A boat travels north at a speed of 20 mph and a bearing of N 32 degrees E. Another boat travels at a speed of 28 mph and a bearing of S 42 degrees E. After 2 hours, how far apart are the boats

Answer:

complement of acute angle = 2x - 46

Step-by-step explanation:

supplementary angles sum to 180° , that is

acute angle + supplement = 180

acute angle + (2x + 44) = 180 ( subtract 2x + 44 from both sides )

acute angle = 180 - (2x + 44) = 180 - 2x - 44 = 136 - 2x

complementary angles sum to 90° , that is

acute angle + complement = 90

136 - 2x + complement = 90 ( subtract 136 - 2x from both sides )

complement = 90 - (136 - 2x) = 90 - 136 + 2x = 2x - 46

Yes, Timothy is correct because triangle AKLM was dilated by using a scale factor of 1.5 centered at the origin.

In Mathematics, dilation can be defined as a type of transformation that is typically used for enlarging or reducing the size of a geometric object but not its shape, based on the scale factor.

For the given coordinates of the preimage triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) would be calculated as follows:

Coordinate K (-1, 3) → Coordinate K' (-1 × 1.5, 3 × 1.5) = Coordinate K' (-1.5, 4.5).

Coordinate L (8, 4) → Coordinate L' (8 × 1.5, 4 × 1.5) = Coordinate L' (12, 6).

Coordinate M (10, -3) → Coordinate M' (10 × 1.5, -3 × 1.5) = Coordinate M' (15, -4.5).

In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph above, therefore, Timothy is correct.

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The function g(t)=100(t-4)/84.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

g(0) = 4

g(1)= 4 + .84x

g(2)= 5.85

g(t) = mt+c

c = 4

g(t) = t-c/m = t-4/0.84 = 100(t-4)/84

Hence, the g(t)=100(t-4)/84.

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The ratio of the vertical lenght to the horizontal length of both triangles   from the graph is the same which is numerical equal to 1/2 and the slope of the line is 1./2.

A triangle is a plane shape that has three sides.

For triangle PRQ,

Ratio of the vertical lenght to the horizontal length of triangle PRQ(r) = Vertical length(v)/Horizontal length (h)

From the graph,

Given:

Substitute into equation 1

Similarly, for triangle SUT,

From the graph,

Given:

Substitute into equation 2

The slope the line is the same as the ratio of the vertical lenght to the horizontal length of both triangles

Therefore,

Slope of the line = 1/2

Hence, the ratio of the vertical lenght to the horizontal length of both triangles  is 1/2 and the slope is 1./2.

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The nth term of the given Quadratic Sequence is n² + 2n.

Given, a sequence of numbers i.e. 3, 8, 15, 24, 35

Now, we have to find the nth term of this quadratic sequence

Let, the quadratic sequence be defined as,

f(x) = ax² + bx + c

Now, as we have f(1) = 3

So, a + b + c = 3 ... (1)

also, we have f(2) = 8

So, 4a + 2b + c = 8 ... (2)

also, we have f(3) = 15

So, 9a + 3b + c = 15 ... (3)

On solving Eq (1) & (2), we get

3a + b = 5 ... (4)

also, On solving Eq (3) & (2), we get

5a + b = 7 ... (5)

Now, on solving Eq (4) & (5), we get

2a = 2

a = 1

On substituting the value of 'a' in Eq. (5), we get

b = 2

So, the quadratic sequence be f(x) = x² + 2x.

Hence, the Quadratic Sequence f(x) = x² + 2x and the nth term be

n² + 2n.

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The point (0, 1) and (-2.5, 6) is the solution to y = 2x² + 3x + 1 and y = -2x + 1

From the information, we want to solve the system by graphing. y = 2x² + 3 x + 1 and y = - 2 x + 1.

An equation is an expression that is used to show the relationship between two or more numbers and variables.

Given the quadratic and linear equation, y = 2x² + 3x + 1 and y = -2x + 1, the solution is at the intersection of both equations. Here, the intersection point of the equations is the solution of the system i.e. (-2.5,6) and (0,1). Therefore, the point (0, 1) and (-2.5, 6) satisfies this equation.

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The table of values for the total cost is:

# of Rides, x    Total cost, y

0                             $8

1                              $11

2                               $14

3                               $17

4                                $20

5                                $23

The table of values create a linear function. This is because the table of value increases by a constant value.

The total cost is the sum of the amount the carnival charges, the number of rides and the cost per ride.

Total cost = cost to enter + (cost per ride x number of rides)

Total cost for 0 ride = $8 + ($3 x 0) = $8

Total cost for 1 ride = $8 + ($3 x 1) = $11

Total cost for 2 rides = $8 + ($3 x 2) = $14

Total cost for 3 rides = $8 + ($3 x 3) = $17

Total cost for 4 rides = $8 + ($3 x 4 ) = $20

Total cost for 5 rides = $8 + ($3 x 5) = $23

The table of values creates a linear function. This is because the total cost increases by a constant amount.

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38 grams is equal to option d 1.3376 ounces.

Given,

We have to convert 38 grams to ounces

1 gram = 0.0352 ounce

Difference between ounce and gram;

In the United States and a few other nations, i.e., anyplace that is not metric, ounces are the main unit of mass used. It turns out that 1 ounce has a lot more mass than 1 gram if you're wondering how an ounce and a gram compare. In actuality, 28.35 grams are almost equal to 1 ounce.

Here,

1 gram is given as 0.0352 ounce

We have to convert 38 grams

Then,

38 x 0.0352 = 1.3376 ounces

That is,

38 grams is equal to option d 1.3376 ounces.

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Answer:

1.3376

Step-by-step explanation:

i did the 3.06 test and got it right

Answer:

6261

Step-by-step explanation:

it was 6261 because I have to do a i test at

Answer:

7

Step-by-step explanation:

First, we need to get rid of the square root. To do this, square both sides.

(x - 5)^2 = √((x - 3)^2)

x^2 - 10x + 25 = x - 3

Next, continue simplifying

x^2 - 10x + 25 - x + 3 = 0

x^2 - 11x + 28 = 0

(x - 7)(x - 4) = 0

x - 7 = 0         and        x - 4 = 0

x = 7              and        x = 4

Next, plug in these values into the equation

x = 7 ---> 7 - 5 = √(7 - 3)

              2 = √4

              2 = 2

x = 7 is a possible value

x = 4 ---> 4 - 5 = √(4 - 3)

               -1 = √1

x = 4 is an extraneous solution and not a possible value.              

Answer:

7 is the only solution

Step-by-step explanation:

x-5=square root x-3

7-5=square root 7-3

2=square root of 4

2=2

7 is a solution

4-5=square root 4-3

-1= square root of 1

-1=1

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On solving the equations y = (-1/2)x + [tex]4\frac{1}{2}[/tex] and 3x - 4y = 12 graphically , the solution is (6 , 3/2) .

In the question ,

it is given that

the equations are y = (-1/2)x + [tex]4\frac{1}{2}[/tex]  and 3x - 4y = 12

which can be written as y = (-1/2)x + 9/2  and 3x - 4y = 12

to plot the graph of the given equations , we need intercept .

For the equation y = (-1/2)x + 9/2

when x= 0  , y = (-1/2)(0) + 9/2 = 9/2

when y = 0 ,

0 = (-1/2)x + 9/2

(1/2)x = 9/2

x = 9

the points are (0 , 9/2) and (9 , 0)

For the equation 3x - 4y = 12

when x = 0 , 3(0) - 4y = 12

-4y = 12

y = -3

when y = 0 , 3x -4(0) = 12

3x = 12

x = 4

the points are (0,-3) and (4,0) .

after plotting the lines on the graph , we can see that the both the lines intersect at the point (6 , 3/2) ,

Therefore , On solving the equations y = (-1/2)x + [tex]4\frac{1}{2}[/tex] and 3x - 4y = 12 graphically , the solution is (6 , 3/2) .

The given question is incomplete , the complete question is

Consider this equation y = (-1/2)x +  [tex]4\frac{1}{2}[/tex]  and 3x - 4y = 12 .

Solve the system by graphing. label each graph.

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Answer:

This is a complementary angle, which adds up to 90 degrees

8x + 7x = 90

15x = 90

x = 6

Answer:

part A=3x-23=28

part B=17

Step-by-step explanation:

3x-23=28

3x=23+28

3x=51

x=17

value of the slope is 22.3 % per Kg

Charging a single, fixed price for a given service is known as flat rate pricing.

The U.S. Postal Service charges a $21.90 flat rate.

additional $4.90 per kilogram.

slope rate =[tex]\frac{4.90}{21.90} X 100 = 22.3 %[/tex] %

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By the concept of function, the value of g(x) obtained is

g(x) = 3f(x) is the required function

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here, from the graph, it can be seen that

g(1) = 3 and g(-1) = 3

Let g(x) = [tex]kx^2[/tex]

g(1) = 3

[tex]k(1)^2 = 3\\k = 3[/tex]

So g(x) = [tex]3x^2[/tex] = 3f(x) is the required function

Option B is correct

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Complete Question

If f(x) = x², which equation represents function g?

A. g(x)=1/3f(x)

B. g(x)=3f(x)

C. g(x)=f(1/3x)

D. g(x)=f(3x)

The diagram has been attached here

Solving the system of linear inequalities, we get

-4x+3y<15 = (0,5),(-15/4,0)

-6x-4y<12 = (0,-3),(-2,0)

What is a system of linear inequalities?

At least two linear inequalities in the same variables make up a system of a linear inequality in two variables. The graph of a linear inequality is the graph of all solutions to the system, and the solution of a linear inequality is the ordered pair that resolves all inequalities in the system.

Here, we have

Given inequalities

-4x+3y<15 and -6x-4y<12

Now we solve  the system of linear inequalities

For, -4x+3y<15

When we put x= 0, we get

y = 5

and if we put y = 0 , we get

x = -15/4

For, -6x-4y<12

When we put x= 0, we get

y = -3

and if we put y = 0 , we get

x = -2

Hence,  Solving the system of linear inequalities, we get

-4x+3y<15 = (0,5),(-15/4,0)

-6x-4y<12 = (0,-3),(-2,0)

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Answer:

x^(9/7)

Step-by-step explanation:

inverse function f(x) = (x^(1/9))^7 = x^(9/7)

The required, example of being "underwater" on a car is option B, owing $8600 on a car that's worth $8200.

Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.

Here,
Being "underwater" on a car means owning more on a car than it is currently worth.

Based on the given options, the example of being "underwater" on a car is option B, owing $8600 on a car that's worth $8200.

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Answer:

$151.50 deducted

Step-by-step explanation:

Walter used his bank's ATM to withdraw $150. This was the sixth time he used the ATM in June. His bank does not charge for the first five ATM uses each month. After that, the fee is $1.50 for each use. What is the total he should subtract from his balance including fees?

1 charge of $1.50 + withdrawal of $150

= $151.50 deducted

Vertex of the given parabola : (1,-9), Axis of Symmetry: x = 1, Y-intercept : (0, -8), x-intercept(s) :  (-2,0) and (4,0), and Concavity: opens up.

A parabola is a U-shaped curve this is drawn for a quadratic function,

f(x) = ax² + b x + c. The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.

The graph of the parabola is given in the question.

According to the given graph, the required solution would be as:

Vertex of the given parabola : (1,-9)

Axis of Symmetry : x = 1

Y-intercept : (0, -8)

x-intercept(s) :  (-2,0) and (4,0)

Concavity: opens up

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Answer:

x = 16

y = 10

Step-by-step explanation:

x+5y =46 [1]

x-y =-14 [2]

x=-14+y [3]

put [3] into [1],

x+5y =46

-14+y+5y=46

6y = 60

y = 10

put y=10 into [1]

x+5(10)=46

x = 16

Answer:

angles 4 is 88 degrees

Angles 3 is 92 degrees

Step-by-step explanation:

all 3 of angles of a triangle equal 180

47+45=92

180-92=88

Angles 4 is 88 degrees

Now since 3 is on a flat plane next to 4 we subtract 88 from 180 to find angle 3

180-88=92

92 degrees is angle 3

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Answer:

slope=-5; y-int=4

Step-by-step explanation:

The slope-intercept form:

y=mx+b

m=slope b=y-int

y=-5x+4

slope=-5 y-int=4

Answer:

slope = -5; y-int= 4

Step-by-step explanation:

You find the slope by comparing the given equation to y=mx+b where m is equal to the slope.

You find the y-intercept by setting x=0 and solving for y

y=-5(0)+4

y=0+4

y=4

Step-by-step explanation:

y-3=5/3(x+6)

y-3=5/3x+10

y=5/3x+13

No further work can be done.

The required equation in slope-intercept form is given as y = 5/3x + 13.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Slope intercept form is given as y = mx + c, where m is the slope of the line and c is y-intercept of the line.

Here,
Given equation,

y − 3 = 5/3(x + 6)

Following distributive Property
y - 3 = 5/3x + 5/3(6)

Following Simplification,
y - 3 = 5/3x + 5(6/3)
y - 3 = 5/3x + 10

Addition 3 on both sides,
y - 3 + 3 = 5/3x + 10 + 3
y = 5/3x + 13

Thus, the required equation in slope intercept form is given as y = 5/3x + 13.

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Answer: 18

Step-by-step explanation:

The annual percentage yield (APY) is equal to 58.2%.

In Mathematics, annual percentage yield (APY) can be defined as the effective (real) rate of interest that is earned by an individual or business organization on an investment over a period of one year.

Generally speaking, annual percentage yield (APY) is calculated by considering the effect of compound interest. Mathematically, annual percentage yield (APY) can be calculated by using this formula:

Annual percentage yield (APY) = (1 + r/n)^{n} - 1

Where:

Substituting the given parameters into the formula, we have;

Annual percentage yield (APY) = (1 + 0.057/4)^{4} - 1

Annual percentage yield (APY) = (1 + 0.01425)^{4} - 1

Annual percentage yield (APY) = (1.01425)^{4} - 1

Annual percentage yield (APY) = 1.0582 - 1

Annual percentage yield (APY) = 0.0582.

Annual percentage yield (APY) = 58.2%.

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Answer: x = 45 degrees

Step-by-step explanation:

We can see that there is a straight line. A straight line is 180 degrees.

We also see a 90-degree angle. There are 2 angles that equal the same amount.

This gives the equation below:

90 + 2x = 180.

Now, we subtract 90 from both sides.

2x = 90.

Now, we divide both sides by 2.

x = 45.

This means that our final answer is 45 degrees.

A statement which could be a representation of the events for the simulation is: Assign the numbers 1-7 to represent a made goal and the numbers 8-10 to represent a missed goal.

A simulation can be defined as a model which is designed and developed to imitate the operation of an existing (proposed) real-life system or natural phenomenon, in order to enhance the ability to study, analyze, and make informed decisions about it.

Since this soccer player made 67% of her goal attempts last season, the number of goals the player will make out of 10 attempts in a game is given by:

Number of goals = 67/100 × 10

Number of goals = 0.67 × 10

Number of goals = 6.7 ≈ 7 goals.

Therefore, this soccer player would score seven (7) goals while missing three (3) goals. Also, the 7 goals would be represented by 1 - 7 while the missed goals would be represented by 8 - 10.

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