Write a rational function that meets the following criteria:Vertical Asymptote only at x = 4Horizontal asymptote at y = 3No "holes"

Answer:

Side of the square (a) = 3½ = 7/2 m

Area of the square

= a²

= (7/2)²

= 49/4

= 12.25 m²

Hope it helps ⚜

In the given function H(p) = p/5 + 15, the independent variable is "p" ,

The independent variable in this function is denoted by "p." The independent variable can also be referred to as the input variable, which means that it is the value that is inputted into the function to produce an output. In this specific function, "p" represents the price of a good or service.

It is important to distinguish between the independent and dependent variables in a function. The dependent variable is denoted by "H(p)" in this case, and it is the output of the function. The value of the dependent variable is determined by the independent variable. In this function, "H(p)" represents the total cost of the good or service, which is dependent on the price "p." p is the input variable representing the price of the good or service.

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The value of angle x is 133 degree

And the equation of line be of the form,

⇒  y - y₁ = 133(x - x₁)

In the given line,

one angle is of 47 degree

And other is x degree

To find the value of x,

Since we know that,

The angle  of line is 180 degree.

Therefore,

⇒ x + 47 = 180

⇒         x = 133 degree

Therefore slope of this line be 133 degree

Now let this line is  passing through (x₁, y₁)

Hence,

The equation of  line be,

⇒ y - y₁ = (slope)(x - x₁)

⇒  y - y₁ = 133(x - x₁)

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The net price of the saws that Black & Decker Manufacturing sold to True Value Hardware on a chain discount of 8/3/1 is $3,357.21.

A chain discount refers to a type of discount offered to customers, which is sequentially applied to the list price to arrive at the net price.

Chain discounts involve a series of trade discounts applied in sequence.

List price = $3,800

Chain discount = 8/3/1

First net price = $3,496 ($3,800 x 1 - 8%)

Second net price = $3,391.12 ($3,496 x 1 - 3%)

Third net price = $3,357.21 ($3,391.12 x 1 - 1%)

Thus, the net price based on a chain discount of 8/3/1 is $3,357.21.

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On graph B, the group of birds seems to have twice as much as the group of mammals.

The change in scale on the y-axis from 50 to 85 in increments of 5 in Graph A to 0 to 80 in increments of 10 in Graph B makes the differences between the groups appear larger in Graph B.

As a result, the height of the bar for birds is approximately twice as much as the height of the bar for mammals in Graph B, which may not be apparent in Graph A.

Therefore, the correct option is (a) On graph B, the group of birds seems to have twice as much as the group of mammals.

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Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

The greatest common factor is the largest number that goes into both numbers. In this case, that is 7.

Step-by-step explanation:

\( \red{\frak{Given}} \begin{cases} & \sf{The\ measure\ of\ one\ angle\ of\ traingle\ is\ {\pmb{\sf{10^{\circ}}}}.} \\ & \sf{The\ other\ two\ angles\ are\ in\ the\ ratio\ of\ {\pmb{\sf{3\ :\ 14}}}.} \end{cases}\)

We know that,

Angle sum property,

\(\rule{200}{3}\)

\( \sf \dashrightarrow {10^{\circ}\ +\ 3x\ +\ 14x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {10^{\circ}\ +\ 17x\ =\ 180^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 180^{\circ}\ -\ 10^{\circ}} \\ \\ \\ \sf \dashrightarrow {17x\ =\ 170^{\circ}} \\ \\ \\ \sf \dashrightarrow {x\ =\ \dfrac{\cancel{170^{\circ}}}{\cancel{17}}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{x\ =\ 10^{\circ}.}}}}_{\sf \blue {\tiny{Value\ of\ x}}}} \)

∴ Hence, the value of x is 10°. Now, let us find out the other two angles of the triangle.

\(\rule{200}{3}\)

Second AnglE :

∴ Hence, the measure of the second angle of triangle is 30°. Now, let us find out the third angle of triangle.

\(\rule{200}{3}\)

Third AnglE :

∴ Hence, the measure of the third angle of the triangle is 140°.

Answer:

Step-by-step explanation:

Answer:

3(x + 5y) - 2(x + y)

3x + 15y - 2x - 2y

x + 13y

(3x + 15y) + (-2x + -2y)

x + 13y

The quadratic functions x² = 16, (x - 4)² = 169 and 4x² - 225 = 0 have solutions 4, (17 or -9) and (7.5 or -7.5) respectively.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x² term is written first, followed by the x term, and finally, the constant term is written. The numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.

In the first function;

1. x² = 16

take the square roots of both sides;

x = √16

x = 4

2. (x - 4)² = 169

Open the bracket

x² - 8x + 16 = 169

Solving for x

x = 17 or x = - 9

3. 4x² - 225 = 0

4x² = 225

x = 7.5 or x = -7.5

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The amount which Guillermo will have to pay on a monthly basis to keep his home insurance is; $270.83

From the information given;

In essence, his annual home owner insurance premium is 0.52% of the house value and can be evaluated as follows;

Therefore, his annual premium is set at $3,250.

However, we are required to determine what will Guillermo have to pay on a monthly basis.

Therefore, we have; $3,250 spread equally over 12 months.

Therefore, we have; $3,250/12 = $270.83

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The amount that Guillermo will pay monthly to keep his home insurance is $270.83.

An insurance premium is a charge that the insurer demands from the insured periodically as part of the pooling of risks under an insurance contract.

House value = $625,000

Insurance premium rate = $0.52 per $100

Annual premium = $3,250 ($625,000 x $0.52/$100)

Monthly premium = $270.83 ($3,250/12)

Thus, the amount that Guillermo will pay monthly to keep his home insurance is $270.83.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}\)

\(A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}\)

The ladder will reach a Height of approximately 43.46 meters on the building.

To find out how high on the building the ladder will reach, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder forms a right triangle with the ground and the building. The base of the ladder is 7 meters, the height of the building is what we need to find, and the length of the ladder is given as 44 meters.

Using the Pythagorean theorem, we can set up the equation:

(Height of the building)^2 + 7^2 = 44^2

Simplifying the equation, we have:

(Height of the building)^2 + 49 = 1936

Subtracting 49 from both sides, we get:

(Height of the building)^2 = 1887

To find the height of the building, we take the square root of both sides:

Height of the building = √1887

Calculating the square root of 1887, we find that the height of the building is approximately 43.46 meters.

Therefore, the ladder will reach a height of approximately 43.46 meters on the building.

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The minimal surface area box has the following measurements: side of base = 5√2/2, height = 5√2, and minimal surface area = 25√2 + 50.

(a) Let x be the side of the square base and y be the height of the box. Then the volume of the box is given by V = x²y = 125, and the surface area is given by S = 2x² + 4xy. We want to minimize S subject to the constraint that V is fixed at 125.

Using the volume equation, we can solve for y in terms of x: y = 125/x². Substituting this expression for y into the surface area equation, we get S(x) = 2x² + 4x(125/x²) = 2x² + 500/x.

To minimize S(x), we take the derivative with respect to x and set it equal to zero:

S'(x) = 4x - 500/x² = 0

Solving for x, we get x = 5√2/2. Substituting this value into the expression for y, we get y = 5√2.

Therefore, the dimensions of the box with minimal surface area are: side of base = 5√2/2, height = 5√2, and minimal surface area = 25√2 + 50.

(b) Let x be the side of the square base and y be the height of the box. Then the surface area of the box is given by S = 2x² + 4xy = 44, and we want to maximize the volume V = x²y.

Using the surface area equation, we can solve for y in terms of x: y = (44 - 2x²)/4x. Substituting this expression for y into the volume equation, we get V(x) = x²(44 - 2x²)/4x = (11x² - x⁴/2).

To maximize V(x), we take the derivative with respect to x and set it equal to zero:

V'(x) = 22x - 2x³/2 = 0

Solving for x, we get x = √11. Substituting this value into the expression for y, we get y = (√11 - √2)²/2.

Therefore, the dimensions of the box with maximal volume are: side of base = √11, height = (√11 - √2)^²/2, and maximal volume = 11(√11 - √2)²/4.

(c) Using Newton's Method, we can approximate the root of f(x) = x³ - 12 starting with an initial guess of x₀ = 2:

x₁ = x₀ - f(x₀)/f'(x₀) = 2 - (2₃ - 12)/(32₂) = 1.833333

x₂ = x₁ - f(x₁)/f'(x₁) = 1.833333 - (1.833333³ - 12)/(31.833333²) = 2.005917

x₃ = x₂ - f(x₂)/f'(x₂) = 2.005917 - (2.005917³ - 12)/(3*2.005917²) = 2.000007

Therefore, the approximated root of f(x) = x³ - 12 using Newton's Method with an initial guess of 2 is x₃ = 2.000007.

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Answer:

5.95%

Step-by-step explanation:

Bond 1:

I = 250(.05)5

I = $62.50

Bond 2:

62.5 = 350(3)r

62.5 = 1050r

r = 62.5/1050

r = 5.95%

Answer:

5.95%

Step-by-step explanation:

Answer:

Ax+By=C and 7.5 lb of Thistle

Step-by-step explanation:

The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.

To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.

The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.

To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:

Impact on income = Loss - Avoidable costs

Impact on income = $205,000 - ($1,295,000 + $119,000)

Impact on income = $205,000 - $1,414,000

Impact on income = -$1,209,000

The negative sign indicates a decrease in income.

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Answer:

V≈718.38

Step-by-step explanation:

The volume of this cone is 718.38 cubic centimeters.

Have a nice day!

Answer:

\(\theta=79.7^{\circ}\)

Step-by-step explanation:

Given that,

v = 2i - j and w = 3i + 4j

We need to find the angle between v and w.

Magnitude of |v|, \(|v|=\sqrt{2^2+(-1)^2} =\sqrt5\)

Magnitude of |w|, \(|w|=\sqrt{3^2+4^2} =5\)

The dot product of v and w,

\(u{\cdot}w=2(3)+(-1)4\\\\=2\)

The formula for the dot product is given by :

\(u{\cdot}w=|u||w|\cos\theta\\\\\cos\theta=\dfrac{u{\cdot}w}{|u||w|}\\\\=\dfrac{2}{\sqrt5\times 5}\\\\\theta=\cos^{-1}(\dfrac{2}{\sqrt5\times 5})\\\\\theta=79.69^{\circ}\\\\=79.7^{\circ}\)

So, the angle between u and v is \(79.7^{\circ}\).

Answer:

The angle between two vectors

 \(\alpha = cos^{-1} (\frac{2}{5\sqrt{5} } )\)

  ∝ = 79.700°

Step-by-step explanation:

Explanation

Given V =  2i - j and w = 3 i + 4 j

Let '∝' be the angle between the two vectors

           \(cos \alpha = \frac{v^{-} .w^{-} }{|v||w|}\)

         \(cos \alpha = \frac{(2i-j).(3i+4j) }{\sqrt{2^{2}+1^{2} )\sqrt{3^{2} +4^{2} } } }\)

        \(cos \alpha = \frac{(2(3)-4(1) }{\sqrt{5 )\sqrt{25 } } } = \frac{2}{\sqrt{5})5 } = \frac{2}{5\sqrt{5} }\)

          \(cos\alpha = \frac{2}{5\sqrt{5} } \\\alpha = cos^{-1} (\frac{2}{5\sqrt{5} } )\)

 The angle between two vectors

        ∝ = 79.77°

The option (b) set y equal to a constant other than zero to get the curve of points where the slope is that constant.

A slope field is a visual representation of the slopes of a function's derivative at different points on the xy-plane. The slope at a particular point in the xy-plane is given by the derivative of the function at that point.

To match the given equations with their corresponding slope fields, you need to analyze the behavior of the slopes and isoclines. An isocline is a curve in the plane along which the slope of a function is constant. Isoclines are useful in constructing slope fields by hand, as they help in determining the slope at different points.

To start with, set y equal to zero and observe how the derivative behaves along the x-axis. Similarly, set x equal to zero and observe the behavior of the derivative along the y-axis. These observations will give you an idea of the direction and magnitude of the slope at different points in the xy-plane.

Next, consider the curve in the plane defined by setting y' = 0. This curve represents the points in the picture where the slope is zero. These points are known as critical points or equilibrium points. They are essential in analyzing the stability and behavior of a system.

These curves are called isoclines and can be used to construct the slope field picture by hand.

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Complete Question:

Match the following equations with their slope field. Clicking on each picture will give you an enlarged view. While you can probably sove this problem by guessing, it is useful to try to predict characteristics of the slope field and then match them to the picture Here are some handy characteristics to start with- you will develop more as you practice. Set y equal to zero and look at how the derivatiwe behaves along the x axis. Do the same for the y axis by setting x equal to 0. Consider the curve in the plane defined by setting y' = 0-this should correspond to the points in the picture where the slope is zero. Setting y equal to a constant other than zero gives the curve of points where the slepe is that constant. These are called isoclines, and can be used to construct the slope field picture by hand.

, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: The fraction 3/9

Now we can simplify the fraction further by dividing both the numerator and denominator by 3

let p=3/9

then p=3/3 / 9/3

       p= 1/3

Hence, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

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The difference between the given expression is -255/16

Functions are written in terms of variable. For instance y = f(x) is a function of y.

Given the expression below

a^2-b^4

Given the following parameters

a= -1/2 and b=2.

Substitute the given parameters to have:

(-1/2)^2 - 2^4

Expand the resulting expression to have:

(1/16) - 16

(1-256)/16
-255/16

Hence the difference between the given expression is -255/16

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Answer:

The answer is "\(\frac{5\pi}{6}\)"

Step-by-step explanation:

Please find the graph file.

\(h= y=2x-x^2\\\\r= x\\\\Area=2\pi\times r\times h\\\\= 2 \pi \times x \times (2x-x^2)\\\\= 2 \pi \times 2x^2-x^3\\\\volume \ V(x)=\int \ A(x)\ dx\\\\= \int^{x=1}_{x=0} 2\pi (2x^2-x^3)\ dx\\\\= 2\pi [(\frac{2x^3}{3}-\frac{x^4}{4})]^{1}_{0} \\\\= 2\pi [(\frac{2}{3}-\frac{1}{4})-(0-0)] \\\\= 2\pi \times \frac{5}{12}\\\\=\frac{5\pi}{6}\\\\\)

Answer:The function is linear because we are dealing with a straight line.

Step-by-step explanation:

Answer: 400,00 km

Step-by-step explanation: 1:50,000 = 8:x

8 * 50,000 = 400,000

So, 8km on the map is 400,000 km in real life.

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Answer:

\(y=\dfrac{1}{4}x+\dfrac{7}{2}\)

Step-by-step explanation:

Given equation:

\(y=-4x-5\)

If two lines are perpendicular to each other, their slopes are negative reciprocals.

The slope of the given equation is -4.

Therefore, the slope of the perpendicular line is ¹/₄.

\(\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}\)

Substitute the found slope and point (-2, 3) into the point-slope formula to create the equation of the perpendicular line.

\(\implies y-3=\dfrac{1}{4}(x-(-2))\)

\(\implies y-3=\dfrac{1}{4}(x+2)\)

\(\implies y-3=\dfrac{1}{4}x+\dfrac{1}{2}\)

\(\implies y=\dfrac{1}{4}x+\dfrac{7}{2}\)

Answer:

80in3

Step-by-step explanation:

12 x 4 = 48

48 / 2 = 24

24 x 10 =240

240 / 3 = 80

           So your answer is 80in3

Answer: 80in

Step-by-step explanation:

Answer:

2^1 × 5^2 × 7^1 = 350

Step-by-step explanation:

2, 5, 7 are prime

first step is to divide the number 350 with the prime factor 2

continue dividing the number 175 by the next smallest prime factor

stop until you can't divide anymore

https://www.cuemath.com/numbers/factors-of-350/

Answer:

m, n and p

Step-by-step explanation:

Given

\(2m^2 + 3mn + 4p\)

Required

List out the variables

Literally, the variables are the alphabets in the expression

And they are:

m, n and p