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To graph a 3 dimensional coordinate system, you must first identify the three axis, often labeled x, y, and z.

A coordinate system is a system used to describe the position or location of a point in space. Coordinate systems are used in mathematics, physics, engineering, and other sciences to describe the position of objects, lines, or points in a given space. Coordinate systems are based on a set of axes, which are defined by a set of numbers, letters, or symbols. Common coordinate systems include Cartesian, polar, and cylindrical. In each system, the axes are used to describe the position of an object relative to the origin point. Coordinate systems are used to accurately describe the location of objects in space and can help to simplify many different mathematical operations.

Then, you will plot points along each of the three axis. For example, if the point is at (2,3,4), then you will plot the point two units away from the origin on the x-axis, three units away from the origin on the y-axis, and four units away from the origin on the z-axis. Once you have plotted all the points, you will connect them with lines to form a graph.

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The area of the shaded region would be 4π - 8 square units.

What is the area of a circle?

The area of a circle is given by the formula: A = πr^2, where A is the area, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle. The radius is the distance from the center of the circle to its edge.

In the given figure we have to find the height of the triangle and that will be the radius of the triangle.

In the triangle LMO,

Angle opposite to 45 = 1/√2* hypotenuse

MO = 1/√2 * 4

MO =2√2

Radius of the circle= 2√2

Area of the triangle = 1/2* MO * LN

                                  = 1/2 * 2√2*4√2

                                  = 8

Area of semi-circle =1/2 * πr²

                      =1/2 * π(2√2)²    

                     = 4π  

Area of shaded region = 4π - 8

Hence, the area of the shaded region would be 4π - 8 square units.

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The product (x+5)(x - 1)(x+2) is equal to  x³ +6x² + 3x - 10 (C)

According to the Product Rule, the derivative of a product of two functions is equal to the product of the first function times the second function's derivative plus the second function times the first function's derivative.

The sum rule explains how many different methods there are to choose between two distinct groups of options. The product rule explains how many different methods there are to choose from each of two sets of options. Both laws apply to bigger sets families in general.

In the given question:-

=(x+5)(x - 1)(x+2)

=(x+5)(x^2+x-2)

=x^3+6x^2+3x-10

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Using the substitution method we will see that the solution is:

a = 69

b = 55.5

Here we want to solve the system of equations below:

-3a + 4b = 15

5a - 6b = 12

We can isolate one of the variables in one of the equations, I will isolate b on the first one.

4b = 15 + 3a

b = (15 + 3a)/4

Now we can replace this on the other equation:

5a - 6*(15 + 3a)/4 = 12

Now we can solve that equation for a.

5a - (6/4)*15 - (6/4)*3a = 12

5a - (3/2)*15 - (9/2)*a = 12

(1/2)*a = 12 + (3/2)*15

a = 2*(12 + (3/2)*15)

a = 24 + 45

a = 69

And the value of  b is:

b = (15 + 3a)/4

b = (15 + 3*69)/4 = 55.5

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Work Shown:

x = his age now

x+11 = his age 11 years into the future

x-7 = his age 7 years ago

The equation to set up is

x+11 = 3(x-7)

since his age 11 years into the future is triple that of his age 7 years ago.

-------

Let's solve for x.

x+11 = 3(x-7)

x+11 = 3x-21

x-3x = -21-11

-2x = -32

x = -32/(-2)

x = 16

He is currently 16 years old.

11 years from now he'll be 16+11 = 27, and 7 years ago he was 16-7 = 9.

Note that 9*3 = 27 to help confirm the answer.

Answer:

16

Step-by-step explanation:

3(x-7)=x+11

Plug into equation and find value of x

Answer: The equation -x = 1 has only one solution, x = -1.

This can be shown by solving the equation for x:

-x = 1

x = -1

To show that this equation has only one solution, we can plug in -1 for x and check that the equation is true:

-(-1) = 1

1 = 1

So x = -1 is the solution.

No other values of x would work here and make the equation true.

Step-by-step explanation:

Accordingly, the cylinder's volume would be 115.45 cubic inches given its parameters.

By multiplying the base area and height of a cylinder, one may get its volume. The radius of the circular base equals half its diameter, and the area of the base is equal to the area of a circle, which is denoted by the formula A = r2. As a result, a cylinder's volume equals:

Cylinder volume equals (r2)

h = 12 inches, where r = D/2 = 3.5 inches, 2 inches, and 1 inch.

Cylinder volume equals (1.75")2. ( 12 in )

147/4 in3 or 115.45353 in3 is the volume of the cylinder.

Accordingly, the cylinder's volume would be 115.45 cubic inches given its parameters.      

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Cost is equal to Selling price plus Loss ( when selling price and loss is given )Therefore, the cost price (C.P.) is 350.

Cost is the same as the selling price plus the loss ( when selling price and loss is given ).

The Profit and Loss Percentage Formula

Profitability (P%) is calculated as (Profit /Cost Price) / 100.

Loss percentage (L%) Equals 100 divided by (Loss / Cost price).

S.P. = {(100 + P%)/100}

if SP > CP, then CP

If SP > CP, S.P. = (100 - L%)/100 CP

C.P. = {100/(100 + P%)}

if SP > CP, then SP

C.P. = SP (if SP > CP)/100/(100 - L%)

Loss percent = 10%

To find:

The C.P.

Solution:

Let x be the C.P.

We have,

S.P. = 315

Loss percent = 10%

S.P = C.P - 10% 0f C.P

315 = X- 0.1X

315 = 0.9 X

Divide both sides by 0.9.

315/0.9 =X

350  = x

Therefore, the cost price (C.P.) is 350.

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Answer:

Length = 18inch

Width = 15inch

Step-by-step explanation:

(Process/Explanation Below)

⇒ 66 ÷ 2 = 33  (We divide by 2 because we need to find two measurements which are our length and width)

⇒ 33 - 3 = 30  (Since the width is 3inches smaller than the length we have to subtract by 3.)

⇒ 30 ÷ 2 = 15in width  (This is our width because since a rectange has 2 sides we have to divide by 2.)

⇒ 5 + 3 = 18in length (This is our length because it says the length is 3inches longer than the width and the width is 15inches.)

Yes, mathematics plays a crucial role in the insurance industry. Actuarial science, which uses mathematical and statistical methods to assess and manage risk, is the foundation of the insurance industry.

Actuaries use mathematical models to calculate the likelihood of future events, such as accidents, illnesses, or natural disasters, and use this information to price insurance policies and estimate the company's potential losses.

The insurance industry also uses mathematical models to assess and manage the risk of potential losses, set prices for their products, and make investment decisions. For example, insurance companies use simulations to estimate the likelihood of different scenarios and the potential impact on their financials.

Additionally, underwriters use mathematical models to assess the risk of insuring a particular individual or business, they take into account factors such as the individual's age, health, and occupation when determining the price of the policy.

Insurance companies also use statistical models and Machine learning algorithms to detect patterns of suspicious behavior that could indicate fraud.

In summary, the mathematical basis for insurance is the use of mathematical and statistical models and techniques, such as probability and statistics, to assess and manage risk and make financial decisions in the insurance industry.

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Therefore ,As a result, the answer to the above  equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

At time zero, Kadeesha stepped outside and drove 3 minutes at a speed of 1 block per minute to the store.

after traveling six blocks at her normal speed of three blocks per minute

She spent 5 minutes stopping at the bank as a result. She then sped home at a rate of three blocks per minute.

She therefore begins at (19,8), travels 8 blocks back in 2 minutes, and ends at (21,0).

Therefore ,As a result, the answer to the above  equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).

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On solving the provided question, we can say that by trigonometry angle of evolution = x = [tex]tan^{-1}(1.2)[/tex]

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

by trigonometry

B = 50m

P = 28m

Tan(x) = 50/281.7857142857 = 1.2

angle of evolution = x = [tex]tan^{-1}(1.2)[/tex]

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The 4 properties of solutions are:

1) Consistency

2) Validity

3) Feasibility

4) Stability

In mathematics, a solution to an equation or system of equations is a set of values that can be substituted into the equation(s) to make the statement(s) true. The four properties of a solution are:

1) Consistency: A solution exists and is unique, or multiple solutions exist.

2) Validity: The solution(s) must satisfy the equation(s) and any constraints or boundary conditions.

3) Feasibility: The solution(s) must be within the domain of the equation(s) and any constraints or boundary conditions.

4) Stability: The solution(s) should be insensitive to small changes in the equation(s) or initial conditions.

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Answer:

119 cm²

Step-by-step explanation:

Area of white triangle:

             base = 9 cm

           height = 14 cm

       [tex]\sf \boxed{Area \ of \ triangle = \dfrac{1}{2}*base *height}[/tex]

                                    [tex]\sf =\dfrac{1}{2}*9*14\\\\ = 9*7\\\\= 63 \ cm^2\\[/tex]

Area of trapezium:

          [tex]\sf \boxed{Area \ of \ trapezium =\dfrac{(a+b)*h}{2}}[/tex]

Here, a and b are the parallel sides of trapezium & h is the height.

           a = 9 cm ; b = 17 cm and h =14 cm

[tex]\sf Area \ of \ trapezium = \dfrac{(9+17)*14}{2}[/tex]

                           [tex]= \dfrac{26*14}{2}\\\\\\=13*14\\\\= 182 \ cm^2[/tex]

Area of shaded region = area of trapezium - area of white triangle

                                      = 182 - 63

                                      = 119 cm²

Answer:

area of shaded region = 119 cm²

Step-by-step explanation:

the outer figure has one pair of parallel sides and is a trapezium.

the shaded area (A) is calculated as

A = area of trapezium - area of white triangle

the area of a trapezium is calculated as

area = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here h = 14 , b₁ = 9 , b₂ = 17 , then

area = [tex]\frac{1}{2}[/tex] × 14 × (9 + 17) = 7 × 26 = 182 cm²

the area of the triangle is calculated as

area = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

here b = 9 and h = 14 , then

area = [tex]\frac{1}{2}[/tex] × 9 × 14 = 4.5 × 14 = 63 cm²

then area of shaded region (A) is

A = 182 - 63 = 119 cm²

The length of the side BD is;  8

The measure of the angle DAB is; ∠DAB = 53°

Two triangles are said to be congruent by any of the following postulates;

1) SSS (Side Side Side) Congruence Postulate.

2) SAS (Side Angle Side) Congruence Postulate.

3) ASA (Angle Side Angle) Congruence Postulate.

4) AAS (Angle Angle Side) Congruence Postulate.

5) HL (Hypotenuse Leg) Congruence Postulate

Now, for the given triangles that are congruent, we can say that;

∠ADC ≅ ∠ACB

∠DAB ≅ ∠CAB

BD ≅ BC

AC ≅ AD

Thus;

BD = 8

∠DAB 53°

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Answer:

6[tex]x^{2}[/tex] + 8x

Step-by-step explanation:

4x(3x + 2) = 12[tex]x^{2}[/tex] + 8x  is the area of the big rectangle

2x(3x) = 6[tex]x^{2}[/tex]  is the area of the small rectangle.

Subtract the small rectangle from the large rectangle to find the area of the shaded region

12[tex]x^{2}[/tex] + 8x - 6[tex]x^{2}[/tex]

6[tex]x^{2}[/tex] + 8x

Professional librarians should be accessible to pupils, according to administrators

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In mathematics, two straight lines can mean a number of things depending on the context. In general, a straight line is a geometric object that has no curvature and extends infinitely in both directions.

When two straight lines are considered together, they can either be parallel, meaning they will never intersect, or they can be intersecting, meaning they will cross at exactly one point. If the two lines are parallel, they will have the same slope, and if they are intersecting, the lines will have different slopes.

The slope-intercept equations for the two straight lines in analytical geometry are written as y = mx + b, where m is the slope, x and y are the coordinates of a point on the line, and b is the y-intercept.

In conclusion, two straight lines can have different meanings in mathematics depending on the context, such as parallel or intersecting, which can be represented by their equations in slope-intercept form.

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Answer:

Step-by-step explanation:

x36 + 24

x39x² + 24x - 28

x3(x2 + 9x - 28/3)

x3(x + 28/3)(x - 3)

To reflect a line over the line y = -2, we can first graph the line and then apply a transformation. A reflection in the y = -2 line can be thought of as a reflection in the x-axis, followed by a translation 2 units upward.

The transformation for a reflection over the line y = -2 is given by (x, y) → (x, -y - 4). To reflect a point (x, y) over the line y = -2, we substitute the coordinates of the point into the transformation and solve for the reflected point.

For example, to reflect the point (3, 4) over the line y = -2, we would substitute the coordinates into the transformation to get (3, -4 - 4) = (3, -8).

To reflect a line, we can reflect each point of the line over the line y=-2 and plot the reflected points.

In conclusion reflecting a line over y=-2 is done by applying a transformation (x, y) -> (x, -y - 4) to each point of the line, this can also be thought of as reflecting the line over x-axis and then translating 2 units upward.

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Answer: 75

Step-by-step explanation:

Answer:

-16

Step-by-step explanation:

Answer:

m = [F(y2) - F(y1) ] / [[F(x2) - F(x1)]      slope of a line

[9 - 6] / [x - 1] = 1       that an increase in x equals the increase in y

Obviously, x must equal 4 so 3 / 3 = 1 or when x increases by 3, y must also increase by 3 for m to equal 1

The area of a 60°-30°-90° triangle can be found by using the formula A = (1/2) × b × h.

In this triangle, b is the length of the side opposite the 60° angle, and h is the length of the side opposite the 30° angle. For example, if the side opposite the 60° angle has a length of 8 and the side opposite the 30° angle has a length of 7, the area of the triangle can be calculated as A = (1/2) × 8 × 7 = 28. Therefore, the area of the triangle is 28 units squared.

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The population of the Boom town increased by 25% compared to last year, present population is 6000 then last year population is equal to 4800.

As given in the question,

Given population of the present year is equal to 6000

Let us consider 'x' be the last year population.

Increased in population compared to last year = 25%

Required equation is given by :

x + (25/100)x = 6000

⇒ (125 / 100 )x = 6000

⇒ x = ( 6000 × 100 ) / 125

⇒ x = 4800

Therefore, the population of the last year as per given data of the present year is equal to 4800.

The above question is incomplete, the complete question is:

Compared to last year, the population of Boom Town has increased by 25%. The population is now 6,000. What was the population last year?

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Answer: THE ANSWER IS 12

Step-by-step explanation:

HOPE IT HELPS =D

The distance across the river (BD) is 800 yards

An equation is an expression that shows the relationship between two or more numbers and variables. Types of equation are linear, quadratic, cubic and so on.

From the image shown, triangle ABC and triangle ADE are similar triangles. For similar triangles, the ratio of corresponding sides are proportional to each other. Hence:

AD/AB = DE/BC

substituting values:

AD / 200 = 500/100

AD = 1000 yards

AD = AB + BD

substituting:

1000 = BD + 200

BD = 800 yards

The value of BD is 800 yards

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The rate of change for a linear function, also known as the slope, can be found by calculating the change in the y-coordinate (rise) divided by the change in the x-coordinate (run) between two points on the line. The slope of a line describes how steep the line is and whether it is increasing or decreasing.

In this case, the slope of the linear function can be found by using the coordinates of points E and F:

Slope = (y2 - y1) / (x2 - x1)

Slope = (-8 - 27) / (5 - 0)

Slope = -35/5

The slope of the linear function is -35/5 or -7.

The initial value of a linear function is the y-intercept, which is the point where the line crosses the y-axis. To find the y-intercept, we can use the slope and one point on the line (in this case point E (0,27)):

y = mx + b

27 = -7(0) + b

b = 27

The y-intercept of the linear function is 27.

So, the linear function starts at point E (0,27) with an initial value of 27, and has a rate of change or slope of -7.

Answer: 439.2 miles

Step-by-step explanation:

213.5/3.5=61

61*7.2=439.2 miles in total

The simplified expression is

14x + 9.6 + 4.1y

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

12x -3.7 + 2x + 13.3 + 4.1y

Combining the like terms.

(12x + 2x) - 3.7 + 13.3 + 4.1y

14x + 9.6 + 4.1y

Thus,

The final expression is 14x + 9.6 + 4.1y.

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The interest rate for first loan is 5% and for the second loan is 7%.

The amount of first loan = $5000

Let the rate of interest for first loan = r

The interest from first loan = ($5000 × r)/100

= 50 r

The amount of second loan = $5000

Let the rate of interest for second loan = r+2

The interest from first loan = ($8000 × (r+2))/100

= 80 r + 160

Total interest = 50 r + 80 r + 160

= 130 r + 160

As per the question statement combined annual interest = $810

810 = 130 r + 160

r = (810-160)/130

r = 5%

Rate of second loan = r+2 = 5+2

= 7%

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