Which rational function has the most solutions in common with the function y=2x+6

An exponential decay function that shows the relationship between y and t is y = 16,000 (0.74)^t.

An exponential decay function is one of the two types of exponential functions, including an exponential growth function.

Exponential functions are depicted as y = abˣ, where "a" is a constant, b is the base and x is the variable exponent.

The purchase value of a car = $16,000

Annual decreasing rate in value = 26%

Decayed value after 1 year = 0.74 (1 - 26%)

Let the number of years after the purchase = t

Let the resale value of the car after t years = y

Resale value after t years, y = 16,000 x (1.074)^t

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B. y = 5x² represents a proportional relationship.

In a proportional relationship, the ratio of the dependent variable (y) to the independent variable (x) is constant. In this equation, as x increases, y also increases by a constant factor (5 times x). This indicates that the two variables are proportional to each other.

In A. y = 4x + 1 and C. y = 9, there is no constant ratio between y and x, so they do not represent proportional relationships.

The median of the given standard data set 9, 3, 10, 12, 4, 5, 12, 2 will be calculated approximately to 7. So , the median of the dataset is 7.

The median is a measure of central tendency that gives us an idea of where the "middle" of a data set lies. In other words, it gives us a value that separates the data set into two equal parts, with half of the values being above the median and the other half being below the median.

To find the median of a data set, the first step is to arrange the values in ascending or descending order. This makes it easier to identify the middle value(s) in the data set.

If the data set has an odd number of values, then there is a single middle value and that value is the median. For example, if we have the data set: 1, 2, 3, 4, 5, the median would be 3 because it is the middle value in the ordered set.

If the data set has an even number of values, then there are two middle values and the median is the average of those two values. For example, if we have the data set: 1, 2, 3, 4, 5, 6, the median would be the average of 3 and 4, which is (3 + 4) / 2 = 3.5.

So, in the case of the data set: 9, 3, 10, 12, 4, 5, 12, 2, we arrange the values in ascending order: 2, 3, 4, 5, 9, 10, 12, 12. Since there are 8 values, which is an even number, there are two middle values: 5 and 9. The median is the average of these two values, which is (5 + 9) / 2 = 7.

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(x^2 - 7x - 18)/(x + 2) = x - 9 can be simplified by multiplying both sides of the equation of x + 2. The new equation is x^2 - 7x - 18 = x^2 - 7x - 18. Therefore the equation's solution is all real numbers.

There are a total of 198 numbers with three digits in monotone order.

For non-decreasing order, we can choose any three digits from 0-9, and arrange them in increasing order. The total number of ways to do this is 10 choose 3, which is 120. For non-increasing order, we can choose any three digits from 1-9, and arrange them in decreasing order. The total number of ways to do this is 9 choose 3, which is 84. However, we have double counted the numbers that are all the same digit, such as 111, 222, etc. There are 9 of these numbers, so we need to subtract them from our total.

So the total number of numbers with three digits in monotone order is 120 + 84 - 9 = 198.

Therefore, there are 198 numbers with three digits in monotone order.

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To grow 80000 bacteria, it will take 4.152 hours.

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Given,

Initial number of bacteria = 4500

Number of bacteria get doubled each hour

Function for population growth of bacteria is given by

N = 4500(2ˣ)

x is time in hours

Future population is N = 80000

Then

80000 = 4500(2ˣ)

800 = 45 . 2ˣ

taking log on both sides

log 800 = log (45 . 2ˣ)

log(mn) = log m + log n and log mⁿ = nlogm

log800 = log45+ x log2

2.9030 = 1.653 + x . 0.3010

x = (2.9030 - 1.653)/0.3010

x = 4.152

Hence, it will take 4.152 hours to grow 80000 bacteria.

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The balance of the account will be 1500 in a period of 8.31 years.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

(a) The final amount in a compound interest is,

A = P(1 + [tex]\frac{r}{n}[/tex] )^ (nt), where,

A : Final amount

P : Principal amount

r : Rate of interest

t : Time in years

n : number of times compounded in a year

Given A = $1500, P = $1000, r = 0.05, n = 1

The equation is,

1500 = 1000 (1 + 0.05)^t

(b) 1500 = 1000 (1 + 0.05)^t

1500 / 1000 = (1.05)^t

1.5 = (1.05)^t

Taking logarithm on both sides,

㏒ (1.5) = t ㏒ (1.05)         [since ㏒ (a)ᵇ = b ㏒ (a)]

t = ㏒ (1.5) / ㏒ (1.05)

t = 8.31 years

Hence the amount will be $1500 in 8.31 years.

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Answer:

My friend didn't factorise the x in 4xy out.

Step-by-step explanation:

15x-20xy= 5x(3-4y)

The value of x and y in the right triangle are as follows:

x = 15√3 units

y = 30 units

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles of a right angle triangle is 180 degrees.

The side x and y can be found using trigonometric ratios,

tan 60° = opposite / adjacent

tan 60° = x / 15

cross multiply

x = 15 tan 60°

x = 15 × √3

x = 15√3 units

Let's find y as follows:

cos 60° = adjacent / hypotenuse

cos 60° = 15 / y

cross multiply

y = 15 / cos 60

y = 15 ÷ 1 / 2

y = 15(2)

y = 30 units

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I got 9 7/9 by using a calculator

B. 5/12

B. 5/12

B. 5/12

B. 5/12

B. 5/12

B. 5/12

B. 5/12

Answer: B

Step-by-step explanation:

Here's how to subtract 3/12 from 4/6:

4/6−3/12

Step 1

We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 4 by 12, and get 48.

Then we multiply 3 by 6, and get 18.

Next we give both terms new denominators -- 6 × 12 = 72.

So now our fractions look like this:

48/72−18/72

Step 2

Since our denominators match, we can subtract the numerators.

48 − 18 = 30

So the answer is:

30/72

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

30/72÷ 2 =15/36

Let's try dividing by 2 again...

Nope! So now we try the next greatest prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

15/36÷ 3 =5/12

Let's try dividing by 3 again...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

No good. 7 is larger than 5. So we're done reducing.

There you have it! The final answer is:4.6−3/12=5/12

Answer:

Step-by-step explanation:

Let x be the number of $1.78 paperback books and y be the number of $2.51 hardcover books that were sold. The total number of books is x + y = 30 and the total amount of money earned is $62.16. The cost of the paperback books is x * $1.78 and the cost of the hardcover books is y * $2.51.

So, we have the following system of equations:

x + y = 30 (the total number of books is 30)

x * $1.78 + y * $2.51 = $62.16 (the total amount of money earned is $62.16)

This system of equations can be used to determine the number of $1.78 paperback books and the number of $2.51 hardcover books that were sold at the yard sale.

Answer:

  W = 680 in

Step-by-step explanation:

You want the length of side w in ∆VWX, where w = 680 in, X = 15°, and V = 116°.

As written, this seems to be a problem in reading comprehension. You are asked for one of the values that is given in the problem statement:

  W = 680 inches

__

Additional comment

The attachment shows the solution of the triangle. In this, we have used ∆ABC ≅ ∆VWX.

The transformations and the order are a shift of 8 units left and 5 units up

From the question, we have the following parameters that can be used in our computation:

f(x) = (x - 8)^2 + 5

The parent function is given as

y = x^2

When these functions are compared, we  have

y = x^2 is shifted right by 8 units and shifted up by 5 units to get f(x)

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The weekly salary for weekly sales of $3,000, $2,340, and $4,675 of the employee is $420, $393.6 and $487 respectively.

Table is attached

A commission is the extra pay to the person in the form of incentives.

Given that, an employee who receives a weekly salary of $300 and a 4% commission is paid according to the equation y = 0.04s + 300, where s represents the total weekly sales.

We are asked to find and make a table for employee's weekly salary for weekly sales of $3,000, $2,340, and $4,675.

We are given values of s,

so, weekly salary for weekly sales of $3,000

y = 0.04(3000)+300

= $420

Weekly salary for weekly sales of $2,340

y = 0.04(2340)+300

= $393.6

Weekly salary for weekly sales of $4,675

y = 0.04(4675)+300

= $487

Hence, the weekly salary for weekly sales of $3,000, $2,340, and $4,675 of the employee is $420, $393.6 and $487 respectively.

Table is attached

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The image point after the translation would be (10, - 1).

Given is the coordinate point of (5, 1).

We can write the translation rule as -

(x, y) → (x + 5, y - 2)

We can write the image point as -

(5, 1) → (5 + 5, 1 - 2)

(5, 1) → (10, - 1)

Therefore, the image point after the translation would be (10, - 1).

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A test of nonverbal intelligence is a type of cognitive assessment that measures an individual's ability to solve problems and think abstractly without the use of language.

Unlike traditional intelligence tests that rely heavily on verbal abilities such as vocabulary, reading, and verbal reasoning, nonverbal intelligence tests use visual-spatial and abstract reasoning tasks that do not require the use of language.

Nonverbal intelligence tests can be particularly useful for individuals who have language or communication difficulties, such as those with speech and language disorders, or those who are non-native speakers of the language in which the test is administered. They can also be used to assess individuals who have difficulty with traditional tests due to visual or hearing impairments.

Examples of nonverbal intelligence tests include Raven's Progressive Matrices, the Naglieri Nonverbal Ability Test (NNAT), and the Universal Nonverbal Intelligence Test (UNIT). These tests typically involve completing visual pattern recognition and completion tasks, spatial reasoning tasks, and other nonverbal problem-solving tasks.

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-9(k-5+2k-8) and -27k+117 are equivalent expressions since the solution of -9(k-5+2k-8) = -27k+117.

Equivalent expressions are algebraic expressions that produce the same answer when being simplified. They are said to be a similar expression for whatsoever process used to solve the expression, either by substitution of values or applying mathematical property, they tend to produce equivalent expressions at the end. The equality sign is used between two algebraic expressions that are said to be equivalent.

Given that:

= -9(k-5+2k-8)  

Open brackets

= -9k + 45 - 18k + 72

= -27k + 117

Therefore, we can say  -9(k-5+2k-8) and -27k+117 equivalent expressions are equivalent expressions.

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The surface area of a solid object is a measure of the total area that the surface of the object occupies.

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Area = length x breadth

To find the surface area of the postal box, we first find the area of each sides of the box and add them together.

Top and bottom area = L x B = 12 x 8 = 96inches² x 2 = 192inches²

Front and back areas = L x B = 12 x 2 = 24inches² x 2 = 48inches²

Area of the sides = L x B = 8 x 2 = 16inches² x 2 = 32inches²

Total surface area will be 192 + 48 + 32 = 272inches²

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Slope of lines 3x - 5y = 2 and 3x + 5y = -2 are m₁ = 3/5 and m₂ = -3/5 respectively.

The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line. The net change in the y coordinate is Δy and the net change in the x coordinate is Δx. Therefore, the change in y-coordinate for a change in x-coordinate can be written as

Line slope is a measure of the steepness or direction of a line in the coordinate plane.  

m = Δy/Δx

where,m is the slope

Given,

equations of the line

3x - 5y = 2

Moving 3x to RHS
-5y = -3x + 2

y = (3/5)x - 2/5

comparing with slope intercept equation of the line y = mx + c

slope m₁ = 3/5

Now, equation

3x + 5y = -2

moving 3x to RHS

5y = -3x - 2

y = (-3/5)x - 2

comparing with slope intercept equation of the line y = mx + c

slope m₂ = -3/5

Hence, m₁ = 3/5 and m₂ = -3/5 are slope of lines 3x - 5y = 2 and 3x + 5y = -2 respectively.

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The account with compound interest of 7.2 % quarterly after 5 years is given by A = $ 1,428.75

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after compound interest be represented as A

Now , the equation will be

The initial principal amount = $ 1000

The rate of interest r = 7.2 %

The number of times interest is applied n = 4 ( quarterly )

The number of years b = 5 years

A = P ( 1 + r/n )ⁿᵇ

Substituting the values in the equation , we get

A = 1000 ( 1 + 0.072/4 )⁴ˣ⁵

On simplifying the equation , we get

A = 1000 ( 1 + 0.018 )²⁰

On further simplification , we get

A = 1000 ( 1.018 )²⁰

A = $ 1,428.75

Hence , the amount after 5 years is $ 1,428.75

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The value of the number one-tenth more than 13.7 is 13.8.

In geometry, a polygon is a type of plane figure and is defined as a closed polygonal chain made up of a finite number of straight-line segments. A region that is enclosed by a bounding plane, a bounding circuit, or both are referred to as a polygon. The portions of a polygonal circuit are referred to as its edges or sides.

Given that numbers are one-tenth and 13.7.

More means add two numbers.

One-tenth = 1/10

The number one-tenth more than 13.7 is

1/10 + 13.7

= 0.1 + 13.7

= 13.8

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Answer: a = 2 because 1 + 1 = 2

Step-by-step explanation:

Sam travels on the highway for approximately 1.4 hours.

We know that Sam's total travel time is 1.5 hours plus the time he spends on the highway, which we'll call "x" hours. So his total travel time can be represented as:

Total travel time = 1.5 + x

We also know that the total distance he travels is 140 miles. We can use the formula:

distance = rate x time

to set up two equations, one for his travel on city roads and one for his travel on the highway. Let's start with the city roads:

distance = rate x time

distance = 35 mph x 1.5 hours

distance = 52.5 miles

So Sam travels 52.5 miles on city roads, which means he still has to travel:

140 miles - 52.5 miles = 87.5 miles

on the highway. Now we can set up an equation for his travel on the highway:

distance = rate x time

87.5 miles = 65 mph x x hours

Solving for x, we get:

x = 87.5 miles / (65 mph)

x ≈ 1.35 hours

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I have solved the question in general, as the given question is incomplete:

The complete question is:

Sam is driving a distance of 140 miles from his house to visit Melissa. Sam takes city roads , on which can he travel an average of 35 mph for a total of 1.5 hours . Sam also takes the highway , on which he travels an average of 65 mph for a total of x hours . approximately how long does Sam travels on the highway , to the nearest tenth of an hour ?

The volume of the triangular solid is 128/3 cubic units.

The cross-sections of the triangular solid along the y-axis are equilateral triangles with side length equal to the width of the triangular base at that y-coordinate. The width of the triangular base at y = h is equal to 8 - 4h/4. So, the side length of the equilateral triangle at y = h is 8 - 4h/4.

Let's call the height of the equilateral triangle at y = h as "x". Then, using the Pythagorean theorem, we can find the relationship between x and the side length:

x^2 = (8 - 4h/4)^2 - (x/2)^2

Expanding and simplifying the right-hand side:

x^2 = 64 - 16h + h^2/16 - x^2/4

Multiplying both sides by 4:

4x^2 = 256 - 64h + h^2 - x^2

Solving for x^2:

3x^2 = 256 - 64h + h^2

Taking the square root of both sides:

x = √(256 - 64h + h^2)/√3

So, the height of the equilateral triangle at y = h is equal to x = √(256 - 64h + h^2)/√3.

The volume of the triangular solid can be found by integrating the cross-sectional area over the height of the triangular base:

V = (1/3) ∫[0, 4] x^2(y) dy

= (1/3) ∫[0, 4] (√(256 - 64h + h^2)/√3)^2 dh

= (1/3) ∫[0, 4] (256 - 64h + h^2)/3 dh

Evaluating the definite integral:

V = (1/3) * [(256h/3 - 32h^2/2 + h^3/3) |_0^4]

= (1/3) * [(256/3 * 4 - 32/2 * 4^2 + 4^3/3) - (256/3 * 0 - 32/2 * 0^2 + 0^3/3)]

= (1/3) * (256 - 128 + 64/3)

= 128/3.

Correct Question :

The base of s is the triangular region with vertices (0, 0), (8, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles. What is the volume of the triangular solid.

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No, the equations 1/5 + 2 = 6 and 1/5(x + 2) = 6 do not represent the same situation.

To solve the first equation, we can subtract 2 from both sides to get 1/5 = 4, and then multiply both sides by 5 to get 1 = 20.

This equation is not true, so there is no solution. To solve the second equation, we can multiply both sides by 5 to get x + 2 = 30, and then subtract 2 from both sides to get x = 28.

This is the solution to the equation. So, while both equations contain the same numbers and operations, they represent different situations and have different solutions.

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Answer:

Step-by-step explanation: n The graph is of an absolute value function. Step-by-step explanation: For x ≥ 0, the graph is given by. ⇒ x + 2y = 6. ⇒. ⇒ ........ (1).

Missing: 50 ‎32 ‎2₁

Hope that helps:)

Answer:i got u mate

The answer is a _10×+8y=15

Step-by-step explanation:

The maximum index of refraction of the fluid that will still cause total internal reflection within the prism is nf = n/sinΘc.

Total internal reflection is a phenomenon in which light passes through a medium with a higher index of refraction and bounces back into the same medium instead of exiting it. This is possible when the angle of incidence is greater than the critical angle of the material.

In the case of a prism surrounded by a fluid, the maximum index of refraction of the fluid that will still cause total internal reflection within the prism can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two materials.

The critical angle of the prism can be calculated as the angle at which the sine of the angle of refraction becomes equal to 1. The critical angle can be calculated using the equation:

sinΘc = 1/n

where n is the index of refraction of the prism.

The maximum index of refraction of the fluid can then be found by rearranging Snell's law and substituting the critical angle into the equation:

nf = n/sinΘc

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Answer:

x=46

Step-by-step explanation:

this is how you set up the problem

3x-6+x-2=180

then you combine like terms

4x-6-6=180

then combine like terms again

4x-4=180

then you have to get 4 to the other side

4x-4=180

+4 +4

which leaves you with 4x=184

which you then divide both sides by 4

which leaves you with

x=46

I hope this helps you!!!

Answer:

x=46 =))))))))))))))))))))))))))))))))))(((()((((()()(