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The distance of the ship from lighthouse found using sine law at both locations are 14.12 miles and 4.8 miles.

What is sine law?

The sine law asserts that the ratio of a triangle's side length to the sine of its opposing angle, which is constant for all three sides.

From the given figure we can find θ = 30 - 10 = 20°

According to sine law, we can write the following equation,

[tex]\frac{9.6}{sin \theta} = \frac{x}{sin \angle ABL} = \frac{y}{sin \angle LAB} \\[/tex]

From the figure, we get that ∠LAB= 10° (alternate angles)

∠LBC = 30°

∠ABL = 180 - 30 = 150°

θ = 20°

Substituting above values in the equation we get ,

[tex]\frac{9.6}{sin 20} = \frac{x}{sin 150} = \frac{y}{sin 10} \\\\\frac{9.6}{0.34} = \frac{x}{0.5} = \frac{y}{0.17}[/tex]

Solving the above we get,

x = 14.12

y = 4.8

Therefore the ship began 14.12 miles from the lighthouse and after travelling 9.6 miles south it is at 4.8 miles from the lighthouse.

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Tony purchased 12 books and 6 magazines for a total of $240.

An equation is a mathematical statement that expresses two or more mathematical expressions as equal. It typically consists of an equals sign (=), two or more variables, and a number or operation that links them. Equations are often used to solve problems, model real-world situations, and to make predictions.

He bought 12 books for $12 each, and 6 magazines for $12 each. Thus, the total cost of 18 books and magazines was $240.

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Answer:

-26/25

Step-by-step explanation:

I took the quiz and I got an A+

Answer:

5 7/16

Step-by-step explanation:

First off, make all the numbers have the same denominator.

In this case, the best one would be 16.

For 9 3/4, the four goes into 16 four times. So you multiply the 3 by four, and get 12 in the numerator. So it is now 9 12/16.

Next we have 3 1/8. 8 goes into 18 2 times. So you multiply 1 by 2 and get 2 in the numerator. So it is now 3 2/16.

Now, lets add the two together:

3 2/16+9 12/16 =

12 14/16

Now we know the sum of the two numbers.

Lets subtract this from 18 7/16:

18 7/16-12 14/16

=

5 7/16

This is your answer!

Hope this helps! :)

1). The relation given; { (−1, 8), (0, 15), (1, –4), (2, 0) } as given is a function.

2). The relation given; { (-5, 2), (5, 2), (0, -3), (3,-8) } as given is a function.

3). The relation given; { (-2, 7), (6, 2), (−2, −3), (0, 9) } as given is not a function.

4). The relation given; { (7,2), (4,-6), (2,-2). (4,-9) } as given is not a function.

5). The relation given; { (2, 3), (2, 4), (2, 5), (2,6) } as given is not a function.

6). The relation given; { (1,4), (2, 4), (3, 4), (4, -4) } as given is a function.

It is important to know that a function is a special kind of relation in which case no one input value, x is assigned more than one output value.

On this note, when a relation is such that one of its input values is assigned two or more output values; such relation is not a function.

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On solving the provided question we can say that - The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.

The order of rotational symmetry is the maximum number of rotations that a geometry may fit in. 360°A°, where A° is the smallest angle by which a figure may be rotated from its rotated shape to match its original shape, represents the degree of rotational symmetry. (180 degrees) A shape's degree of rotational symmetry is determined by how many times a perfect circle may be turned while maintaining its appearance. Only when a triangle is back in its original beginning position will a full 360° revolution appear the same.

If a geometric figure maps onto itself when rotated around an angle at its center, it possesses rotational symmetry.The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.

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The three ways to purchase a vehicle include: (1) On lease  (2) On hire purchased and (3) On cash basis

A vehicle can be purchased on the following ways:

Lease:  This involves granting the user access on the property over a period of time before he could make payment

Hire purchase:  In this method, the buyer deposits first initial money while he agrees with the seller to make the payment of the balance on installment basis

Cash:  In this method the buyer pays cash at prompt or on the point of purchase

Advantages include:

It places the buyer on good life without cash

He enjoys the luxurious life

Disadvantages:

He can run away with the vehicle

The seller looses in cash of accident taking the life of the buye

Additional expenses include

Cost of maintenance

Repairs

Fueling

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Answer:

4.6

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve this system of equations, you can use the substitution method.

In this method, you solve one of the equations for one of the variables in terms of the other variable. Then you substitute this expression into the other equation. This will give you a single equation in one variable, which you can solve to find the value of that variable. Finally, you can substitute this value back into one of the original equations to find the value of the other variable.

To solve this system using substitution, we can solve the second equation for y:

y = x - 4

Then, we substitute this expression for y in the first equation:

x + (x - 4) = 8

Combining like terms, we get:

2x - 4 = 8

Adding 4 to both sides, we get:

2x = 12

Dividing both sides by 2, we find that:

x = 6

Now we can substitute this value back into one of the original equations to find the value of y. Let's substitute it into the second equation:

x - y = 4

Substituting 6 for x, we get:

6 - y = 4

Subtracting 6 from both sides, we find that:

y = 2

So the solution to the system of equations is x = 6 and y = 2.

Answer:

x=6, y = 2

Step-by-step explanation:

If you add 2 expressions, 2x = 12, so x = 6.

So the other one y = 2.

Answer:

15

Step-by-step explanation:

Due to it being a parallelogram 6x-10=3x+5 which makes it 3x-10=5 when you subtract both sides by 3x then you add 10 to both sides to make 3x = 15 which gets you x = 5 finally you put this into 4x-5 which is 4*5-5,  20-5=15 so the answer is 15

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Answer:

(2 2) is answer of this question

Answer:

(2,2) is the solution to both lines A and B

Step-by-step explanation:

this is because they both intersect at point (2,2)

Answer:

85 degrees

Step-by-step explanation:

180=x+4x-20

180=5x-20

200=5x

x=40

C=2(40)+5

C=80+5

C=85

Answer:

C you all welcome:)

Step-by-step explanation:

A was wrong sorry to tell you

Answer:

x = 9    if there is any confusion, please ask questions

Step-by-step explanation:

so in math, a complementary angle is when two angles add up to 90 degrees.

to find this, you have to do 90-81

90 - 81 = 9

Answer: 7

Step-by-step explanation:

9/6 = 1.5

1200 x 1.5 = 1800 (t-shirts a work day)

12 600/1800 = 7

7 work days

Answer:

D No, because the cards are not being replaced in the deck after they are turned over, the independence condition has not been met.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

lucky guess

Answer:

$576.19

Step-by-step explanation:

On solving the provided question, we can say that - the value of x and y by the linear equation will be x = 12 and y = -21

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here, we have

3x-2y = 3

-4x + 5y = -11

and on solving we got

x = 12 and y = -21

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The vertex of the parabola -x² - 2x + 10 = 0 occurs at (-1,11), It is a maximum value.

Given the equation of the parabola;

-x² - 2x + 10 = 0

First, the maximum of a quadratic function occurs at;

x = -b/a, if a is negative, the maximum value of the function is f( -b/2a)

f_max(x) = ax² + bx + c occurs at;

x = -b/2a

Now, find the value of x = -b/2a

Plug in a = -1 and b = -2

x = -( -2/2(-1) )

x = -( -2/-2) )

x = -( 1 )

x = -1

Hence;

f(x) = -x² - 2x + 10

f( -1 ) = -( -1 )² - 2( -1 ) + 10

f( -1 ) = -1 + 2 + 10

f( -1 ) = -1 + 12

f( -1 ) = 11

Therefore, maximum occurs at (-1,11).

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Answer:

Hello, their has been a update to brainly. we no longer accept images, **** off

Step-by-step explanation:

Answer:

4+m

Step-by-step explanation:

You can't put them together 'cause they aren't like terms, so you just keep the sign that put them together in the first place.

9514 1404 393

Answer:

  (b)  6

Step-by-step explanation:

Eliminating parentheses gives ...

  4x -8 = 16

Dividing by 4, we have ...

  x -2 = 4

  x = 6 . . . . . . add 2

There is a $1,000 additional interest earned on a $100,000 CD (Commercial Paper) for 9 months than for 6 months.

The additional interest earned for a 9-month CD over a 6-month CD can be computed using the subtraction operation.

Firstly, the interests on the 9-month CD and 6-month CD are worked out separately, using the interest formula: Principal x Rate x Time.

The interest for the 6-month CD is subtracted from the interest for the 9-month CD.  The result is the difference or additional interest earned.

Commercial Deposit = $100,000

Annual Percentage Rate = 4%

Monthly Percentage Rate = 0.333% (4%/12)

Interest for 9 months = $3,000 ($100,000 x 4% x 9/12)

Interest for 6 months = $2,000 ($100,000 x 4% x 6/12)

The difference in interest earned = $1,000 ($3,000 - $2,000) or ($100,000 x 4% x 3/12)

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APY = 4%

Setting x=2 in the function is the simplest approach to discover f(2). However, you might plot the graph of f(x) and the vertical line x=2 to visually solve this.

Set x=2 in the function for the quickest and easiest method to discover f(2). Plotting the graph of f(x) and the vertical line x=2 would allow you to visually answer this problem. Next, the graphs' intersection will represent the answer. The "x" in "f (x)" is known as "the function's argument" or simply "the argument" in function notation.

As a result, if they ask for a "argument" and offer you the equation "f (2)," all you have to say is "2." Now (1) f(2)=2(2+1)=2×3=6.If our function's value is f(2), then we should calculate its value when x=2. Example. If x = 2, then f(2) = 2 + 7 = 9. F(x) = x + 7. GF(2), also known as the Galois field of two elements, or F2, the chemical formula for fluorine. F2 is a tornado intensity category on the Fujita scale.

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He cut 16 pieces

I really hope this helps :D

120:36 is equivalent to 10:3

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"The trick with ratios is to always multiply or divide the numbers by the same value.

Given here the ratio is 120:36≡10:3

 Hence,  120:36 is equivalent to 10:3                                

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The solutions to the equation 4(x² − 5) − 1 = 3 are ±√6

From the question, we have the following parameters that can be used in our computation:

4(x 2−5)−1=3

Express properly

This gives

4(x² − 5) − 1 = 3

Subtract -1 from both sides of the equation

So, we have the following representation

4(x² − 5) = 4

Divide both sides by 4

This gives

x² − 5 = 1

Subtract -5 from both sides of the equation

So, we have the following representation

x² = 6

Take the square root of both sides

x = ±√6

Hence, the solution is ±√6

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Answer:

A = 1/4

Step-by-step explanation:

Answer:

A = 1/4 is the correct answer