A rectangular garden has a length of 20 yards and a width of 42 yards. A diagonal path runs from one end of the garden to the other. How long is the diagonal path? a. B. C. 50 yd. D.

The greatest integer function has the domain of a set of all real numbers (R), and its range is the set of all integers (Z).

The greatest integer function gives the greatest integer, which is less than or equal to a given number. The greatest integer less than or equal to a given number x can be represented as ⌊x⌋. Mathematically, the greatest integer function ⌊x⌋ is defined as follows:

⌊x⌋ = a, where a ≤ x < a + 1 and 'a' is an integer.

The greatest integer function has the domain of the set of all real numbers (R), and its range is the set of all integers (Z).

--The given question is incorrect; the correct question is

" What is the domain and range of the greatest integer function?"--

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The constant of proportionality in the given equation as represented in the task content is; 0.25.

It follows from the task content that the constant of proportionality of the given equation as required in the task content be identified.

Since the given equation in the task content is;

p = 0.25q

As evident in the equation above, there exists a directly proportional relationship between the quantities p and q.

Hence, the constant of proportionality in the give. equation is; 0.25.

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Answer:

  (b)  Domain: all real numbers; Range: {-24}

Step-by-step explanation:

You want the domain and range of the function f(x) = -24.

The domain of the function is the set of values of x for which it is defined. The function f(x) is defined for all x, so the domain is all real numbers.

The range is the set of output values of the function. This function has only one output value: -24. The range of the function is {-24}.

The word "logarithm" is derived from the Greek meanings for "ratio" (logos) and "number" (arithmos).

In the 17th century, Scottish mathematician John Napier (1550-1617) developed logarithms as a tool for computing. He derived the phrase from the Greek words for ratio (logos) and number (arithmos).

Before mechanical (and later electronic) computers were developed, logarithms were essential for simplifying calculations in astronomy, navigation, surveying, and afterwards engineering. A logarithm is a mathematical formula that calculates how many times the base, or initial number, must be multiplied by itself to produce the target number. As a result of the relationship between logarithms and geometric progressions.

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The factors considered when deciding to make a good and service are

a)Determining who has the greatest need

b)finance of prospective buyer

d) way to produce items at a lower cost or higher quality

When deciding how to make goods and services, it's important to take into consideration the needs of the customers. Identifying who has the greatest need for the product is crucial in determining how to design and produce it.

Another important factor is the cost of production, a way to produce the item at a lower cost or higher quality must be considered as it will affect the final price and the competitiveness of the product in the market.

While maximizing profit is always a goal, it should not be the only deciding factor when determining how to make goods and services, as other factors such as customer need and production cost also play important roles.

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The formula of the nth term in the arithmetic sequence is a(n) = 3 + (n-1)9.

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a fixed constant, called the common difference, to the preceding term.

The sequence can be represented by the general term an = a1 + (n-1)d, where a1 is the first term and d is the common difference

In an arithmetic sequence, the difference between consecutive terms is constant. Therefore, if a(1) = 3 and a(2) = 12, the common difference (d) is 12 - 3 = 9.

The nth term of an arithmetic sequence is given by the formula:

a(n) = a(1) + (n-1)d

where:

a(n) is the nth term of the sequence

a(1) is the first term of the sequence

d is the common difference

n is the position of the term in the sequence

So, for the given sequence, the nth term a(n) of the arithmetic sequence is:

a(n) = a(1) + (n-1)d = 3 + (n-1)9

This means that the nth term of the arithmetic sequence is found by adding the common difference (9) to the first term (3), and then multiplying the result by (n-1) which indicates the position of the term in the sequence.

Therefore, a(n) = 3 + (n-1)9 is the formula of the nth term in the arithmetic sequence.

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Answer:

x = 0.45882352

Step-by-step explanation:

-1.95 = -1.7 x/0.4

-1.95 = -4.25x

x = 0.45882352

The unit rate is 120 words per minute and 185 words per minute

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

a) For the first graph, using the points (3, 360) and (2, 240)

Unit rate = Slope = (240 - 360) / (2 - 3) = 120 words per minute

a) For the second graph, using the points (0, 0) and (1, 185)

Unit rate = Slope = (185 - 0) / (1 - 0) = 185 words per minute

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Equivalent sets must have the same cardinality, i.e., n(A) = n(B) where, n(A ) and n(B) are the number of elements in set A and set B respectively.

Equivalent Sets means that there should be a one-to-one correspondence between the elements of both sets. Equal sets and equivalent sets are two different concepts. A is equivalent to B if A and B are two sets such that n(A) = n(B). This means that two equal sets are always equal, but the opposite of the same may or may not be true.

Statement: Set A and Set B are equivalent.

Proof: Let us consider two sets A and B. Let 'a' be any member of A. We need to show that "a" is also a member of B. Then let "b" be any member of B. We must show that b is also a member of A. If the members of A and B are defined by an algorithm or set of features, it must be shown that algorithms that define elements of A also define elements of B, and vice versa.

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Complete question:

How do you prove equivalent sets?

Hey there!

Answer:

There isn't any options to choose from, however an equivalent expression to the given expression above would be [tex]13h[/tex].

Hope this helps! If not, comment below and lmk what else I can do to better assist you.

A factor is a number that divides exactly into another number, leaving no residue. The factors of 12, for instance, are 1, 2, 3, 4, 6, and 12. Particularly in the areas of number theory, algebra, and arithmetic, factors play a crucial role in mathematics.

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Complete Question :

What do you mean by Factor?

The components of the polynomial given as 122 9z - 4 + 3 are (4 - 3). (3- 1) 122 - 92 - 4a + 3 polynomial the provided polynomial has been factored 922 think about the polynomial 12z 4a + 3.

Taking 34 common terms from the first two terms and 1 common term from the last two terms, we get 3a2(4z - 3) - 1(4* - 3) when we factorise using grouping of terms. Taking (4x-3) common once more, we have (4z - 3)(322- 1). Therefore, (4z - 3) is the factor of the provided polynomial 12a - 9z'- 42 + 3. (3r - 1).

The given polynomial, 12x3-9x2-4x+3, has the components (4x-3) (3x2) - 12x3-9x2-4x+3 polynomial the provided polynomial has been factored. The term "factor" refers to a number that, when multiplied or divided, yields a specific number. Think about the polynomial 12x3-9x2-4x+3. We'll factorise based on a collection of terms, Using the first two terms' 3x2 common value and the last two terms' -1 common value, we arrive to.

Complete question:

What is 9x2 factored?.What distinguishes the two polynomials and its conclusion?

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The expression 9x² can be factored as 3x². The expression 9x² can be factored by dividing both 9 and x² by their greatest common factor of 3.

In other words, 9x² can be written as 3 * (x²) which is equivalent to 3x². Factoring is a useful technique for simplifying expressions and solving equations, as well as for understanding the relationship between different terms in a polynomial.

By factoring an expression, we can see how it can be written as a product of simpler expressions, which can sometimes make it easier to manipulate or solve for a particular variable.

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Complete Question:

What is 9x²  factored?.

The 3 4 5 triangles angles are applicable for the right angle triangle.

The sum of all angles of triangle is 180 degree.

A 3 4 5 triangle is right angle triangle in which 3 and 4 is the base and perpendicular, where 5 is the hypotenuse of that triangle.

Properties of 3 4 5 triangle.

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Answer:

x = 6

Step-by-step explanation:

6x²/x³ = 1/1

6/x = 1

x = 6

Answer:

44 degrees

Step-by-step explanation:

if it's worded the way I think. You definitely have the wording mixed up but you add both angles together and set equal to 90.

Hope it helps! :)

A right angle does not always have two equal sides, only in the case of an isosceles triangle it will have two equal sides.

A triangle is said to have a right angle if one of the angles is 90 degrees. Right triangles are those having angles at 90 degrees, which are referred to as right angles.

The Pythagorean rule may be used to understand the relationship between the different sides of this triangle. The biggest side, also known as the hypotenuse, is the side that forms the right angle.

The right triangles are further divided into isosceles and scalene right triangles based on the other angle values.

Thus, A right angle does not always have two equal sides, only in the case of an isosceles triangle it will have two equal sides.

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Step-by-step explanation:

x² - 9

1. There is no common factor other than 1.

2. √x² = x; √9 = 3

3. a = x; b = 3

4. x² - 9 = (x - 3)(x + 3)

The answer is:

The given parameters are:

Start = 24 inches

Rate = 6 inches/second

The function model of the height is determined using a linear function:

h(t) = Start + Rate × t

Where: t represents the time in seconds

So, we have:

h(t) = 24 + 6 × t

This gives

h(t) = 24 + 6t

After 22 seconds, the height of the periscope will be

h(22) = 24 + 6 × 22

Multiply

h(22) = 24 + 132

Add

h(22) = 156

Hence, the maximum height is 156 inches.

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The complete question is:

what function models the height of the periscope lens at time t? If the periscope reaches its maximum height after ascending for 22 seconds, what is the maximum height in feet? ( 24 inches above the surface and ascends at 6 inches per sec.)​

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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The value of the stock will be $1,179.98 in 2024 (After rounding the answer off to the nearest dollar).

It is given that steve bought $2,000 worth of stocks in 2019 and its values have been decreasing by 10% each year,

So in 2020 the value will become

$(2,000-(10% of 2,000))

=$(2,000-(200))

=$1,800

in 2021,

$(1,800-(10% of 1,800))

=$(1,800-(180))

=$1,620

in 2022,

$(1,620-(10% of 1,620))

=$(1,620-(162))

=$1,458

in 2023,

$(1,458-(10% of 1,458))

=$(1,458-(145.8))

=$1,312.2

and finally in 2024,

$(1,312.2-(10% of 1,312.2))

=$(1,312.2-(131.22))

=$1,179.98

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Answer: Sorry!

Step-by-step explanation:

Hello! Will you please include the instructions? If you do, I can help you!

The area of the courtroom is the sum of the areas of a rectangle and a triangle equal 45 m².

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

From the given diagram of the courtroom, its total area should be the sum of the area of a rectangle with a length of 9 m and width of 4 m and a triangle with a height of 3m and a base of 6 m.

Therefore,

The area of the courtroom is,

= (9×4) + (1/2)×3×6 m²      [area of triangle = (1/2)×base×height, area of  

                                                          rectangle is (length×width)]

= 36 + 9 m².

= 45m².

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Answer:

87 students

Step-by-step explanation:

We know

12 out of every 15 students owns a cell phone, so the ratio of student who owns cell phone is 12:3. For every 15 students, there are 12 own cellphones, and 3 do not.

To find there are 435 students surveyed, how many do not own a cell phone? We take

435 / 15 = 29

3 x 29 = 87 students

So, 87 students do not own a cellphone.

Answer:

10cm

Step-by-step explanation:

same gghshbsbbsnsnnsbsbxbbxbdbbxbxbbdbdbdbbdbdndndnndndndnnfnfbbdhdn

The total price including tax, Fawaz has to pay is $36 round to the nearest cent.

To find the total price of the phone including tax, we need to add the tax amount to the price of the phone. The tax rate is 9%, which means that for every $1 of the price of the phone, $0.09 will be added as tax. To find the total price including tax, we can use the following formula:

Total price = Price of the phone + (Price of the phone x Tax rate)

Given the information in the problem, we know that:

Price of the phone = $33

Tax rate = 9% (expressed as a decimal)

Plugging these values into the formula, we get following equation:

Total price = $33 + ($33 x 0.09)

To solve for total price, we need to calculate ($33 x 0.09)

= $3

Total price = $33 + $3

Total price = $36

So the total price including tax, Fawaz has to pay is $36 round to the nearest cent.

In simple words, we have multiplied the price of the phone with the tax rate and then added the tax amount with the price of the phone to get the total price including tax.

Note: The tax rate is given as 9% which is equal to 0.09 in decimal form.

Therefore, The total price including tax, Fawaz has to pay is $36 round to the nearest cent.

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Total price = $33 + ($33 x 0.09)

To solve for total price, we need to calculate ($33 x 0.09)

= $3

Total price = $33 + $3

Total price = $36

So the total price including tax, Fawaz has to pay is $36 round to the nearest cent.

The y - intercept of 2x + y = -2 is -2.

Given straight line is 2x + y = -2.

We know that standard slope form of straight line is y = mx + c

Now we transform given equation to standard form of straight line :

The point at which a straight line cut the y-axis is called the y-intercept. Any point on the y-axis has a x-coordinate of zero.

Therefore, x-coordinate of y-intercept  is 0.

For finding y-intercept, we can substitute x by 0 and solve for y:

Therefore, the y - intercept of 2x + y = -2 is -2.

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The statements about his solution that are true include:

1) He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

2) He did not multiply the numerator and denominator by the correct number to equal 1,500.

5) He should have multiplied the numerator and denominator by 75, not 30,  because 20 x 75 = 1,500

From the information, Josiah kept track of how many songs of each genre were played in an hour from his MP3 player and the counts are displayed in the table below.

In this case, it should be noted that he should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

In this case, the correct options are 1, 2 and 5.

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The interval in which the graph increasing is (10,∞). The correct option is D.

The absolute value or modulus of a real number x denoted |x| in mathematics, is the non-negative value of x regardless of its sign. Specifically, if x is a positive number,|x|=x.

In discrete mathematics, and more specifically in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way. The objects correspond to mathematical abstractions known as vertices, and each pair of related vertices is known as an edge.

The given absolute function is h (x) =lx-10l+6. When we plot the graph of the function it is observed that the graph is increasing from 10 to ∞. The graph is attached with the answer below.

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Answer:

5 in

Step-by-step explanation:

20 ft-9[tex]\frac{1}{2}[/tex] in+ 2[tex]\frac{1}{2}[/tex] in = 21 ft   meaning, Tim has to jump 2[tex]\frac{1}{2}[/tex] in more inches just to get to 21 ft, then...

He needs to jump an additional    2[tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] = 2[tex]\frac{2}{4}[/tex] = 2[tex]\frac{1}{2}[/tex] in to break the record.  Note:  he needs to jump at least [tex]\frac{1}{4}[/tex] in farther than the record because jumps only are measured to the nearest [tex]\frac{1}{4}[/tex] inch.

Therefore Tim must jump 2[tex]\frac{1}{2}[/tex] in + 2[tex]\frac{1}{2}[/tex] in = 5 in farther to break the record.