An article is sold for Rs. 2970 after allowing a discount of
10%. Find the marked price of the article.

The domain of the function f(x)= -long(5-x)+b is Dom(f) = [– ∞,  5]., range is all real numbers except for x = 5.

IF function is the process or state of instruction that text inputs performance is specific task and produce an output functional key components of programming language allowing the quarter to create complex commands with simple instruction for example a function can be used to add two numbers together or to generate a random number function can also be combined to create more complex sequence of instruction.

The range of this function is all real numbers as the long function will never return a negative value. The value of b determines the exact range of the function, as it shifts the graph up or down.

The formula is: f(x) = - log(5 - x) + b.

Limitation for the f domain:

5 – x > 0

x < 5

Hence, f's domain is

Dom(f) = {x ∈ R:  x < 5}

Alternatively by notating intervals,

Dom(f) = [– ∞, 5].

Secondly, we wish to demonstrate that there is always an x Dom(f) for any given y R.

y = f(x) (x)

Once we've demonstrated that, we can say that f's operating range is R. (all real numbers).

How to find x in an equation:

[tex]y = f(x)\\y = - log(5 - x) + b\\y - b = - log(5 - x) (5 - x)\\-(y - b) = log(5 - x) (5 - x)\\b - y = log(5 - x) (5 - x)\\5 - x = 10^{(b - y) (b - y)}\\x = 5 - 10^{(b - y) (b - y)}\\[/tex]

Because y is not constrained, the range of f is R. (all real numbers).

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Answer: rectangle

Step-by-step explanation: because i have eyes

Answer:

Step-by-step explanation:

No, the number of students at the school is not proportional to the number of teachers. In a proportional relationship, two quantities have a constant ratio. However, in this case, the number of teachers is not directly proportional to the number of students because there is a fixed number of teachers regardless of the number of students. Even if the number of students changes, the number of teachers remains the same.

A more appropriate way to describe the relationship between the number of teachers and students at the school is to say that there are 2 teachers for every 48 students, or that the ratio of teachers to students is 2:48, which simplifies to 1:24.

Answer:

Step-by-step explanation:

S=24000x(1.043)^t

Due to length restrictions, we kindly invite to read the explanation below for further details on equivalence of trigonometric expressions.

In this problem we find five case of trigonometry expressions whose equivalence must be proved by means of algebra properties and trigonometric formulas. Now we proceed to show the solution for each case:

Case 3:

tan θ · cos θ

(sin θ / cos θ) · cos θ

sin θ

Case 5:

(1 - cos θ) · (1 + cos θ)

1 - cos² θ

sin² θ

Case 6:

(1 + sin θ) · (1 - sin θ)

1 - sin² θ

cos² θ

Case 7:

(sec θ + tan θ) · (sec θ - tan θ)

sec² θ - tan² θ

1

Case 10:

(tan θ + cot θ) / tan θ

1 + cot θ / tan θ

1 + cot² θ

csc² θ

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Answer:

Missing measure for angle B = 74°

Missing measure for angle C = 74°

Step-by-step explanation:

Side AB = Side AC

∴∠B° = ∠C°

Two sides out of three of this triangle are equal to each other, therefore this is an isosceles triangle

Let x° = ∠B° = ∠C°

Sum of interior angles of a triangle = 180°

                                      ∴32° + x° + x° = 180°

                                     = 32° + 2x° = 180°

                                      = 2x° = 180° - 32°

                                      = 2x° = 148°

                                      = x° = [tex]\frac{148}{2}[/tex]

                                      = x° = 74°                

                            ∴∠B° = ∠C° = 74°  

The length and the width of the playground 12 yards and 17 yards respectively.

As per the data given in the question the area of the playground is 204 square yards.

Area = 204 square yards.

The width of the playground is 5 yards longer than its length.

Let the length of the playground be 'l' yards.

Then the width of the playground will be (l + 5) yards.

The formula for the area of the playground is Length × Width.

A = Length × Width

204 = l (l + 5)

204 = [tex]l^{2}[/tex] + 5l

[tex]l^{2}[/tex] + 5l - 204 = 0

[tex]l^{2}[/tex] + 17l - 12l - 204 = 0

l (l + 17) -12 (l + 17) = 0

(l + 17) (l - 12) = 0

(l + 17) = 0 or (l - 12) = 0

l = -17 or l = 12

Length cannot be the negative value.

So the value of the length is 12 yards.

Then width = l + 5

Width = 12 + 5

Width = 17 yards

Therefore length is 12 yards and width is 17 yards.

Option (b) is correct.

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The area of a playground is 204 yd2. The width of the playground is 5 yd longer than its length. Find the length and width of the playground.

a.) length 17 yd, width 22 yd

b.) length 12 yd, width 17 yd

c.) length 22 yd, width 17 yd

d.) length 17 yd, width 12 yd

The number of arrangements of 6 balls with 2 red balls and 2 blue balls, we need to consider the number of ways to choose 2 red balls from the 4 available red balls and the number of ways to choose 2 blue balls from the 4 available blue balls.

These are both combinations, and we can use the formula for combinations to calculate them:

C(n, k) = n! / (k! (n-k)!).

For the red balls, C(4, 2) = 4! / (2! (4-2)!) = 6.

For the blue balls, C(4, 2) = 4! / (2! (4-2)!) = 6.

The total number of arrangements of 6 balls with 2 red balls and 2 blue balls is the product of the number of arrangements for each type of ball:

C(4, 2) * C(4, 2) = 6 * 6 = 36

So, there are 36 arrangements of 6 balls with 2 red balls and 2 blue balls.

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The graph of this piecewise function is a step function, with steps at x=1 and x=2, where the value of the function changes.

The cost of parking for hours is a function of the number of hours. It can be modeled by a piecewise function, where the cost depends on the number of hours you park.

Here's the piecewise function for the cost of parking in dollars:

f(x) = {5, if 0 < x <= 1

{10, if 1 < x <= 2

{12, if x > 2

The graph of this piecewise function is a step function, with steps at x = 1 and x = 2, where the value of the function changes. The value of the function is constant in each interval (0, 1), (1, 2), and (2, infinity).

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Answer:

-4

Why? I subtract the numbers. How to do that is by looking at the table. You always use two ordered pairs. Let's choose (-3,12) and (-2,8).

Step 1: Choose two ordered pairs (you can choose any two, it doesn't matter).

Now, subtract the y's together and subtract that x's together. So, what is 12-8? That's obvious, it's 4. Alright, how about -3-(-2)? Well, two negatives make a positive, so the problem is actually -3+2. So, what's that? Correct, -1. And, since slope is y/x, the answer would be -4/1, or -4.

7. The percentage of the seats taken by 18,460 attendees out of 34,000 capacity spectators of the Bidvest Wanderers Cricket Stadium is 54%.

8. If a bus can seat 60 passengers and some passengers got off, leaving 0.4 of the seats occupied, the number of passengers who got off the bus is 36, representing 60 percent.

9a) The population that speak Mandarin more than English is 526,200,000.

9b) If the world population is approximately 7 000 000 000 (7 billion), the percentage of the entire population that speaks Spanish is 5.00%.

The percentage represents the ratio of one value compared to another.

The percentage is determined as the quotient from dividing the numerator by the denominator and multiplying by 100.

7) The spectator capacity of the Bidvest Wanderers Cricket Stadium = 34,000

Attendees at a one-day match = 18,460

Percentage of seats taken = 54.3% (18,460/34,000 x 100)

8) Bus passenger capacity = 60

The percentage of seats occupied = 0.4

The number of passengers who got off the bus = 36 (60 x (1 - 0.4)

9) Most Commonly Spoken World Languages:

Mandarin 867 200 000 people

English 341 000 000 people

Spanish 350 000 000 people.

a) The more Mandarin speakers than English = 526,200,000 (867,200,000 - 341,000,000)

b) World Population = 7 billion

Percentage of Spanish speakers to World Population = 5.00% (350,000,000/7,000,000,000 x 100)

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Answer:$1. 45

Step-by-step explanation:

The bill is $1

the quarter is .25

and the nickels together are .20

add everything together its 1.45

First, we need to know the value of each coin. The top coin is a quarter, and its value is $0.25. The four coins below are nickels, and they have a value of $0.05. The dollar bill at the bottom has a value of $1.00.

If we have one quarter, we start with a value of $0.25.

[tex]$0.25[/tex]

Now, we add on the nickels.

[tex]0.25 + 0.05+ 0.05+ 0.05+ 0.05 = 0.45[/tex]

Now we have a total of $0.45.

Adding the dollar would look like this:

[tex]1.00 + 0.45 = 1.45[/tex]

Therefore, the value of all the money in the picture is $1.45.

Step-by-step explanation:

To find the volume of this solid, we will use the method of cylindrical shells. We will integrate the cross-sectional area of the equilateral triangles over the height of the solid.

The height of the solid is given by the difference between the upper and lower bounds of the base, which are y = 4 and y = x^2, respectively. The cross-sectional area of an equilateral triangle with sides of length 2x is given by (x^2 * √3)/4.

So, the volume of the solid is given by the integral:

V = ∫[x^2, 4] (x^2 * √3)/4 dx

Using the antiderivative of x^2 * √3 / 4, which is (2x^3 * √3)/(12), we can find the definite integral:

V = [2x^3 * √3]/12 from x^2 to 4

Evaluating the definite integral and simplifying, we get:

V = 16 units^3

So, the volume of the solid is 16 units^3.

Answer:

the volume of the solid is 16 units^3

Step-by-step explanation:

Answer:

[tex]5.98xy-8y[/tex]

Step-by-step explanation:

Distribute the y

[tex]5.98xy-5.81y-2.19y[/tex]

Combine like-terms

[tex]5.98xy-8y[/tex]

The answer to our inquiry is that 180 grams of zinc contain a particular compound.

Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were going to compare another data item (A) to this other data point (B).

The zinc to copper ratio in a particular compound is 4: 11.

Copper weighs 495 grammes in the chemical.

How much zinc does it chemically contain in grammes.

Assume that y is the scalar multiple of zinc and copper.

as stated

The proportion of zinc over copper in a certain compound is 4 to 11.

Copper weighs 495 g in the chemical.

Equation is than

11y = 495

11y = 495

y = 495/11

y = 45

Zinc in a particular chemical = 4y

= 4x45

= 180 grams

Therefore 180 grams of zinc contain in a certain chemical .

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Answer:

  (x, y) = (-3, -5)

Step-by-step explanation:

You want to solve the given system of equations by elimination.

To eliminate a variable from the equations, we need to add them in such a way that the coefficients for one of the variables have a total of zero.

Here, we observe that the y-coefficients are the same, so subtracting one equation from the other will cancel the y-terms. We want the result of that subtraction to give an equation with x having a positive coefficient, so we elect to subtract the second equation from the first:

  (2x -3y) -(-5x -3y) = (9) -(30)

  7x = -21 . . . . . simplify (y-terms are gone, x-term has positive coefficient)

  x = -3 . . . . . . . divide by 7

The value of y can be found from either equation. We choose to use the first one:

  2x -3y = 9

  2(-3) -3y = 9 . . . . . . substitute -3 for x in the first equation

  -15 = 3y . . . . . . add 3y-9

  -5 = y . . . . . . . divide by 3

The solution is (x, y) = (-3, -5).

The zeroes of the given function are + 1 and - 1 respectively.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is the function as -

y = x² - 1

For the zeros of the function substitute {y} = 0. We get -

x² - 1 = 0

x² = 1

x = ± 1

Therefore, the zeroes of the given function are + 1 and - 1 respectively.

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It is formatted a bit weird.

u = the radius (im pretty sure)

area of a circle = pi(u)^2

circumference of a circle is 2pi(u)

22/7 = pi

Area = (22/7)(u)^2

Circumference = 2(22/7)u

Answer:

The equation that shows inverse variation is (Choice C) y = (1/8)x.

Step-by-step explanation:

The equation that shows inverse variation is (Choice C) y = (1/8)x.

The toddler crawled a total of 24 feet (2 yards = 6 feet and 8 more feet).

The question asks how many feet the toddler traveled. To answer this question you need to convert yards to feet then add the measurements together. One yard is equivalent to three feet, so the toddler traveled two yards which is six feet. The toddler then stopped and continued to crawl eight more feet. To figure out the total distance the toddler traveled, you need to add the two measurements together. Six feet plus eight feet is equal to fourteen feet. Therefore, the toddler traveled a total of twenty-four feet.

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Answer:The student made a mistake and explain the specific error that was made. Support your answer using the correct vocabulary. The mistake has been done in Step 2.

PART A: There is a mistake in Step 2, Distributive Property has been employed incorrectly.

7 has to multiply by both the terms inside the bracket, but it has been multiplied with the first term only.

7(-2 x-8 y)=-14 x-56 y and 7(-2 x-8 y) -14 x-8 y

Hence, -5(x-16 y)+7(-2 x-8 y)=-5 x+80 y-14 x-56 y

PART B :

The given equation is

-5(x-16 y)+7(-2 x-8 y)

Applying distributive property to the above equation that states A(B+C)=AB+AC, we get :

-5 x+80 y-14 x-56 y

Now, Writing the terms with the same variable together, we get

(-5 x-14 x)+(80 y-56 y)

Proceeding with solving terms inside the brackets according to BODMAS, we get,

-19 x+24 y

Hence , −5(x − 16y) + 7(−2x − 8y) = -19x +24y

The correct answer for the measures of the sides of the triangle is (D) 8 cm, 10 cm, and 4√41 cm.

The sine of an angle is a mathematical function that describes the relationship between the lengths of the sides of a right triangle and the angles within that triangle. In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

Let's call the side opposite the angle with sine 4.5 "a", and the side adjacent to that angle "b". Using the definition of sine, we can write the following equation:

sin(θ) = a/c

where c is the length of the hypotenuse. We can substitute 4.5 for the sine:

4.5 = a/c

Cross multiplying, we get:

4.5c = a

So, given the length of c, we can find a.

The only option that gives a positive value for c is (D), with c = √41 cm. In this case, a = 4.5 * √41 = 4√41 cm, which matches the value in the answer choices.

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The number of star wars that Amy has is 255 and Carly has is 85

Linear equation:

The linear equation is a combination of algebraic terms that are used to find unknown quantities in a word problem. To solve the given problem represent the unknown value with a variable and form a linear equation according to the given condition. Now solve the equation for the value of the variable.

Here we have

Amy has three times as many star wars toys as Carly.  

Let Amy have 'x' star wars and Carly have 'y' star wars

From the given data, x = 3y  

It is also given that both have 340-star wars toys in total

=> y + 3y = 340

=> 4y = 340

=>  y = 85

Hence, the number of star wars that Carly has = 85

Number of star wars that Amy has = 3(85) = 255

Therefore,

The number of star wars that Amy has is 255 and Carly has is 85

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The ratio of the number of astronauts on Earth to the total number of astronauts is 7 : 30.

A ratio is a mathematical expression that compares two or more values by dividing the size of one value by the size of another.

Ratios can be expressed in several different forms, including fractions, decimals, or percentages, and can be used to compare quantities, measurements, or other values in a meaningful way.

Ratios provide a way to express the relationship between two or more values in a compact and concise format, and can be used in a variety of fields, including mathematics, science, finance, and engineering.

If the space program has 23 astronauts in outer space and 7 astronauts on Earth, then the ratio of the number of astronauts on Earth to the total number of astronauts is:

7 : (23 + 7) = 7 : 30

You can simplify the ratio to 7/30 or approximately 0.23 or 23%.

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It depends on the thickness of the aluminum bar. Generally, a hacksaw blade with 18 teeth per inch is used to cut off aluminum from 1'' square bar.

The number of teeth a hacksaw blade should have to cut off a piece of aluminum from 1'' square bar depends on the thickness of the aluminum bar.

2. Generally, a hacksaw blade with 18 teeth per inch is used to cut off aluminum from 1'' square bar.

For example, if the aluminum bar being cut is thin (1/8'' or less) then a hacksaw blade with 18 teeth per inch should be used. On the other hand, if the aluminum bar is thicker (greater than 1/8''), then a hacksaw blade with fewer teeth per inch should be used. The fewer teeth per inch the hacksaw blade has, the thicker the aluminum bar it can cut through. It is important to choose the correct hacksaw blade for the job in order to ensure a clean and safe cut.

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Answer:

  n ∈ ℕ . . . (Natural numbers)

Step-by-step explanation:

You want the domain of the relation s(n) = 7+3n so that it defines the sequence 10, 13, 16, ....

The domain of a function is the set of "input" values for which the function is defined. Here, the function is intended for use with values of n that are Natural numbers:

  domain = ℕ

__

Additional comment

In general, the domain of any function that defines a sequence will be Natural numbers. That is, values of n will be 1, 2, 3, ....

Occasionally, the sequence represents a relation that is of interest for values of n other than positive integer values. In such a case, the domain may be Whole numbers, or Real numbers.

Answer:

Option 4
y = 2x + 3

Step-by-step explanation:

Equation of a line in slope intercept form is
y = mx + b
where m = slope and b = y-intercept

Slope m = rise/run = Δy/Δx with Δy = change in y values between any two points on the line and Δx = corresponding change in x values

b is the y-intercept, value of y when x = 0 and indicates the point at which the line crosses the y-axis

Let's take two distinguishable integer points on the line

(0, 3) and (1, 5) are two points

rise = Δy = 5 - 3 = 2
run = Δx = 1 - 0 = 1

So slope = 2/1 = 2

Since y = 3 at x = 0, y-intercept b = 3

Equation of line is
y = 2x + 3

Option 4)

Answer:

4)y=2x+3

You can see this clearly as the y-intercept is 3 and going two spaces up and one to the side is the slope.

Step-by-step explanation:

The area of the forest decreases by 6.25% each year, and after 15 years, the area will be approximately 1089 km.

The area of a forest is a crucial aspect of understanding its size and its impact on the environment.

In this question, we are know that the forest with an initial area of 2500 km, which decreases by 6.25% each year. Our task is to find the area of this forest after 15 years. To do this, we need to perform a calculation that takes into account the decrease in area each year.

Mathematically, we can represent the area of the forest after n years as:

A = 2500 * (1 - 0.0625)ⁿ

Where n is the number of years that have passed. To find the area after 15 years, we can plug in n = 15:

A = 2500 * (1 - 0.0625)¹⁵

Using the calculator provided, we find that the area of the forest after 15 years is approximately 1089.38 km. Rounding this to the nearest square kilometer, we get 1089 km.

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Answer: The distance between these two points is 5.

Step-by-step explanation:

Yay! Love doing distance formula questions!

Okay, so first off, the distance formula goes as follows:

d = [tex]\sqrt(x^{2} - x^1)^2 + (y^{2}-y^1)^2[/tex]

Basically you just plug in your coordinates to the formula.

Step 1:

[tex]\sqrt(-5 + 5)^{2} + (2-7)^{2}[/tex]

Step 2: Distribute the exponent to both parenthesis to get [tex]\sqrt{25}[/tex].

Step 3: Factor the number, which would result in [tex]\sqrt{5^2}[/tex].

As a result of this, your answer would be 5.

The quantity of lunch specials conceivable is 2 sandwiches * 2 beverages * 3 treats = 12.

The lunch exceptional at Teresa's Café incorporates a sandwich, a beverage, and a sweet. There are 2 choices for sandwiches, 2 choices for beverages, and 3 choices for treats. To decide the quantity of conceivable lunch specials, we want to track down the quantity of blends of these things. The recipe for mixes is n! /(r! * (n - r)!). Nonetheless, since every thing is chosen just a single time, we can basically duplicate the quantity of choices for every thing. For this situation, there are 2 choices for sandwiches, 2 choices for beverages, and 3 choices for pastries, so 2 * 2 * 3 = 12 potential lunch specials.

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