Explain the concept of extraneous solutions. Give examples with the different types of functions explored.

The solution of the equations are x = √1 = ± 1

Now, According to the question:

The given equation is [tex]9x^4 - 2x^2 - 7 = 0[/tex]

Using the substitution rule we put [tex]x^{2}[/tex] = u .

The given equation now changes to

[tex]9u^2 - 2u - 7 = 0[/tex]--- (1)

Equation(1) is a simple quadratic equation which can be solved by factorization as follows:

[tex]9u^2 - 2u - 7 = 0[/tex]

(9u + 7)(u - 1) = 0

Therefore

9u + 7 = 0 → u = -7/9

u -1 = 0→ u = 1

Since u = [tex]x^{2}[/tex] implies

x = √-7/9 = ± i√7/9

x = √1 = ± 1

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The complete question is this:

What are the solutions of the equation [tex]9x^4 - 2x^2 - 7 = 0[/tex]? use u-substitution to solve.

Answer:

7 : 1 or 7/1

.........................

Answer:

x = 8

Step-by-step explanation:

∠ B ≅ ∠ D

∠ A ≅ ∠ C

Then

Δ BAD ≅ Δ DCE ( AA postulate )

Then the ratios of corresponding sides are equal, that is

[tex]\frac{BA}{DC}[/tex] = [tex]\frac{BD}{DE}[/tex] , substitute values

[tex]\frac{x}{4}[/tex] = [tex]\frac{12}{6}[/tex] = 2 ( multiply both sides by 4 to clear the fraction )

x = 8

Answer:

3: C

4: "What are five of your favorite songs?"

Step-by-step explanation:

3: (a) already says how many students participate, (b) already said how many activities there were, & (c) it never talked about the movies

4: You'll be able to figure out the different types of music they enjoy listening to by asking this question.

Answer:

Part 1: A

Part 2: Five favorite songs

Area of quadrilateral is 24 units and it is known as parallelogram.

A point in the plane is one-to-one connected to an ordered pair of real numbers (x, y) using point plotting. The 2-dimensional Cartesian coordinate system is as a result obtained.

A parallelogram results from plotting the four points.

the lower side is between (-6,-3) and (-2,-3)

0 to 3 is at the top (4,3)

As a result, the base length is 4 because the distance

between (-6,-3) and (-2,-3) = 4

the separation between (0,3) and (4,3)

The sides are the lines that connect (0,3) to (-6,-3)

along with (4,3) to (-2,-3).

Vertical height ranges from -3 to 3 or 6.

The parallelogram's area is given by base*height = 4(6) = 24.

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Answer:

50 miles.

Step-by-step explanation:

You can visualize this as a triangle. the west route is one leg and the south route is the other. The distance from the starting point is the hypotenuse. 48^2+14^2=c^2, c=50.

Answer:

50

Step-by-step explanation:

[tex]48^{2} + 12^{2} = x^{2} \\X= 50[/tex]

The amount of eroded rock in cubic kilometres is 1 km3.

To calculate the amount of eroded rock in cubic kilometres, we need to find the volume of the area that has been eroded. The volume of a rectangular shape is found by multiplying the length, width, and height (or depth) together.

In this case, the area that has been eroded is 10 km long, 5 km wide, and 20 m deep. However, we need to convert the depth from meters to kilometres to match the units of the other measurements. Since 1 km = 1000 m, we can convert the depth by dividing by 1000:

20 m / 1000 = 0.02 km

Now that all of the measurements are in kilometres, we can find the volume by multiplying them together:

10 km * 5 km * 0.02 km = 1 km3

So the amount of eroded rock in cubic kilometres is 1 km3.

Complete Question:

The amount of eroded rock is measured in cubic kilometres (km3). A cubic kilometre is a cube that measures 1 km on each side. How many km3 of rock were eroded in an area that is 10 km long, 5 km wide, and 20 m deep?

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Answer:

Step-by-step explanation:

a.

a = 1 > 0  ← that means the parabola opens up, so the vertex is minimum of the function

b.

  [tex]f(x)=x^2+10x+20\\\\f(x)=\underline{x^2+10x+25} - 25+20\\\\f(x)=(x+5)^2-5[/tex]

The probability that a bag of flour passes inspection is 0.05.

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true. In this case, the probability of an event us usually represented as a number between 0 and 1.

In this case, the odds that a bag of flour weighs enough to pass inspection are 1:20. The probability that a bag of flour passes inspection will be:

= 1/20

= 0.05

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Complete question

The odds that a bag of flour weighs enough to pass inspection are 1:20. What is the probability that a bag of flour passes inspection?

Answer:

The correct answer is 0 or choice A on edge

Step-by-step explanation:

right on edge

Therefore, value of r(x) as x approaches Infinity : zero

[tex]\bold{\lim_{x \to \infty} r(x)=0}[/tex]

"A function is a special relationship where for each input and their is single outputs."

"Limit is defined as the value that a function approaches for the given input value."

For given situation,

We have been given a function,

r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction

We can rewrite it as,

[tex]r(x)= \frac{ax^b+8}{cx^d}[/tex] , where a, b, c, and d are positive integers and b < d.

We need to find the value of r(x) approach as x approaches Infinity.

This means, we need to find the value of the limit [tex]\lim_{x \to \infty} r(x)[/tex]

Now, we find the value of limit for given function.

[tex]\lim_{x \to \infty} r(x)[/tex]

=  [tex]\lim_{x \to \infty} \frac{ax^b+8}{cx^d}[/tex]

= [tex]\lim_{x \to \infty} (\frac{ax^b}{cx^d} + \frac{8}{cx^d})[/tex]

= [tex]\lim_{x \to \infty} \frac{a}{cx^(d-b)} + \lim_{x \to \infty} \frac{8}{cx^d}[/tex]                          ...............(since d > b)

= [tex]0 + 0[/tex]

= [tex]0[/tex]

Therefore, [tex]\bold{\lim_{x \to \infty} r(x)=0}[/tex]

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a) The greatest number of students who will get the refreshment is 210.

b) Each student will get 0.5 hot dogs.

c) Each student will get 0.6 cans of fruit juice.

a) To find the greatest number of students who will get the refreshment , we need to find the least common multiple of hot dogs and fruit juice.

The least common multiple is 210, which is the multiple of 105, and 126 is the least.

So the greatest number of students who will get the refreshment is 210.

b) To find the number of hot dogs each student will receive, we need to divide the total number of hot dogs (105) by the greatest number of students who will get the refreshment (210)

105/210 = 0.5

So each student will get 0.5 hot dogs.

c) To find the number of fruit juices each student will receive, we need to divide the total number of fruit juice (126) by the greatest number of students who will get the refreshment (210)

126/210 = 0.6

So each student will get 0.6 cans of fruit juice.

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[tex]y=2x^2+16x+33\\\\y=2x^2+16x+32+1\\\\y=2(x^2+8x+16)+1\\\\y=2(x+4)^2+1\\\\or\\\\y=2x^2-16x+33\\\\y=2x^2-16x+32+1\\\\y=2(x^2-8x+16)+1\\\\y=2(x-4)^2+1[/tex]

Answer:

x=12

Step-by-step explanation:

10x-18+6x+6=180

16x-12=180

16x=180+12

16x=192

x=192/16

x=12

plz mark as brainliest

Answer:

[tex]\sqrt{13}[/tex]

Step-by-step explanation:

d = √(7-4)²+(3-1)²

= √3²+2²

= √9+4

= √13

When subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

In mathematics, an equation is an expression or a statement made up of two algebraic expressions with the same value that are separated by the equal sign. It is a mathematically quantified version of an otherwise expressed statement. Equations can take many different forms. Equations are used to compare two expressions.

To Subtract -2a+7b=-5 from the other equation so the b-terms become opposites, we need to make +7b to -7b

This is only possible when the other term has 14,

Lets solve

 2a + 7b = - 5

- 4a + 14b = -10

-2a -7b = 5

Thus, when subtracted -2a+7b=-5 from the other equation so the b-terms become opposites, we get 2a -7b = 5 as the result.

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The provided phrase, x3+4x2+ 7x+ â' 2 has four terms. and coefficient are 1 , 4 ,7 for the expression

What does the phrase mean?

Expressions are made up of terms. A term might be either a constant, a variable, or a combination of both.

What kind of phrase would that be?

A single letter, a single positive or negative integer, or a number of variables multiplied but never added or subtracted might be the only variable. A number is placed in front of some nouns that have variables. The number used before a sentence is called a coefficient. single-word illustrations: Three times in one phrase.

The mathematical operator + separates the four components in the equation x3+4x2+ 7x+â' 2.

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Binomial is the referred to the polynomial algebraic expression that has two terms.

An expression with two dissimilar terms joined by an addition or subtraction operator is called a binomial in algebra. Since there are two terms, for instance, 2xy + 7y is a binomial. According to the quantity of terms present, algebraic expressions can be divided into different types, such as monomial, binomial, trinomial, etc.

An expression in algebra with two terms is called a binomial. Alternatively stated, a binomial expression is an algebraic expression made up of two terms that are dissimilar and have constants and variables. Using mathematical operators like + (plus) and - (minus), these terms are joined. Depending on how many terms it contains, an algebraic expression is classified as a binomial, monomial, trinomial, quadrinomial, etc.

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The degree of the polynomial [tex]5x^{3} + 4x^{2} + 7x[/tex]  is 3 , that means it is a third degree polynomial called as cubic polynomial  .

What is Degree Of Polynomial ?

The degree of the polynomial is defined as  the highest power of the polynomial expression. But, if the polynomial has multiple variables, the degree of polynomial can be found by adding the powers of the different variables  in the polynomial expression.

For Example : the degree of polynomial ⇒  [tex]9x^{2} + 7x + 2[/tex] is  2 .

The polynomial is given as : [tex]5x^{3} + 4x^{2} + 7x[/tex] , we have to find the degree ,

So , we can see that the the term having the highest power of the given polynomial is [tex]5x^{3}[/tex] , and the degree is 3 .

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Answer:

hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Step-by-step explanation:

Answer:

C)

hope this helped

Step-by-step explanation:

Answer:

x > -5

( -5, ∞)

Step-by-step explanation:

6 - 11x < 61

Subtract 6 from both sides

-11x < 55

Divided both side by -11. When divided by a negative number the < switch to >

So, the answer is

x > -5

Or

(-5,  ∞)

Answer:

the answer is C

Step-by-step explanation:

since we have 8 sides multiply 6 by 8 u get 48 so the answer must be 6+6+6+6+6+6+6+6+48

Answer: C

Step-by-step explanation:

This is because an octagon has 8 total sides and each side is 6 in long. So to find perimeter you have to add all the sides up.

The slope of a logarithmic graph depends on the type of logarithm used.

For a logarithmic function in the form y = log(b,x) where b is the base of the logarithm, the slope of the graph is undefined for x=0 and for x<0 because logarithmic functions are not defined in those cases.

For a natural logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

For a common logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.

It's important to note that logarithmic functions are not linear functions, and therefore they do not have a constant slope, the slope of a logarithmic graph will change throughout the graph.

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The flowchart to find the biggest of 3 numbers is mentioned below:

A flowchart is a type of diagram that represents an algorithm, process, or workflow. It is a visual representation of the steps and decisions involved in a problem-solving or decision-making process. Flowcharts use a variety of symbols and shapes to represent different types of steps and decisions, such as inputs, outputs, process steps, and decision points. They are used to communicate the logic of a program or process to different stakeholders, such as developers, managers, and users.

An algorithm is a set of instructions or a step-by-step procedure for solving a problem or completing a task. It is a well-defined sequence of operations or actions that are taken in order to achieve a specific goal or outcome. Algorithms can be expressed using natural language, pseudocode, or programming languages. The steps in an algorithm must be unambiguous and have a clear stopping point.

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Answer:

7:13

Step-by-step explanation:

Answer:

if im thinking correctly ratios can be written in 3 ways

Step-by-step explanation:

so it could be 7/13, 7 to 13, or 7:13

Answer:

B, 6

Step-by-step explanation:

As there are 2 service options and 3 regular options All you do is multiply them:

2×3=6

Heres a different way to show it:

FS = Full service

SS = self service

R = regular

M = Midgrade

P = Premium

FS,R FS,M FS,P

SS,R SS,M SS,P

So it's 6

Answer:

B. 6

Step-by-step explanation:

Full/self service = 2 options

regular/mid/premium = 3 options

2 x 3 = 6

r = (sin theta + C)^(-1) where C is an arbitrary constant of integration.

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation. Assuming that a function's rate of change with regard to x is inversely proportional to y, we may write it down as dy/dx = k/y.

r = (cos(theta) - d/d(theta) of sec(theta)) / sec(theta)

The differential equation assists us in presenting a relationship between the changing quantity with respect to the change in another variable. The derivative represents nothing more than a rate of change. Be a function with the form: y=f(x), where x is an independent variable, f is an unknown function.

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Answer:

55

Step-by-step explanation:

So lets take our 50 dollars.

Next, take your increase of 5%. Remember, 5% is 0.05, and it is a increase of 5%, so we are multipling 50 by 1.05.

Before we start multiplying, lets recall that this occurs twice(2 years), but this doesnt mean we multiply 50 by 1.10. No, we just mutiply 50 by 1.05 2 times:

50*1.05

=

52.5

52.5*1.05

=

55.25

So your answer is 55 dollars(rounding down).

Hope this helps!

Answer:55

Step-by-step explanation: