How do you find the domain and range given points on a graph?.

1: Convert the mixed number into an improper fraction.

2: Rewrite the whole number as a fraction with the denominator 1.

3: Multiply two fractions by multiplying the numerators and denominators separately.

4: Convert it into simplified form if required.

Now, According to the question:

A mixed number is a whole number and a proper fraction represented together.  It generally represents a number between any two whole numbers.

To multiply a mixed number with a fraction, first, convert the mixed number to a fraction and then multiply the two fractions. Two fractions can be multiplied by multiplying the numerators and denominators separately to get a fraction as an answer. The fraction can be written in its simplest form by removing any common factors between the numerator and denominator.

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Answer:

Etymology

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello! You know that the price of a new car is $29,990 and the sales tax rate is 6.5%.  To calculate the tax you will have to pay, you have to multiply 0.065 by 29,990.  You have to move the decimal space two spaces to the left to get rid of the percentage.  29,990 x 0.065 = 1949.35.  The sales tax being charged for the car is $1949.35.  The total cost of the car including tax is $29,990 + $1949.35, which equals $31939.35. Hope this helps!

Answer:

  y = 250(0.96^n)

Step-by-step explanation:

You want an equation for the number of students in the senior class after n years, when it has 250 students now and decreases at 4% per year. You also want to know the number of years until the class is 100 students.

The exponential equation will have the form ...

  y = a·b^x

where 'a' is the initial value, 'b' is the growth factor, and x is the independent variable.

You have an initial value of 250, a growth factor of (1+(-4%)) = 0.96, and an independent variable of 'n', representing the number of years the population has been declining. The equation is ...

  y = 250(0.96^n)

The population will reach 100 students when n has the value that satisfies ...

  100 = 250·0.96^n

  0.4 = 0.96^n . . . . . . . . . divide by 250

  log(0.4) = n·log(0.96) . . . . . take logarithms

  n = log(0.4)/log(0.96) ≈ 22.45

The senior class will have about 100 students in 22.45 years.

__

Additional comment

The growth factor used in these exponential equations is (1 + growth rate), where the growth rate is the fractional change in the period of interest. The independent variable (x or n) is the number of such periods. Here, the fractional change is given as -4%, a 4% per year decrease. This tells us a period is 1 year. Of course -4% is the decimal fraction -0.04.

The exact solutions of an quadratic equation, 9x² - 4 is equals to the values of x, i.e., x = 2/3, - 2/3.

In algebra, a quadratic equation is any equation that can be written in standard form as ax² + bx + c = 0, where x represents an unknown variable, and a, b, and c are known constants, where a ≠ 0. The solutions of a quadratic equation represent x values, where values stratified the equation . Quadratic formula is used to find the solution of standard equation and it can be written as, x = (- b ±√b² - 4ac)/2a .

We have, an quadratic equation,9x²- 4=0

Comparing it with standard equation ax² + bx + c = 0, we get, a = 9 , b = 0 , c = - 4

Using the quadratic formula to determine the solution of it , x = (- b ±√b² - 4ac)/2a

=> x = { -0 ±√0 - 4×9×(-4)}/2×9

=> x = ±(√144/18)

=> x = ± 12/18 = ± 2/3

Hence, the required solution are x = ± 2/3.

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The perimeter of the isosceles triangle is 128.8/(√35 +2) cm.

What is an isosceles triangle?

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.

We are given that the base of an isosceles triangle is equal to 1/3 of the lateral side.

Also, the height of the base together with the height is 9.2 cm.

Let the lateral side be 'x' and the height be 'h'

So, the base is x/3

Since the height of the triangle, divides it into two right angled triangles, therefore,

x^2= h^2 + (x/6)^2

⇒h^2 = x^2 - (x/6)^2

⇒h^2 = √[x^2 - (x/6)^2]

We are given h+b=9.2 cm

So,

⇒√[x^2 - (x/6)^2] + x/3 = 9.2

⇒x√35/6 + x/3 = 9.2

⇒(x√35 +2x)/6 = 9.2

⇒x√35 +2x = 55.2

⇒x(√35 +2) = 55.2

⇒x = 55.2/(√35 +2)

So, the base is 1/3*55.2/(√35 +2) = 18.4/(√35 +2)

Perimeter = 2*55.2/(√35 +2) + 18.4/(√35 +2)

= (110.4 + 18.4)/(√35 +2)

= 128.8/(√35 +2) cm

Hence, the perimeter of the isosceles triangle is 128.8/(√35 +2) cm.

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The simplified exponential expression for this problem is given as follows:

-9h^7g^5.

The exponential expression for this problem is defined as follows:

2h²g^4h^5g - 7hg²h^6g³ - 4g²h³h^4g³.

When two terms with the same base and different exponents are multiplied, the bases are kept while the exponents are added.

Hence the terms are simplified as follows:

Hence the simplified expression is given as follows:

2h^7g^5 - 7h^7g^5 - 4h^7g^5.

(2 - 7 - 4)h^7g^5.

-9h^7g^5.

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An ordered pair contains one point's coordinates. The name of a point in an ordered pair is (x, y).

The first number stands for the x-coordinate, and the second for the y-coordinate. To graph a point, a dot must be placed at the ordered pair's coordinates. The name of a point in an ordered pair is (x, y). The first number stands for the x-coordinate, and the second for the y-coordinate. To graph a point, a dot must be placed at the ordered pair's coordinates.

A set of ordered pairs is any pair of components that are wrapped in brackets and exist in a specific sequence. If there are two components, "a" and "b," the two distinct pairings are "(a, b)" (b, a). A and B are referred to as the first and second elements, respectively, in an ordered pair (a, b). The relationship between the input or domain and the output or range is described by the function rule. If and only if there is only one value in the range for each domain value, a relation is a function.

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Step-by-step explanation:

DISCUSSION QUESTIONS (DQ's).

1. Is division always a negative in a religious faith? Why or why not?

The multiplicative inverse of 'a' is stipulate by a-1 or 1/a. on other side, the multiplicative inverse of a number is expounded as 1 divided by the number.

The multiplication inverse of 6 is 1/6.

hence, the multiplicative inverse of -6 is -1/6.

The multiplicative inverse is defined as the reciprocal of a given number. It is used to define mathematical expressions.

The word 'inverse' concludes something opposite/contrary in effect, order, position. or direction. A number when multiplied by its multiplicative inverse results in 1.

The multiplicative inverse formula is called that the multiply of a number and its reciprocal is 1.

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Answer:

D. y = 5x

Step-by-step explanation:

This graph shows a linear relationship between the number of sandwiches bought (x) and their cost (y). In this question, we are asked to define the relationship between x and y using an equation. Since this relationship is linear and thus has a constant of proportionality, we can represent it in the form: y = mx, where m is the ratio of the cost of sandwiches to the number of sandwiches. We can solve for m with the formula:

m = rise / run

So, the value m of the given line is:

m = 10 / 2

m = 5

Hence, the equation that displays the proportional relationship between the number of sandwiches bought (x) and their cost (y) is D. y = 5x.

Answer:

1.

-x² + 2x

Step-by-step explanation:

x² + x - 2.

=x³ - x² + 2x - 2.

1

=-x² + 2x.

note: x³ cancel x² and x, and -2 cancel -2.

The true statement is D)Census. It's pretty easy to survey all the students at a high school.

All units or participants in the target population under the survey are statistically compiled as part of the census method's process.

Population in this context refers to the total collection of observations associated with a specific study.

For instance, if university students are asked for input on the teaching staff, the latter group will be considered the study's population.

The targeted population is used to choose the various sample entities. With this approach, a predetermined number of observations that come from a bigger pool of populations are statistically analyzed.

Different types of sample methodology can be used, including basic random sampling, systematic sampling, cluster sampling, stratified sampling, and more.

By the above observations, we can conclude that This given situation is a Census as we can survey it among a collection of people that is the batch of senior students and it is easy to survey as there will be a few members of seniors in a school.

Therefore,

The true statement is D)Census. It's pretty easy to survey all the students at a high school.

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Answer:

Step-by-step explanation:

Simplify the following:

(sqrt(48))/(sqrt(42))

Rationalize the denominator. (sqrt(48))/(sqrt(42)) = (sqrt(48))/(sqrt(42))×(42^(1 - 1/2))/(42^(1 - 1/2)) = (sqrt(48)×42^(1 - 1/2))/42:

(sqrt(48)×42^(1 - 1/2))/42

Combine powers. (sqrt(48)×42^(1 - 1/2))/42 = sqrt(48)×42^((1 - 1/2) - 1):

sqrt(48)×42^((1 - 1/2) - 1)

Put 1 - 1/2 over the common denominator 2. 1 - 1/2 = 2/2 - 1/2:

sqrt(48)×42^((2/2 - 1/2) - 1)

2/2 - 1/2 = (2 - 1)/2:

sqrt(48)×42^(((2 - 1)/2) - 1)

2 - 1 = 1:

sqrt(48)×42^(1/2 - 1)

Put 1/2 - 1 over the common denominator 2. 1/2 - 1 = 1/2 - 2/2:

sqrt(48)×42^(1/2 - 2/2)

1/2 - 2/2 = (1 - 2)/2:

sqrt(48)×42^((1 - 2)/2)

1 - 2 = -1:

sqrt(48)×42^((-1)/2)

sqrt(48) = sqrt(2^4×3) = 2^2 sqrt(3):

2^2 sqrt(3) 1/sqrt(42)

2^2 = 4:

4 sqrt(3) 1/sqrt(42)

Rationalize the denominator. (4 sqrt(3))/(sqrt(42)) = (4 sqrt(3))/(sqrt(42))×(sqrt(42))/(sqrt(42)) = (4 sqrt(3) sqrt(42))/42:

(4 sqrt(3) sqrt(42))/42

The gcd of 4 and 42 is 2, so (4 sqrt(3) sqrt(42))/42 = ((2×2) sqrt(3) sqrt(42))/(2×21) = 2/2×(2 sqrt(3) sqrt(42))/21 = (2 sqrt(3) sqrt(42))/21:

(2 sqrt(3) sqrt(42))/21

sqrt(3) sqrt(42) = sqrt(3×42):

2/21 sqrt(3×42)

3×42 = 126:

(2 sqrt(126))/21

sqrt(126) = sqrt(3^2×14) = 3 sqrt(14):

2/21 3 sqrt(14)

3/21 = 3/(3×7) = 1/7:

Answer: (2 sqrt(14))/7

Count 6 point from zero to the left side from zero for negative (-6) and for 5 count 5 points right from the zero on the number line.

A number line in mathematics is a horizontal straight line with numbers spaced equally apart along that line. Some will have a defined beginning and end. We refer to these as closed number lines. Number lines may also be left empty or blank. A number ladder is almost a vertical number line.

Number lines are frequently used in elementary and middle school to help students develop skills like counting, adding, and subtracting numbers. They are typically introduced in kindergarten.

Additionally, it is very easy to read number lines. The values provided enable kids to compare and visualise the relationships between the numbers shown on the line, despite the fact that it isn't a ruler and the space between the numbers isn't fixed. In turn, this promotes the growth of number sense.

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The measure of length PQ will be 22 units.

A triangle's third side is stated to be parallel to the line segment uniting its two midpoints, and it is also half as long as the third side.

Given:

PQ = 5x + 62, and MN = 6x-4

Now, using Mid- Point Theorem

PQ= 1/2 MN

-5x+ 62 = 1/2( 6x - 4)

-5x+ 62 = 3x - 2

-5x- 3x = -2 - 62

-8x = -64

x= 8

PQ= 5x+ 62 = -5(8) + 62 = -40 + 62 = 22

Hence, the measure of PQ is 22 units.

The missing image is attached below.

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The logarithmic function

[tex] f(x) = log_{b}(x) [/tex] is represent the inverse of an exponential function f(x)= bˣ.

A logarithmic function involves logarithms. Its basic form is

[tex]f(x) = log_{a}(x) ,[/tex] , where a > 0. It is Log functions include natural logarithm (ln) or common logarithm (log). For example f(x) = ln(x). An exponential function is defined as a mathematical function in the form f(x) = aˣ , where “x” represent a variable and “a” is a constant number which is known as the base of the function and it's value always be greater than zero. Transcendental number e is mostly used as a base of exponential function base is f. We have, the logarithmic function

[tex]f(x) = log_{b}(x) [/tex] , is the inverse of an exponential function f(x) =bˣ, and which means that

[tex]y = log_{b}(x) [/tex], is bʸ = x. The expression bʸ = x is said to be the “exponential form” for the logarithm

[tex]y = log_{b}(x) [/tex].

Here, b is called the base (of the logarithm) and it should be positive constant.

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Complete question:

What function is

[tex]f(x)= log_{b}(x) ?[/tex]

Answer:

2 weeks

Step-by-step explanation:

The next week Mr Blair’s class will have written 5 letters because his class wrote one more letter, while Ms Stevenson’s class will have written 4 letters because her class wrote 2 more letters. This next week Mr Blair’s class will write another letter leaving them at 6 letters, and Ms Stevenson’s class will write 2 more letters leaving them at 6 letters also. So all in all, in 2 weeks, the two classes will be at equal amounts and caught up to each other.

Answer: 183sr3, 370sr3

Step-by-step explanation:

The domain is actually the set of all "x" values, whereas the range is the set of all "y" values in an ordered pair.

Given,

What is the definition of the word "domain"?

Remember which of the following symbols corresponds to which ordered pair: (x, y).

If an x value has more than one y value connected with it, such as in the relation (4, 1), (4, 2), where the x value of 4 has y values of 1 and 2, a collection of ordered pairs is not a function.

Thus, the connection is referred to as a function if there is only one y value for every x value.

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Answer:

A = 42

Step-by-step explanation:

If 6 / 7 = A / 49, then:
(multiply both sides of the equation by 49)
A = 49 * 6 / 7
A = 42

You can also solve by the rule of proportions (see picture):
7 * A = 6 * 49
A = 6 * 49 / 7
A = 6 * 7 = 42

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Answer:

2 ...

Step-by-step explanation:

since LM = 8

and LN = 10

therefore MN = LN - LM .

MN = 10 - 8 .

MN = 2

Answer:

The slope is simply the gradient of the two points . use the gradient equation (Y2-Y1/X2-X1) to find the answer ;⁠)

The pizza pie cost  $16.50.

We have the following information. An equation is a mathematical statement that asserts the equality of two expressions. It is written in the form of "left-hand side = right-hand side," where both sides are expressions that are made up of numbers, variables, and mathematical operations.

Gentiana spent $10 on her entrance fee, so she has $40 - $10 = $30 left.

25% of $30 is $30 x 0.25 = $7.50.

She spent $7.50 on a Movie.

20% of $30 is $30 x 0.20 = $6.

She spent $6 on popcorn.

So, the total amount spent on Movie and popcorn is $7.50 + $6 = $13.50.

Therefore, the pizza pie cost $30 - $13.50 = $16.50

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25% of $30 is $30 x 0.25 = $7.50.

She spent $7.50 on a Movie.

20% of $30 is $30 x 0.20 = $6.

She spent $6 on popcorn.

So, the total amount spent on Movie and popcorn is $7.50 + $6 = $13.50.

Therefore, the pizza pie cost $30 - $13.50 = $16.50

Answer:

Below in bold.

Step-by-step explanation:

To do this we keep dividing by successive primes, using the lowest prime that divides exactly.

2) 12600

2) 6300

2) 3150

3) 1575

3) 525

5) 175

5) 35

7        <---we end up with a prime number so tha's the end of the process

So, 12,600 = 2*2*2*3*3*5*5*7 or 2^3*3^2*5^2*7.

Answer:

Step-by-step explanation:

Y = e−x

Answer: A negative exponential function or y = e−x, is otherwise known as exponential decay

Step-by-step explanation: I hope this helps!

Answer:

x^2 + 6x + 9 and x^2 + 8x + 16 are examples of perfect-square trinomial

Step-by-step explanation:

1. x2 + 6x + 9

(x + 3)^2

= (x + 3)(x + 3)

= x2 + 6x + 9

2. x^2 + 8x + 16

x^2 + 8x + 16

= x^2 + 2(x)(4) + 4^2

= (x + 4)^2

To calculate std deviation in R you can create a list of values or import a CSV file to find the standard deviation.

It is simple to compute an average and standard deviation in R. The mean() and sd() functions compute the average and standard deviation, respectively.

The positive square root of the variance is the standard deviation. One of the fundamental techniques used in statistical analysis is standard deviation. Standard deviation, also known as SD or indicated by the symbol "," indicates how far a value deviates from the mean value.

A low standard deviation indicates that the values are often within a few standard deviations of the mean, whereas a large standard deviation indicates that the values are much outside of the mean. Learn how to determine a random variable's standard deviation as well as the standard deviation of data that has been grouped and ungrouped.

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Different quadrilaterals have different properties to get proven.

what are quadrilaterals?

A quadrilateral is a polygon with four sides, four vertices, and four angles.

It is formed by joining four non-collinear points. The sum of the interior angles of quadrilaterals is always equal to 360 degrees. The word quadrilateral is derived from the Latin words ‘Quadra’ which means four and ‘Latus’ means ‘sides’. Not all the four sides of a quadrilateral need to be equal in length. Hence, we can have different types of quadrilaterals based on sides and angles.

Now,

Five special quadrilaterals are shown below in the image, along with their definitions and pictures, and points for them to get proven.

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Yes. Zero is a real value of x.

Given,

Real value of x;

The non-negative value of a real number x, regardless of its sign, is its absolute value (or modulus), | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5.

How do you discover the true worth?

The influence of price level changes is subtracted from the nominal value of a good, service, or time-series data to create real value, which provides a more accurate view of economic trends. A deflator is used to alter the nominal value of time-series data, such as GDP and incomes, in order to produce real values.

Here,

The real value of x includes 0.

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