What is ideal or real solution?

For Quadratic equation, It is possible to know if there are 2 real solutions by examining the discriminant that is [tex]b^2-4ac[/tex] of the equation [tex]ax^2+bx+c[/tex].

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

discriminant : [tex]b^2-4ac[/tex]

if [tex]b^2-4ac[/tex] is positive, Both solutions are real.

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[tex]24x+15=25x+45[/tex]

Subtract 25x from both sides:

[tex]24x+15-25x=25x+45-25x[/tex]

[tex]-x+15=45[/tex]

Subtract 15 from both sides:

[tex]-x+15-15=45-15[/tex]

[tex]-x=30[/tex]

Divide both sides by -1(to remove negative from variable):

[tex]\dfrac{-x}{-1} =\dfrac{30}{-1}[/tex]

[tex]\fbox{x = -30}[/tex]

Answer:

[tex] \sf \: x = - 30[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ 24x + 15 = 25x + 45

Then the value of x will be,

→ 24x + 15 = 25x + 45

→ 24x - 25x = 45 - 15

→ -x = 30

→ [ x = -30 ]

Hence, the value of x is -30.

After solving, the smallest number of yellow marbles are 4.

In the given question, all of Marcy's marbles are blue, red, green, or yellow.

One third of her marbles are blue, one fourth of them are red, and six of them are green.

We have to find the smallest number of yellow marble.

The 6 green marbles and yellow marbles of the total marbles = 1 - (1/3) - (1/4)

The 6 green marbles and yellow marbles of the total marbles = 5/12

Now, suppose the total number of marbles is x

We know the number of yellow marbles is 5/12 x-6 and a positive integer.

Therefore, 12 must divide x

Trying the smallest multiples of 12 for x.

We see that when x = 12

We get there -1 yellow marbles, which is impossible.

However, when x = 24 here are

= 5/12 x - 6

= 5/12*24 - 6

= 4

So, the yellow marbles are 4 which must be the smallest possible.

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The fraction of the two squares that is shaded exists 5/16 area shaded.

A diagonal is a line segment connecting two opposite corners (vertexes) of a polygon, however it is not an edge (side). In other words, it connects any two non-adjacent polygonal vertices. Therefore, by connecting any two vertices in a polygon directly (i.e., without using a side), we create a diagonal.

A line segment known as a diagonal joins two polygonal vertexes (corners), although it is not an edge (side). To put it another way, it joins any two polygonal vertices that are not adjacent. Therefore, by connecting any two vertices in a polygon directly (i.e., without using a side), we create a diagonal.

The triangle on the bottom exists 1/2 × 1/2 × 1/2  of the original area of the lower square = 1/8 of the lower square

2 square =  [1/2 (square) + 1/8 (square) ] / 2 square  

= 5/16 area shaded

Therefore, the fraction of the two squares that is shaded exists 5/16 area shaded.

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The fraction of the two squares that is shaded exists 5/16 area shaded.

A diagonal is a line segment that joins two opposed polygonal corners (vertexes), although it is not an edge (side). In other words, it joins any two polygonal vertices that are not neighbouring. As a result, we can make a diagonal by directly joining any two vertices of a polygon (i.e., without utilising a side).

Although it is not an edge, a line segment known as a diagonal connects two polygonal vertexes (corners) (side). In other words, it connects any non-adjacent pair of polygonal vertices. As a result, we can make a diagonal by directly joining any two vertices of a polygon (i.e., without utilising a side).

The triangle on the bottom exists 1/2 × 1/2 × 1/2  of the original area of the lower square = 1/8 of the lower square

2 square =  [1/2 (square) + 1/8 (square) ] / 2 square  

= 5/16 area shaded

Therefore, the fraction of the two squares that is shaded exists 5/16 area shaded.

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Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , 5) and a "p" distance of negative 2 units, since it's opening to the left, so

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=5\\ p=-2 \end{cases}\implies 4(-2)(~~x-0~~) = (~~y-5~~)^2\implies {\Large \begin{array}{llll} -8x=(y-5)^2 \end{array}}[/tex]

A hat symbol (^) is used to represent an estimated value in regression analysis.

We know that in regression analysis, the predicted values are the y-hat values.

Here y is the output variable or dependent variable

A 'hat' symbol (^) is used to denote an estimator.

A ^ symbol is placed over the variable name to denote the estimated value.

In matrix system, a hat matrix is nothing but the projection matrix.

It projects the vector of observations, y, onto the vector of predictions, y^

We know that a vector has magnitude and direction. A ^ symbol is used is represent the direction of unit vector.

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Answer:

Points identify starting and ending positions, and a line (in this case line segment) connects such points to show the distance between the two points.

Step-by-step explanation:

Using the calculator there are various methods according to the calculator we used and the approach we follow, Basic answer is to select N and generate random number.

Random sampling is a method of selecting a sample from a population in such a way that each member of the population has an equal probability of being selected. This ensures that the sample is representative of the population, and reduces bias in the sampling process. In simple random sampling, a random sample is drawn from a larger population by using random number generators, tables of random numbers, or other methods that ensure that each member of the population has an equal chance of being selected.

A sample is a portion or a subset of a population that is selected for the purpose of studying characteristics of the population. The sample is used to make inferences or conclusions about the population from which it was drawn. The sample is usually smaller in size than the population, and it is selected through a process called sampling. The process of sampling is used to select a sample that is representative of the population, meaning that the sample has similar characteristics as the population.

Define the population size (N) and the sample size (n) that you want to obtain.

Use the calculator's random number generator to generate a random number between 1 and N. This will be the first element of your sample.

Repeat step 2 to generate the remaining elements of the sample, making sure that each element is different from the previous ones.

Record the elements of the sample, which are the random numbers that have been generated.

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Answer:

a ≥ -5

Step-by-step explanation:

Think like this is a number line

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

-6              -5           -4            -3        -2          -1       0         1        2         3   4

and all the inequality says is for it to be bigger than -6 so than is -5, -4, -3, -2 -1, 0,1 and so on. So the answer is a>-6 or a≥-5

Answer: 12

Step-by-step explanation: 3/4 divid by 3

The mean of negatively skewed facts can be less than the median. If the information graphs symmetrically, the distribution has 0 skewness, no matter how lengthy or fat the tails are.

What is a curve ?

Curve can be defined as the path on which it is usually generated by the equation.

In statistics, a negatively skewed (also called left-skewed) distribution is a sort of distribution wherein more values are targeting the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.

negatively skewed distribution refers to the distribution kind where greater values plot at the graph's proper facet, the tail of the distribution is longer on the left aspect, and the suggest is decrease than the median and mode. It is probably 0 or poor due to the data being distributed negatively.

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Therefore the rounded numbers are 23.54 and 0.9160.

An integer containing one or more "0"s at the end in a certain base is said to be round. In this way, 590 is more rounded than 592 but less rounded than 600. A round number is frequently understood to stand for a value or values close to the nominal value given in both formal and informal language.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold mathbb Z.

a. To round 23.54 to five decimal places, we look at the sixth decimal place, which is 4. Since 4 is less than 5, we leave the fifth decimal place as is, and the number rounded to five decimal places is 23.54.

b. To round 0.916 to five decimal places, we look at the sixth decimal place, which is 1. Since 1 is greater than or equal to 5, we increase the fifth decimal place by one, and the number rounded to five decimal places is 0.9160.

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To solve x easily, shift the variables to one side, and shift all the other values including constants to the other side.

Solve for x means finding the value of x in an equation involving one variable that is x or with different variables like finding x in terms of y. Whatever the case is you are required to find  the value of x, for which the given equation holds true.

For example, if the equation is given as: 2x - 50 = 4

Now solve the tjis equation for x by keeping the term with variable x to one side, and shifting all the other values such as constants to the other side.

now

2x = 4 + 50

2x = 54

x = 54/2

x= 27

This is the required value of x which is obtained after solving the equation for x.

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Answer: B. 3750

Step-by-step explanation:

We start by converting the percentage 25% to the decimal 0.25.

Next, we multiply the original price by this decimal (5000*0.25=1250)

And Finally, Since it is a loss we subtract the 1250 from the original price.

5000 - 1250 = 3750

Answer: 8

Step-by-step explanation: Based on the given conditions, formulate 25/5+3 Reduce  the sum or difference: to 8 therefore the answer is 8

Answer:

down below

Step-by-step explanation:

The quotient means the total amount that comes from dividing two things. In this case, the problem is asking for 25 and 5 to be divided. 25 divided by 5 is 5. You can check this by multiplying 5 and 5 to get 25. So, you know it's right. Now, take 5 and add 3 to it. 5 + 3 = 8. So, the answer is 8.

Hope this helps! :)

The log function with base 10 is called the “common logarithmic functions” and the log with base e is called the “natural logarithmic function”. The logarithmic function is defined by, if logab = x, then ax = b.

The log with a base "e" (log e) is the same thing as In

The natural logarithmic function log e  refers to its logarithmic function of the base of the constant e. For this equation to be equivalent in logarithm;

We can say that:

log e = ln

Logarithm may alternatively be defined as the exponent power to which a base must be raised in order to produce a given number.

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The total amount of payment for calls is Rs 648

From the problem, the following information is deduced to help solve the problem

the minimum charge of 175 calls is Rs 180 and Rs 1.50 per calls for additional calls

The total call reading

= present reading - former reading

= 7577 - 5577

= 2000

the number of 175 calls in 2000

= 2000 / 175

= 11 3/7 approximately 12

Total cost of calls

175 calls = Rs 180 + Rs 1.50 * 12

= 180 + 1.50 * 12

= Rs 180

Adding other charges to Rs 180

= 180 * 1.1 + 180 * 1.3 + 180 * 1.2

= Rs 648

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{35}{m}=\cfrac{m}{7}\implies 245=m^2\implies \sqrt{245}=m\implies \sqrt{7^2\cdot 5}=m\implies 7\sqrt{5}=m[/tex]

we can find out the polynomial by the degree of the Polynomial.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division

Degree of polynomial

The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.

Types of polynomial

Depending upon the number of terms, polynomials are divided into the following categories:

1-Monomial

2-Binomial

3-Trinomial

4-Polynomial containing 4 terms (Quadronomial)

5-Polynomial containing 5 terms (pentanomial ) and so on.

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The four types of problem solving can be named as Trial and Error , Algorithms , Inductive Reasoning and Deductive Reasoning .

What is Problem Solving ?

The Problem solving can be defined as the act of defining a problem , finding cause of problem, identifying, prioritizing and selecting the alternatives for solution and implementing it .

The four types of problem solving are :

(i) Trial and Error : It is defined as trying the different ways of doing something until we find the best solution .

(ii) Algorithms : The algorithm can be defined as a  set of step by step procedures which provides correct answer to a particular problem.

(iii) Inductive Reasoning : It is defined as a process where we come to a conclusion where a general statement is reached from specific result.

(iv) Deductive Reasoning : It is defined as a process where we get specific results from general statements .

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Answer:

b.x=30

c.x=21

Step-by-step explanation:

When selecting four coins from a jar containing quarters, loonies, and toonies, there are a total of 27 unique combinations.

This can be calculated by using the formula for combination, which is nCr.

In this case,

n is the total number of coins in the jar (3) and

r is the number of coins selected (4).

Therefore, 3/(4(3-4)) = 3/0 = 3/1 = 3,

which is the number of possible combinations in the jar for the quarters, loonies, and toonies. When you multiply 3 by 3, you get 9, and when you multiply 9 by 3 again, you get 27.

Therefore, there are 27 unique coin combinations when selecting four coins from the jar.

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The number of points is simply 5 times this random variable, and E(C*Y) = C*E(Y), where C is a constant and Y is a random variable, according to expected value principles. As a result, E(X) = 5*2 = 10.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

The number of dice that are showing an even number is a binomial random variable with n = 4, and p = 1/2 (because half the faces on the die are even and half are odd).

The expected value of this random variable is n*p = 4*1/2 = 2.

The number of points is simply 5 times this random variable, and by the rules of expected value, E(C*Y) = C*E(Y), where C is a constant and Y is a random variable. Thus E(X) = 5*2 = 10.

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The linear function in the option is − x / 3 + y / 7 = 11.

A linear function is a function that represents a straight line on the coordinate plane.

Linear function can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's select the linear function from the options:

− 3 / x + y / 7 = 11

-3x⁻¹ + 1 / 7 y = 11 (Not a linear function)

− x / 3 + 7 / y = 11

- 1 / 3 x + 7y⁻¹ = 11 (Not a linear function)

− x / 3 + y / 7 = xy (Not a linear function)

− x / 3 + y / 7 = 11

- 1 / 3 x + 1 / 7 y = 11 (This is the linear function)

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The length of XY, with the area of the rectangular surface of the prism 720 sq.cm, XX' 20 cm and XY : XZ: YZ = 5:3:4, is 12 cm.

Area of the rectangular surface of the prism = 720 sq. cm

XX' = 20 cm

XY : XZ: YZ = 5:3:4

As we know, area of prism = 3 × area of rectangle

⇒720 = 3 × area of rectangle

⇒area of rectangle = 720/3

⇒XY × XX' = 240

⇒XY × 20 = 240

⇒XY = 240/20

⇒XY = 12 cm

Thus, the length of the XY is 12 cm.

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Three possible solutions when solving a system of equation are: one solution, no solution, and infinite solutions.

The 3  possible solutions of a system of equations are:

- Unique or one solution

- Infinite solutions

- No solution

In case of   a system of linear equations, we can determine the type of its solution as follows:

- If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equation will have one solution.

-  If the slopes are the same but the equation of the lines are different, the lines are parallel, hence they will not intercept. Therefore, there is no solution.

- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.

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The area of the garage door on the blueprint is 0.55 ft^2.

The size of a patch on a surface is determined by its area. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given in question,

Scale factor = 0.05

Since this scale factor is for length.

The scale factor for the area = 0.05*0.05

                                          = 0.0025

Original Area = 220

The area on the blueprint = 0.0025*220

                                       = 0.55

Hence, the area of the garage door on the blueprint is 0.55 ft^2.

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The inverse of the logarithmic function f x log9x is f-1(x)=9^x.

The inverse of a logarithmic function is the exponential function. To find the inverse of the logarithmic function f x log9x, we can use the following equation: f-1(x)=9^x. This equation states that the inverse of the logarithmic function f x log9x is the exponential function f-1(x)=9^x.

The inverse of the logarithmic function f x log9x is f-1(x)=9^x, which is the exponential function.This means that for any value of x, the inverse of the logarithmic function f x log9x is equal to 9 raised to the power of x. For example, if x=2, then the inverse of the logarithmic function f x log9x is 9^2, or 81. Similarly, if x=3, then the inverse of the logarithmic function f x log9x is 9^3, or 729. In general, the inverse of the logarithmic function f x log9x is 9 raised to the power of x, for any value of x.

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Answer: f –1(x) = 9x

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

To start, we will substitute 8 in for w. So, we get:

[tex]5 - \frac{32}{8}[/tex]

Then, we simplify our fraction, giving us:

5 - 4

Then, 5 - 4 = 1. So our answer is 1.

Hope this helped!

Answer:

5 - (32/w) = 1

Step-by-step explanation:

Given expression,

→ 5 - (32/w)

Now we have to use,

→ w = 8

Let's solve the expression,

→ 5 - (32/w)

→ 5 - (32/8)

→ 5 - (4)

→ 5 - 4

→ 1 => final value

Therefore, the answer is 1.