex]

[tex]\implies y=\dfrac{1}{2}x +2[/tex]

Substitute the equations for z and y into the equation for x and solve for x:

[tex]\implies x=2z-y-24[/tex]

[tex]\implies x=2(x+9)-\left(\dfrac{1}{2}x +2\right)-24[/tex]

[tex]\implies x=\dfrac{3}{2}x-8[/tex]

[tex]\implies \dfrac{1}{2}x=8[/tex]

[tex]\implies x=16[/tex]

Substitute the found value of x into the equation for z and solve for z:

[tex]\implies z = 16 + 9[/tex]

[tex]\implies z = 25[/tex]

Substitute the found value of x into the equation for y and solve for y:

[tex]\implies y=\dfrac{1}{2}(16) +2[/tex]

[tex]\implies y=8+2[/tex]

[tex]\implies y=10[/tex]

Therefore, the ages of Elliot, Miya and Cara are:

The nearest integer that is a solution, gotten through graphing of the quadratic function x² + 2x - 2 = 5, is x = -4

Quadratic equations when plotted on a graph follows a parabolic path.

To plot the functions there will be table of values that is used in making the graph. The table of values is solved as follows

x² + 2x - 2 = 5 rearranging the equation will result to x² + 2x - 7 = 0

For x = -20,  y = (-20)² + 2 * -20 - 7 = 353

For x = 0,  y = (0)² + 2 * 0 - 7 = -7

For x = 20,  y = (20)² + 2 * 20 - 7 = 433

x      y

-20  353

0      -7

20    433

The graph is plotted and attached. From the graph the solution is

x = -3.828, to the nearest integer = -4

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Answer:

Step-by-step explanation:

i have no idea

A) The linear equation is:

y = (3/4)*x + 3

B) The sets with only positive elements are:

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Here, we do know that the y-intercept of the linear equation is (0, 3), then we know that b = 3.

Then the line is something like:

y = a*x + 3

We also know that the line passes through (-4, 0), then we can replace these values in the equation above to get:

0 = a*-4 + 3

4a = 3

a = 3/4

Then the linear equation is:

y = (3/4)*x + 3

The sets where all the numbers are positive are:

{x| x ∈ N}

Where N is the set of the natural numbers, these are all the integers equal to or larger than 1, so all are positives.

{y| 0 < y < 1}

There we can see that y must be larger than zero, so all the elements are positive.

{y| 3 ≤ y ≤22}

Here the elements are between 3 and 22, so all of these are positve.

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The graph of the system of linear equations is attached with the answer.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given is the system of linear equations as given -

- 2x + y = 10

x + 2y = 5

The given system of linear equations is -

- 2x + y = 10

x + 2y = 5

Refer to the graph of the system of linear functions attached. The point (-3, 4) is the solution set of this system of equation.

Therefore, the graph of the system of linear equations is attached with the answer.

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Answer:2009#73

Step-by-step explanation:

3939+373

Ie,ek

The solution to the equation log₇343 = 3 is 7³ = 343

An equation is used to show the relationship between numbers and variables.

The logarithm can be defined as the exponent that raises a base to get a particular number. The law of logarithm states:

logₓm = n is the same as xⁿ = m

Given the equation:

log₇343 = 3

Applying the law of logarithm gives:

7³ = 343

The solution to the equation is 7³ = 343

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Answer:

x = 55

Step-by-step explanation:

Since the sides of the shape are parallel, AngleC and AngleD will add up to 180° (see "parallel lines cut by a transversal" or maybe you have learned a big pile of parallelogram theorems)

Use this relationship to set up an equation.

2x + 20 + 50 = 180

combine like terms

2x + 70 = 180

subtract 70

2x = 110

divide by 2

x = 110/2

x = 55

x is 55

Answer:

The value of x is 55°

Step-by-step explanation:

Since we know that opposite angles of a parallelogram are equal

The sum of any two adjacent angles is supplementary. This means, ∠A + ∠B = 180°, ∠B + ∠C = 180°, ∠C + ∠D = 180°, and ∠D + ∠A = 180.

So,

∠C + ∠D = 180°

(2x + 20)° + 50° = 180°

2x + 70° = 180°

2x + 70° - 70° = 180° - 70°

2x = 110°

2x/2 = 110°

x = 55°

Thus, The value of x is 55°

Answer:

(-∞, 1] or {x|x<=1}

Step-by-step explanation:

The unit rate is 18 commercials per hour.

A division is a process of splitting a specific amount into equal parts.

On Saturday morning, Wendy watched one and a half hours of her favorite shows on television.

During the shows there were 27 commercials.

We need to find the unit rate of commercials per hour.

To find this we have to divide 27 by number of hours

27/[tex]1\frac{1}{2}[/tex]

Convert [tex]1\frac{1}{2}[/tex] to improper fraction

27/(3/2)

When whole number is divided by fraction, the denominator is multiplied with whole number

27×2/3

54/3

18

Hence, the unit rate is 18 commercials per hour.

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Answer:18 commercials per hour

Step-by-step explanation:

On solving the provided question we cans ay that -  order when writing it on the number line: = -1.25, -0.75, 0.25, 1.5, 2

A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.

The numbers on the number line must be

[tex]6/3 = 2\\-3/4 = -0.75\\1.5 = 1.5\\0.25 = 0.25\\-5.4 = -1.25\\[/tex]

In ascending order, t

[tex]-1.25 = -5/4\\-0.75 = -3/4\\0.25\\1.5\\2 = 6/3[/tex]

order when writing it on the number line:

-1.25, -0.75, 0.25, 1.5, 2

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7½

7×2+1/2

14+1/2

15/2

12½

12×2+1/2

24+1/2

25/2

4.8

Divide 250 by 2 which is 125 then do 600 divided by 125. Then your answer should be 4.8.

The value inside the square root should be greater than or equal to zero. Then the domain of the function will be [7, ∞).

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The domain means all the possible values of x and the range means all the possible values of y.

The function is given below.

f(x) = √x

The function after the transformation, then we have

f(x) = √(x - 7) + 2

The value inside the square root should be greater than or equal to zero. Then the domain of the function will be given as,

x - 7 ≥ 0

x ≥ 7

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Answer:

157[tex]ft^{3}[/tex]

Step-by-step explanation:

Volume =  the area of the base times the height.

Area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]

a = [tex]\pi[/tex][tex](5^{2})[/tex]   I am going to use 3.14 for [tex]\pi[/tex]

a = 3.14(25)

a = 15.7

Volume = 15.7 x 10 = 157

Answer:

785 ft२

Step-by-step explanation:

volume =3.13*5२*10

=3.14*25*10

=785 ft२

Answer:

75%

Step-by-step explanation:

To find the percent of change that Target marks the shoes up for, you need to calculate the difference between the cost of the shoes to Target and the price at which they sell it to the public, and then divide that difference by the cost of the shoes to Target. Finally, you need to multiply the result by 100 to express the answer as a percentage.

Using this formula, the percent of change that Target marks the shoes up for is:

(35 - 20) / 20 * 100 = 15 / 20 * 100 = 0.75 * 100 = 75%

This means that Target marks the shoes up by 75% of their cost.

From the exponential function, the average rate of change from year 1 to year 4 is 62.43, the average rate of change from year 5 to year 8 is 67.57 and the rate of change per year is 65

An exponential function is a type of function that involves a variable in an exponent. It is of the form f(x) = a⋅b^x where a and b are constants and b > 0, b ≠ 1. The input to the function, x, is the exponent that the base, b, is raised to. The output, f(x), is the result of raising the base to the exponent.

In this problem, we have to calculate the rate of increase per year.

Data;

rate = 2%

P = 3000

The exponential growth can be calculated by;

A = P(1 + r)ⁿ

In year 1

A = 3000(1 + 0.02)¹

A = 3060

In year 4

A = 3000(1 + 0.02)⁴

A = 3247.3

a)

The average rate of change from year 1 to year 4 will be

A = [3000(1 + 0.02)⁴ - 3000(1 + 0.02)¹] / 4 - 1

A = 62.43

The average rate of change from year 1 to year 4 is 62.43

b)

The average rate of change from year 5 to year 8 is calculated as

A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)⁵] / 8 - 5

A = 67.57

C)

The rate of change increase can be calculated as;

A = [3000(1 + 0.02)⁸ - 3000(1 + 0.02)¹] / 8 - 1

A =65

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Using an inverse trigonometric function, we will find that the solution is:

θ = 1.047

Here we want to solve the equation:

1 - cos(θ) = 1/2

Such that θ ∈  [0,2pi)

Now let's return to our equation:

1 - cos(θ) = 1/2

1 - 1/2 = cos(θ)

1/2 = cos(θ)

Now we could apply the inverse cosine function to both sides, then we will get:

Acos(1/2) = Acos(cos(θ))

1.047 = θ

That is the solution.

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By adding the weight of the triangle, the weight of the circle heavier than that of the square.

The linear equation that results from examining the weights will contain the following parameters.

Let t stand for the triangle.

Let c stand for the circle.

Let's use the shape square.

left side of the equation = 6s + 3t

right side of the equation = 3s + 3c

equating both sides

6s + 3t = 3s + 3c

6s - 3s + 3t = 3s + 3c

3s + 3t = 3c

3(s + t) = 3c

dividing all through by 3

s + t = c

10 + t = c

Because of the resulting equation, we can conclude that the the circle is weightier than the square by the weight of the triangle

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Answer:

(0.5, 3)

Step-by-step explanation:

Just entered it into a desmos graphing calculator online

1] Answer: y = -[tex]\frac{1}{2}[/tex]x + 3

Step-by-step explanation:

➜ This line is going down from the top left to the bottom right, so it will have a negative slope.

➜ Using rise over run, we get a slope of -2/4. This simplifies to -1/2.

➜ The line intercepts the y-axis at 3.

2] Answer: y = 3x

Step-by-step explanation:

➜ This line is going down from the bottom left to the top right, so it will have a positive slope.

➜ Using rise over run, we get a slope of 3/1. This simplifies to 3.

➜ The line intercepts the y-axis at 0.

3] Answer: y = x - 4

Step-by-step explanation:

➜ This line is going down from the top left to the bottom right, so it will have a negative slope.

➜ Using rise over run, we get a slope of 2/2. This simplifies to 1.

➜ The line intercepts the y-axis at -4.

The linear equation in this case is . The [tex]$3 x^2+4 x+4=0$[/tex] answer is [tex]x=-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}, x=-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}[/tex] and [tex]$3 y^2+2 x+4=0: \quad$[/tex]: quadratic [tex](h, k)=(-2,0), p=-\frac {1} {6}[/tex] , is the solution.

[tex]$3 x^2+4 x+4=0 \quad: \quad x=-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}, x=-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}$[/tex]

[tex]$3 x^2+4 x+4=0$[/tex]

Apply the quadratic formula to the problem. [tex]$x_{1,2}=\frac{-4 \pm \sqrt{4^2-4 \cdot 3 \cdot 4}}{2 \cdot 3}$[/tex]

Simplify [tex]$\sqrt{4^2-4 \cdot 3 \cdot 4}: \quad 4 \sqrt{2} i$\\[/tex]

[tex]$x_{1,2}=\frac{-4 \pm 4 \sqrt{2} i}{2 \cdot 3}$[/tex]

Distinguish the answers

[tex]x_1=\frac{-4+4 \sqrt{2} i}{2 \cdot 3}, x_2=\frac{-4-4 \sqrt{2} i}{2 \cdot 3}\\x=\frac{-4+4 \sqrt{2} i}{2 \cdot 3}: \quad-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}\\x=\frac{-4-4 \sqrt{2} i}{2 \cdot 3}: \quad-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}[/tex]

The following are the quadratic equation's solutions:

[tex]x=-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}, x=-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}[/tex]

2) [tex]$3 y^2+2 x+4=0: \quad$[/tex] A parabola with a focal length of and a vertex at (h,k)=(-2, 0) [tex]$|p|=\frac{1}{6}$[/tex]

[tex]$3 y^2+2 x+4=0$[/tex]

[tex]$4 p(x-h)=(y-k)^2$[/tex] is the common formula for a right-to-left parabola with a vertex at (h, k) and a focal length of |p|.

Rewrite [tex]$3 y^2+2 x+4=0$[/tex]  using the proper form: [tex]$4\left(-\frac{1}{6}\right)(x-(-2))=(y-0)^2$[/tex]

The following are characteristics of parabolas:

[tex](h, k)=(-2,0), p=-\frac {1} {6}[/tex]

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Answer:

11

Step-by-step explanation:

Based on the given conditions, formulate: 25 - 14

Calculate the sum or difference: 11

get the result: 11