A U.S. Coast Guard Response Boat leaves Charleston, South Carolina at 1:30 p.m. heading due east at an average speed of 20 knots (nautical miles per hour). At 4:30 p.m., the boat changes course to N 18°18°E. At 8:00 p.m. what is the boat's bearing and distance from Charleston, South Carolina? Round all units to the nearest hundredth.
Bearing from Charleston, South Carolina:
Distance from Charleston, South Carolina:

Answer: Add 40 to both sides to collect like terms on each side of the equation

Step-by-step explanation: That's the first step

g(x, y) = f(xy) is a differentiable function.

We'll show that g(x, y) = f(xy) is a differentiable function by finding its partial derivatives with respect to x and y.

Given that f is a differentiable function of r, we know that f'(r) exists for all values of r. Now, let's find the partial derivatives of g(x, y) with respect to x and y:

1. ∂g/∂x:
Using the chain rule, we get ∂g/∂x = (∂f/∂r) * (∂r/∂x). Since r = xy, ∂r/∂x = y. Thus, ∂g/∂x = f'(xy) * y.

2. ∂g/∂y:
Similarly, we get ∂g/∂y = (∂f/∂r) * (∂r/∂y). Since r = xy, ∂r/∂y = x. Thus, ∂g/∂y = f'(xy) * x.

Since both partial derivatives ∂g/∂x and ∂g/∂y exist, we can conclude that g(x, y) = f(xy) is a differentiable function.

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The equation 3+7+2=+2 is actually not true, but false.

The equation 3+7+2=+2 is actually not true, but false. This is because the sum of 3, 7, and 2 is 12, not 2.

In general, an equation is considered true if the expressions on both sides of the equal sign are equivalent in value. In this case, the expressions on the left-hand side (3+7+2) and the right-hand side (+2) are not equivalent, and therefore the equation is false.

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The given ratio 5:11 can be used to describe a relationship between the beads on each necklace. The relationship that this ratio can describe is the relative number of beads of different colors.

Let’s see how this relationship was obtained:

We know that the ratio of 5:11 can be expressed in fraction form as 5/11.

Since there are two different colors of beads, let’s assume that there are 5 beads of one color (let’s call it color A) and 11 beads of another color (let’s call it color B).

Hence, the ratio of 5:11 can describe the relationship between the number of beads of color, A to the number of beads of color B on each necklace.

In other words, the ratio of 5:11 tells us that for every 5 beads of color A, there are 11 beads of color B.

This ratio can be used to describe the relative number of beads of different colors on the necklace.

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According to the graph, the range, which is the set of values that y can take, comes from negative infinite and stops at approximately 2. It means that y will always be greater than negative infinite but less than 2, this represented as inequation is:

Answer:

In counting to a base, when we get to the point where the base integer comes up, we replace by 10, on the first time and by 10 at every other time the integer is about to come up

We now this in base 10 as when we get to 10 we input 10 and so and so till we get to 99 where since we are in base 10 the next number is 100 because that is the highest we can go while in base 11 100 in base is equivalent to 91

So we have for base 5

1 , 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44, 100, 101, 102, 103, 104, 110, 111, 112, 113, 114, 120, 121, 122, 123, 124, 130, 131, 132, 133, 134, 140, 141, 142, 143, 144, 200

We see that on getting to 4 instead of the next digit to be 5 we replace it with 10 because 5 cannot be displayed in base 5

Similarly after 14 is 20 because 5 cannot be displayed at 24 the next number is 30 because 5 cannot be displayed

at 34 the next  40, while at 44 the next is (we could have written 50 but 5 is 10 in base 5 so we write 100) 100

At 144, we note that 44 = 100 + 44, therefore, the next number will be 100 + 44+ 1 = 100 + (45 but 45 = 100 in base 5) 100 so that the next number is 200

Base 2

In base 2 we have;

1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 100111, 101000, 101001, 101010, 101011, 101100, 101101, 101110, 101111, 110000, 110001, 110010

We see that there are no 2s and after 11 we get 100 just like after 99 we get 100 in base 10 and after 44 we get 100 in base 5

So we need to still have an idea of the number system just as we did for base 10

Step-by-step explanation:

Solution of the equation x² -11x -5 =0 using quadratic formula is equal to x = (11 ±√141)/ 2 .

As given in the question,

Given equation is equal to

x² -11x -5 =0

Solving the given equation using quadratic formula we get,

Standard quadratic equation is

ax² + bx + c =0

D = √b² -4ac

D >0 two distinct roots.

Roots given by:

x = ( -b ± √b² -4ac) /2a

Here a = 1 , b= -11, c= -5

D = √ (-11)² -4(1)(-5)

   = √121+20

   =√141 >0

Two distinct roots.

x = (-(-11) ± √141) /2(1)

  = (11 ±√141) /2

Therefore, Solution of the equation x² -11x -5 =0 using quadratic formula is equal to x = (11 ±√141)/ 2 .

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To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.

Looking at the histograms described:

The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.

The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.

The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.

The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.

Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.

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A student drove from her home to the university and get back to her home. The distance of her home and the university is 12 km. Her average speed for the entire trip is:  3.16 km/hours

The relation between speed, distance, and time is given by:

d = v x t

Where:

d = distance

v = speed

t = travelled time

In this problem, the distance of round trip, from her home to university and back home is:

d = 2 x 12 km = 24 km

The time needs to make this round trip = t = 7.6 hours

Hence, the average speed is:

average speed = distance/time

average speed = 24 / 7.6

average speed = 3.16 km/hours

Your question is incomplete. Most likely it was:

A student drove to the university from her home and noted that the odometer reading of her car increased by 12.0 km.

(c) if she drove back home using the same path she took out to the university and arrives 7.6 h after she first left home, what was her average speed for the entire trip, in kilometers per hour?

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Answer:

Step-by-step explanation:

(x - 8)/2 = -5

x - 8 = -10

x = -2

(y + 6)/2 = 10

y + 6 = 20

y = 14

(-2, 14)

Answer:

B

Step-by-step explanation:

step

Answer:

(B). 50°

Step-by-step explanation:

(5x + 55)° = (2x + 100)°

5x + 55 = 2x + 100

5x - 2x = 100 - 55

3x = 45

x = 15

5(15) + 55 = 130°

m∠2 = 180° - 130° = 50°

Answer:

The midpoint of the line segment AB

is at (−1, 0).

Step-by-step explanation:

In a general sense the midpoint formula for a line segment whose endpoints are

\( \sf ( x_1 + x_2) (y_1 + y_2)\)

would be the mean of the abscissa and the ordinate as seen in the formula below:

\( \sf \: (x_m, \: y_m) = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} )\)

When the line segment lies on one axis, then the there would be only one non-zero value in the ordered pair.

Assuming that the line segment AB

is in the x-axis, then the coordinates of the points would be:

\( \sf \: A(−2, 0)B(0,0)\)

To get the midpoint, substitute the points above in the formula for the midpoint:

\( \sf \: (x_m, \: y_m) = ( \frac{x_1 + x_2}{2} , \frac{y_1 + y_2}{2} ) \\ \sf \: = ( \frac{ - 2 + 0}{2} ),0 \\ \sf \: = ( \frac{ - 2}{2} ), 0 \: \: \: \: \: \: \: \: \\ \sf \: ( - 1, 0)\)

The midpoint of the line segment AB

is at (−1, 0).

Answer:

it would be “>”, 100% guaranteed.

Answer:

answer is >

Step-by-step explanation:

hope this is helpful

After 1.8 years, the value equals the amount she paid for the car.

The value will be $ 22,131.10.

To solve the problem, find both the expense equation and depreciation equation.

The exponential depreciation equation will be:

\(y=25,900(1-0.082)^x\)

Where x represents time in years.

The expense equation will be: y=550 x+10,000

Where x represents the number of months that have passed

If x represents time in years in the expense equation, then it determines the yearly payment rather than the monthly payment.

Over the course of the year, Nina will have paid 550(12) or $ 6,600 in car payments.

The new yearly expense equation will be: y=6,600 x+10,000

Where x is time in years.

Use the two equations to find the point of intersection which will give the time she paid for the car and the value paid by her.

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Answer:

-3n⁹

Step-by-step explanation:

= \(\sqrt[3]{-27n^(27)}\)

= \(\sqrt[3]{-27} * \sqrt[3]{n^{27}}\)

= (-3) × n⁹

= -3n⁹

Answer:

√50 is the odd one out.

Step-by-step explanation:

√50 is irrational while the others are rational.

Jutin chooses a function J(x) = 3x - 1 that when he uses the number 7 as an input, then the output is 20.

As per the given data, Jutin chooses a function in which he uses the number 7 as an input, then the output is 20.

Here we have to determine which function Jutin has to use.

Now we have to substitute the value that x = 7 in all the given functions.

First function:

F(x) = 2\(x^{5}\)

F(7) = 2 \((7)^{5}\)

F(7) = 2 (16807)

F(7) = 33614 which is not equal to 20.

Second function:

G(x) = \(x^{2}\) - 19

F(7) = \((7)^{2}\) - 19

F(7) = 49 - 19

F(7) = 30 which is not equal to 20.

Third function:

H(x) = 13 - x

H(7) = 13 - 7

H(7) = 6 which is not equal to 20.

Fourth function:

J(x) = 3x - 1

J(7) = 3(7) - 1

J(7) = 21 - 1

J(7) = 20

The correct function is J(x) = 3x - 1

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Answer:

aa

Step-by-step explanation:

aa

Answer:

x^2 -12x+36

Step-by-step explanation:

(x - 6)^2

(x-6)(x-6)

FOIL

x^2 - 6x-6x+36

Combine like terms

x^2 -12x+36

Answer:

we conclude that:

Step-by-step explanation:

A dilation is a transformation which generates an image that is the same shape as the original object but in a different size.

The image can be obtained by multiplying the measure of the original object by a scale factor.

If the scale factor > 1, the image is stretched

If the scale factor < 1, the image is reduced

If the scale factor = 1, the image and object will be congruent

For example, if we multiply the measure of the coordinates of the vertex A(2, 2) of a triangle by a scale factor of 2, the image A' is stretched as the scale factor > 1.

Dilation with scale factor 2, multiply by 2.

A(2, 2) → (2(2), 2(2)) = A'(4, 4)

So, the image point A'(4, 4) is enlarged.

Dilation with scale factor ½, multiply by ½.

A(2, 2) → (2(1/2), 2(1/2)) = A'(1, 1)

So, the image point A'(1, 1) is reduced.

Therefore, we conclude that:

The new total bill including the tip of 15% is $59.01.

To find the amount of the tip, we can multiply the total bill by the percentage as a decimal:

tip = 0.15 * $51.31 = $7.70

To find the new total including the tip, we can add the tip to the original bill:

new total = $51.31 + $7.70 = $59.01

So the new total, including a 15% tip, will be $59.01.

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The parabola's vertex is located at (-2, 8). The parabola's graph is then depicted below.

Let a be the leading coefficient and the parabola's vertex be the point (h, k). The parabola's equation will therefore be stated as,

y = a(x - h)² + k

The parabola's equation is stated as,

y = -(x + 2)² + 8

The downward-pointing parabola is represented by the negative sign.

The vertex of the parabola is at (-2, 8), according to the equation above. The parabola's graph is then depicted below.

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Answer:

m<E = 1/2 ( WP - KA )

m<E = 1/2 ( 162 -56 )

m<E = 1/2 (106)

m<E = 53

Answer:

1: The ladder

2:                                        

3:                              

Step-by-step explanation:

It takes approximately 18.001 seconds (or approximately 18 seconds) for the bike traveling at 20 km/h to cover a distance of 100 meters.

To determine how many seconds, it takes for a bike traveling at 20 km/h to cover a distance of 100 meters, we need to convert the speed from kilometers per hour to meters per second and then calculate the time.

First, let's convert the speed from kilometers per hour to meters per second.

1 kilometer is equal to 1000 meters, and 1 hour is equal to 3600 seconds.

Speed in meters per second = (20 km/h) * (1000 m/km) / (3600 s/h)

Calculating:

Speed in meters per second = (20 * 1000) / 3600 ≈ 5.556 m/s

Now that we have the speed in meters per second, we can calculate the time it takes to travel 100 meters using the formula:

Time = Distance / Speed

Time = 100 m / 5.556 m/s

Calculating:

Time ≈ 18.001 seconds

Therefore, it takes approximately 18.001 seconds (or approximately 18 seconds) for the bike traveling at 20 km/h to cover a distance of 100 meters.

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If the discriminant is negative, then neither of the solutions is a real number.

Since the discriminant is a negative number 7, then there is/are no real solutions to the quadratic equation.