A man on the deck of a ship observes that the angle of elevation on the top of the cliff is 40° find the distance between the man and the cliff if the cliff is 50 m high

By setting y = 0 and factoring, we can determine the roots of other polynomial functions. Because there is only one value of x for which x - 3 = 0 and no values of x for which x2 + 3x + 9 = 0.

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

By setting y = 0 and factoring, we can determine the roots of other polynomial functions. Because there is only one value of x for which x - 3 = 0 and no values of x for which x2 + 3x + 9 = 0, the equation y = x3 -27 = (x - 3)(x2 +3x2 + 9) has only one root (x = 3). (the discriminant is negative).

To know more about polynomials visit:

https://brainly.com/question/11536910

#SPJ4

The value of the number in the statement is 8

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

A mathematical statement represented as

Five times the difference of twice a number and three is twenty-five

Represent the number with x

So, we have

Five times the difference of twice x and three is twenty-five

When represented as an equation, we have

5(x - 3) = 25

Divide both sides by 5

This gives

x - 3 = 5

Add 3 to both sides

x = 8

Hence, the number is 8

Read more about word problem at

https://brainly.com/question/1781657

#SPJ1

Answer: i’m the biggest bird

Step-by-step explanation:

i’m the biggest bird

A Riemann sum is a method used to approximate the definite integral of a function. A definite integral is a measure of the area between a function and the x-axis over a certain interval. The Riemann sum formula is used to approximate this area by breaking up the interval into a number of subintervals (or "rectangles") and summing the areas of each rectangle. The formula for a Riemann sum is given by:

∑ f(x_i) * Δx

where f(x) is the function being integrated, x_i is the right endpoint of the i-th subinterval, Δx is the width of the subinterval, and the sum is taken over all the subintervals.

The Riemann sum formula is defined with a limit, as the number of subintervals approaches infinity and the width of subintervals approaches zero, the Riemann sum formula becomes the definite integral.

There are different ways to calculate Riemann sum, such as Left Riemann Sum, Right Riemann Sum, Midpoint Riemann Sum, and Trapezoidal Riemann Sum, each one of them has different ways to calculate x_i, thus leading to different results, but all of them approach the definite integral as the number of subinterval increases.

Learn more about Riemann sum here: https://brainly.com/question/30184175

#SPJ4

A 5 cm pentagon has a perimeter of 25 cm.

A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter. The perimeter of a thing is the distance surrounding it. Your house, for example, has a fenced-in yard. The perimeter of the barrier is its length. A perimeter is the length of a two-dimensional shape's border. It is sometimes defined as the total of the lengths of all the object's sides. The perimeter of such form is the algebraic sum of the lengths of each side. We have formulae for the various geometric forms.

Here,

side of pentagon=5 cm

perimeter of pentagon=5*side

=5*5

=25 cm

The perimeter of a 5 cm pentagon is 25 cm.

To know more about perimeter,

https://brainly.com/question/7720055

#SPJ4

Answer:

7

2 meats + 5 cheeses

= 7 choices

Answer:

Step-by-step explanation:

2

Therefore , the solution of the given problem of expressions comes out to be n= 19.

Addition, subtraction, division, and the term multiply are examples of numerical computations that are possible. The words are arranged as follows: An equation, a calculator, and an integer or variable A mathematical expression is mainly composed of constants, numbers, and processes (such as additions, subtraction, multiplying, or dividing, etc.). Contradictory claims or expressions and variable are possible.

Here,

Given : a^15.a^4

to find a^n

thus,

=>a^15.a^4 = a^n

=> a^(15+4) = a^n

=> a^19 = a^n

So, on comparing above expression

We get ,

n= 19

thus , n=19 is the solution for this problem

Therefore , the solution of the given problem of expressions comes out to be n= 19.

To know more about expressions visit :-

brainly.com/question/14083225

#SPJ1

The correct ratios are

sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex] ,  tan(C) =[tex]\sqrt{3}[/tex] , sin(B) = [tex]\frac{1}{2}[/tex]

Consider the below figure attached to this question.

In triangle ABC, ∠A=90°, ∠B=30° and ∠C=60°, AC=9 and BC=18.

Using Pythagoras' theorem we get

hypotenuse² = perpendicular² + base²

BC² = AB² + AC²

⇒(18)² = AB² + 9²

⇒324 - 81 = AB²

Taking square root on both sides.

⇒√243 = AB

∴ √3 =AB

Trigonometric ratios are

[tex]sin(C) = \frac{opposite}{hypotenuse} = \frac{AB}{BC} = \frac{9\sqrt{3} }{18} =\frac{\sqrt{3} }{2}[/tex]

[tex]cos(B) = \frac{base}{hypotenuse} = \frac{AB}{BC} = \frac{9\sqrt{3} }{18} =\frac{\sqrt{3} }{2}[/tex]

[tex]tan(C) = \frac{opposite}{basee} = \frac{AB}{AC} = \frac{9\sqrt{3} }{9} =\sqrt{3}[/tex]

[tex]sin(B) = \frac{opposite}{hypotenuse} = \frac{AC}{BC} = \frac{9 }{18} =\frac{1}{2}[/tex]

[tex]tan(B) = \frac{opposite}{base} = \frac{AC}{AB} = \frac{9 }{9\sqrt{3} } =\frac{1 }{\sqrt{3} }[/tex]

Therefore, the correct ratios are

sin(C) = [tex]\frac{\sqrt{3} }{2}[/tex] , tan(C) = [tex]\sqrt{3}[/tex] , sin(B) =[tex]\frac{1}{2}[/tex]

Read more about trigonometric ratios:

https://brainly.com/question/10417664

#SPJ4

The complete question is:

Which trigonometric ratios are correct for triangle ABC? Select three options.

1. sin(C) = StartFraction StartRoot 3 EndRoot Over 2 EndFraction

2. cos(B) = StartFraction StartRoot 2 EndRoot Over 3 EndFraction

3. tan(C) = StartRoot 3 EndRoot sin(B) = One-half

4. tan(B) = StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction.

Set-builder notation: {x | x ∈ D} (where D is the domain) and {y | y ∈ R} (where R is the range), Interval notation: (a, b) (where a and b are the minimum and maximum of the domain) and [c, d] (where c and d are the minimum and maximum of the range) , Graphical notation: The domain and range are represented by a graph.

Set-builder notation is a way of representing the domain and range of a function. It uses curly brackets surrounding the domain and range variables, separated by a vertical bar. The form is {x | x ∈ D} (where D is the domain) and {y | y ∈ R} (where R is the range). This notation is useful when the domain and range are not easily written as a set of numbers.

Interval notation is another way of representing the domain and range of a function. It uses parentheses to represent the domain and square brackets to represent the range. The form is (a, b) (where a and b are the minimum and maximum of the domain) and [c, d] (where c and d are the minimum and maximum of the range). This notation is useful when the domain and range are quickly written as a set of numbers.

Graphical notation is a third way of representing the domain and range of a function. In this case, the domain and range are represented by a graph, with the x-axis representing the domain and the y-axis representing the range. This notation is useful when visualizing the relationship between the domain and range of a function.

Set-builder, interval, and graphical notations are all ways of representing the domain and range of a function. Set-builder notation is useful when the domain and range are not easily written as a set of numbers, while interval notation is useful when the domain and range are quickly written as a set of numbers. Graphical notation is useful when visualizing the relationship between the domain and range of a function.

Learn more about domain here

https://brainly.com/question/13113489

#SPJ4

The baker can make 13 loafs of bread using 85 cups of flour using 6 1/4 c of flour for each loaf of bread.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

A baker has 85 cups (c) of flour to make bread she uses 6 1/4 c of flour for each loaf of bread.

Now, The fraction 6 1/4 can be written as 25/4.

Therefore, The number of bread loaf the baker can make is,

= (85/25/4).

= 85×(4/25).

= (17×4)/5.

= 68/5.

= 65/5 + 3/5.

= 13 + 3/5.

So, he can make 13 bread loafs.

Learn more about Baker here

https://brainly.com/question/14862486

#SPJ4

The equation of the tangent line to the circle through the point (-6,8) has equation = Y = 0.75x + 3.5

For circles that have a center at (0,0), the equation is  [tex]x^{2} + y^{2} = r^{2}[/tex]

[tex]x^{2} + y^{2} = 10^{2}[/tex]

[tex]x^{2} + y^{2}[/tex] = 100

We check if the point (-6,8) is a circle

[tex]x^{2} + y^{2}[/tex] = 100

[tex]-6^{2} + 8^{2}[/tex] = 36 + 64 = 100

So the point is exactly at circle line, as picture below

We solve the gradient of a normal line (n)

Mn = [tex]\frac{y2 - y1}{x2 - x1}[/tex] = [tex]\frac{8 - 0}{-6 - 0}[/tex]  = [tex]- \frac{8}{6}[/tex]

For perpendicular lines the gradient is

Mp = [tex]- \frac{1}{Mn}[/tex]  = [tex]\frac{- 1 }{-\frac{8}{6} }[/tex] = [tex]\frac{6}{8} = \frac{3}{4}[/tex]

The standard equation of a linear line is

Y =  mx + c

We need to find constant (c). We substitute x and y with point (-6,8)

So, x = -6 and y = 8

C = y - mx

C = 8 - ¾(-6) = 8 – [tex]\frac{18}{4}[/tex] = 3.5

With m = Mp =  [tex]\frac{3}{4}[/tex] and c = 3,5    

So, Y =  mx + c

      Y =     [tex]\frac{3}{4}[/tex] x + 3.5

      Y = 0.75x + 3.5

More about The equation of the tangent line at

https://brainly.com/question/28994498

#SPJ4

Rachel has 0.41 quarters that can be obtained using the equation Q + D + N = T.

We can start by using the following equation to find the number of quarters Rachel has: Q + D + N = T

Where Q is the number of quarters, D is the number of dimes, N is the number of nickels, and T is the total amount of money in dollars. We know that T is $4.65, and we know that Rachel has twice as many nickels as quarters, and three more quarters than dimes.

Let's assume that Rachel has x number of quarters

So we can write the above equation as:

x + (x+3) + 2x = 4.65

4x+3 = 4.65

4x = 1.65

x = 0.4125

Rachel has 0.4125 quarters, Which is not possible as it is a decimal. So we need to round it off to the nearest whole number.

Rachel has 0.4125 quarters which is equivalent to o.41 quarters.

Therefore, Rachel has 0.41 quarters that can be obtained using the equation Q + D + N = T.

To learn more about equations,

Visit; brainly.com/question/29657983

#SPJ4

The perimeter of the polygon is 29.43

Polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. The simplest polygons are triangles (three sides), quadrilaterals (four sides), and pentagons (five sides).

Given here:  P(–4, 3), Q(1, 3), R(2, –3), S( 5, –3), and T(-7, -1).

PQ=[tex]\sqrt{(1+4)^{2} +(3-3)^{2} }[/tex]  =5

QR=[tex]\sqrt{1^{2} +9^{2} }[/tex] =9.055

similarly we can calculate the distance of the other edges and the perimeter of the polygon can be found out as PQ+QR+RS+ST+PT=29.43

Hence, The perimeter of the polygon is 29.43

Learn more about polygons here:

https://brainly.com/question/24464711

#SPJ1

The  quotient of the fraction is -3/4 * p²/q²

We should know that when a number is divided by another number, the result is the quotient of the number

We have to find the quotient of the following division, -3/4 * p²/q²

This implies that (15p⁻⁴q⁻⁶)/(-20p⁻¹²q⁻³)

Now, (15p⁻⁴q⁻⁶)/(-20p⁻¹²q⁻³) will give

3/4p[(⁻⁴(⁻¹²)]q²(⁻⁶-(⁻³)]

We know that  all the terms in the expression are in product form, so we can treat them separately}

Hence  we know the property of exponent as aˣ/aᵇ=a(ᵇ⁻ˣ]

Hence this implies that -3/4 * p⁶/q²

Learn more about quotient on https://brainly.com/question/16134410

#SPJ1

Answer:

x<3

Step-by-step explanation:

3x+5<14

Your first step is to simplify the inequality.

To do this, always look to see if you can subtract any numbers from both sides to isolate a variable.

You can subtract 5 from both sides to isolate the 3x on one side.

After that, you will get 3x<9

Next, you must divide both sides by 3 to try and get x by itself, completing the inequality.

9/3 = 3

Your are left with: x<3

Done!

Answer:

x < 3

Step-by-step explanation:

3x + 5 < 14  subtract 5 from both sides

3x + 5 - 5 < 14 - 5

3x < 9  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] < [tex]\frac{9}{3}[/tex]

x < 3

Answer:

Step-by-step explanation:

A conclusion or a hypothesis presented on an unproven foundation in mathematics is referred to as a conjecture, conjectures 6,it is divisible by 2,4,9,12.

Therefore the result is 6,it is divisible by 2,4,9,12.

To know more about  conjecture visit:

brainly.com/question/14392383

#SPJ1

The length and width of the rectangle with 88 feet perimeter are 33 feet and 11 feet respectively

An equation is used to show the relationship between numbers and variables.

The perimeter of a shape is the sum of the distance along its sides. For a rectangle:

Perimeter = 2(length + width)

Let L represent the length and W represent the width of a rectangle with a perimeter of 88 feet

If the length of the rectangle is 3 times its width, hence:

L = 3W

Perimeter = 2(L + W)

88 = 2(L + W)

But L = 3W:

88 = 2(3W + W)

44 = 3W + W

4W = 44

W = 11 feet

L = 3W = 3(11) = 33 feet

The length and width are 33 feet and 11 feet respectively

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Horizontal lines called latitudes are used to measure distances north or south of the equator. Vertical lines known as longitudes are used to determine the west or east of the meridian in Greenwich, England. Latitude and longitude work together to help cartographers, geographers, and others find specific locations on the globe.

Any location's distance from the equator may be determined using its latitude, which is based on its degree. We can locate any point on Earth using longitude and latitude. The GPS or Global Positioning System uses these coordinates.

The grid system that enables us to locate absolute or precise places on the surface of the Earth is made up of latitude and longitude. Latitude and longitude can be used to pinpoint certain locations. Landmark identification also benefits from knowledge of latitude and longitude.

To know m ore about latitude refer to:

https://brainly.com/question/30046637

#SPJ4

Answer:

The mean is lower than the median which is lower than the mode.

Step-by-step explanation:

Answer:

20 ducks

Step-by-step explanation:

4+5=9

4/9:x/45

9*5=45

4*5=20ducks

On solving the provided question we can say that by coordinates-  (4,-8)(4,−8) ; y - y1 = m(x-x1) => y - x 12 = 0

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

by coordinates-

(4,-8)(4,−8)

y - y1 = m(x-x1)

y +8 = x - 4

y - x 12 = 0

To know more about coordinates  visit:

https://brainly.com/question/27749090

#SPJ1

The algebraic formula to represent Giselle's profit is $b*1 - $18.72, or $b - $18.72, where $18.72 is spent on supplies.

A statement that contains at least two numbers or variables, along with at least one mathematical operation, is referred to as a mathematical expression. Any one of the following mathematical operations could be used: addition, subtraction, multiplication, or division. The following are an expression's fundamental parts: : (Number/Variable, Math Operator, Number/Variable). A statement that includes at least two numbers or variables, at least one mathematical operation, and the word "expression" is referred to as a mathematical expression. Let's review expressive writing. The alternative number, which is known as x, is 6 more than half of the given number. This sentence is denoted by the phrase x/2 + 6 in mathematics.

given

number of bracelets = b

profit = $b*1 - $18.72

The algebraic formula to represent Giselle's profit is $b*1 - $18.72, or $b - $18.72, where $18.72 is spent on supplies.

To know more about expression visit :-

https://brainly.com/question/14083225

#SPJ1

To find the height of an obtuse angle in a triangle, you can use the following steps:

It is important to note that the hypotenuse of the right triangle (the base) must be the side opposite to the obtuse angle, and the other two sides should be the legs of the triangle. Also, the altitude can fall inside or outside of the triangle, it does not affect the calculation of the height.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/343682

#SPJ4

Correct option is D, To satisfy triangle inequality theorem, 4 < c < 42.

Triangle inequality is a theorem in Euclidean geometry that states any two triangle sides added together must be greater than or equal to the third side; it is represented by the symbols a + b c.

The basic tenet of the theorem is that a straight line connects any two places.

According to the triangle inequality theorem, any two sides' sums in a triangle must be bigger than the length of the third side.

If a, b, and c are the lengths of a triangle's sides, then the sum of a and b's lengths is greater than c's length. Similar to how a+ c > b, b + c > a.

To learn more about Triangle inequality theorem from given link

https://brainly.com/question/309896

#SPJ1

Rationales that may be involved : [tex]$\pm 1, \pm \frac{1}{2}, \pm 3, \pm \frac{3}{2}, \pm 5, \pm \frac{5}{2}, \pm 15, \pm \frac{15}{2}$[/tex] and real roots in reason: [tex]$1,-1,-\frac{15}{2} \mathrm{~}$[/tex] .

We can use the theorem of rational zeros since all coefficients are integers.The constant term's coefficient, or trailing coefficient, is 15, and The plus and minus signs can be used to find its components. [tex]$\pm 1, \pm 3, \pm 5, \pm 15$[/tex]  . The options for p are as follows. The maximum degree of the term's coefficient, or the leading coefficient, is -2.

The plus and minus signs can be used to find its components. [tex]$\pm 1, \pm 2$[/tex] . The possible possibilities for q are as follows.

Discover each potential value for [tex]$\frac{p}{q}: \pm \frac{1}{1}, \pm \frac{1}{2}, \pm \frac{3}{1}, \pm \frac{3}{2}, \pm \frac{5}{1}, \pm \frac{5}{2}, \pm \frac{15}{1}, \pm \frac{15}{2}$[/tex]

These could be the rationale for the following: [tex]$\pm 1, \pm \frac{1}{2}, \pm 3, \pm \frac{3}{2}, \pm 5, \pm \frac{5}{2}, \pm 15, \pm \frac{15}{2}$[/tex]                                                      rationales that may be involved: [tex]$\pm 1, \pm \frac{1}{2}, \pm 3, \pm \frac{3}{2}, \pm 5, \pm \frac{5}{2}, \pm 15, \pm \frac{15}{2}$[/tex] .

real roots in reason: [tex]$1,-1,-\frac{15}{2} \mathrm{~}$[/tex].

To learn more about rational roots refer to :

https://brainly.com/question/17754398

#SPJ1

All the angles from the polygon path made by the students are;

∠1 = 96°

∠2 = 90°

∠3 = 162°

∠4 = 132°

∠5 = 60°

The images of the polygon are missing and so i have attached them. From the attached image, we can see we have;

Triangle (3-sided polygon)

Square (4-sided polygon)

Pentagon (5-sided polygon)

Hexagon (6 sided polygon)

Now, we know that formula for external angle of a polygon with n sides is 360/n.

Thus, for the 6-sided polygon, the ∠5 = 360/6

∠5 = 60°

Since ∠4 is shared by the pentagon and hexagon, then;

∠4 = (360/5) + 60

∠4 = 72° + 60°

∠4 = 132°

Since ∠3 is shared by the square and pentagon, then;

∠3 = 90 + 72

∠3 = 162°

∠2 = 90° because external angles of a square = 360/4 = 90°

Learn more about polygon on:

https://brainly.com/question/1592456

#SPJ1

The value of x in the angle  is -6

                  m ∠B = (x +53)°

                 m ∠C = (x +53)°

         2 (x + 53) + 86 = 180

          2x + 106 + 86 = 180

                 2 x + 192 = 180

                            2x = 180- 192

                            2x = -12

                             x = -6

To learn more about isosceles triangle, refer:

https://brainly.com/question/1475130

#SPJ1

Answer:

Step-by-step explanation:

The center of a hyperbola is located at the point where the two foci (focii) are located. In this case, the center of the hyperbola is located at point (3,-2), which is option D.