A cruise ship maintains a speed of 22 knots (nautical miles per hour) sailing from San Juan to Barbados, a distance of 600
nautical miles. To avoid a tropical storm, the captain heads out of San Juan at a direction of 28° off a direct heading to
Barbados. The captain maintains the 22-knot speed for 15 hours, after which time the path to Barbados becomes clear of
storms.

(a) Through what angle should the captain turn to head directly to Barbados?

(b) Once the turn is made, how long will it be before the ship reaches Barbados if the same 22-knot speed is maintained?

(round to one decimal place)

The results of the division between the two functions are listed below:

a) (h / g) (- 1) = - 1 / 15

b) x = 7 / 8 is not in the domain of (h / g) (x).

Herein we have two functions h(x) and g(x), the former is a quadratic equation and the latter is a linear equation and the division between the two functions is described below:

(h / g) (x) = h(x) / g(x), for all x such that g(x) ≠ 0

If we know that h(x) = 2 · x² - 3 and g(x) = - 8 · x + 7, then the division between the two functions is:

(h / g) (x) = (2 · x² - 3) / (- 8 · x + 7)

Now we evaluate the function at x = - 1:

(h / g) (- 1) = [2 · (- 1)² - 3] / [- 8 · (- 1) + 7]

(h / g) (- 1) = (- 1) / 15

(h / g) (- 1) = - 1 / 15

To determine the value of x such that does not belong to g(x), we need to solve the following expression:

g(x) = 0

- 8 · x + 7 = 0

8 · x = 7

x = 7 / 8

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You travel from the United States to Spain if and only if you have a passport. When both sides of a biconditional statement have the same truth value, the statement is said to be true.

What does a biconditional mean?

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You travel from the United States to Spain if and only if you have a passport. When both sides of a biconditional statement have the same truth value, the statement is said to be true.

When both sides of a biconditional statement have the same truth value, the statement is said to be true. A double-headed arrow indicates the biconditional operator. If both the initial conditional assertion and the opposite statement are true, a statement is said to be biconditional.

"An A is guaranteed if you receive a perfect score on the final." ... Last but not least, it is a widely recognized principle that the conditional and biconditional operators have. A statement is logically true if it cannot logically be wrong. If a sentence can be expressed in the form "P if and only if Q," it is a biconditional assertion.    

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Answer:

SAS, ASA, SSS, ASA, Yes

Step-by-step explanation:

The system of equations does not have any solutions since the values on both sides of the final expression are different and the lines will not cross.

A system of equations, usually referred to as an equation system, is a collection of finite equations for which common solutions are sought.

Given the system of equations below;

x + 2y = 4............ 1

3x + 6y = 18 ........... 2

From equation 1:

x = 4 - 2y .........3

Substitute equation 3 into 2 to have:

3(4 - 2y) + 6y = 18

3(4) - 3(2y) + 6y = 18

12 - 6y + 6y = 18

12= 18

Since the values on both sides of the resulting expression is different, hence the given system of equation has NO solutions showing the lines  will not cross on the graph.

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The distance Manatee will swim in 5 hours is 25 miles.

Distance can be defined as the length between two points.

To calculate the distance manatee can swim in 16 hours, we use the equation below

Make y₂ the subject of the equation

Where:

Substitute these values into equation 2

Hence, manatee can swim a distance of 25 miles.

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Complete question: A manatee can swim an average of 10 miles every 2 hours how far can it swim in 5 hours. Assume the distance y in miles is proportional to the number of hours x the manatee swam.

Answer:

in the picture

Step-by-step explanation:

hope it helped

Answer: He should shade 3 and leave 4 unshaded.

Step-by-step explanation:

The measure of the exterior angle x of the polygon is x = 105°  .

In the question ,

it is given that ,

in the figure, the measure of external angles are 75° , 90° , 90° and x .

we know that By Polygon Exterior Angle Sum Theorem states that the sum of measure of all exterior angle of a polygon is 360° ,

So , 75° + 90° + 90° + x = 360°

75° + 180° + x = 360°

255° + x = 360°

Subtracting 255 from both the sides , we get

x = 360° - 255°

x = 105°

Therefore , The measure of the exterior angle x of the polygon is x = 105°  .

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After differentiation of function with respect to y, the value of y'(1) is 0.225.

In the given question we have to find the value of derivative of y at 1.

The given function is [tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]

To find the derivative of y at 1 we have to firstly derivate the given function with respect to y.

Now writing the given function in the y form

[tex]\frac{x^2}{36}+\frac{y^2}{64}=1[/tex]

Subtract x^2/36 on both side, we get

[tex]\frac{y^2}{64}=1-\frac{x^2}{36}[/tex]

Multiply by 64 on both side, we get

[tex]y^2=64-64\times\frac{x^2}{36}[/tex]

[tex]y^2=64-\frac{16x^2}{9}[/tex]

Differentiating with respect to y on both side

[tex]2y\frac{dy}{dx}=0-\frac{16\times2x}{9}[/tex]

[tex]2y\frac{dy}{dx}=\frac{32x}{9}[/tex]

Simplifying

dy/dx = 16x/9y

We can write dy/dx as y' so

y' = 16x/9y

We have to find the value of y'(1).

Since the y is the function of x so we put x=1 and we know y(1)=7.89, so

y'(1) = 16*1/9*7.89

y'(1) = 16/71.01

y'(1) = 0.225

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The like terms in the expression are -8x^2,-10x,14 and -6. The like terms are 14 and -6

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 5x + y, the two terms are 5x and y.

In the expression 14-8x^2-6-10x, there are 4 terms in it: 14, -8x^2, - 6, - 10x.

out of the four terms only two are alike because of they are both constant. This like terms are -6 and 14.

10x and -8x^2 are unlike terms because x^2 is a different term from 10x.

Therefore the like terms are -6 and 14

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An equation that models the relationship between the amount of time taken by Rick's bus ride and Matt's bus ride is M = t/3 + 3, which is shown in the graph attached below.

In order to write this equation, we would assign variables to the amount of time taken by Matt's bus ride and Rick's bus ride to school respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation as follows;

Matt's bus ride Time = 3 minutes more than 1/4 the time of Rick's bus ride

M = (1/4 × t) + 3

M = t/3 + 3

Based on the graph shown in the image attached below that models the relationship between the amount of time taken by Rick's bus ride and Matt's bus ride, we can reasonably and logically deduce that the y-intercept is equal to 3 and the slope of the graph is equal to 1/4.

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The function which is representative of the transformation of the parent function f(x) = log4x by reflecting it over the x-axis, stretching it vertically by a factor of two, and shifting it up five units is g(x) = -2log4(x) + 5. Option C is correct.

The reflection over the x-axis is given by the transformation:

f₁(x) = - f(x)

Therefore, the first step we get is:

f₁(x) = - log(4x)

Stretching by a factor n along the y-axis is given by the transformation:

f₂(x) = n · f₁(x)

Therefore, we will get:

f₂(x) = -2 · log(4x)

Shifting a function up of a quantity n is given by:

f₃(x) = f₂(x) + n

Therefore, we will get:

f₃(x) = -2 · log(4x) + 5

So,

g(x) = -2 log4(x) + 5

Thus, the function which is representative of the transformation of the parent function f(x) = log4x by reflecting it over the x-axis, stretching it vertically by a factor of two, and shifting it up five units is g(x) = -2log4(x) + 5. Option C is correct.

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Answer:

m∠X=75.75

Step-by-step explanation:

A triangle's angles combine to 180 degrees. Subtract 62.45+41.8 from 180.

The measure of the exterior angle of the triangle is given by ∠A = 104.25°

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ΔXYZ

Let the measure of the exterior angle be m∠A

Now , the measures of the angles of the triangle are

The measure of angle ∠Y = 62.45°

The measure of angle ∠Z = 41.8°

The measure of angle ∠X = m∠X

Now , for a triangle , the sum of the interior angles = 180°

So ,

m∠X + m∠Y + m∠Z = 180°

Substituting the values in the equation , we get

m∠X + 62.45° + 41.8° = 180°

Subtracting 104.25 on both sides of the equation , we get

m∠X = 75.75°

Now , the measure of angle exterior to m∠X be ∠A = 180° - m∠X

The measure of m∠A = 180° - 75.75°

The measure of m∠A = 104.25°

Therefore , the measure of ∠A = 104.25°

Hence , the exterior angle of the triangle is ∠A = 104.25°

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Coordinate of circumcenter of the given triangle = (3, 2)

What is circumcenter of a triangle?

Circumcenter of a triangle is the point of intersection of the perpendicular bisectors of every sides of the triangle.

Let the coordinate of circumcenter be (x , y)

Distance of Circumcenter from (4,2) =

[tex]\sqrt{(x - 4)^2 + (y-2)^2[/tex]

Distance of Circumcenter from (3, 3) =

[tex]\sqrt{(x - 3)^2 + (y-3)^2[/tex]

Distance of Circumcenter from (2,2) =

[tex]\sqrt{(x - 2)^2 + (y-2)^2[/tex]

By the problem,

[tex]\sqrt{(x - 2)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 2)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 4x + 4 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\6x - 4x +6y -4y = 18-8\\2x +2y = 10\\x+ y = 5\\[/tex]..... (1)

Again,

[tex]\sqrt{(x - 4)^2 + (y-2)^2} = \sqrt{(x - 3)^2 + (y-3)^2}\\(x - 4)^2 + (y-2)^2} = (x - 3)^2 + (y-3)^2}\\x^2 - 8x + 16 + y^2 -4y + 4 = x^2 -6x + 9 + y^2-6y + 9\\8x - 6x +4y -6y = 20-18\\2x -2y = 2\\x- y = 1\\[/tex]...... (2)

Adding (1) and (2)

[tex]2x = 6\\x = \frac{6}{2}\\x = 3[/tex]

Putting the value of x in (1),

3 + y = 5

y = 5 - 3

y  = 2

Coordinate of circumcenter = (3, 2)

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The slope between points (17,8) and (17,24) is (B) undefined.

We know that the slope of a line passing through two points (a,b) and (c,d) is given by,

m = (d-b)/(c-a)

So here given points are (17,8) and (17,24)

Then, a=17, b=8, c=17, d=24

Now the slope between these two points is given by,

m = (24-8)/(17-17) = 16/0

So the slope value does not exist or infinity.

Hence the slope between the points (17,8) and (17,24) is Infinity or undefined.

Thus, the correct option is (B).

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Answer:

[tex]x=\frac{(y-h)^{2} }{g^{2} }[/tex]

Step-by-step explanation:

       [tex]y=g\sqrt{x} +h\\\\[/tex]

[tex]-g\sqrt{x} =h-y[/tex]

    [tex]\sqrt{x} = -\frac{h-y}{g}[/tex]

    [tex]\sqrt{x} =\frac{y-h}{g}[/tex]

   ∴ [tex]x=\frac{(y-h)^{2} }{g^{2} }[/tex]

the area of the original square garden is 80 square meters.

Let the side of the original square be a. We are given that the area of the new garden was (a - x)(a + x) = a² - x² = 64.

We want to find the area of the original square, so the value of a².

(1) The area of the new garden was 80 percent of the area of the original square garden --> 64 = 0.8a² --> a² = 80. Sufficient.

(2) x = 4 --> a² - 4² = 64 --> a² = 80. Sufficient.

the area is the quantity that expresses the quantity of a location on the aircraft or on a curved surface. The place of an aircraft region or plane vicinity refers back to the location of a form or planar lamina, at the same time as floor area refers to the place of an open surface or the boundary of a 3-dimensional object. location may be understood as the quantity of fabric with a given thickness that might be vital to style a model of the form, or the amount of paint necessary to cowl the surface with an unmarried coat. it's by far the two-dimensional analog of the duration of a curve (a one-dimensional idea) or the volume of a strong (a three-dimensional concept).

place plays a vital position in current mathematics. further to its apparent importance in geometry and calculus, the place is associated with the definition of determinants in linear algebra and is a simple asset of surfaces in differential geometry. In analysis, the vicinity of a subset of the plane has defined the use of the Lebesgue measure, though no longer every subset is measurable. In the trendy, region in better mathematics is visible as a unique case of quantity for two-dimensional regions.

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The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system.

What ordered pair is a solution to the system of linear equations?

An equation is said to linear when it is in ax+ by = c form where a , b and c are real numbers . System of linear equation consist of a set of two or more equation with same variables. such as ,

a₁ x + b₁ y = c₁

a₂ x + b₂ y = c₂

A solution to a linear system is an ordered pair (x ,y) that solves both the equations .

To check that an ordered pair is a solution ,we have to substitute the corresponding values of our variables (x ,y) into our equations and see if they satisfy both the equations.

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Answer:

Step-by-step explanation:

Between 9 and 10.

Why?

Because sq of 9 is 81 and sq of 10 is 100 which gives us the gesture that sq.rt of 84 is between 9&10.  

Hence, Two integers are 9 and 10.

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Answer:

90 degrees

Step-by-step explanation:

The question asks for the temp after an hour and a half. This is the same as 90 minutes. With this, you plug 90 in for t.

This is what it looks like:

T(t)=69e^-0.0174(90) + 76

Then you solve for T(t)

T(t)=69e^-1.566 +76

T(t)=69(0.2088) +76

T(t)=14.41265 +76

T(t)=90.41265

Then round to 90 degrees

The distance between the two cities, Ottawa and Toronto, as determined by Greg and Max is 280.37 miles.

What is a Speedometer?

What is Distance?

How is Distance Calculated?

The distance between two locations can be calculated using the formula,
d = s x t,------ (1)

where [tex]d[/tex] is the distance travelled, [tex]s[/tex] is the average speed, and [tex]t[/tex] is the total time.

In the given question, it is given that Greg and Max travel from Ottawa to Toronto with an average speed of 40 mph and 30 mph for the return trip.

So, [tex]s_{1}=40 mph[/tex] and [tex]s_{2}=35mph[/tex].

The total travelling time for the round trip, T = 15h  ------(2)

Let the distance from Ottawa to Toronto be x.

From (1), we get that, the formula for the time taken is,

[tex]t=\frac{d}{s}[/tex]

So, the time taken to travel from Ottawa to Toronto,

[tex]t_{1} =\frac{d}{s_{1} } \\\implies t_{1} =\frac{x}{40}[/tex]      ------- (3)

And, the time taken for the return trip (back from Toronto to Ottawa),

[tex]t_{2} =\frac{d}{s_{2} } \\\implies t_{2} =\frac{x}{35}[/tex]      --------(4)

Here, the total time travelled from the round trip is equal to the sum of the time taken to travel from Ottawa to Toronto and back from Toronto to Ottawa.

T = t_1 + t_2------(5)

Substituting the values of (2), (3), and (4) in (5), we get

15 = x/40 + x/35
--> 15 = 0.0535x

Simplifying,

x = 15/0.0535
--> x = 280.37 miles

Therefore, the distance between the two cities as determined by Greg and Max is equal to 280.37 miles.

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Answer:

1 and 3

Step-by-step explanation:

where the dots on the graph are, you can read that in 5 minutes, 3 pages are edited. in 10 minutes, 6 pages.
so statement 1 is correct.
when every 10 minutes 6 pages are edited, divide both by 10 to get what is edited per minute. -> 6/10 pages are edited per minute.

Three Expression equivalent to 12x + 8 are,

                  4 ( 3x+2 ) ,  12 (x + 2/3) ,    8 (2x/3 + 1)      

Equivalent expressions:

                                        Equivalent expressions are expressions that work the same even though they look different.

                                                                                    If two or more algebraic expressions are equivalent, then all expressions will give the same value if we put different value of variable.

Here,

         given expression is "  12x + 8 "

               we have to write three equivalent expression to 12x + 8

a.

       If we take 4 common we will get,

                      12x + 8 = 4 ( 3x+2 )

    so,

       one of the expression equivalent to 12x + 8  is 4 ( 3x+2 )

b.

     If we take 12 common then,

                   12x + 8 = 12 (x + 8/12)

                                = 12 (x + 2/3)

      one of the expression equivalent to 12x + 8  is 12 (x + 2/3)

c.

  If we take 8 common then,

                   12x + 8 = 8 ( 12x/8 + 1)

                                = 8 (2x/3 + 1)

    one of the expression equivalent to 12x + 8  is 8 (2x/3 + 1)

Hence,

           Three Expression equivalent to 12x + 8 are,

                   4 ( 3x+2 ) ,  12 (x + 2/3) ,    8 (2x/3 + 1)    

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the length of each rope would be 4.9 inches.

One of the four fundamental operations in mathematics is division; the other three are addition, subtraction, and multiplication. Simply put, division is the process of dividing a large group into smaller ones so that each group has the same number of items. In mathematics, it is a procedure for equal sharing and grouping.

Callies has a rope of length = 14.7 inches,

she cut the rope into pieces = 3

let 'x' be the length of each rope,

if each piece is of the same length, the length of the original rope would be 3x.

this implies, 3x = 14.7 inches,

x = 4.9 inches.

therefore, the length of each rope would be 4.9 inches.

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(complete question)

Callie has a rope that is 14.7 inches long. She cut the rope into 3 pieces. If each piece is the same length, how long is each piece of rope?

The answer is [tex]a^{-3}=\frac{1}{x^{3} }[/tex]

Exponent

An exponent is a number that has a power. In numbers with exponents, there are several rules. This rule is used to calculate the exponents operation.

The rules are, including:

[tex]a^{m}a^{n}=a^{m+n} \\\frac{a^{m} }{a^{n} }=a^{m-n}\\( a^{m}) ^{n}=a^{mn}\\ (ab)^{m}= a^{m}b^{m} \\\frac{a}{b} ^{m}=\frac{a^{m} }{b^{m} } \\a^{-m}=\frac{1}{a^{m} }\\ \sqrt[n]{a^{m} } =a^{\frac{m}{n} }[/tex]

From the properties rules, the rules that can be used in the problem are

[tex]a^{-m}=\frac{1}{a^{m} }[/tex]

From the properties above, it can be concluded that negative exponents mean one per number to that power. Do not reverse with the cube root, where the cube root the one per is the power, not the base number.

If the question is asked [tex]a^{-3}[/tex]

then it can be directly substituted in the rule above.

With that rule, let's find the number that equivalent with [tex]4^{-3}[/tex].

[tex]a^{-3}=\frac{1}{x^{3} }[/tex]

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Answer:

$124.80

Step-by-step explanation:

$58.23 + $66.57 = $124.80

Step-by-step explanation:

you take the specific number (males prefer cycling = 0.22) and the fitting total.

note there are 2 possibilities for that total :

all males

all people preferring cycling

the way it was phrased I would say the reference is all males.

the conditional relative frequency is then

0.22 / 0.54 = 0.407407407... ≈ 0.41

but if the meaning would be rather about how many of all people preferring cycling are male, then we would have

0.22 / 0.37 = 0.594594595... ≈ 0.59

both results are in your answer options.

I think the intended result is 0.41, because I understand the problem that way :

find the conditional relative frequency that a student athlete surveyed prefers cycling, given that the student is male.

the other should be phrased like

find the conditional relative frequency that a student athlete surveyed is male, given that the student prefers cycling.

If they have 50 plants growing in the garden. The number of vegetable plants they have is :20.

Using this formula to find the number of vegetable plants

Number of vegetable plants = Percentage of vegetable plants  × Number of plants in the garden

Let plug in the formula

Number of vegetable plants = 40% × 50

Number of vegetable plants = 20

Therefore the number of vegetable plants is 20.

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Step-by-step explanation:

55/12

hope this helps:)

Makayla spend $29.87 if he was in the river for 4(1/2) hours.

Given, Makayla rents a kayak.

She pays a rental fee of $12.99 plus $3.75 for each hour that he spends in the water.

Now, we have to find that how much did she pay if she was in the river for 4(1/2) hours.

Let the no. of hours in the water be, x

So, Rental fee = 12.99 + 3.75x

As, she was in the water for 4(1/2) hours i.e. 9/2 hours

the rent will be = 12.99 + 3.75(9/2)

Rent = 12.99 + 1.875(9)

Rent = $29.865

Hence, Makayla spend $29.87 if he was in the river for 4(1/2) hours.

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