What are the formulas of polynomials Class 9?.

The inverse of the function f(x) and its domain include the following: D. f⁻¹(x) = (x + 4)²; x ≥ 0.

In order to determine an inverse function or the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;

f(x) = √x - 4

y = √x - 4

x = √y - 4

√y = x + 4

Taking the square of both sides of this inverse function, we have:

f⁻¹(x) = (x + 4)²

For the domain of this function, we have the following:

f(x) = √x - 4

When x= 0, we have:

f(0) = √0 - 4

f(0) = 0.

In conclusion, the domain of this function cannot be equal to -4 because it is impossible to find the square root of a negative number.

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We can rewrite the given linear equation to have the different numbers of solutions as:

a) 3x + 8 = 3x + 4

b) 3x + 8 = 3x + 8

c) 3x + 8 = 3x +x

Here we have the linear equation:

3x + 8 = 3x + ?

Notice that the first term (the one that depends of x) is equal in both sides, so the equation will not be true only if the second term is a constant and is different to 8, so for example we could write:

3x + 8 = 3x + 4

b) Infinite solutions means that we have the same thing in both sides, so here we can add 8

3x + 8 = 3x + 8

Is true for all values of x, thus, it has infinite solutions.

c) The equation will have one solution only if the coefficients of the variable x are different in both sides, then here we can add "x"

3x + 8 = 3x +x

3x + 8 = 4x

That equation has a single solution:

8 = 4x - 3x

8 = x

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The answers to each part is mentioned above.

Given is that Aiko works in the fish department of a pet store. She must drain, clean, and refill two reef tanks. The first tank hold 175 gallons of water and drains at a rate of 25 gallons per hour. The second tank holds 200 gallons of water and drains at a rate of 30 gallons per hour.

Equation for tank {1} -

y = 175 - 25x

Equation for tank {2} -

y = 200 - 30x

For the solution we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5

and

y = 200 - 150

y = 50

For the same amount of water we can write -

175 - 25x = 200 - 30x

- 25x + 30x = 200 - 175

5x = 25

x = 5 hours

In tank (1), there is : 175 - 25 x 5 = 50 gallons

In tank (2), there is : 200 - 30 x 5 = 50 gallons

Therefore, the answers to each part is mentioned above.

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The equivalence class of a is [a] = {x ∈ A: (a, x) ∈ R}. This includes all elements of A that are related to 'a'.

An equivalence class is the name we give to the subset S that includes all elements that are equivalent to each other. If there is an equivalence relation between any two elements, they are called equivalent.

Equivalence class properties : The relation ~ is an equivalence relation if and only if:

When our relation ~ satisfies the above three properties, we can write the definition of an element equivalence class as follows [a] = { x ∈ X | and ~ x}. Consider an example, If X were the set of all polygons and the equivalence relation ~ was defined as "having the same number of sides", the set of all triangles, the set of all quadrilaterals, the set of all pentagons, etc., are represents the equivalence classes.

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Complete question:

What is equivalence class ?

4t + 0.2 = 6(t+x) this system of equations can be used to find when Carson catches up with Arturo.

What is a system of equations?

A solution to a system of equations is a set of values for the variable that satisfy all the equations simultaneously. In order to solve a system of equations, one must find all the sets of values of the variables that constitute solutions of the system.

The system of equations that can be used to find when Carson catches up with Arturo is:

distance = speed x time

For Arturo:

distance = 4t + 0.2

For Carson:

distance = 6(t+x)

where t is the time in hours that Arturo has been walking, x is the time in hours that Carson has been jogging, and distance is measured in miles.

Equating the two equations to find when they meet:

4t + 0.2 = 6(t+x)

And solving for x, the time in hours that Carson has been jogging.

x = (4t + 0.2 - 4t)/6 = 0.2/6 = 1/30

This is the time in hours that Carson has been jogging when he catches up with Arturo.

Hence, 4t + 0.2 = 6(t+x) this system of equations can be used to find when Carson catches up with Arturo.

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27500 ≥ 120x + 12600 is the inequality that can be used to determine x, the great 120-kilogram crates that can be loaded onto the shipping container.

A relation that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. [1] Most frequently, size comparisons are made between two numbers on the number line. Different notations can be used to represent various kinds of inequalities, including:

A is smaller than b, as shown by the symbol a < b.

When the expression a > b is used, it means that a is greater than b.

The greatest weight that can be loaded into a container = 27500kg

Shipment weight already present in the container = 12400kg

Amount of weight that can be loaded = 27500 - 12400 = 15100kg

Weight of each crates = 120 kg

Let x be the maximum number of 120 kg crates that can be loaded to the container

Weight of 'x' number of 120 kg crates = 120x

Therefore, the required inequality is as follows

27500 ≥ 120x + 12600 (since the maximum amount of weight of crates that can be put in the container should be less than or equal to the total weight of the maximum number of crates that can be loaded into the container).

Thus, 27500 ≥ 120x + 12600 is the inequality that can be used to determine  x, the great 120-kilogram crates that can be loaded onto the shipping container.

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The results for each operation are given as follows:

x-2/9=6 5/9 -> x = 61/9.

J+1/2=3 9/14 -> J = 22/7.

x-1/8=5/24 -> x = 1/3.

The first step to solve the expressions is to transform the mixed numbers to fractions, hence:

Then the solution for the first expression is of:

x = 59/9 + 2/9

x = 61/9.

The solution for the second expression is of:

J = 51/14 - 1/2

J = 51/14 - 7/14

J = 44/14.

J = 22/7.

The solution for the third expression is of:

x = 5/24 + 1/8

x = 5/24 + 3/24

x = 8/24

x = 1/3.

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A line is a one-dimensional shape that is straight. The equation of the line that describes the shark's length is [tex]y = \frac{13}{3}x + 20\\[/tex].

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by:

[tex]y = mx + c[/tex]

where,

x is the coordinate of the x-axis,

y is the coordinate of the y-axis,

m is the slope of the line, and

c is constant.

Given when the shark was born the length of the shark was 20 inches, therefore, the coordinates can be written as (0,20).

Similarly, the length of the shark is 46 inches, while the age of the shark is 6 months. Therefore, the coordinates can be written as (6,46).

Now, the slope of the line can be written as,

m = (46-20)/(6-0) = 13/3

Now, the equation of the line can be written as  [tex]y = \frac{13}{3}x + c[/tex], further, substitute the value of any point in the equation of the line, therefore,

20=13/3(0)+c

c=20

Hence, the equation of the line that describes the shark's length is :

[tex]y = \frac{13}{3}x + 20\\[/tex].

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The expressions that could be equivalent to x^2+bx-36 where b is negative is option 1: (x + 3)(x - 12) and option 5: (x - 9)(x + 4).

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is - x² + bx - 36

The first expression is - (x + 3)(x - 12)

Solve using the multiplication property -

= (x + 3)(x – 12)

= x(x - 12) + 3(x - 12)

= x² - 12x + 3x - 36

= x² - 9x - 36

The second expression is - (x - 2)(x + 18)

Solve using the multiplication property -

= (x - 2)(x + 18)

= x(x + 18) - 2(x + 18)

= x² + 18x - 2x - 36

= x² + 16x - 36

The third expression is - (x - 13)(x - 3)

Solve using the multiplication property -

= (x - 13)(x - 3)

= x(x - 3) - 13(x - 3)

= x² - 3x - 13x + 39

= x² - 16x + 39

The fourth expression is - (x + 4)(x + 9)

Solve using the multiplication property -

= (x + 4)(x + 9)

= x(x + 9) + 4(x + 9)

= x² + 9x + 4x + 36

= x² + 13x + 36

The fifth expression is - (x - 9)(x + 4)

Solve using the multiplication property -

= (x - 9)(x + 4)

= x(x + 4) - 9(x + 4)

= x² + 4x - 9x - 36

= x² - 5x - 36

Therefore, the choices for b being negative is x² - 5x - 36, and x² - 9x - 36.

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Select all expressions that could be equivalent to x^2+bx-36 where b is negative.

(x + 3)(x - 12)

(x - 2)(x + 18)

(x - 13)(x - 3)

(x + 4)(x + 9)

(x - 9)(x + 4)

A function is decreasing on some interval of its domain if f(a) < f(b) for all a, b in that interval such that a > b.

A function f(x) decreases on an interval I if f(b)<=f(a) for all b>a, where a,b in I. If f(b)<f(a) for all b>a, the function is said to be strictly decreasing. Conversely, a function f(x) increases on an interval I if f(b)>=f(a) for all b>a with a,b in I. If f(b)>f(a) for all b>a, the function is said to be strictly increasing. If the derivative f^'(x) of a continuous function f(x) satisfies f^'(x)<0 on an open interval (a,b), then f(x) is decreasing on (a,b). However, a function may decrease on an interval without having a derivative defined at all points. For example, the function -x^(1/3) is decreasing everywhere, including the origin x=0, despite the fact that the derivative is not defined at that point.

A function is increasing on some interval of its domain if f(a) > f(b) for all a, b in that interval such that a > b. A function is decreasing on some interval of its domain if f(a) < f(b) for all a, b in that interval such that a > b. More casually put: a function is increasing if the graph rises to the right. It is decreasing if the graph falls to the right.

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Answer:

11 months

Step-by-step explanation:

It looks like you are trying to create a function that represents the number of members the fitness club has over time, assuming that each month they add 25 new members to the club.

You can use the function f(x) = 225 + 25x, where x represents the number of months from the current time.

The function starts with an initial value of 225 members, which represents the number of members the club already has. Then, for each additional month represented by x, the function adds 25 new members to the total, represented by 25x.

So, if the fitness club wants 500 members in 9 months, you can set f(9) = 500 and solve for x

f(9) = 225 + 25x = 500

25x = 500 - 225

25x = 275

x = 11

So, the club will reach 500 members in 11 months if they continue to add 25 members per month

The probability of drawing a constant, replacing it, and then drawing a vowel is given as follows:

105/676.

A probability is obtained as the division of the number of desired outcomes by the number of total outcomes.

In the context of this problem, we have that:

Hence the probability of drawing a constant, replacing it, and then drawing a vowel is calculated as follows:

p = 21/26 x 5/26 = 105/676.

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The lowest positive whole number that should replace the question mark on the pinner such that the probability of pinning an odd number greater than 6 is 1/4 is 9.

It could be determined by calculating the probability of pinning an odd number greater than 6 out of the total number of possible outcomes.

If we consider the lowest positive whole number greater than 6 is 7, then we have 7,9,11,13,15,17,19,21,23,25 and so on.

Out of these numbers, 1/4 are odd numbers greater than 6. So the lowest whole number that could replace the question mark on the pinner is 9.

This is applicable for any situation where the probability of an event occurring out of a set of possible outcomes needs to be determined, and the lowest value for which that probability is a certain ratio needs to be found. In this case, the event is pinning an odd number greater than 6, and the set of possible outcomes is all positive whole numbers greater than 6. The probability being considered is 1/4, and the question is what is the lowest value that can replace the question mark on the pinner such that this probability is achieved.

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Answer:   [tex]\text{x}^3\text{y}[/tex]

This is the same as writing x^3y

===================================

Explanation:

When finding the GCF, we look for the smallest exponent for each variable.

The x terms of the given expressions are x^3 and x^5. The smallest exponent here is 3, so x^3 is part of the GCF.

The y terms are y^2 and y. Think of y as y^1, which shows 1 is the smallest exponent. We'll have y as part of the GCF.

-----------

We found that...

The overall GCF is x^3y which can be written as [tex]\text{x}^3\text{y}[/tex]

Side note: We ignore the coefficients since they are 1 for each monomial.

Answer: Slope = - 1/3, the y-intercept = -4

Step-by-step explanation:

Pick two coordinates: (-1, -1), (2, -2)

Find the slope: y2 -y1 / x2 - x1  

                         -2 - (-1) / 2 - (-1) = - 1/3

Slope intercept form: y = mx + b

Substitute in what you know to find b:

-1 = -1/3 (-1) + b           substitution property

-1 = 1/3 + b                 distributive property

-3 = 1 + b                    multiplication property

-4 = b                         subtraction property

The degree of the polynomial 2x² 5x² 7 is 4.

The biggest sum of all the exponents for all of variables in a term is the polynomial's degree. Any polynomial's degree is determined solely by its variables; coefficients are to be disregarded. The highest exponential power in a polynomial equation is called the polynomial's degree.

When x is the variable with the highest power n in an nth degree polynomial function with real coefficients, where n can take whole number values.

One of the key ideas in mathematics is the degree of polynomials, which establishes the maximum number of possible solutions and the frequency with which a function will cross the x-axis on a graph.

A polynomial with many variables is of a certain degree: Find the term with the highest degree by averaging the exponents of all the variables in each phrase. That will be regarded as the polynomial's degree.

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The simplified expression of the given expression is 6x + (-21).

What is simplified expression?

Simplified expression is that expression which does not contains any like terms. When in an expression, all the like terms are combined and all of the specified brackets are solved, then only unlike terms are left in the simplified expression which cannot be further reduced.

We are given  expression as 6 + 2(x-8) + 3x -11 + x

Now, on simplifying the expression, we get

⇒ 6 + 2x - 16 + 3x - 11 + x

⇒ 6x - 21

⇒ 6x + (-21)

Hence, the simplified expression of the given expression is 6x + (-21).

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Since, there are multiple questions so the question I answered is attached below.

Answer:

Hugo earns $11.50 per hour

Step-by-step explanation:

57.50/5 = 11.50

Answer:$11.5 per hour

Step-by-step explanation: $57.50 / 5 hour shift = $11.5 per hour

Answer:

$16.47

Step-by-step explanation:

125×18=2250

these are the pages printed

2250÷500=4.5

these are the reams of paper needed

$3.66 ×4.5=$16.47

this is the money needed

The ratio of unshaded squares to shaded squares is 15:10. This means that for every 15 unshaded squares, there are 10 shaded squares. This can also be simplified to 3:2, which means that for every 3 unshaded squares, there are 2 shaded squares.

It is important to keep in mind that the ratio is not equal to the fraction, it's just a way to express the relationship between the two.

Answer:

15:10

Step-by-step explanation:

15:10 which means that for every 15 unshaded squares there are 10 shaded squares which can also be simplified to 3:2 which means pretty much the same thing, for every 3 unshaded squares there will be 2 shaded ones. A ratio is not a fraction, so i advise not treating it like one.

Answer:11 miles

Step-by-step explanation:

so, no matter what you pay $5, and each mile is $4, so you pay $49 dollars. First do 49 - 5, which equals 44, and 44 ÷ 4 = 11, so the answer is 11 miles

The two column proof showing that ΔKLG ≅ ΔMLG is as detailed below.

A two-column proof is defined as a geometric proof consists of a list of statements, and the reasons for which we know those statements to be true.

Statement 1: GL ⊥ KM

Reason 1: Given

Statement 2: KG  ≅ MG

Reason 2: Given

Statement 3: ∠GLK and ∠GLM are right angles

Reason 3: Definition of right angles

Statement 4: GL ≅ GL

Reason 4: Reflexive Property

Statement 5: ΔKLG and ΔMLG are right triangles

Reason 5: definition of right triangles

Statement 6: ΔKLG ≅ ΔMLG

Reason 6: HL Congruency postulate

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By evaluating and using the quadratic equation we will have:

1) 7 seconds.

2) Yes, it will pass.

3) 24.5 meters, after 3.5 seconds.

To find this, we need to solve the quadratic equation:

h = -2t^2 + 14t = 0

Taking t as a common factor we can write:

t*(-2t + 14) = 0

-2t +14 = 0

14 = 2t

14/2 = t

7 = t

The ball will be 7 seconds on the air.

2) To check this we need to evaluate the quadratic equation on t = 3

h = -2*3^2 + 14*3 = 24

The height is of the ball is larger than the height of the tree.

3) What is the maximum height of the ball?

This happens at the vertex of the quadratic equation:

h = -2t^2 + 14t

The two roots are t = 0 and t = 7, then the vertex is at t = (7 - 0)/2 = 3.5

And the maximum height is:

h = -2*3.5^2 + 14*3.5 = 24.5

The maximum height is 24.5 meters.

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Answer:

So the final solution is q < 9 and the inequality is False.

Step-by-step explanation:

To solve the given inequality, you first need to simplify the left-hand side of the inequality:

9 + 8 = 17

so the inequality becomes:

17 > 20 or 2q - 5 < 13

Since 17 is not greater than 20, this inequality is false.

Next, we need to solve the other inequality:

2q - 5 < 13

To isolate the variable on one side of the inequality, we need to add 5 to both sides:

2q < 18

Then, we divide both sides by 2:

q < 9

So the solution is q < 9

So the final solution is q < 9 and the inequality is False.

The prime numbers of 36 are 2 and 3 and the Prime factorization expression of 36 is equals to 2 × 2 × 3 × 3.

Prime factorization is a method of representing a number as a product of prime factors. A prime factor of a number is a factor that is prime. The numbers are called factors of 36 that divide 36 evenly. In other words, if we multiply two numbers and get the result equals to 36. So, factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Steps for Prime Factorization of 36 :

Step 1: In first step, divide the number i.e., 36 by its smallest prime factor. So, by divisibility rules, 2 is the smallest prime factor of 36. So, we get, 36 ÷ 2 = 18

Step 2: Here need repeatedly divide the quotient by 2 until we get a number that is no more divisible by 2. So, we divide 18 again by 2 which is 18 ÷ 2 = 9.

Step 3 : Now, 9 is not completely divisible by 2, so, we proceed with the next prime factor of 36, which is 3. That is 9 ÷ 3 = 3

Step 5: Divide the quotient by 3 again which is 3 ÷ 3 = 1. Now, we need not proceed further as we have obtained 1 as our quotient. Therefore, the prime factorization of 36 is expressed as 2 × 2 × 3 × 3 = 2² × 3²; where 2 and 3 are prime numbers and the prime factors of 36.

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To find the discriminant and nature of the roots of a quadratic equation, you can use the quadratic formula.

Write the quadratic equation in the form of ax² + bx + c = 0, where a, b, and c are constants, and x is the variable.

Calculate the discriminant using the formula

b² - 4ac.

Use the discriminant to determine the nature of the roots:

If the discriminant is greater than 0, the roots are real and distinct.

If the discriminant is equal to 0, the roots are real and identical (i.e., the equation has only one root).

If the discriminant is less than 0, the roots are complex and not real numbers.

To find the roots of the quadratic equation, you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The plus-minus sign indicates that there are two possible solutions, and the square root of the discriminant is used to find them.

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Step-by-step explanation:

the arc angle KLI = 142°.

that means that the arc angle KJI = 360 - 142 = 218°.

this is twice the inscribed opposite angle on the arc (L).

so,

(a)

angle KLI = 218/2 = 109°

(b)

for the same reason

angle LKJ is half of the arc angle LIJ.

arc angle LIJ = 2× angle LKJ = 2×66 = 132°

that means

arc angle LKJ = 360 - 132 = 228°

angle LIJ = half of arc angle LKH = 228/2 = 114°

FYI for such an inscribed quadrilateral there is Akari the rule that the sum of opposite angles have to be 180°.

so, angle LIJ is opposite of angle LKJ.

angle LIJ = 180 - angle LKJ = 180 - 66 = 114°

Answer:

7 feet per second

Step-by-step explanation:

The change in elevation of the parachutist is -35 ft in 5 seconds. To find the change in elevation per second, we can divide the total change by the number of seconds.

Change in elevation per second = -35 ft / 5 seconds = -7 ft/s

So the parachutist's elevation changes by -7 ft/s each second.

It means the elevation of the parachute is decreasing by 7 feet per second.

Step-by-step explanation:

16x - 4y = 12

4x - y = 3

4x = 3+y

x= 3+y/4

for y = 1

x= 3+1/4 = 1

y = 2

x=3+2/4 = 5/4 = 1.25

y = 3

x = 3+3/4 = 6/4 = 1.5