What is domain and range with example?.

If the product is positive integers is 32118, then the king's age is 53, his number of children is 6 and is length of boat is 101m.

What is integer?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

The puzzle demands for three numbers - x, y, z which represent the king's number of children, age and length of boat respectively.

It will be advantageous to conceive the problem thus: We have but one unknown; this unknown, however, is not a number but a tripartite unknown, a triplet (x, y, z) of numbers.

It is very important to split the condition that is expressed by the statement of the problem into appropriate clauses. This needs careful con-sideration of details and considerable regrouping. After several trials (which we skip to save space) we may arrive at the following two clauses:

(r1), x, y, and z are positive integers different from 1 and such that -

xyz = 32118

(r2) 4 ≤ x < y < 100

Begin with (r1) which leaves only a finite number of possibilities, whereas (r2), which does not restrict z at all, leaves an infinite number.

Therefore, we examine (r1). Now, 32118 is divisible by 6, and so we easily decompose it into prime factors:

32118 = 2 × 3 × 53 × 101

For a decomposition into three factors we have to combine two of the four primes. Therefore, there are only six different ways to decompose the number 32118 into a product of three factors all different from 1:

6 × 53 × 101

3 × 101 × 106

3 × 53 × 202

2 × 101 × 159

2 × 53 × 303

2 × 3 × 5353

Of these six possibilities, the remaining requirement (r2) rejects all except the first one, and so we obtain -

x = 6 , y = 53 and z = 101.

Therefore, the values of x, y and z are 6, 53 and 101 respectively.

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9x² + 24x + 16 is equal to (3x + 4)².

This is a  perfect square trinomial equation.

Option B is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

9x² + 24x + 16

This can be written as,

(3x)² + 2 x (3x) x 4 + 4²

This is the perfect square trinomial of (3x + 4)².

[ (a + b)² = a² + 2ab +  b² ]

Thus,

9x² + 24x + 16 is a  perfect square trinomial equation.

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Answer:

67.5°

Step-by-step explanation:

180 -45 = 135

135 / 2

k= 67.5

The value of x = 3 and y = 1 is the solution.

Two or more algebraic equations that have a common variable and are solved simultaneously are referred to as simultaneous equations (that is, simultaneously). For instance, the simultaneous equations x + y = 5 and x - y = 6 are created by concurrently solving two equations that have the same unknown variables, x and y. Multiple techniques, including the substitution method, elimination approach, and visual methods, can be used to solve simultaneous equations.

We have 2 equations,

2x - y = 5 (equation 1)

3x + 2y = 11 (equation 2)

We can solve the given equations simultaneosuly.

Multiplying equation 1 by 2,

4x - 2y = 10

Adding the 2 equations,

4x - 2y = 10

3x + 2y = 11

⇒ 7x = 21

⇒x = 3

Substituting the value of x = 3 in equation 1,

2x - y = 5

⇒ 6 - y = 5

⇒ y = 1

Hence, the values of x and y are 3 and 1 respectively; this is the solution of the equation.

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Answer: When we have a function in formula form, it is usually a simple matter to evaluate the function. For example, the function f(x)=5−3x2 f ( x ) = 5 − 3 x 2 can be evaluated by squaring the input value, multiplying by 3, and then subtracting the product from 5.

Step-by-step explanation:

Functions is an important branch of math, which connects the variable x with the variable y. Functions are generally represented as y = f(x) and it states the dependence of y on x, or we say that y is a function of x.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE x}\% of \textit{\LARGE y}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE x}}{100} \right)\cdot \textit{\LARGE y} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{a\% of a}}{\left( \cfrac{a}{100} \right)a}\implies \cfrac{a^2}{100} \\\\[-0.35em] ~\dotfill[/tex]

[tex]a\div \cfrac{a^2}{100}\implies \cfrac{a}{1}\div \cfrac{a^2}{100}\implies \cfrac{a}{1}\cdot \cfrac{100}{a^2}\implies \cfrac{a}{a^2}\cdot \cfrac{100}{1}\implies \cfrac{1}{a}\cdot 100\implies \cfrac{100}{a}[/tex]

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If you would like to know what is a divided by a% of a, you can write it as follows:

a divided by a% of a:

a/ (a% of a) = a/ (a% a) = a/ (a/100* a) = a/(a^2/100) = a * (100/a^2) = 100 / a

The correct result would be 100/a.

Eliud was running 125 miles per week, and now he is running 20% more. To determine how many miles Eliud is now running per week, the equation is 125 plus 125 times 0.2, which equals 150 miles per week.

125 + (125 x 0.2)

=125 + 25

= 150

Eliud was previously running 125 miles per week. To determine how many miles he is now running per week, an equation needs to be solved. The equation is 125 plus 125 times 0.2, which equals 150 miles per week. This is because 20% of 125 is 25, so 125 plus 25 is 150. Therefore, Eliud is now running 150 miles per week, which is an increase of 25 miles per week from his previous running amount. This increase of 25 miles per week is equivalent to 20% more than he was previously running. Solving this equation reveals that Eliud is now running 150 miles per week, which is an increase of 20% from his previous mileage.

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The expression that represents the shaded length of the number line would be = 3/20 × 9/20. That is option C.

A number line is defined as the graduates line that is used to represent the position of both positive and negative real numbers.

The shaded length of the number line contains 20 bars with a total of 9 shaded bars.

There are a total number of 3 per each bar of the number line, therefore, the shaded length of the number line would be = 3/20 × 9/20.

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Answer:[tex]\sqrt{5x[/tex]

Step-by-step explanation:

output of the given input/output relationships is 36 and 25.

To illustrate a function, an input-output table can be used, as in the example below. The same function rule connects every pair of numbers in the table. To find each output number, multiply each input number (-value) by 3. ( -value).

Input-output analysis table: what is it?

The table of input-output analysis measures the flows of outputs from one industry as inputs into another (in rows) (in columns). In the input-output analysis paradigm, the original demand shift and its direct, indirect, and induced implications can be used to examine the overall economic impact of an event.

output = input +29

input= 7

output = input +29=7+29=36

input= -4

output = input +29= -4+29=25.

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Answer:

Step-by-step explanation:

Yes, the anti-logarithm which is also called an antilog is the inverse of the logarithmic transform.

The antilogarithm, also referred to as an antilog, is the inverse of the logarithm transform. Since the base-10 logarithm of 1000 is 3, the anti-logarithm of 3 is 1000. To find the anti-logarithm of a base-10 logarithm, raise it by ten.

We are aware that an exponential is the inverse of a log function. We know that f(x) = log sub(x) has the inverse, f(y) = b, as a result (y). When working with the natural log, the inverse of f(x) = ln(x) is f-1(y) = ey if the base is e.

A logarithm's and an antilog's basis is 2.7183. The natural logarithm and antilog should be calculated by multiplying the logarithm and antilog, whose bases are 10 and 2,303, respectively.

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The correct option is A. The standard form of the polynomial function in number 3 is f(x) = 5[tex]x^{7}[/tex] +[tex]x^{4}[/tex] + 3x.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

What is the standard form of the polynomial function in number 3?

A. f(x) = 5[tex]x^{7}[/tex] +[tex]x^{4}[/tex] + 3x

B. f(x) = 5[tex]x^{7}[/tex] + 3x + [tex]x^{4}[/tex]

C. f(x) = [tex]x^{4}[/tex] + 5[tex]x^{7}[/tex] + 3x

D. f(x) = 3x + 5[tex]x^{7}[/tex] + [tex]x^{4}[/tex]

Let the circum-circle of the cyclic quadrilateral PQRS be O.

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Answer: 3

Step-by-step explanation:

5x = 15

Divide both sides by 5:

x = 3 :>

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5x = 15}[/tex]

[tex]\textbf{DIVIDE 5 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{5x}{5} = \dfrac{15}{5}}[/tex]

[tex]\textbf{SIMPLIFY it}[/tex]

[tex]\mathsf{x = \dfrac{15}{5}}[/tex]

[tex]\mathsf{x = 3}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

17.031g/mol

Step-by-step explanation:

pay attention in class

The probability of getting number 6 on a single roll of the fair die is 1/6; not getting 6 is 5/6; getting number 10 is 0 and getting any number of 1-6 is 1.

a) The probability of getting the number 6 on a single roll of a fair die numbered 1 to 6 is 1/6, or approximately 0.17. This is because there is a single outcome (rolling a 6) out of a total of 6 possible outcomes (rolling any number from 1 to 6) that will result in rolling a 6.

b) The probability of getting the number 10 on a single roll of a fair die numbered 1 to 6 is 0, because the die only goes up to 6.

c) The probability of not getting the number 6 on a single roll of a fair die numbered 1 to 6 is 5/6, or approximately 0.83. This is because there are five outcomes (rolling any number from 1 to 5) out of a total of 6 possible outcomes (rolling any number from 1 to 6) that will not result in rolling a 6.

d) The probability of getting one of the numbers 1, 2, 3, 4, 5, or 6 on a single roll of a fair die numbered 1 to 6 is 1 because there is only one outcome out of one possible outcome that is not getting one of the numbers 1, 2, 3, 4, 5 or 6.

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The end behavior of the rational polynomial function [tex]f(x) = \frac{6x^3 - x^2 + 7}{2x + 5}[/tex] is,

{x → ∞, y → ∞ and x → - ∞, y → ∞}.

A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.

The graph's final behavior is determined by a polynomial function's degree and leading coefficient.

Given, A rational polynomial function [tex]f(x) = \frac{6x^3 - x^2 + 7}{2x + 5}[/tex].

Now A cubic function divided by a linear function would result in a quadratic function, And as the coefficients of the highest degree terms of both the highest terms are positive the coefficient of the highest term of the quadratic function will also be positive and it's graph will be a parabola that opens upwards and symmetric about the y-axis.

Therefore, The end behavior will be when x tends to positive infinity y goes to positive infinity and when x tends to negative infinity y goes to positive infinity.

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The required measure of the angles x and y is given as 50°.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,

As it can be seen, x and y are alternate-opposite equal angles,
x = y

Now,
Adding complementary angles to 180°,
x + 60 + 70 = 180
x = 180 - 130
x = 50°

So,
x = y = 50°

Thus, the required measure of the angles x and y is given as 50°.

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In 36 months the populations of the 2 cities be the same .

What is additive comparison?

In an additive comparison, we question or state how much more (or less) one amount is in contrast to the other to determine the relationship between the two numbers. Additive comparison issues are typically word problems that can be resolved by creating an equation.

The comparison approach is a technique for rewriting each equation with the same variable as the subject in order to solve systems of independent equations. The initial variable to isolate can be any of the variables. Every equation is now an isolated-subject equation with an isolated variable.

Let,

  if in about x month, the population of the towns will be equal .

the equation will be;

                          70,000 + (150-100)x = 61,000 - 200x

                        ⇒  70,000 + 50x = 61,000 - 200x

                        ⇒ 250x = 9000

                       ⇒ x = 9000/250

                      ⇒ x = 36

So, in 36 months the populations of the 2 cities be the same .

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All 3 angles of a triangle always add up to 180 degrees.

This is because a triangle is a three-sided polygon and the sum of the angles in any polygon is always 180 degrees multiplied by the number of sides minus 2. Therefore, in a triangle, which has three sides, the sum of the angles is 180 x (3-2) = 180 degrees. This rule is known as the "triangle angle sum theorem" and is a fundamental property of triangles. It is important to note that this rule applies to all types of triangles, whether they are right triangles, acute triangles, or obtuse triangles. Understanding this theorem is crucial in solving geometric problems related to triangles.

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The radical equation solution is x= -1.

What is radical equation?

The unknown is a component of the radicand of a radical expression in a radical equation. Equations with an uncertain value enclosed by a radical sign are referred to as radical equations (also known as irrational) equations. Radical expressions are those that fall inside the square root. Radical inequality refers to an inequality contained within a radical.

Here the given radical equation is

=> [tex]\sqrt{2x+3} -\sqrt{x+2}[/tex] = 0

=> [tex]\sqrt{2x+3} = \sqrt{x+2}[/tex]

Now taking square on both sides then,

=> [tex](\sqrt{2x+3})^2 = (\sqrt{x+2})^2[/tex]

=> 2x+3 = x+2

=> 2x-x = 2-3

=> x = -1

Hence value of the x is -1.

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If the fifth day of the month is two days after Monday, then the fifth day would be Wednesday. Additionally, the 19th would be a Wednesday, that is, the day before the 19th would be Tuesday the 18th.

To identify the day of the week that coincides with the date 19 and 5 we must have the information as a reference:

The fifth day is two days after Monday.

According to the information above, the fifth day would be a Wednesday. Additionally, we must use this information to organize the rest of the days of the month as shown below:

According to the above, the 19th would be Wednesday and the day before this would be Tuesday the 18th.

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Step-by-step explanation:

for first image →

Option B ) 8n + 4

for second image →

Option A ) The number of minutes Dylan practises each weekdays

Satisfying all the given situations, there were 156 candidates in the examination.

We can use the principle of inclusion-exclusion to solve the problem.

The principle of inclusion-exclusion states that the total number of elements in the union of two or more sets is equal to the sum of the number of elements in each set, minus the number of elements in their intersection.

Here, let A be the set of candidates who offered biology, B be the set of candidates who offered history, and C be the set of candidates who offered mathematics.

Using the principle of inclusion-exclusion, the total number of candidates, N, can be found as follows:

N = (A U B U C) = (A + B + C) - (A ∩ B + B ∩ C + A ∩ C) + (A ∩ B ∩ C)

where A U B U C is the union of the three sets, A ∩ B is the intersection of A and B, and so on.

Given that:

|A| = 52, |B| = 60, |C| = 96

|A ∩ B| = 21, |A ∩ C| = 22, |B ∩ C| = 16

|A ∩ B ∩ C| = 7

Therefore,

N = (52 + 60 + 96) - (21 + 22 + 16) + 7

N = 156

Hence, there were 156 candidates in the examination.

The problem seems incomplete, it must have been

"In a certain examination, 52 candidates offers biology,60 offers history,96 offers mathematics, if 21 offered both biology and history,22 offered mathematics and biology, and 16 offered mathematics and history. If 7 candidates offered all the subject. how many candidates were there for the examination​?"

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If two of the angles and one of the sides of an oblique triangle are known, the Law of Sines can be used to find the missing lengths or angle measurements.

We cannot utilize the formulas specified for right triangles to solve oblique triangles; instead, new formulas must be used. We'll look at how the Law of Sines can be applied to resolve oblique triangles.

The Sine Rule:

The ratios of the length of a side to the sine of the angle opposite the side must all be the same if A, B, and C are the measurements of the angles of an oblique triangle and a, b, and c are the lengths of the corresponding sides.

[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]

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The sum of the interior angles of a 21-gon (21 sides) is 3420°.

What are Interior angles?

Any angle that is created between two of a polygon's adjacent sides is said to be its internal angle. The internal angle of a polygon is what we might refer to as the angle measured at the interior portion of a polygon.

The polygon has 21 sides.

we can find the sum of all interior angles of the polygon by using this formula :

S = 180 ( n - 2)

So, S = 180 (21 - 2)

        = 180 × 19

        = 3420°.

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The inequality |y -8 | + 11 > 19 can be solved to get the compound inequality:

y > 16

y < 0

Here we want to solve the inequality:

|y - 8| + 11 > 19

To solve the inquality, we need to isolate the variable, we can start by subtracting 11 in both sides, then we will get:

|y - 8| + 11 - 11 > 19 - 11

|y - 8| > 8

Now we can decompose that into two inequalities so we get:

y - 8 > 8

y - 8 < -8

Solving these two we will get:

y > 8 + 8 = 16

y < -8 + 8 = 0

The the solution is the compound inequality:

y > 16

y < 0

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Answer:

5p

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