Find the length of BC.

Answer: The distance of the ship from the lighthouse is 546.4 feet.

Step-by-step explanation:

What is the angle of elevation?

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

The beacon light is 126 feet high, the angle of elevation to the beacon is 13° and the distance from the lighthouse to the ship = x

These from a right-angled triangle,

from trigonometry

tan 13 = 126/x

making x the subject of the equation we have

x tan 13 = 126

x = 126/tan 13

but tan 13 = 0.2308

x = 126/0.2308

x = 546.4 feet

In conclusion, the ship's distance from the lighthouse is 546.4 feet.

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Answer: (1,-2) , (5,-35)

Step-by-step explanation:

x = 1

1. g(x) = 5 - 7x

This can also be written as g(1) = 5 - 7x

This means that we plug in 1 for all the "x"s. So we get:

g(1) = 5 - 7(1)

7(1) = 7

5 - 7 = -2

x = 1 is true and that means y = -2 (because g(x) also means y

x = 5

1. g(x) = 5 - 7x

This can also be written as g(5) = 5 - 7x

This means that we plug in 5 for all the "x"s. So we get:

g(5) = 5 - 7(5)

7(5) = 35

5 - 35 = -30

x = 5 is true and that means y = -35

I think this is what the question meant, hope this helps!

The numbers that result in the top and bottom numbers are: -3.83 and 7.83

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

x y= -30............ (1)

and, x + y= 4 ...................(2)

So, x + (-30/x)= 4

x² - 30 = 4x

x² -4x -30 = 0

Solving the Quadratic Equation

x= (4 ±√4² - 4(1)(-30) / 2)

x= (4 ± √136)/ 2

x= (4 ± 11.66)/2

x= (4+ 11.66)/2  or x= (4- 11.66)/2

x= 15.66/2 or x= -7.66/2

x = 7. 83 or x= -3.83

So, For y=7.83

x+ y = 4

x= -3.83

For y=-3.83

x+y=-4

x+(-3.83)= 4

x= 7.83

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The asymptote of the graph is given as 3

As one or both of the x or y coordinates go to infinity, a line is said to be an asymptote of a curve in analytic geometry when the distance between the curve and the line approaches zero.

The value of x from the graph here is given as 3. The curve cuts across the x axis at 3. This is the value as x moves towards positive infinity

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If one angle is 67° and the other is 52°, the other two angles are equal and the angle has a value of 120°.

A place where two lines converge creates an angle. They are quantified in degrees and are denoted by the symbol °. Four essential types are reflex, acute, right, and obtuse angles. A circle has 360 degrees. One terminal exists when two rays (half-lines) are merged form an angle. The rays are referred to as the angle's sides, occasionally as its legs, and occasionally as its arms, while the latter is referred to as the angle's vertex. The place where all points of an angle converge is known as the vertex.

given

total interior angles = 360°

m/C = 67° , m/D = 52°

67° +  52° + 2x = 360 °

119 + 2x = 360 °

2x =  360 ° - 119°

x = 120°

if one angle is 67° and the other is 52°, the other two angles are equal and the angle has a value of 120°.

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In ACDE, mzC = 67° and mzD = 52°. Which statement about the sides of ACDE must be true?

DE > CD > EC

DE > EC > CD

EC > CD > DE

EC > DE > CD

CD > DE > EC

CD > EC > DE

As a result, the East Pacific Rise rate of change extends by around 6 to 16 centimeters annually, compared to the Mid-Atlantic Ridge's 2 to 5 cm.

The relation of one quantity's changes to someone else's change is known as the rate of change. The rate of change in linear relationships is constant. Here are a few instances with varying rates: Every week, forty rats are added to the rat population. When an automobile is moving at 68 km, its distance traveled grows by 68 mph over time. When calculating the change in distance for a car employing 27 miles per gallon, the duration is multiplied x 27 mile for each gallon.

Here,

Using the data in the inquiry

Conclusion: As a result, we may say also that East Pacific Rise is expanding more quickly than the Mid-Atlantic Ridge.

The East Pacific Rise expands roughly 6 to 16 centimeters year, whereas the Mid-Atlantic Ridge distributes about 2 to 5 centimeters annually.

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For the given equations 7x+6y=16 and 4x-2y=1 the value of x is 1 and y is 3 / 2.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the two equations are 7x+6y=16 and 4x-2y=1. The solution of the equations by elimination method is calculated as,

7x + 6y = 16

4x -2y = 1

Cross-multiply the two equations by the coefficients of variable y.

-14x -12y = -32

-24x + 12y = -6

____________

-38x = -38

x =1

The value of y will be calculated as,

4x - 2y = 1

4 -2 y = 1

y = 3 / 2

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Therefore , the solution of the given problem of expression comes out to be 589418163090.78.

Multiplying, dividing, adding, and subtracting are necessary math operations. When combined, the following expression would appear: A mathematical operator, some data, and an equation Values, variables, and functions make up a statement of fact's constituent parts, such as additions, deductions, multiplications, divisions, etc. It is possible to contrast and compare words and phrases.

Here,

Given :

=> 2 x/y [tex]3^{z}[/tex]

At x = 72 , y=23 , z=23

So,

Putting values

=> 2*72/23 * 3²³

=> 589418163090.78

Therefore , the solution of the given problem of expression comes out to be 589418163090.78.

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The correct answer is (option A)

We are trying to find the greatest common factor of 6 and 10 so we need to divide 10 and 6:

→ 10/6

→ = 1.6

→ = 2

Now we are rounding the number 1.6. 6 is close to 10 so it would equal 10 = 2

Therefore, the correct answer is (option A)

The gradient vector field of f(x, y) = tan(3x − 4y) is ∇f = (3 [tex]sec^2[/tex](3x − 4y) , −4 [tex]sec^2[/tex](3x − 4y)).

The gradient vector field of f(x, y) = tan(3x − 4y) is given by ∇f = (3 [tex]sec^2[/tex](3x − 4y) , −4 [tex]sec^2[/tex](3x − 4y))

The gradient vector field, also known as the gradient of a scalar function, is a vector-valued function that describes the direction of the steepest increase of a scalar function at a given point. It is represented by the symbol ∇ and is defined as the vector of partial derivatives of the function with respect to each variable.

To find the gradient vector field of f(x, y) = tan(3x − 4y), we take the partial derivatives with respect to x and y:

∂f/∂x = 3 [tex]sec^2[/tex](3x − 4y)

∂f/∂y = −4 [tex]sec^2[/tex](3x − 4y)

The gradient vector field is a useful tool in vector calculus and can be used to find the direction of the maximum increase of a scalar function, the direction of a vector field, the direction of a level curve, the equation of a tangent plane, and many other applications.

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A right Riemann sum has the formula  A=∑ni=1Δxf(xi) A = ∑ i = 1 n Δ x f ( x i ) where x is the width of each of the n rectangles and f(xi) is the height.

A specific method of approximating an integral with a finite sum in mathematics is known as a Riemann sum. Riemann is the name of a German mathematician who lived in the 19th century. Approximating the area of functions or lines in graphs, as well as the length of curves and other approximations, is a highly typical application. The picked points in each subinterval of the partition are all in the upper Riemann sum, given an interval partition. The interval is often separated into subintervals of equal size.

Riemann  sum formula is A=∑f(xi)Δx A = ∑ f ( x i ) Δ x ,

where A is the curve's area under the evaluable interval,

f(xi) f ( x i ) is each rectangle's height (or the average of the two heights in the case of a trapezoid)

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On solving the provided question, we can say that By addition, people could be at a game = 42,500 - 275 = 42225

The other three fundamental operations are subtraction, multiplication, and division. Addition is one of the four basic operations. The sum or total of these combined values is obtained by adding two integers. The process of merging two or more numbers is known as addition in mathematics. Numbers are added together to form addends, and the outcome of this operation, or the final response, is referred to as the sum. This is one of the crucial mathematical operations we employ on a regular basis. You would add numbers in a variety of circumstances. Combining two or more numbers is the foundation of addition. You can learn the fundamentals of addition if you can count.

By addition,

Stadium capacity = 42,500

General admission seating = 31,750

Reserved seating = 10,475

42,500-( 31,750 + 10,475 ) =42,500- 42225 = 275

people could be at a game = 42,500 - 275 = 42225

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The slope of the table is 2.

What is slope?

An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x). The ratio of how much y grows as x grows by a certain amount is known as the slope of a line. A line's slope, or the amount by which y rises as x rises, indicates how steep a line is. The slope is constant (the same) along the line.

Here using given table we can find slope by taking any two points then,

[tex](x_1,y_1)=(6,0) and (x_2,y_2)=(4,-4)[/tex]

Now using slope formula m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> m = [tex]\frac{-4-0}{4-6}[/tex]

=> m = [tex]\frac{-4}{-2}[/tex]

=> m = 2

Hence the slope of the given table is 2.

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The slope of points that are given on the table is 2.

The slope of a line indicates how steep it is. "rise over run" is used to calculate slope mathematically (change in y divided by change in x). The slope of a line is the ratio of how much y grows as x grows by a certain amount. The slope of a line, or the amount by which y rises as x rises, indicates the steepness of the line. Along the line, the slope is constant (the same).

Using the given table, we can find the slope by taking any two points and then,

(x1,y1) = (6,0) and (x2,y2) = (4,-4)

Using the slope formula m = y2-y1/x2-x1,

Then,

m = -4-0/4-6

m = -4 /-2

=> m = 2

As a result, the slope of the given table is 2.

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The sine of an angle is the ratio of height to the hypotenuse. The value of sin 50° = 0.7660.

What is an angle?

An angle is a figure in Plane Geometry generated by two rays or lines that share a common endpoint. The term "angle" is derived from the Latin word "angulus," which meaning "corner". The two rays are referred to as the sides of an angle, while the common terminus is referred to as the vertex.

The sine of an angle is the ratio of height to the hypotenuse of a right triangle.

The reference angle is 50.

Now sin 50 = 0.766044.

The 5 digits after the decimal point is 4. 4 is less than 5 thus the 4 digits after the decimal point remain the same.

sin 50 = 0.7660

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Solving the provided question, we can say that from given number line, value of y is 5 and RS is 33 ST is 28.

A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.

RS + ST = RT

10y+ 11 = 61

loy = 50

putting values

RS 5 33

ST 4 * 5 + = 28

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To find the mass of the lamina, we need to integrate the density function over region D. The density function is given by? (x, y) = 7ky, where k is a constant. The region D is bounded by y = [tex](1 ? x^2)[/tex]  and y = 0, and the limits of integration are [tex]0 < = y < = (1 - x^2)[/tex] .

So, the mass of the lamina is:

[tex]m = ∫∫?(x, y) dx dy = ∫∫ 7ky dx dy\\= 7k ∫∫ y dx dy = 7k * ∫ (1 - x^2) dy dx\\= 7k * ∫(0 to 1 - x^2) y dy\\= 7k * (1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/2 * [((1-x^2)^3/3] - 0))= 7k * (1/2 * (1/3 - x^6))[/tex]

To find the center of mass (x bar, y bar) of the lamina, we need to find the x and y coordinates of the center of mass.

The x-coordinate is given by

[tex](x bar) = 1/m * ∫∫ x ?(x, y) dx dy = 1/m * ∫∫ x * 7ky dx dy \\= 7k * ∫ (x * y) dx dy\\= 7k * (x * 1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (x * 1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (x * (1/2 * (1/3 - x^6))\\The y-coordinate is given by\\(y bar) = 1/m * ∫∫ y ?(x, y) dx dy = 1/m * ∫∫ y * 7ky dx dy= 7k * ∫ (y^2) dx dy\\= 7k * (1/3 * ∫(0 to 1 - x^2) y^3 dy)\\= 7k * (1/3 * [y^4/4] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/3 * (1/4 - x^6/2))[/tex]

It's worth noting that the mass and center of mass of the lamina depend on the constant k, which is not specified in the problem.

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An inequality that describes a possible length in yards of the rectangular parking lot is L < 6.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Since the city wants the width of the parking lot to be 5 yards and the area of the rectangular parking lot to be more than 30 square yards, an inequality that models a possible lengths of the rectangular parking is giving by;

A > LW

30 > 5L

Dividing both sides of the inequality by 5, we have:

6 > L

L < 6

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Answer:

There is only one solution and the solution is (0,4).

Step-by-step explanation:

The given system has equations;

and

We equate the two equations to determine their point of intersection;

We put x=0 into the first equation to get;

There is only one solution and the solution is (0,4).

The required special segment in triangles that are matched in the triangles is given as perpendicular bisector, altitude, median, and midsegments.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

The question seems to be incomplete, so we assume that there are two congruent triangles.
For the congruent triangles, special segments in triangles are congruent to each other.

Thus, the required special segments in triangles that are matched in the triangles is given as perpendicular bisector, altitude, median, and midsegments.

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Description               Interval notation           Set builder notation

5.                               (-∞, -4]                               {x | x ≤ -4 |

6.                               (-∞, ∞)                              { x | x all real numbers }

7.                               (-11/3, 17/3]                       { x | x -11/3 < x ≤ 17/3 }

Continuous sets of real numbers can be represented using interval notation by the numbers that bound them. When written, intervals resemble ordered pairs in several ways.

In interval notation ( ) means open interval, [ ] represents closed interval  

Numbers on the square brackets are included in the notation while numbers of the braces (open interval) are not included

Set builder notation is a type of mathematical notation used to describe sets by naming its components or highlighting the requirements that each member of the set must meet.

Set builder notation used curtly brackets to carry out the information.

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12

Step-by-step explanation:

bc i did the math

Answer: The answer is 12.

Step-by-step explanation:

The answer is twelve because if you divide 1.5 by 4, it equals 0.375, and then you divide 4.5 by 0.375, you get 12! hope this helps!

Answer:

The volume of sphere N is 400cm3/8 = 50cm3

Step-by-step explanation:

The volume of a sphere is given by the formula: V = 4/3 * π * r^3

where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.

Given that the volume of sphere M is 400cm3 and the radius of sphere N is half the radius of sphere M, we can write an equation to find the volume of sphere N:

Vm = 4/3 * π * rm^3 = 400cm3

We know that radius of sphere N is half of sphere M so

rn = rm/2

So the volume of sphere N can be found by substituting the value of radius of sphere N in the sphere volume formula:

Vn = 4/3 * π * (rm/2)^3

Vn = 4/3 * π * (rm^3)/8

Vn = (Vm)/8

So, the volume of sphere N is 1/8th of the volume of sphere M, which is 400cm3.

The volume of sphere N is 400cm3/8 = 50cm3

The average rate of change of g(x)=3x^2-5x from x=4 to x=8 is 90

From the information given, we have that;

g(x) = 3x² - 5x

To determine the rate from x = 4 to x = 8

First, substitute the value of x as 4, we get;

g(4) = 3(4)² - 5(4)

expand the bracket, we get;

g(4) = 48 - 20

Subtract the values

g(4) = 28

For g(8), we get;

g(8) = 3(8)² - 5(8)

expand the bracket

g(8) = 192 -- 40

subtract the values

g(8) = 152

The average rate is;

= 152 + 28/2

= 90

Hence, the value is 90

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Answer:  C. the domain is 2 to 5 because it's the x axis

Step-by-step explanation:

Each of the numbers on the left should be matched with all appropriate number sets on the right as follows:

In Mathematics, there are six (6) common types of numbers and these include the following:

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 6, 12, 1/2, 0.5, √16, -2, etc.

Additionally, -2 can be classified as both a rational number and an integer.

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Therefore , the solution of the given problem of domain comes out to be

Domain =[-∞,∞) and Range: (-∞,∞].

A function's domain is the range of possible arguments that it may accept. These integers indicate the cin of a polynomial like f. (x). The range of potential values that can be used with a function is known as its domain. The number that the method returns after inserting the x value belongs to this set. The formula for a function with y as the predictor variables and x as the regression coefficient is y = f. (x). When a single value of y can be successfully produced from a value of x, that x values is said to fall within the domain of the function.

Given : f(x) = -x+3-2

after being streamlined, y = -x + 1

To Locate: What are the function's domain and range?

Solution:

In relation to the Domain:

=> -x + 1 < 0

=>  -x < -1

Domain =[-∞,∞) thus.

for the range

=> -x + 1 < 0

=>  -x < -1

=>f(x)=  -x -1 Consequently, Range: (-∞,∞]

Therefore , the solution of the given problem of domain comes out to be

Domain =[-∞,∞) and Range: (-∞,∞].

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Answer:

66.15

Step-by-step explanation:

70 dollars - discount + fee

discount = 10% of total = 10% of 70 = 0.1 * 70 = 7

fee = 5% of discounted price

discounted price = original - discount = 70 -7 = 63

fee = 5% of 65 = 0.05 * 65 = 3.15

70 - 7 + 3.25 = 66.15

The radius of the globe with a volume of 904.78 in³ is 6 in.

The amount of space occupied within a sphere is referred to as its volume. Every point on the surface of the sphere is equally spaced from its centre, making it a three-dimensional round solid figure.

The fixed point and fixed distance are referred to as the sphere's centre and radius, respectively.

Given that the volume of the sphere is 904.78 in³. The radius of the sphere is calculated as,

Volume = ( 4 / 3 )πr³

r³ = ( 3 x volume ) / 4π

r³ = ( 3 x 904.78 ) / 4π

r³ = 2714.34 / 4π

r³ = 216

r = 6 in

Hence, the radius of the globe is 6 in.

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