Which rules define the function graphed below? y=2x+3, y=-1/3x+3

The equation of line is y = 14.24375x + 296.8875 , where x is the number of days and y is the total weight gain in x days

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 18 , 40.5 )

Let the second point be Q ( 50 , 496.3 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 496.3 - 40.5 ) / ( 50 - 18 )

Slope m = 455.8 / 32

Slope m = 14.24375

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 40.5 = 14.24375 ( x - 18 )

On simplifying the equation , we get

y - 40.5 = 14.24375x - 256.3875

Adding 40.5 on both sides of the equation , we get

y = 14.24375x + 296.8875

where x is the number of days

Hence , the equation of line is y = 14.24375x + 296.8875

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The inequality that shows the least amount he needs is  4x + 22 ≥ 85.50 which shows he needs at least $15.875

The Inequality that will represent this problem is 4x + 22 ≥ 85.50, where x is the number of windows Jonathan washes.

To solve the inequality, we'll start by subtracting 22 from both sides:

4x ≥ 63.50

And finally, dividing both sides by 4:

x ≥ 15.875

So, Jonathan needs to wash at least 15 windows in order to save up enough money to buy the boxed set.

b.

The graph on the number line showing x ≥ 15.875 is attached below

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If the diameter of the tub is 8 inches, then the height of gallon tube is,  5.25 inches

Surface area is the sum of the areas of all the faces (or surfaces) of a three-dimensional object. It is a measure of how much area the surfaces of an object take up in two dimensions. The surface area of a solid can be found by adding up the areas of its faces.

The surface area of a cylinder can be expressed as:

SA = 2πr² + 2πr x h

where r is the radius of the cylinder, h is its height, and π is the constant pi (3.14).

The diameter of the tub is 8 inches, which means the radius is 4 inches. We are also given that the total surface area is 232.36 square inches.

So we can write:

232.36 = 2(3.14)(4²) + 2(3.14)(4)(h)

Simplifying and solving for h, we get:

232.36 = 100.48 + 25.12h

131.88 = 25.12h

h = 131.88/25.12

h ≈ 5.25 inches

Therefore, the height of the ice cream tub is approximately 5.25 inches.

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As said, 48 model automobiles are driven by Jim at the moment, and the ratio might alter to 19:13.

An organisation of the integers a and b stated as a/b is still a ratio if b is truly not comparable to 0. Two ratio with the same value are established by the percent formula. As an illustration, you might write your ration as follows: 1:3 when there is 1 man and 3 females.

You know there's an 8:6 ratio between the grand total of model cars Jim and Terrence possess.

As a result, you can respond to the assignment as follows: Assume Jim owns x different car models.

8/6 = x/36

x = 36*8/6

x = 288/6

x = 48

The new percentage of Jim's against Terrence's model vehicles will be as follows because both Jim & Terrence sell ten of their model cars:

(48-10)/(36-10) = 38/26 = 19/13

Jim's to Terrence's miniature automobiles will now be in a 19:13 ratio.

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Using subtraction operator, the distance between the house and the ducks is 21 feet

Trigonometric ratios are mathematical ratios that relate the sides of a right triangle to its angles. The three primary trigonometric ratios are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan.

In this case, we don't need to use trigonometric ratio since the duck and house with the tree are on the same length. We can simply use a basic arithmetic operation to find the distance between the ducks from the house.

Using subtraction, the distance between the ducks and the house will be

distance = 47 - 26

distance = 21 feet

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Yes, sorting the tiles with positive coefficients and tiles with negative coefficients together can help simplify an expression that involves all tiles.

When sorting the tiles, the positive coefficients are grouped together and the negative coefficients are grouped together. This makes it easier to perform operations such as addition and subtraction on the tiles and simplify the expression.

For example, if you have two tiles with positive coefficients and one tile with a negative coefficient, it becomes easier to see that the expression can be simplified by subtracting the negative tile from the sum of the two positive tiles.

Additionally, grouping the positive and negative coefficients together makes it easier to see any patterns or relationships that may exist between the coefficients and terms in the expression, which can further aid in simplification.

In summary, sorting the tiles with positive coefficients and tiles with negative coefficients together can help simplify an expression by making it easier to perform operations on the tiles and identify patterns and relationships between the coefficients and terms.

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The amount of money that needs to be deposited now into an account to obtain $6,200 in 15 years is $2,928.67.

Mathematically, continuous compounding interest can be calculated by using this mathematical expression:

P(t) = P₀e^{rt}

Where:

Substituting the given parameters into the continuous compounding interest formula, we have;

P(t) = P₀e^{rt}

$6,200 = P₀e^{0.05 × 15}

$6,200 = P₀e^{0.75}

Principal, P₀ = 6,200/e^{0.75}

Principal, P₀ = 6,200/2.11700001661

Principal, P₀ = $2,928.67.

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Using Euler's formula, the expressions can be rewritten as Im = sin(e^j) - sinh(1), exp(e^j) = e^(cos(1) + j*sin(1)) and e^[(1/2)√(2)e^(j(π/4+2π*n))] respectively

1.

Cos(e^j) can be expressed using Euler's formula as:

Cos(e^j) = (e^(je^j) + e^(-je^j)) / 2

= (cos(e^j) + cosh(1)) + j(sin(e^j) - sinh(1))

Re = cos(e^j) + cosh(1)

Im = sin(e^j) - sinh(1)

2.

exp(e^j) can also be expressed using Euler's formula as:

exp(e^j) = e^(cos(1) + j*sin(1))

3.

(sqrt(j))^sqrt(j) can be written as:

(sqrt(j))^sqrt(j) = e^[(1/2)√(2)e^(j(π/4+2π*n))]

where n is an integer. This is because the logarithm of a complex number has infinitely many possible values due to the periodicity of the exponential function.

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P(12,8)

Move  8 units to the left (X) and  12  units down(Y).

P'(12-8, 8-12)

P'(4, -4)

If you don't how to do translation try plotting (12,8).

Answer:

x = 2.4 inch

Step-by-step explanation:

Tall retangular prism = lwh = 6 x 9 x 3 = 162 in^3

378 - 162 = 216

Long rectangular prism = lwh = (15)(6)(x) = 90x

216 = 90x

x = 2.4

Answer:

$29.68 to drive 350 miles

Step-by-step explanation:

To find the cost of driving 350 miles, we first need to calculate the amount of gasoline required for driving 350 miles. We can use the formula:

gasoline = distance ÷ miles per gallon

Plugging in the given values:

gasoline = 350 ÷ 33

gasoline = 10.606060606060606

So, we need 10.61 gallons of gasoline to drive 350 miles.

Next, we multiply the amount of gasoline needed by the cost per gallon to find the total cost:

total cost = gasoline × cost per gallon

total cost = 10.61 × 2.80

total cost = 29.6780

Therefore, it would cost approximately $29.68 to drive 350 miles when gasoline costs $2.80 per gallon and your car gets 33 miles per gallon.

Answer: 350 mi * 1 gal / 33 miles * $2.80 / 1 gal  = 29.69$

which means the cost is 2.8*(350/33)=29.69$

Step-by-step explanation:

Here, 2.80$/1 Gal.

Now we need to cancel out gallons, so we add a ratio with gallons.

2.80$/1 Gal. x 1 Gal/33 mi.

Now add the last data element to cancel out miles.

2.80$/1 Gal. x 1 Gal/33 mi. x 350 mi.

Cancelling out units and numbers gives,

(2.80$ x 350)/33. Continue reducing to an answer:

980$/33 = 29.69$

Answer:

Note that 0.01 is the decimal form of 1%, so 0.01 multiplied by 7 yields 7%. So, if we were to find 1% of 250, which is 2.5, we can multiply the value by 7, which is 17.5.

Therefore, 7% of 250 is 17.5

The required simplified expression for "Two times the sum of a number and five" is 2x + 10.

An algebraic expression is defined as when the expression is formed with help of variables such as x, y z, and so on. in the format of x + y + z or in any mathematical operation.

Here,
The phrase "Two times the sum of a number and five" can be written as

= 2(x + 5)

This is an algebraic expression that represents the value of two times the sum of the unknown number (represented by "x") and five.

We can simplify this expression by distributing the 2

= 2(x + 5) = 2x + 10

Therefore, the simplified expression for "Two times the sum of a number and five" is 2x + 10.

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Answer:

3

Step-by-step explanation:

In this triangle ABC, the leg lengths are AC and BC, being x and x+7, respectively. So, the area can be listed as: 15 = (1/2) * x * (x+7). Simplifying that gets x^2 + 7x = 30 -> x^2 + 7x - 30 = (x-10)(x-3). So, x = 3 since it cannot be negative.

Answer:

1. 32 divided by 2 is 16

2.  2 x 16 = 36

Step-by-step explanation:

The number of blue marbles in the representative sample which contains 2 green marbles is 8.

What is meant by a representative sample?

A subset of a population that aims to correctly reflect the traits of the larger group is called a representative sample. Because the results accurately mirror those you would get from interviewing the full population, it is known as a representative sample.

Because samples comprise more manageable, smaller representations of the broader group, they are helpful in statistical analysis when population numbers are huge.

Given the total number of green and blue marbles is 8 and 32 respectively.

So the ratio of green marbles to blue marbles = 8:32 = 1:4

Now, this ratio is maintained when we form a representative sample.

Given there are 2 green marbles in a representative sample.

Then the number of blue marbles x is:

2 : x = 1 : 4

2 : x = 2 : 8

x = 8

Therefore the number of blue marbles in the representative sample is 8.

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Answer: Since the speed of personal computers is expected to double every 18 months, we can use exponential growth to calculate the increase in speed over time. We can start by finding the growth factor, which is equal to 2 raised to the power of the number of doublings. In this case, the number of doublings over 6 years can be calculated as follows:

6 years / 1.5 years = 4 doublings

So the growth factor is:

2^4 = 16

This means that the speed of personal computers will be 16 times faster in 6 years compared to now.

Step-by-step explanation:

Option (c) is correct answer.

(C) DE = 12, DF = 16 and m∠D = 35

which states, length of DE is 12 units , length of DF is 16 units and m/D=35 degrees.

If two figures possess the same shape but not necessarily the same size, they are considered to be similar. We may remark that all circles are similar as an example. Equilateral triangles and squares are similar to one another. Although similar figures need not be congruent, all congruent figures are similar.

Property 1:

Two triangles are similar if their respective sides have the same ratio and their corresponding angles are equal.

Property 2:

The corresponding angles of two similar triangles will have equal values . Equiangular triangles are what they are called.

Now by property 1,

The pairs of  corresponding sides of similar triangles are proportional .

Therefore, in the given triangles,

[tex]\frac{AB}{DE} =\frac{AC}{DF} \\\\\frac{AB}{AC} =\frac{DE}{DF} \\\\\frac{9}{12} =\frac{DE}{DF} \\\\\frac{3}{4} =\frac{DE}{DF}[/tex]

Therefore, in the given options, option (c) satisfies the condition.

Hence, DE = 12 , and DF = 16.

By property 2 we know that , corresponding angles of similar triangles are equal.

hence, /A=/D

therefore, /D=35.

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Answer: To find the limit of the expression 3√x-1/x-1 as x approaches 1, we can use L'Hopital's Rule. L'Hopital's Rule is a method for finding the limit of indeterminate forms, such as 0/0 or ∞/∞, by taking the derivative of the numerator and denominator.

In this case, the expression is of the form 0/0, so we can use L'Hopital's Rule:

lim 3√x-1/x-1 = lim (3/2)((x-1)^(1/2)) / 1 = 3/2

So the limit of the expression 3√x-1/x-1 as x approaches 1 is equal to 3/2.

Step-by-step explanation:

The trait would be MOST useful for these farmers is to be considered as the fast growth rate.

The main goal of science that should create knowledge and understanding.

Since the plan for using the breeding to produce a new type for the wheat for farmers that lived in the northern areas.

The growth rate of a value (GDP, turnover, wages, etc.) measures its change from one period to another (month, quarter, year). It is very generally expressed as a percentage.

The annual average rate of change of the gross domestic product (GDP) at market prices based on constant local currency, for a given national economy, during a specified period of time.

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Answer:

Below

Step-by-step explanation:

5000   *   2.4 x 10^-6  =

12 000 x 10^-6  g

= .012 g

On solving the prοvided question, we can say that 4.75 miles were ran on day four.

A mathematical equation is a formula that jοins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equatiοn in algebra.

Fοr instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences οn either side of a letter is described by a mathematical formula. Often, there is only οne variable, which alsο serves as the symbol. for instance, 2x – 4 = 2.

On day one, Justin ran two miles.

He ran two miles on the second day, or 75% of it. Divide by 100 and multiply by 75 to get the percentage of two miles that is 75%.

On the secοnd day, I ran 1.5 miles, or 2 / 100, or 0.02 x 75. (I've run 3.5 miles so far)

He ran 1.5 miles further on the third day than the previous one:

1.5 + 1.5 = 3 (6.5 miles jogged sο far) (6.5 miles jogged so far)

The total number of miles run was 9.25, thus tο find the solution, we must subtract 6.5 from 9.25.

4.75 miles were ran οn day four, or 9.25 minus 6.5.

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On solving the provided question, we can say that the trigonometry sin3θcos2θ+cos3θsin2θ = 4sin3(1−2cos2θ)+sinθ

The area of mathematics knοwn as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, arοund the third century BC. frοm the use of geometry in astronοmical study.

The area of mathematics knοwn as exact methods deals with specific trigonometric functions and hοw they might be used in calculations. There are six popular trigonοmetric functions in trigonometry. Sine, cosine, tangent, cοtangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics οf triangles, particularly right triangles, is called trigonοmetry. The study of geοmetry, however, is the characteristics of all geοmetric figures.

the trigonometry

sin3θcos2θ+cοs3θsin2θ=4sin3(1−2cos2θ)+sinθ

Use the variation cοs2θ=1−sin2θ to express sin(5θ) in terms of sinθ

sin5θ=4sin3θ(1−2(1−sin2θ))+sinθ(8(1−sin2θ}

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Answer:

r = 5

Step-by-step explanation:

25 - 3r = 10 ( subtract 25 from both sides )

- 3r = - 15 ( divide both sides by - 3 )

r = 5

the solution from the replacement set is 5

The value in 6 years is $3050.43

The term depreciation refers to an accounting method used to allocate the cost of a tangible or physical asset over its useful life.

Using the formula:

Value = P(1-r)^n

From the question, the original value is $9,000, the depreciation rate is 16.5% or 0.165, and the time is 6 years. Plugging in the values:

Putting the values into the formula

Value = 9000(1-0.165)^6

Value = 3050.43

Hence, the value of the car after 6 years will be $3050.43

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The height that a ladder reaches is determined by the length of the ladder and its distance from the base of the building.

The ladder can be thought of as the hypotenuse of a right triangle, with the height that the ladder reaches up the building being one of the other sides and the distance of the ladder from the building being the other side.

So, the formula for the height that a ladder reaches can be expressed as:

Height =

Where "Ladder Length" is the length of the ladder, and "Distance from Base" is the distance of the ladder from the building.

Using this formula, we can calculate the height that the 14-foot ladder reaches when set up 4 feet from the base of the building:

Height = ([tex]14^2 - 4^2)^0.5[/tex]

= [tex](196 - 16)^0.5[/tex]

= [tex]180^0.5[/tex]

= 13.416407864

Rounding to the nearest tenth of a foot, the height the ladder reaches is 13.4 feet.

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1.The athlete that did the most sit-up per minute is D'andrea with 44 sit up per minute

2. 22 Miles in 20 minutes < 38 Miles in 30 minutes

3. The rate that could be Jessica rate is 1 tile in 3 minutes

4. The best rate to find the best value of card is 6 greeting cards for $23.40

5. Elias can fold 3boxes in a minute and Dionne can fold 3.5 boxes in a minute.

A rate is a special ratio in which the two terms are in different units. For example, if a 12-ounce can of corn costs 69¢, the rate is 69¢ for 12 ounces. This is not a ratio of two like units, such as shirts. This is a ratio of two unlike units: cents and ounces.

Rate per minute is the quantity divide by no of minute.

For example Casey did 93 sit up in 3 minute, His rate = 93/3 = 31 sit up per minute.

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Answer:

  -5x⁵ +2x² -3/x³

Step-by-step explanation:

You want the quotient and remainder of (-15x⁸ +6x⁵ -9)/(3x³).

The quotient and remainder can be found by dividing term by term.

  [tex]\dfrac{-15x^8+6x^5-9}{3x^3}=\dfrac{-15x^8}{3x^3}+\dfrac{6x^5}{3x^3}-\dfrac{9}{3x^3}\\\\\\=\boxed{-5x^5+2x^2-\dfrac{3}{x^3}}[/tex]

__

Additional comment

The exponent rule is (a^b)/(a^c) = a^(b-c).

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