A ship sails at a speed of 36 nautical miles per hour due east. An hour later it changes its direction to N 32° E and continues at the same speed and direction for a half hour. At this point, what are the ship's distance and direction of bearing from the starting point? Round your answers to the nearest hundredth:
The ship is____________ nautical miles from the starting point at a directional bearing of N _______ ° E.

To find the measure of angle G in triangle FGH, we can use the fact that the sum of angles in a triangle is always 180 degrees.

First, we can find the measure of angle H using the fact that the sum of angles in a triangle is 180 degrees:

H = 180 - F - G

H = 180 - 72 - G

H = 108 - G

Next, we can use the Law of Cosines to find the length of side FG:

FG^2 = GH^2 + FH^2 - 2(GH)(FH)cos(F)

FG^2 = 8^2 + 13^2 - 2(8)(13)cos(72)

FG^2 = 169.21

FG ≈ 13.01 ft

Finally, we can use the Law of Cosines again to find the measure of angle G:

cos(G) = (FG^2 + GH^2 - FH^2) / (2(FG)(GH))

cos(G) = (169.21 + 64 - 169) / (2(8)(13))

cos(G) = 0.7686

G ≈ 40.6 degrees

Therefore, the measure of angle G in triangle FGH is approximately 40.6 degrees.

ΔPQR has:  PM is a median

So: MR = QM = 3 cm

ANSWER:  MR = 3 cm

Ok done. Thank to me :>

We are given the equation of a parabola. Let's remember the general form for this equation:

The given equation is:

Therefore, the coefficients are:

Now we will rewrite the equation to the form:

First we will change the equation in the following way:

Now we can factor:

since the term (x+5)^2 is multiplied by a positive constant, this means that the parabola opens up.

The vertex of the parabola is the point (h,k), in this case, we have:

The axis of symmetry for a parabola is x = h, therefore, the axis of symmetry for this parabola is:

The y-intercept is the point where x = 0, therefore, making x zero in the equation we get:

Therefore the y-intercept is y = 8.

The equation of the linear function is y=8x+(-8).

What do you mean by equation?

A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.

According to data in the given question,

We have points (0,-8) and (1,0), thus

\(m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\=\frac{(0-(-8))}{1-0} \\=8\)

Then

y=8x+b

Points (0,-8) means that when x=0, y=-8 and we use this to find b,

y=8x+b

-8=8(0)+b

-8=0+b

b=-8

So, y=8x+(-8)

Therefore, the equation of the linear function is y=8x+(-8).

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Answer:

C) 4

Step-by-step explanation:

1 + x/2 = 3

x/2 = 2

x = 4

The value of x is 4.

Start with 4. Half of 4 is 2. Add 1. You get 3. 4 makes the problem work, so 4 is the answer.

Answer: C) 4

Answer:

✔️ <1 and <3 => Vertical angles

✔️<2 and <6 => alternate exterior angles

✔️<2 and <4 => corresponding angles

✔️<3 and <7 => alternate interior angles.

✔️<4 and <3 => consecutive interior angles.

✔️<7 and <6 => linear pair angles.

Step-by-step explanation:

✔️ <1 and <3 are opposite angles formed when two straight lines intersect. They both share the same vertex. Thus, they are vertical angles, which are congruent to each other.

<1 and <3 are vertical angles.

✔️<2 and <6 are alternate exterior angles.

<2 and <6 both lie outside the straight lines cut across by the transversal, and they also lie in the side of the transversal alternating each other

✔️<2 and <4 are corresponding angles.

They both take the same position on the same side of the transversal.

✔️<3 and <7 are alternate interior angles.

They are alternating angles along the transversal that are located just within the two lines intersected by the transversal.

✔️<4 and <3 are consecutive interior angles.

They are angles on the same side of the transversal but lie within the two straight lines intercepted by the transversal.

✔️<7 and <6 are linear pair angles.

They are angles on a straight line, and sum up to 180°.

Answer:

I do believe it is C

Step-by-step explanation:

since 6,5 + 2.4 = 8, 9

Answer:

f(-3) = 4

Step-by-step explanation:

f(-3) = 3-2-(-3)

f(-3) = 3-2+3

f(-3) = 4

Answer:

it was skewed to the right

Step-by-step explanation:

i just answered the quistion and D was not the answer

Answer:

  (x, y) = (1120, 700)

Step-by-step explanation:

You want the number of discount (x) and premium (y) tickets to be sold so that a total of 1820 tickets are sold for $40 and $45, respectively, and they generate revenue of $76,300.

The equations reflect the relationships stated in the problem:

  x + y = 1820 . . . . . . the total number of tickets sold is 1820

  40x +45y = 76,300 . . . . . total sales must be $76,300

It usually works well to substitute for the variable representing the lower-price tickets:

  40(1820 -y) +45y = 76300 . . . . . . substitute for x using the first equation

  5y = 3500 . . . . . . . . . . . . . . subtract 72800, simplify

  y = 700 . . . . . . . . . . . . divide by 5

  x = 1820 -700 = 1120

The numbers of tickets of each type sold are (x, y) = (1120, 700).

The answer would be 0.25.

The symbol √ is called the radical symbol or the square root symbol. It is used in mathematics to represent the square root of a number. For example, the square root of 25 is represented as √25, which equals 5. Similarly, the cube root of a number can be represented using the radical symbol with a small 3, such as ∛27, which equals 3.

In mathematics, a fraction is a number that represents a part of a whole or a collection. It is written as one integer divided by another integer, with a horizontal line between them. The number on the top is called the numerator, and the number on the bottom is called the denominator. Fractions can represent numbers less than one, such as 1/2 or 3/4, or numbers greater than one, such as 5/3 or 7/4. They are used in many everyday situations, such as measuring quantities, dividing food, or expressing probabilities.

First, we simplify the term inside the square root:

√25 = 5

So, 6 - √25 = 6 - 5 = 1

Now we can substitute in the expression:

(6 - √25) / 4 = 1 / 4 =0.25

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Answer:

Top right

Step-by-step explanation:

4x7=28

The model on the top left shows that Caleb saw 4 more meteors, 7 times.

Answer:

the bottm left

i did the i ready

Step-by-step explanation:

Answer:

A) 11.25

Step-by-step explanation:

6x+2x=90

8x=90

x=90÷8

x=11.25

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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The expression 2√2 is equivalent to 2.83.

A radical, or root, is the mathematical opposite of an exponent, in the same sense that addition is the opposite of subtraction. Mathematically -

\($\underbrace{\sqrt[n]{x} \times \sqrt[n]{x} \times \dots}_{n \text{ times}} = x\)

Given is the expression as -

2√2

We can write -

2√2 = 2\($(2)^{\frac{1}{2}}\)

2√2 = 2 x 1.414

2√2 = 2.83

Therefore, the expression 2√2 is equivalent to 2.83.

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Answer:

x ≈ 1.64 m

y ≈ 3.09 m

So to find the area of floor space we need to know the sides..

So we dont know the side and so to find the side of the cube we need to- (see the above pic)

So by doing this we get 12 as the side...

Now we need to know the area of floor space(as the shape is square) so area is s²= 12×12=144

So therefore area is 144cm² (of floor space)

Note that the limit of the expression as x approaches infinity is 1/2.

start by multiplying both the numerator and denominator by the conjugate  expression

√ (x ² - 9x + 1) + x,

this will eliminates the root in the numerator

lim x->∞ [(√(x ² - 9x + 1) - x)  * (√(x² - 9x + 1) + x)] / (√(x² - 9x + 1) + x)

Expanding the numerator

lim x- >∞ [(x² - 9x + 1) - x^2] / (√(x² - 9x + 1) + x)

Simplifying further:

lim x->∞ [(1 - 9/x + 1/ x²)] / (√(1 - 9/x + 1 /x²) + 1)

we can see that the 1/x ² term approaches zero, and the expression simplifies to

lim x->∞ [(1 - 0)]  / (√(1 - 0) + 1)

= 1/2

So it is correct to state that the limit of the expression as x approaches infinity is 1/2.

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The true statement on the height of the ball when thrown from a building, given the equation, can be found to be A. The ball reaches the ground in 3 seconds.

The equation given of the ball being thrown from a building, gives us the height when solved.

The height of the ball when it reaches the ground is 0 feet so we can insert this in the formula to find the time:
0 = - 5 ( t - 3 ) ( t + 5 )

We can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. So, we can set each factor equal to zero and solve for t:

t - 3 = 0 or t + 5 = 0

Solving for t in the first equation, we get:

t - 3 = 0

t = 3

Seeing as t is 3 seconds the first option is correct.

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The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

n = 4

Step-by-step explanation:

We are given the equation 7n - 2 = 5n + 6, ans we want to solve it for n.

To do this, we need to isolate n one one side.

Let's start by adding 2 to both sides.

7n - 2 = 5n + 6

   +2           +2

_______________

7n = 5n + 8

Now, subtract 5n from both sides.

7n = 5n + 8

-5n   -5n

_______________

2n = 8

Divide both sides by 8 to get the value of n.

2n = 8

÷2   ÷2

________

n = 4

Answer:

I think it's b

Step-by-step explanation:

Answer:

None

Step-by-step explanation:

By using the equation a^2 +b^2=c^2 we can see if it will work.

Substitute a for 6 and b for 2 to get 6^2+2^2=40

when you \(\sqrt{40}\) you don't get 7 therefore you cant make any triangles

Answer:

Step-by-step explanation:

Answer:

(1, -1)

Step-by-step explanation:

To convert polar to rectangular coordinates, use these identities:

Here we were given the point \((\sqrt{2},-\frac{\pi}{4})\) which is our (r, Ф) point

We can now plug these values into our x and y equations to convert to rectangular and find our (x, y) point

So our (x, y) point is (1, -1)

The time it takes for the volume to change when each edge is 10 centimeter would be = 3.3sec

A cube is a type of solid shape that has six number of faces, eight number of vertices and twelve number of edges.

The cube with edges of 3 cm = 1 second

When the cube has edges of 10 cm = X seconds

Make X seconds the subject of formula;

X seconds = 10 × 1/3

X seconds= 3.3sec

Therefore, it will take 3.3 secs for the volume to change when each edge is 10 centimeter.

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Answer:

Three hundred eighty two

Step-by-step explanation:

Answer:

in 18 mins it would be 6 pages and in 6 mins it would be 1 page