Solve the inequality:
x(2x-1)>15

A photo with dimension 5 x 7 in is reduced so that the width becomes 4 in. The reduced size of the length of the photo is 5.6 in.

When two shapes are identical but differ in size, they are considered to be similar shapes. A similar shape can be created by scaling all of the lengths of the original shape. This means they've been stretched or shrunk in the same proportions. This is referred to as the scale factor.

In this case, the original photo and the smaller photo are similar shapes. Hence, the proportion of the corresponding sides have to be the same.

We can find the scale factor as:

Scale factor = reduced width / initial width

                   = 4 in. / 5 in. = 0.8

The length has to be reduces at the same scale factor. Therefore,

reduce length = 0.8 x 7 in = 5.6 in.

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Simplifying the linear inequality, x has a value in the range of -2 to + 1 and can be expressed as -2 < x < 1

A mathematical statement in which the maximum power of the variable is 1 is known as a linear inequality. The equation "ax + b c" or "ax + b > c" is used to describe it, where "a," "b," and "c" are constants and "x" is the variable. The collection of all 'x' values that satisfy the inequality is the solution to a linear inequality. A straight line on a coordinate plane represents the graph of a linear inequality.

In the given problem, the linear inequality is;

1 < x + 3 < 4

To solve for x, we have to subtract 3 from all sides of the inequality

-3 + 1 < x + 3 - 3 < 4 - 3

Simplifying this;

-2 < x < 1

The solution of value of x is between -2 to + 1

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All these antiderivatives are equivalent as they are different ways of solving the same problem and differ only by a constant value.

What is an antiderivative?

An antiderivative, also known as a primitive function or indefinite integral, is the reverse operation of taking a derivative. In other words, if the derivative of a function f(x) is g(x), then f(x) is said to be an antiderivative of g(x).

The antiderivative of sin(x)cos(x) can be found using the product-to-sum identities:

(sin(x)cos(x))' = (sin(x)cos(x))'
                      = (1/2)(cos(2x) - sin(2x)) + C

Another way to find the antiderivative of sin(x)cos(x) is to use the chain rule:
(sin(x)cos(x))' = (sin(x))'cos(x) + sin(x)(cos(x))'
                     = -sin(x)cos(x) + cos(x)sin(x) + C

A third way is to use integration by parts, where we take u = sin(x) and dv = cos(x)dx. This gives us:
(sin(x)cos(x))' = sin(x)cos(x) - ∫cos(x)sin(x)dx + C

Another way is to use the substitution method, where we set u = cos(x) and du = -sin(x)dx. This gives us:
(sin(x)cos(x))' = sin(x)cos(x) + ∫-sin(x)cos(x)du + C

Lastly, we can use the trigonometric identity method where we use sin(2x) = 2sin(x)cos(x) and integrate.
This gives us: (sin(x)cos(x))' = (1/2)sin(2x) + C

Hence, All these antiderivatives are equivalent as they are different ways of solving the same problem and differ only by a constant value.

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DSS help users make decisions by providing them with access to information, analytical tools, and models. ES are designed to emulate the decision-making capabilities of experts in a particular field. Finally, AI systems are designed to mimic human intelligence and behavior.

1. Transaction Processing Systems (TPS)

2. Management Information Systems (MIS)

3. Decision Support Systems (DSS)

4. Expert Systems (ES)

5. Artificial Intelligence (AI)

1. Transaction Processing Systems (TPS): These systems are designed to capture, store, update and retrieve transaction data for business operations. Examples include point-of-sale systems, accounting systems and inventory control systems.

2. Management Information Systems (MIS): These systems are designed to provide managers and decision makers with the information they need to make informed decisions. Examples include financial reporting systems, sales tracking systems, and customer service systems.

3. Decision Support Systems (DSS): These systems are designed to help users make decisions by providing them with access to information, analytical tools, and models. Examples include budgeting systems, forecasting systems, and data mining systems.

4. Expert Systems (ES): These systems are designed to emulate the decision-making capabilities of experts in a particular field. Examples include medical diagnosis systems, legal advice systems, and financial planning systems.

5. Artificial Intelligence (AI): These systems are designed to mimic human intelligence and behavior. Examples include natural language processing systems, robotics systems, and machine learning algorithms.

The five main types of systems are Transaction Processing Systems (TPS), Management Information Systems (MIS), Decision Support Systems (DSS), Expert Systems (ES), and Artificial Intelligence (AI). TPS are designed to capture, store, update and retrieve transaction data for business operations, while MIS provide managers and decision makers with the information they need to make informed decisions. DSS help users make decisions by providing them with access to information, analytical tools, and models. ES are designed to emulate the decision-making capabilities of experts in a particular field. Finally, AI systems are designed to mimic human intelligence and behavior.

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Answer: 180 degrees

Step-by-step explanation:

If there are two parallel lines such as we could see in the problem, you can basically carry some angles to the other corners if these corners show the same direction.

In this case, you can carry "a" angle to the corner which is at the top of the "b" angle. Then, you can notice that a and b angles are complementary to 180 degrees for each other. So, this is the answer.

Note: Actually, you can also realize that these two corners at the intersections of the lines should have the same angle otherwise there would be no parallelism.

Jim can buy 3.75 pounds of kind 1 and 1.25 pounds of kind 2 chocolate for $10 by setting up and solving a system of equations.

The question is asking how much of each kind of chocolate Jim can buy for $10. To solve this, you can set up a system of equations.

Let x = pounds of kind 1, and y = pounds of kind 2

x + y = 5 (total pounds of chocolate)

1.8x + 2.3y = 10 (cost of chocolate)

Solving the system of equations, you get x = 3.75 pounds of kind 1 and y = 1.25 pounds of kind 2. Jim can buy 3.75 pounds of kind 1 and 1.25 pounds of kind 2 for $10.

1.8x + 2.3y = 10

1.8x = 10 - 2.3y

x = (10 - 2.3y)/1.8

x + y = 5

x = 5 - y

(10 - 2.3y)/1.8 = 5 - y

10 - 2.3y = (1.8)(5 - y)

10 - 2.3y = 9 - 1.8y

1.2y = 10 - 9

1.2y = 1

y = 1/1.2

y = 0.833 (rounded to 1.25)

x = 5 - y

x = 5 - 0.833

x = 4.167 (rounded to 3.75)

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Answer:

x = 2√2

Step-by-step explanation:

If is inversely proportional to x², then:

[tex]y \propto \dfrac{1}{x^2} \implies y=\dfrac{k}{x^2} \quad \textsf{(for some constant k)}[/tex]

Given:

Substitute the given values into the found equation and solve for k:

[tex]\implies 2=\dfrac{k}{4^2}[/tex]

[tex]\implies 2=\dfrac{k}{16}[/tex]

[tex]\implies k=32[/tex]

Therefore:

[tex]y=\dfrac{32}{x^2}[/tex]

To find the value of x when y = 4, substitute y = 4 into the found equation and solve for x:

[tex]\implies 4=\dfrac{32}{x^2}[/tex]

[tex]\implies x^2=\dfrac{32}{4}[/tex]

[tex]\implies x^2=8[/tex]

[tex]\implies x=\sqrt{8}[/tex]

[tex]\implies x=\sqrt{4 \cdot 2}[/tex]

[tex]\implies x=\sqrt{4} \sqrt{2}[/tex]

[tex]\implies x=2\sqrt{2}[/tex]

N'  =(-2, 6) will be the coordinates of vertex N' of the image.

A coordinate system is a system made up of a collection of points, lines, or surfaces, where each point is given a specific position, or coordinate.

Given that,

Triangle MNP will be dilated according to the rule  (x,y), where point P is the center of dilation.

The coordinate N = (0, 2)

The rule of dilation with scale factor k =2 and point P is the center of dilation is given by: (x,y) =>(2x-2, 2y-2)

thus, N(0,2)=N'(2(0)-2,2(2)+2) = N'(-2,6)

Therefore, N'  =(-2, 6) will be the coordinates of vertex N' of the image.

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Answer:

The dimensions of the larger triangle are 48 cm * 15 cm.

The following are true assertions concerning the polynomial function: The highest level is a 3. It is trinomial since it has three terms. One of the factors is (x-1).

A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. A polynomial is an expression in mathematics that consists of variables (also known as indeterminates) and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Polynomial equations are expressions that contain many constants and variables. The conventional way to write a polynomial equation is to place the greatest degree first, followed by the constant term.

Here,

f(x)=x³-x²-3

The statements that are true about the polynomial function: The highest degree is 3. It has 3 terms so it is trinomial. It's one of the factor is (x-1).

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Complete question:

which statements are true about the polynomial function f(x)=x^3-x^2-3

The highest level is a 3.

It is trinomial since it has three terms.

One of the factors is (x-1).

f(x) divided by (x+1) has a remainder of 0

The missing side is  6√13 in the given right-angled triangle.

If one of a triangle's angles is a right angle (90 degrees), the triangle is known as a right-angled triangle or just a right triangle, according to the definition of a right triangle. Triangle ABC is a right triangle that contains the base, altitude, and hypotenuse in the example image.

Base AB, altitude AC, and hypotenuse BC are shown in this equation. The largest side and the side that faces away from the right angle in a right triangle is the hypotenuse, and it is this side that is significant.

Given that A right angle triangle has sides 12cm and 18 cm

y = [tex]\sqrt{12^2 + 18^2}[/tex]

y = 6√13

Thus, the missing side y is  6√13.

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The AM = 6 because of Definition of Perpendicular Bisector.

The correct option is A.

Those lines that are perpendicular to each other that means create an angle of 90° at intersecting point are perpendicular lines.

Given:

Kyle is creating a frame for a model car.

He begins by piecing two rods together,

as shown in the attached diagram.

A perpendicular bisector means,

a line intersects another line.

And divide into two same parts.

And angle between two lines is 90°.

Here, the if the one piece of one rod is 6.

Then that means, the rod is divided into 2 equal parts.

Therefore, the definition is the definition of Perpendicular Bisector

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Triangle ΔABC is comparable to triangle ΔABC, which was formed after ABC's dilatation. The appropriate answers are The characteristics of dilations show that angles ∠B =∠ B'.

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the flanks of the hook, that converge at the vertex of both the angle, which is located in the centre. Two rays may combine to form an angle in the plane in which they are positioned. Two planes colliding results in an angle as well. We refer to them as dihedral angles.

Here,

Assuming that A (0, -3), C (0, 5), and B are the triangle's vertices (6, 3)

Set point P to be (0, 0)

There is;

A' = 3/2 * (0,-3) = (0,-9/2) = (0,-4.5) (0,-4.5)

C' = 3/2 * (0,5) = (0, 15/2) = (0,7.5) (0,7.5)

B' = 3/2 * (6,6/3) = (9 , 9/2) = (9,4.5) (9,4.5)

Therefore, on a scale, the image of ABC is bigger than that of the image of A'B'C.

The proportion of the adjacent angles of ABC is given by a factor of 1.5.

since and "A'B'C" are both equal, the angle made by section BC and

BA,

AB/sin(C) = AC/sin(B)

AB/sin(C) = A'C'/A'B' = sin(B)/sin (C)

This means that

sin(B)/sin(C) = sin(B')/sin(C').

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The complete question is "A. Dilate triangle ABC using center p and scale factor 3/2.

B. What do properties of dilations tell you about B'? (please answer B)"

The exact value of  the cosine ( (4π)/3) ] is -0.5.

The exact value of  the cosine function [ Cos ( (4π)/3) ] is calculated by resolving the pi radian into degrees as shown below.

π radian = 180 degrees

The exact value of  the cosine ( (4π)/3) ] is calculated as

Cos ( ( 4π ) / 3 ) = cos ( 4 x 180 / 3 )

cos ( 4 x 180 / 3 )  = cos ( 4 x 60 )

cos ( 4 x 60 ) = cos ( 240 )

cos ( 240 ) = -0.5

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Given line equation y=x+2

Compare above equation with slope intercept form y=mx+b

slope m=1 and y-intercept=(0,2)

Here it is line equation graph

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A formula is used to find a Center of a circle with a (h, k) center and a radius of r has the equation:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

A circle is a collection of all points in a plane that are uniformly distanced from a fixed point. The radius of a circle is the difference between the center and any point itself along the perimeter.

A circle is a closed curve that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center. The equation for a circle with a (h, k) center and a radius of r is:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

This is the equation's standard form. So, if we know the radius and center coordinates of a circle, we can rapidly determine its equation.

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Answer:

See below

Step-by-step explanation:

Better description of what you want.

D)

3 - 2(s - 1) = 13 + 6s  Distribute the -2

3 -2s + 2 = 13 + 6s  Combine like terms

5 - 2s = 13 + 6s  Add 2s to both sides

5 - 2s + 2s = 13 + 6s + 2s

5 = 13 + 8s  Subtract 13 from both sides

5 - 13 = 13 - 13 + 8s

-8 = 8s  Divide both sides by 8

[tex]\frac{-8}{8}[/tex] = [tex]\frac{8s}{8}[/tex]

-1 = s

E)

2(n + 9) = -6 (2n-5) + 8  Distribute the 2 nd the -6

2n + 18 = -12n + 30 + 8  Combine like terms

2n + 18 = -12n + 38  Add 12n to both sides

2n + 12n + 18 = -12n + 12n + 38

14n + 18 = 38  Subtract 18 from both sides

14n + 18 - 18 = 38 - 18

14n = 20  Divide both sides by 14

[tex]\frac{14n}{14}[/tex] = [tex]\frac{20}{14}[/tex]

n = [tex]\frac{20}{14}[/tex]  Divide the numerator and denominator by 2 to simplify

n = [tex]\frac{10}{7}[/tex]

F)

5(4k -3) -5k = 10 +2(3k + 1)  Distribute the 5 and the 2

20k -15 - 5k = 10 +6k +2  Combine like terms

15k - 15 = 12 + 6k  Subtract 6k from both sides

15k - 6k - 15 = 12 + 6k -6k

9k -15 = 12  Add 15 to both sides

9k - 15 + 15 = 12 + 15

9k = 27  Divide both sides by 9

[tex]\frac{9k}{9}[/tex] = [tex]\frac{27}{9}[/tex]

k = 3

The number of 2-button special moves possible with the controller is 42 combinations.

For the given query:

The number of total buttons : 4 + 3 = 7

Number of digits two be formed 2-button special moves.

So,

First place cane be filled with all 7 numbers.

Second place can be filled with remaining 6 numbers.

Thus,

= 7 x 6

= 42 combinations.

Thus, the number of 2-button special moves possible with the controller is 42 combinations.

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Each walkway is around 51 yards long.

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a²+b²=c²

However, it can also be written in the form of c²=a²+b²

In order to find the hypotenuse, you will have the length of two sides, for example, these could be 3 and 4.

As 'C' is always the hypotenuse, you have to work out the two other lengths, and you do this by squaring the numbers.

3²=9 and 4²=16.

As you're looking for C, you've got to add these together

9+16=25

As a²+b²=c², this means that the answer for C is the square root of 25.

√25= 5

Divide the square in half to make a right triangle. Now, use Pythagoras' theorem to solve for the hypotenuse.

a²+b²=c²

⇒ 36²+36²=c²

⇒ 1296+1296=c²

⇒ 2592=c²

∴ c =50.9116

Round to the nearest whole number, we get c = 51 yards.

Thus, each walkway is around 51 yards long.

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The bus 2 will pass bus 1 at 12.30 pm, when both are at 360 miles.

The bus 1 starts half hour earlier than bus 2. But since bus 2 is faster, it will overtake at some point. At 8 am, bus 1 will start. By the time 8.30, it will cover a distance of 40 miles.

Bus 2 starts at 8.30, So it will be at 0 miles.

By 10, the bus 1 will be at 160 miles, bus 2 at 135 miles

By 10.30, the bus 1 will be at 200 miles, bus 2 at 180 miles.

By 11.30, bus 1 will be at 280 miles, bus 2 will be at 270 miles

By 12.30, bus 1 will be at 360 miles, bus 2 will be at 360 miles.

So at the 360 the, the both the buses passes each other.

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Based on the diagram presented, it can be concluded that for every 1 cup of fruit juice, 1.2 cups of iced tea and 0.6 cup of sugar are used.

The diagram shows the three ingredients required to prepare a pitcher of fruit tea and the amount of the ingredients required.

Ingredients required:

Fruit juce: 2.5 cups

Sugar: 1.5 cups

Iced tea: 3 cups

Let's use the rule of three to find the answer:

Sugar required:

2.5 cups = 1.5 cups

1 cup  = x

x= 1.5 / 2.5 = 0.6 cups

Iced tea required:

2.5 cups = 3 cups

1 cup  = x

x = 3 / 2.5 = 1.2

Note: Here you can find the missing diagram:

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The circumference of a circle with a radius of 18 feet is 113.04 ft.

The distance around the circle's edge is referred to as the circumference. It is a basic characteristic of a circle and is incorporated into a number of geometric and trigonometric calculations.

C = 2πr, where C is the circumference, is a mathematical constant, and r is the circle's radius, is the formula for calculating a circle's circumference. An irrational number is one that contains an endless number of decimal places and cannot be stated as a ratio of integers. However, the value of is roughly 3.14 for the majority of practical purposes.

The circle's radius in the provided situation is 18 feet. We can use pi = 3.14 to determine the closest approximation for the circumference of this circle.

C = 2πr = 23.1418 = 113.04 feet.

  So ,the circumference of circle is 113.04 feet.

       Therefore, 113.04 feet is a circle's circumference with a radius of 18 feet.

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Answer:

x = 11 , CE = 98

Step-by-step explanation:

• If 2 chords are congruent, then they are equidistant from its centre , so

CE = FC , that is

10x - 12 = 8x + 10 ( subtract 8x from both sides )

2x - 12 = 10 ( add 12 to both sides )

2x = 22 ( divide both sides by 2 )

x = 11

Then

CE = 10x - 12 = 10(11) - 12 = 110 - 12 = 98

Answer:

A; -6

Step-by-step explanation:

Well, the cube root of 216 is just 6, and because the root is an odd number, we can allow negative numbers as the answer instead of imaginary numbers. Therefore the real cube root of -216 is just -6

As stated in the problem, the equation can be modeled by the equation:

[tex]y=0.35x[/tex]

The problem also defines the meaning of these variables:

y = bounce height in feet

x = release height in feet

Now, the question asks "If the ball is released from a height of 70 feet, what is the height the ball will achieve after the first bounce?"

From this question, we know that we want to solve for bounce height (y). We are also given the release height (x) of 70. Plug this value into the equation we were given at the start.

[tex]y=0.35(70)[/tex]

Now, just multiply the two values together:

[tex]y=24.5[/tex]

Therefore, we now know that the ball achieved a bounce height of 24.5 ft on the first bounce!

a function that transforms the parent root function with a horizontal compression by a factor of 5 and a downward shift of 10 units is: [tex]f(x) = \sqrt[n]{5x} -10[/tex]

The function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the another variable).

A function is described as a relationship between a group of inputs and one output each. A function is, to put it simply, a connection between inputs in which each input is connected to exactly one output.

Parent root function is given by:

[tex]f(x) = \sqrt[n]{x}[/tex]

According to rules-

Combining these 2 transformation gives us the function: [tex]f(x) = \sqrt[n]{5x} -10[/tex]

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The correct option for the given congruence of triangle is:

ΔGTA ≅ ΔQME.

Consider the order in the given triangles: ΔGTA and ΔQME:

GT = QM

TA = ME

AG = EQ

Thus,

ΔGTA ≅ ΔQME

By using the side side side (SSS) congruence.

Therefore, the correct option for the given congruence of triangle is:

ΔGTA ≅ ΔQME.

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The correct number of question is 11.

Answer: 12

Step-by-step explanation:

For the equation to have infinitely many solutions, it must be an identity.

[tex]3(5+x)+kx+8=7(2x+3)+(x+2)\\\\15+3x+kx+8=14x+21+x+2\\\\x(k+3)+23=15x+23\\\\\implies k+3=15 \implies k=12[/tex]

If Young is replacing fencing around his rabbit pens and garden , then to replace the two rabbit pens and his garden the number of feet of fencing required is 76 ft .

The Dimensions of the Rabbit Pen is :

the length of rabbit pen is = 3.5 ft ;

the width of the rabbit pen is = 4.5 ft ;

the Dimensions of the Garden are :

the length of garden is = 12 ft ;

the width of garden is = 10 ft ;

So , Perimeter of Rabbit Pen is = [tex]2\times (Length + Width)[/tex] ;

Perimeter = [tex]2\times (3.5 + 4.5)[/tex]

= 16 ft .

Since there are 2 rabbit pens ,

So , the Perimeter of two rabbit pen is = [tex]16+16[/tex] = 32 ft ;

And , Perimeter of Garden is = [tex]2\times (12 + 10)[/tex] = 44 ft .

Total Perimeter of Pen and Garden is  = [tex]32+44[/tex] = 76 ft .

Therefore , Young would require 76 ft of fencing to replace the two rabbit pen and garden .

The given question is incomplete , the complete question is

Young is replacing the fencing around his rabbit pens and garden. The table shows the dimensions of the different areas. How many feet of fencing will he need to replace two rabbit pens and his garden?

Item             Length(ft)   Width(ft)

Rabbit Pen      3.5             4.5

Garden             12               10

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