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Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions.

Any equation in algebra that can be written in standard form as

ax^2+bx+c=0,

where x stands for an unknown integer and a, b, and c are known quantities, where a 0, is considered a quadratic equation.

The coefficients of the equation are the numbers a, b, and c, which can be separated by naming them, respectively, the quadratic coefficient, the linear coefficient, and the constant coefficient or free term.

Due to the fact that the solutions lie where the parabola crosses the x-axis, quadratic equations frequently have two solutions. The graph will cross twice if the vertex is below the x-axis and the parabola opens up, and it will cross twice again if the vertex is above the x-axis and the parabola opens down.

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Part (a)

Multiply both sides by 2, then add 9 to both sides.

z > 2

2z > 2*2

2z > 4

2z+9 > 4+9

2z+9 > 13 is the final answer for part (a)

--------------------------------------------------------------

Part (b)

We'll start with subtracting 4 from both sides, and then triple each side.

z > 2

z-4 > 2-4

z-4 > -2

3(z-4) > 3*(-2)

3(z-4) > -6 is the final answer for part (b)

--------------------------------------------------------------

Part (c)

Follow similar steps to that of part (a).

z > 2

2z > 2*2

2z > 4

2z+4 > 4+4

2z+4 > 8 is the final answer to part (c)

--------------------------------------------------------------

Part (d)

For now let's ignore the 5 out front and focus on 3z-2

z > 2

3z > 3*2

3z > 6

3z-2 > 6-2

3z-2 > 4

Now multiply each side by 5.

5(3z-2) > 5*4

5(3z-2) > 20 is the final answer to part (d)

--------------------------------------------------------------

Side note: The inequality signs did not flip when multiplying both sides by a positive number. The flip would only happen if we multiplied both sides by a negative number.

A statement of an order relationship between two numbers or algebraic expressions is known as an inequality in mathematics. It can be greater than, greater than or equal to, less than, or less than or equal to.

Using the inequality symbol, a mathematical statement known as an inequality depicts the relationship between two expressions. An inequality symbol denotes that the terms on each side are not equal.

It indicates that the expressions on the left and right should be bigger or less than one another, or vice versa. Literal inequalities are those where the relationship between two algebraic expressions is described by the inequality symbols.

According to the definition, a relationship is considered to be an inequality if it involves two real numbers or algebraic expressions and uses the symbols “>”, “<”, “≥”, “≤”.

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The measures of the missing angles are given as follows:

First we consider that when two angles form a ray, they are supplementary, meaning that the sum of their measures is of 180º.

Then the measures of angles 3 and 5 are given as follows:

The sum of the internal angles of triangle is of:

S(3) = (3 - 2) x 180º = 180º.

Hence the measure of angle 4 is obtained as follows:

m < 4 + 36 + 56 = 180

m < 4 = 180 - (36 + 56)

m < 4 = 88º.

Angles 2 and 4 are congruent, hence the measure of angle 2 is given as follows:

m < 2 = m < 4 = 88º.

The sum of the internal angles of a quadrilateral is of:

S(4) = (4 - 2) x 180º = 360º.

Hence the measure of angle 1 is obtained as follows:

m < 1 + 88 + 144 + 124 = 360

m < 1 = 360 - (88 + 144 + 124)

m < 1 = 4º.

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An example of a pattern rule is "add 3" which means that to find the next term in a sequence, you add 3 to the previous term.

To write a rule for a sequence, you need to identify the pattern. This involves looking at the differences between the numbers and seeing if there is a pattern of increasing or decreasing numbers. Once you have identified the pattern, you can then write a rule that expresses that pattern.

Examples of pattern sequences include the Fibonacci sequence (1,1,2,3,5,8,13,21,34, etc.), the even numbers (2,4,6,8,10, etc.), and the multiples of 3 (3,6,9,12,15, etc.).

To describe the pattern of a sequence, you need to look at the differences between the numbers and the pattern of increases or decreases. For example, in the Fibonacci sequence, the pattern is that each number is the sum of the two numbers before it so 1+1=2, 1+2=3, 2+3=5, etc.

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Answer:

[tex]I'(-0.5,0.25), J'(0.5,0.5), K'(0.5, -0.25)[/tex]

Step-by-step explanation:

Assuming the dilation is centered at the origin, we can use the rule that:

After simplification, the formula 4 (2x - 1) + 3 (2x + 5) becomes 14x + 11.

A number's arithmetic value for each digit can be expressed using the expanding form. Expanded numbers are numerical expressions that consist of the place value of each digit added to the total of the digits. To improve place value comprehension, expanded form is an excellent strategy.

It is given that,

4 (2x - 1) + 3 (2x + 5)

We have to expand and simplify the expression,

= 4 (2x - 1) + 3 (2x + 5)

Multiply the term out of the bracket into the bracket as

= 8x - 4 + 6x + 15

Add comparable terms together so that we can execute mathematical operations like addition and subtraction on the result.

= 14x + 11

As a result, the simplified expression for 4 (2x - 1) + 3 (2x + 5) will be 14x + 11.

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The angle when the secant intersect is as follows:

A secant is a line that intersects a circle in exactly two points.

If two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs.

Therefore,

m ∠GPE = 1 / 2 ( mGE -  mHF)

mGE = 99°

mHF = 41°

m ∠GPE = 1 / 2 (99 - 41)

m ∠GPE = 1 / 2 (58)

Therefore,

m ∠GPE = 29 degrees

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The linear equation for the relationship between the weight and number of months is y = 5.55x + 78.95.

First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., just one variable). Multiple variables may be present in a linear equation. Linear equations with two variables, for example, are used when a linear equation contains two variables.

We know that the sumo wrestler's weight is 140 kilograms after 11 months and he gained weight at a rate of 5.55 kilograms per month.

The equation for the relationship between the weight and number of months can be represented as:

y = 5.55x + b

Where y is the sumo wrestler's weight (in kilogram) after x month, 5.55 is the rate at which he gained weight per month, x is the number of months and b is the y-intercept.

To find the value of b, we can use the point (11, 140) which represents that after 11 months the sumo wrestler's weight is 140 kg, and substitute it into the equation:

y = 5.55x + b

140 = 5.55(11) + b

Solving for b:

b = 140 - (5.55 * 11)

b = 140 - 61.05

b = 78.95

So the complete equation is:

y = 5.55x + 78.95

Where y is the sumo wrestler's weight (in kilogram) after x months.

Therefore, The linear equation for the relationship between the weight and number of months is y = 5.55x + 78.95.

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The pattern shown by the erosion data measurements for the Western Beach is that the width decreases over time, with a steady decrease of about 10 feet per year. The pattern for the Dunes Beach is that the width increases over time, with an increase of about 5 feet per year.

Based on the data, it appears that the beaches will have approximately the same width around year 20. At this point, the Western Beach will have a width of approximately 50 feet and the Dunes Beach will have a width of approximately 90 feet.

To get a better approximation of when the two beaches will have the same width, it would be necessary to gather more data points over a longer period of time and to take into account other factors that may affect the beaches' widths such as the strength of the waves, the composition of the beach, and human interventions that may be taking place.

we can see that the function C(x) = 25x + 75 represents the labor cost (in dollars) for Bob's Auto Repair to replace your alternator, where x is the number of hours. We can use this function to find the cost of replacing an alternator that is estimated to take 5 hours of labor.

C(5) = 25(5) + 75 = 125 + 75 = 200

We also have the labor cost for the main competitor, Budget Auto Repair, in a table format.

Hours Cost

1          $90

2         $130

3         $170

We can see that the cost of labor increases as the number of hours increases. From the information provided it's hard to say which company would be cheaper to hire, however the company with the function C(x) = 25x + 75 would be cheaper if the alternator takes more than 4 hours of labor, otherwise Budget Auto Repair would be cheaper.

It's important to check the warranty, prices of parts, and reputation of both companies. If a company has a good reputation and a good warranty, it may be worth paying a little more for labor.

It's also a good idea to get a second opinion or ask for a quote from both companies before making a decision.

In conclusion, it's hard to say which company would be cheaper to hire based on the information provided, but it's recommended to check the warranty, prices of parts, and reputation of both companies, and to get a second opinion or quote from both companies before making a decision.

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Answer:

[tex]c+d=\langle-3,9\rangle[/tex]

Step-by-step explanation:

We simply add the respective horizontal and vertical components:

[tex]c+d=\langle 6,2 \rangle+\langle-9,7\rangle=\langle6+(-9),2+7\rangle=\langle6-9,9\rangle=\langle-3,9\rangle[/tex]

The proper method of filling a table with a function has been explained below.

Tables are helpful when we have to plot a function or we have to interpolate a function using given data points. A table usually consists of 2 or more 2 variables whose values are arranged either in a row or in a column. For filling a table with the help of a function, firstly we have to define the values of independent variables which we will input into the function to get the dependent variable's values.

When we get the value of independent data we will be inputting one of one those values in the function we will get the values of the function at the given point and hence the function will be filled by the output values.

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Answer:

∠S = 105°

∠T = 95°

Step-by-step explanation:

Cyclic quadrilateral:

   Quadrilateral MNST is a cyclic quadrilateral. In cyclic quadrilateral, the opposite angles are supplementary.

     m∠S + m∠M = 180°

 3x + 2x +  5 = 180

        5x  + 5  = 180           {Combine like terms}

                 5x = 180 - 5     {Subtract 5 from both sides}

                 5x = 175

                    x = 175 ÷ 5  {Divide both sides by 5}

                    x = 35°

∠S = 3x

    = 3 * 35

    = 105°

∠T = 3x - 10

     = (3*35) - 10

     = 105 - 10

     = 95°

Answer: area: 1/2 length * width, perimeter: add the three sides

Step-by-step explanation:

The volume of the chamber follows a pattern. The formula that represents the volume of the nth chamber is 6.3% of the previous chamber.

What is a pattern?

A pattern is a repeated arrangement of numbers, shapes, colours, or other elements. The Pattern can be associated with any kind of event or object. A pattern is defined as a set of numbers that are related to one another in a specific way. Patterns are sometimes referred to as sequences.

Given that:

Chamber 7: 1.207 cm³

Chamber 6: 1.135 cm³

Chamber 5: 1.068 cm³

Chamber 4: 1.005 cm³

Chamber 3: 0.945 cm³

Chamber 2: 0.889 cm³

Chamber 2: 0.836 cm³

                          1.207     1.135     1.068   1.005     0.945      0.889      0.836

First difference:        .072        0.067    0.063   0.060    0.056      0.053

Second difference:            0.005     0.004    0.003     0.004    0.003

Since the difference is not the same, thus the volume is not in a linear pattern. Then find the ratio consecutive volume:

1.207/1.135 ≈ 1.063

1.135/1.068 ≈ 1.063

1.068/1.005 ≈ 1.063

1.005/0.945 ≈ 1.063

0.945/0.889 ≈ 1.063

0.889/0.836 ≈ 1.063

Each chamber is 6.3% greater than the previous chamber. The pattern is exponential functions.

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all are statement except shut the window because sets are statement

square is a rectangle .The sun is a star is a statement

Describe finite set using an example.

What is the set in math?

Sets, in mathematics, are an organized collection of objects and can be represented in set-builder form or roster form. Usually, sets are represented in curly braces {}, for example, A = {1,2,3,4} is a set.

 A1 = { 1}   A2 = { 2 }  A3 = { 3 }..

  U  Ai = { 1 , 2 , ,,}

           = N is not a finite set

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The length of the side WX of the rectangle WXYZ, which is similar to the rectangle ABCD, is 40 inches.

According to the information provided, the rectangles ABCD and WXYZ are very similar to one another, which means they have the same ratio or proportional. If the ratio between two amounts is directly proportional, then as one quantity increases, the other amount also increases, and when one amount decreases, the other amount also decreases.

In this case, we are given that:

AB = 50 inches

BC = 40 inches

XY = 32 inches

To calculate the length of WX, we may apply the formula that is as follows =

AB/WX = BC/XY

50/WX = 40/32

40WX = 50x32

WX = 40

As a result, the length of WX in rectangle WXYZ is 40 inches

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Answer:

4a + 25.2.

Step-by-step explanation:

2/3(6a+9)+19.2

= 2/3 * 6a + 2/3 * 9 + 19.2

= 4a + 6 + 19.2

= 4a + 25.2.

Answer:

f(x)=a(b)^x

Step-by-step explanation:

exponential functions are usually growth or decay,

a represents the base, b is the change, and x is how much time (depending on the question). if b is larger than 1 ex: 1.08, it is growth. if it is less than 1 ex: 0.4, it is decay

The exponential form formula is a^b = c, where a is the base, b is the exponent, and c is the result. In this formula, a is raised to the power of b, resulting in the value c.

Answer:1111

Step-by-step explanation:

11111

The magnified length of the objects is 0.01 meters in decimal form, based on the height of object and magnification power.

The formula to find magnified length is -

Magnification = image height ÷ object height. Here image height is magnified length.

Keep the values in formula -

Image height = 10⁵ × [tex] {10}^{-7} [/tex]

Performing multiplication on Right Hand Side of the equation. Note that power of products will be used to find the magnified length. The exponents will be added.

Image height = [tex] {10}^{5 + (-7)} [/tex]

Performing addition of exponents to find the image height

Image height = [tex] {10}^{-2} [/tex] meters

Writing the image height in decimal form - 0.01 meters

Therefore, the height of image or magnified length is 0.01 meters.

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Answer:

[tex]\huge\boxed{\sf Yes.}[/tex]

Step-by-step explanation:

y = 6x - 9 ---------------(1)

y = 2x + 3 --------------(2)

So,

x = 3, y = 9

Put this in Eq. (1) to verify.

9 = 6(3) - 9

9 = 18 - 9

9 = 9 [Equation satisfied]

Now, put x = 3, y = 9 in Eq. (2)

9 = 2(3) + 3

9 = 6 + 3

9 = 9 [Equation satisfied]

Since, both the equations are satisfied by the values of x and y, we can say that x = 3 and y = 9 is the solution to the system.

[tex]\rule[225]{225}{2}[/tex]

Answer: Yes, it is a solution

Step-by-step explanation:

Plug (x,y) values into the equations.

Plug in (3,9)

y=6x-9  ---->.  (9)=6(3)-9 ----> 9=18-9 ----->   9=9

y=2x+3 ------>.  (9)=2(3)+3 ----> 9=6+3 ----> 9=9

When know (3,9) is a solution because each side has the same value.

Example:

8=9 Not a solution

5=5 A solution

The coordinates of the points after the translation are:

All the points are translated on the same way, so let's analyze the translation of P to P'.

The coordinates of Pare (5, 8), and P' is at (3, 4)

Then the translation is:

(3, 4) - (5, 8) = (3 - 5, 4 - 8) = (-2, -4)

So we just need to subtract 2 to the x-value and 4 to the y-value.

The coordinates of Q and R are:

Q = (7, 8)

R = (8, 5)

Then the translated points are:

Q' = (7 - 2,8 - 4) = (5, 4)

R' = (8 - 2, 5 - 4) = (6, 1)

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Answer: 6 in each batch

Step-by-step explanation: 54/9 = 6

The balanced equation is:

CCl₄ --> C + 2Cl₂

The law of conservation of mass states that when a chemical reaction takes place, the mass of the reactants and products should be equal.

Here is an equation that describes a chemical reaction:

CCl₄ --> C + 2Cl₂

Thus, add 2 atoms of Cl to balance the equation.

Then,

The balanced equation is:

CCl₄ --> C + 2Cl₂

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By setting each factor to 0, you can get the roots, or solutions, of the polynomial equation P(x) = 0 by figuring out what x is. Factor the polynomial equation to find the solution.

Constants and indeterminates are parts of polynomial algebraic expressions.

One could consider polynomials to be a subset of mathematics.

They are used to express numbers in almost all areas of mathematics, and calculus is one of those areas where they are particularly important.

A polynomial is a specific sort of expression.

An expression is a mathematical statement that does not contain the equals sign (=). Let's look at the following descriptions of polynomials' definition and applications.

All the exponents of an algebraic expression called a polynomial must be whole numbers.

Any polynomial must have non-negative integer variable exponents. We cannot divide a polynomial by a variable even though it contains variables and constants.

Hence, By setting each factor to 0, you can get the roots, or solutions, of the polynomial equation P(x) = 0 by figuring out what x is. Factor the polynomial equation to find the solution.

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The solution set of the following equation (- 8x +  x + 15) = ( - 7x + 12) is zero i.e this equation does not have any solution.

Equation is (- 8x + x + 15) = (-7x + 12)

Now solving

(-8x + x  + 7x ) = ( 12 - 15 )

( - 7x +7x) = (-3)

( 0 )= ( - 3)

Since 0 = -3 is not correct, therefore, the equation does not have any solution.

So it is stated that the equation (- 8x +  x + 15) = ( - 7x + 12) does not have any solution in its solution set.

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