Using long division to rewrite each rational function f(x)=2x/x+4

y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find the slope-intercept equation for a line that goes through the point (4,-3)--with a slope of -2

m=-2

Now let us find the y intercept

-3=-2(4)+b

-3=-8+b

-3+8=b

5=b

Hence, y=-2x+5 is the slope-intercept equation for a line that goes through the point (4,-3) and 5 is the value of b.

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Using algebraic equation, the number of hot dogs sold is 40 and the number of  sodas sold is 90.

algebraic equation, statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root.

Given that they sold one hot dogs at $3 and one sodas at $2.

The number of sodas sold was 10 more than two times the number of hot dogs sold.

Let the number of hot dogs sold is x

The number of sodas sold is 2x + 10

The school made total $300. SO that,

x*$3 + (2x+10)*$2 = $300

⇒ 3x + 4x + 20 = 300

⇒ 7x + 20 = 300

subtracting 20 from both side of equation

⇒ 7x = 300 - 20

⇒ 7x = 280

divided both side by 7

⇒ x = 280/7

⇒ x = 40

so the number of hot dogs sold is 40.

and the number of sodas sold is 2x + 10

= 2*40 + 10

= 80 + 10

= 90

The number of sodas sold is 90.

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The correct answer is A, Canada. This is because the select() function allows you to specify the exact variables to be included in the data frame, and Company.Location is one of the variables that was specified in this case.

The first row of the table created using the select() function contains the data for the three selected variables from the original flavors_df data frame. The select() function was used to create a new data frame with only three variables: Rating, and Cocoa.Percent, and Company.Location. This function was used to filter out all the other variables from the original flavors_df data frame, leaving only the three variables of interest.

When looking at the first row of the table, the value in the Company.Location column is Canada, which is the country in the company producing the chocolate is located in.

Complete question:

After previewing and cleaning your data, you determine what variables are most relevant to your analysis. Your main focus is on Rating, Cocoa.Percent, and Company.Location. You decide to use the select() function to create a new data frame with only these three variables.

Assume the first part of your code is:

trimmed_flavors_df <- flavors_df %>%

Add the code chunk that lets you select the three variables.

select(Rating, Cocoa.Percent, Company.Location)

What company location appears in row 1 of your table?

Single Choice Question. Please Choose The Correct Option &#x2714;

A. Canada

B. Scotland

C. France

D. Columbia

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Answer:

second step

Step-by-step explanation:

1/8 is not equal to 2^3 but instead it is equal to 2^-3

Answer: C) x=2 or x=-4/7

The required graph of the function y=x²+4x+3 for the interval -3 ≤ x ≤ 3.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
The given function,
y=x²+4x+3

Since we have given the interval for the value of the x, as -3 to 3
By putting value in the above expression we get y,
put x = -3
y = (-3)² + 4(-3) + 3
y = 9 - 12 + 3
y = 0

Similarly, other values are shown through the map.

Thus, the required graph of the function y=x²+4x+3 for the interval -3 ≤ x ≤ 3.

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The total weight of the wire is 24.32 ounces.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that,

Total length of the wire = 7.6 meters

Weight of each meter of wire = 3.2 ounces

Total weight of the wire = Total meter of the wire × Weight of each meter

                                        = 7.6 meters × 3.2 ounces

                                        = 24.32 ounces

Hence the weight of the total length of the wire is 24.32 ounces.

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For a car worth $38,890.00 a person should invest $23,403.660 for a rate of 10.2% for 5 years if compounded monthly.

What is Compound Interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

The amount is A = $38,890.00

The time period in years is t = 5 years

The rate is given as r = 10.2%

The amount is compounded monthly, so n = 12.

First, convert R as a percent to r as a decimal -

r = R/100

r = 10.2/100

r = 0.102 rate per year,

The formula for compound interest is -

A = P(1 + r/n)^nt

Where,

A = amount

P = principal

r = rate of interest

n = number of times interest is compounded per year

t = time (in years)

Substitute the values into the equation -

A = P(1 + 0.102/12)^(12)(5)

38,890 = P(1 + 0.0085)^(60)

38,890 = P(1 + 0.0085)^(60)

38,890 = P(1.661705)

P = 38,890 / 1.661705

P = 23,403.660

Therefore, the principal value is $23,403.660.

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Miss Saver needs to withdraw $391 each year from her bank.

To solve this problem, we need to

First, we need to determine the total amount of money Miss Saver will have saved using:

Total = $1000 * (1 + 0.05)^30 = 4321.94

Next, we need to determine the future value of this amount after 30 years at an effective annual interest rate of 2%.

This is done using

$4321.94 * (1 + 0.02)^30 = $7828.60

Now, we can determine the annual withdrawal amount, X as follows

X = $7828.59/20 = $391.4295

Rounding up to the nearest integer, X = $391

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Answer: 8:1

Step-by-step explanation:

Since there are 1000 grams in 1 kilogram, we can start by converting the 4 kg of glass to kilograms.

4 x 1000 = 4000, so this means that we have 4000 grams of glass in the bin.

So right now, the ratio of the glass in the bin to the plastic in the bin is 4000:500.

We can simplify: Start by dividing 100 from both numbers. Now, your ratio will look like this: 40:5. We can simplify even further, so divide 5 from both sides to get the ratio 8:1.

I hope this helps!

Answer:

=-16

Step-by-step explanation:

Step 2, divided first within first parentheses

Step 4, subtract first within the parentheses.

（³√27-14÷2) (6-8)²

 =(3-14÷2) (6-8)²

 =(3-7) (6-8)²

 =(-4) (-2)²

 =(-4) 4

 =-16

Answer:

191 i guess

Step-by-step explanation:

πr^2=3.14*4.5^2=63.585

63.585*3(three pieces only)=191 approximately

Her total pay for last week is given as follows:

£506.25.

The total pay is obtained applying the proportions in the context of this problem.

The rates are given as follows:

The number of hours is given as follows:

Hence the total earnings are given as follows:

5 x 7.5 x 10.8 + 7.5 x 13.50 = £506.25.

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The correct answer is option 1. 13.33 cm. In a rectangle ABCD, The length of PC is 13.33 cms.

In a right triangle BPC, we have two sides: BP = AP = 6 cm and PD = 10 cm. Using the Pythagorean theorem, we can find the length of PC:

[tex]PC^2 = BP^2 + PD^2\\= > PC^2 = 6^2 + 10^2\\= > PC^2 = 36 + 100\\= > PC^2 = 136\\= > PC = \sqrt{136} \\= > PC = 13.33 cm[/tex]

In the rectangle ABCD, we have a right triangle BPC. Point P is on side AB and is such that ∠BPC = ∠ADP. Therefore, BP and PD are the corresponding sides of the two right triangles. Using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (PC) is equal to the sum of the squares of the lengths of the other two sides (BP and PD), we can find the length of PC.

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Using concept of linear equation, Pedro hit runs=1483 and Ricky hit runs=1198.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Given,  

Together, teammates Pedro and Ricky got 2681 base hits last season. i.e. P+R=2681 -->1 where P=Pedro and R=Ricky

Pedro had 285 more hits than Ricky i.e. P-R=285 --->2

Solving equation 1 and 2 we get

P=1483 and R=1198

hence,

          Pedro hit runs=1483 and Ricky hit runs=1198.

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Answer:

The function 8(x) is a parabola that opens downward and is centered at (0,0). The domain of 8(x) is x∈R and the range of 8(x) is y∈[0,∞).

To arrive at the new function g(x), follow these steps:

Base Graph: The base graph of 8(x) is shown below.

Vertical Reflection: To reflect the parabola about the x-axis, multiply the function by -1. The new function is g(x) = -8(x).

Horizontal Reflection: To reflect the parabola about the y-axis, multiply the function by -1. The new function is now g(x) = 8(-x).

Horizontal and Vertical Translations: To translate the parabola 4 units to the left and 2 units up, add 4 to the x-coordinates and subtract 2 from the y-coordinates. The new function is g(x) = 8(x-4)-2.

The resulting graph is shown below. The domain of g(x) is x∈R and the range of g(x) is y∈[-2,∞).

On solving the provided question, we can say that so, standard deviation ,we have 2nd > DISTR> Vars> (-10000;37;25;4)

Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed.

[tex]X = N(25,4)\\u = 25, z = 4\\P(X > 35)\\P(X < 35) = P( Z > 35 - 25/ 4) = P(Z > 2.5)\\2nd > DISTR > Vars > normalcdfnormalcdf(-10000;37;25;4)[/tex]

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The piecewise function that defines the graph is given as follows:

A piecewise function is a function that has different definitions, according to the input values assumed by the function.

The different definitions for the function in this problem are given as follows:

To the left of x = -2, the function is increasing with a slope 1, hence it would cross the y-axis at y = 1, and the definition is given as follows:

y = x + 1, x < -2.

At x = 2 and between x = -2 and x = 1, the function is constant.

The piecewise function is given by the image presented at the end of the answer.

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TOYS is a rectangle with diagonals TY and OS intersecting at point J. If angle TYO = 43°, then angle YJS = 68.5°.

Given that TOYS is a rectangle, we know that:

The diagonals TY and OS bisect each other.

The diagonals TY and OS are congruent (equal in length).

Using the information above, we can draw the following interpretation s:

We can see that:

Triangle TYJ is isosceles (because TY = OJ).

Angle TYJ = (1/2) * Angle TYO = (1/2) * 43° = 21.5°

Angle YJS = 90° - 21.5° = 68.5°

So, angle YJS = 68.5°.

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Answer:

[A] The U.S has more people under 18 than China does.

[B] There are more people under 18 than age 45 to 64 in the U.S

[D] There are more people age 19 to 44 than any other age group in the U.S

Step-by-step explanation:

Based on the graph we know that:

Green = U.S

Dark Blue = China

Now let's look at our answer choices:

[A] The U.S has more people under 18 than China does.

Now looking at the graph we can see there are more green than dark blue which means U.S have more people under 18 than China does.

[B] There are more people under 18 than age 45 to 64 in the U.S

Based on the graph and estimate :

Under 18 in U.S = 25

Age 45-64 in U.S = 21 or 22 ish.

As we can see, there are more people under 18 than age 45-64 in the U.S

[C] The population of China is more than 4 times that of U.S

Graph don't really prove enough info to prove China population is more than 4 times of U.S.

But based on the graph, it doesn't look like population of China is more than 4 times that of U.S

[D] There are more people age 19 to 44 than any other age group in the U.S

Based on the graph we can see that out of all the age group - age 19 to 44 have the highest percentage which mean there are more people age 19-44 than any other age group in the U.S

RevyBreeze

According to the information, it can be inferred that the words that complete the sentences are: Radius, 3.14, radius, circumference, and both.

To complete the sentences we must read each of them several times and identify its main theme; this will help us identify the missing term by context.

Additionally, we must read the text on the left side where we will find related information that will help us find the correct terms.

According to the above, the complete sentences would look like this:

In Rachel's method, 4 represents the radius of the rug, and the fraction 11/7 3.14 a good approximation for

In Erik's method, the height of the parallelogram is approximately equal to radius and the length is approximately equal to circumference.

Therefore, both suggested a reasonable method for approximating the area of the rug.

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Answer:

129

Step-by-step explanation:

6+23×4-√81 =6+132-9= 129

Answer:

[tex]C = 16.8954 ^\circ[/tex]

Step-by-step explanation:

Law of Sines

The rule of sines states: If a, b, and c are, respectively, the lengths of a triangle's legs on either side of angles A, B, and C:

[tex]\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}[/tex]

Given:

[tex]C = \sin^{-1} \left[ \dfrac {c \sin B}{b}\right][/tex]

[tex]= \sin^{-1}\left[\frac {{13}{\sin}(28 ^\circ)} {21}\right][/tex]

[tex]= 16.8954 ^\circ[/tex]

Thanks.

Answer:

j=19

Step-by-step explanation:

In the image, it shows that the weight of 5 + j is equal to the weight 24. Using this information, let's create a equation and solve for j:

5 + j = 24   [Subtract 5 from both sides]

j = 19

So, j must equal 19 for both sides of the hanger to be equal.

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Answer:

Below

Step-by-step explanation:

L x H = area

(x+5) (x-2)   =   x^2 +3x -10  cm^2

Answer:

Answer is c

Step-by-step explanation:

To solve the previous exercise step by step, we first need to break down the equation into its components:

z^6−16z^3 +128 = 0

Now, we can use the quadratic formula to solve this equation:

x = (-b ± √(b² - 4ac)) / 2a

In this case, we have:

a = 1 b = -16 c = 128

So, the quadratic formula reduces to:

x = (-(-16) ± √((-16)² - 4(1)(128))) / 2(1)

Simplifying, we get:

x = (16 ± √(256 - 512)) / 2

And finally we get the solutions:

x = (16 ± √(-256)) / 2

Which simplifies to:

x = (16 ± 4i) / 2

And the solutions are:

z = 2, 4i, -2, -4i

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The given triangles OML and ONP are similar triangles by SAS postulate.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
Consider triangle OML and ONP
OL / OP = OM/ON
13.5/3 = 9/2
4.5 = 4.5

And
∠O = ∠O  [common angle]

Thus, both triangles are similar triangle by the SA postulate of similarities.

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2x+6 is the required weight.

The weight of an object is defined as the force acting on the object due to gravity. It is a scalar quantity. Weight is measured in newtons.

In Physics, the gravitational force with which the earth attracts all the masses to its center is called weight.

In the given question,

Let the weight of an object is x.

6 pounds more than twice the weight means the required weight of an object will be the 2×weight of the object(x) + 6 pounds.

Therefore,

2x+6 is the required weight of the object.

The complete question is,

The weight of 1st object is x. The weight of the second object is 6 pounds more than twice the weight. What is the weight of the second object?

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The needed weight is 2x+6.

The force exerted on an object by gravity is known as the weight of the object. It has a scalar value. Newtons are a unit of weight.

Weight is the term used in physics to describe the gravitational force that pulls all masses toward the center of the earth.

In the posed query,

Let's say that an object weighs x pounds.

The needed weight of an object is the weight of the object(x) plus 6 pounds, which is 6 pounds more than twice the weight.

Therefore,

The object must weigh at least 2x+6.

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The complete question is:-

The first item weighs x pounds. The second object weighs 6 pounds more than it does, or more than twice as much. What does the second object weigh?

Answer:

83 and 84

Step-by-step explanation:

Let's call the two integers x and (x + 1), respectively.

x + (x + 1) = 167

2x + 1 = 16

2x = 166

x = 83

The two integers are 83 and 84