determine the equations of the vertical and horizontal asymptotes, if any, for g(x)=x^3/(x-2)(x+1)​

Answer:

[tex]\frac{1}{16} x^2-\frac{1}{2} x-10[/tex]

Step-by-step explanation:

When (x,y) is a point on the parabola, the distance from the focus is equal to its distance from the directrix.

Given point as (4,-7) and  directrix as y=-15 then;

distance to focus=distance to directrix

Apply formula for distance

[tex]\sqrt{(x-4)^2+(y+7)^2} =(y+15)[/tex]

square both sides

[tex](x-4)^2+(y+7)^2=(y+15)^2\\\\\\x^2-8x+16+y^2+14y+49=y^2+30y+225\\\\\\\\x^2-8x+y^2-y^2+14y-30y+16+49-225=0\\\\\\16y=x^2-8x-160\\\\y=\frac{1}{16} x^2-\frac{1}{2} x-10[/tex]

Final answer:

The equation of the parabola with a focus at (4, -7) and a directrix of y = -15 is [tex]y = (1/16)x^2 - (1/2)x - 2.[/tex] However, none of the provided options match this equation, suggesting an error in the options or the interpretation of the question.

Explanation:

To derive the equation of a parabola with a focus at (4, -7) and a directrix of y = -15, we start by noting that the vertex lies midway between the focus and the directrix. The distance from the focus to the directrix is 8 units (|-7 - (-15)| = 8), thus the vertex is 4 units above the focus (at y = -3) and since the focus has an x-coordinate of 4, this is also the x-coordinate of the vertex. Therefore, the vertex is at (4, -3).

Next, we use the standard form of a vertical parabola (x-h)^2 = 4p(y-k), where (h,k) is the vertex and 4p is the distance from the vertex to the focus and the directrix. Because our parabola opens upwards (the focus is below the vertex), and the value of p is half the distance from the vertex to the focus or directrix, p = 4. Substituting h = 4, k = -3, and p = 4 into the equation yields [tex](x-4)^2 = 16(y+3[/tex]). We simplify the equation to:
x^2 - 8x + 16 = 16y + 48

By moving the term 16y to the left and then dividing all terms by 16, we get:

[tex]x^2/16 - x/2 + 1 = y + 3[/tex]

To obtain the standard form y = ax^2 + bx + c, we subtract 3 from both sides:

[tex]y = (x^2/16) - (x/2) + 1 - 3[/tex]

[tex]y = (1/16)x^2 - (1/2)x - 2[/tex]

The closest options provided in the question lack proper coefficients to match the derived equation, indicating a potential error in the provided options or in the interpretation of the question.

Step-by-step explanation:

I have answered ur question

The equation tan(x- pi/6) is equal to (√3tanx - 1)/(√3 + tanx).

To solve the equation [tex]\(\tan(x - \frac{\pi}{6})\)[/tex], we can use the tangent sum formula, which states that for any angles [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:

[tex]\[\tan(A - B) = \frac{\tan(A) - \tan(B)}{1 + \tan(A)\tan(B)}\][/tex]

Let [tex]\(A = x\)[/tex] and [tex]\(B = \frac{\pi}{6}\)[/tex]. We know that [tex]\(\tan(\frac{\pi}{6}) = \frac{1}{\sqrt{3}}\)[/tex] .

Applying these values to the formula, we get:

[tex]\[\tan(x - \frac{\pi}{6}) = \frac{\tan(x) - \frac{1}{\sqrt{3}}}{1 + \tan(x)\frac{1}{\sqrt{3}}}\][/tex]

[tex]\[\tan(x - \frac{\pi}{6}) = \frac{\tan(x) - \frac{1}{\sqrt{3}}}{1 + \tan(x)\frac{1}{\sqrt{3}}} \cdot \frac{\sqrt{3}}{\sqrt{3}}\][/tex]

[tex]\[\tan(x - \frac{\pi}{6}) = \frac{\sqrt{3}\tan(x) - 1}{\sqrt{3} + \tan(x)}\][/tex]

Answer:

Positive; more fruit bars are sold as the temperature rises;

Two bars for every 1 °F  

Step-by-step explanation:

I plotted a scatter chart in Excel and asked it to draw the regression line and include the equation for the line of best fit

The graph has a positive slope, so a positive correlation exists between the temperature and the number of fruit bars sold.

The real-world meaning of the positive slope of the line of best fit is that more fruit bars are sold as the temperature rises.

The equation for the line of best fit is

y = 2.1855x - 101.02

There are approximately two more fruit bars sold for every 1 °F the temperature rises.

Answer:

1--positive

2--2.2

3--1

Step-by-step explanation:

ed

To make each radio cost half its Monday price, the store would need to reduce the Tuesday price by 37.5% on Wednesday.

The store initially reduced its prices by 20% on Tuesday, meaning the radios now cost 80% of their original Monday price. If the goal is for the radios to cost half of their Monday price, we need to figure out what percentage of the Tuesday price will get us there. Since half of the Monday price would be 50%, and we know the price on Tuesday is 80% of the original, we'll divide 50 by 80 to find our answer. This yields 0.625, which as a percentage is 62.5%.

Therefore, the store would need to reduce the Tuesday price by 100% - 62.5% = 37.5% on Wednesday to make each radio cost half its Monday price.

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Answer:

car pooling

Step-by-step explanation:

saves gas, 2 or more can ride fro the same price as 1

Carpooling allows commuter expenses to be shared by sharing a car as the fuel charge and parking charges are reduced​.

Carpool is the sharing of car travel  in order to travel more than one person in the car. The carpool save the need to drive the car by different person for the same location.

Benefits of carpooling-

Hence, carpooling allows commuter expenses to be shared by sharing a car as the fuel charge and parking charges are reduced​.

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Answer:

x = 1.

Step-by-step explanation:

2(5x + 8) = 6x + 20

10x + 16 = 6x + 20

10x - 6x = 20 - 16

4x = 4

x = 1.

To solve the equation 2(5x + 8) = 6x + 20, follow the steps of distribution, simplification, and isolation to find the solution x = 1.

Step 1: Distribute 2 to terms inside the parentheses on the left side of the equation: 10x + 16 = 6x + 20.

Step 2: Combine like terms on each side to simplify the equation: 10x - 6x = 20 - 16, which results in 4x = 4.

Step 3: Solve for x by isolating it: x = 4/4, hence x = 1.

Answer:

9 ft

Step-by-step explanation:

So let's assume the shape is rectangular.

The perimeter of the rectangle with dimensions l and w is: 2w+2l.

We are given 48 feet of wood so we want 2w+2l=48.

Manny wants l to be 15 so insert this into equation: 2w+2(15)=48.

Now we need to solve

2w+2(15)=48

Multiplying 2 and 15:

2w+30=48

Subtract 30 on both sides:

2w     =18

Divide both sides by 2:

 w     =9

We want the width to be 9 ft.

Answer:

B and C cannot be points on the unit circle

Step-by-step explanation:

This like asking which of the points does not satisfy x^2+y^2=1.

Let's look at (-2/3 , sqrt(5)/3)

x=-2/3

y=sqrt(5)/3

We have x^2=4/9 while y^2=5/9, and x^2+y^2=4/9+5/9=9/9=1.

This first one looks great and is on the unit circle.

Let's look at (sqrt(3)/2 , 1/3)

x=sqrt(3)/2

y=1/3

We have x^2=3/4 and y^2=1/9 , and x^2+y^2=3/4+1/9=31/36 (this is not 1).

This point is not on the unit circle.

Let's look at (1,1)

x=1

y=1

We have x^2=1 and y^2=1, and x^2+y^2=1+1=2 (this is not 1).

This point is not on the unit circle.

Let's look at (0.8,-0.6)

x=0.8

y=-0.6

We have x^2=.64 and y^2=.36, and x^2+y^2=.64+.36=1

This point is on the unit circle.

Answer:

B and C

Step-by-step explanation:

FreckledSpots is correct.

3/4 = X/64

Divide 64 by 4, then multiply 3 by that number:

64/4 = 16

3 x 16 = 48

3/4 = 48/64

Answer:

a. 2.14% should have IQ scores between 40 and 60

b. 15.87% should have IQ scores below 80

Step-by-step explanation:

* Lets explain how to solve the problem

- For the probability that a < X < b (X is between two numbers, a and b),

 convert a  and b into z-scores and use the table to find the area

 between the two z-values.

- Lets revise how to find the z-score

- The rule the z-score is z = (x - μ)/σ , where

# x is the score

# μ is the mean

# σ is the standard deviation

* Lets solve the problem

- IQS are normally distributed with a mean of 100 and standard

 deviation of 20

∴ μ = 100 and σ = 20

a.

- The IQS is between 40 and 60

∴ 40 < X < 60

∵ z = (x - μ)/σ

∴ z = (40 - 100)/20 = -60/20 = -3

∴ z = (60 - 100)/20 = -40/20 = -2

- Use the z table to find the corresponding area

∵ P(z > -3) = 0.00135

∵ P(z < -2) = 0.02275

∴ P(-3 < z < -2) = 0.02275 - 0.00135 = 0.0214

∵ P(40 < X < 60) = P(-3 < z < -2)

∴ P(40 < X < 60) = 0.0214 = 2.14%

* 2.14% should have IQ scores between 40 and 60

b.

- The IQS is below 80

∴ X < 80

∵ z = (x - μ)/σ

∴ z = (80 - 100)/20 = -20/20 = -1

- Use the z table to find the corresponding area

∵ P(z < -1) = 0.15866

∵ P(X < 80) = P(z < -1)

∴ P(X < 80) = 0.15866 = 15.87%

* 15.87% should have IQ scores below 80

Answer:

3x^2+14x-2 if you meant f(x)=3x^2+10x and g(x)=4x-2

and I think C was meant to read 3x^2+14x-2

Please correct me if I have mistranslated. Thank you kindly.

Step-by-step explanation:

I kind of wonder if you meant f(x)=3x^2+10x and g(x)=4x-2.

(f+g)(x)=f(x)+g(x)

          =(3x^2+10x)+(4x-2)

          =3x^2+10x+4x-2

          =3x^2+(10x+4x)-2  I paired 10x and 4x together because    they are like terms

         =3x^2+14x-2

Answer:

I can not see it properly

Step-by-step explanation:

Answer:

D. 2.1 + 2x = 7.5

Step-by-step explanation:

The perimeter of a polygon is the sum of the lengths of all sides.

The sides here measure x, x, and y.

The perimeter of the triangle is x + x + y.

We are told the perimeter is 7.5

Now we have

x + x + y = 7.5

or

2x + y = 7.5

We are told y = 2.1, so we substitute 21.1 for y, and we get:

2x + 2.1 = 7.5

or

2.1 + 2x = 7.5

Answer: D. 2.1 + 2x = 7.5

Answer:

The scale factor is 1.

Step-by-step explanation:

Let k be the scale factor of a dilation of triangle ABC to form the image triangle A'B'C'.

The dilation is a magnification if

[tex] |k| > 1[/tex]

In this case, the preimage will be similar to the image triangle.

If

[tex] - 1\: < \: k \: < \: 0 \: \: or \: \: 0 \: < \: k \: < \: 1[/tex]

the dilation is a reduction. The image and pre-image will still be similar.

But if

[tex]k = 1[/tex]

the image is the same as the preimage.

We say the pre-image is congruent to the image triangle.

Answer:

1

Step-by-step explanation:

edge2022

Answer:

The system represents the maximum amount of money that the parks department can spend on trees and the relationship between the number of oak trees, x, and elm trees, y.

Step-by-step explanation:

Compare the given situation and inequality. Oak trees cost $60 each, therefore, the variable associated with 60 in the inequality, x, represents the number of oak trees. Elm trees cost $80 each, therefore the variable associated with 80 in the inequality, y, represents the number of elm trees.

The city has up to $9,600 to spend on trees and the inequality uses a less than symbol. This means that the solution set will be at or below 9,600, which means that it is a maximum.

Consider the second inequality in the system. It shows that x is less than or equal to 3 times y. This is associated with the situation in that the number of oak trees, x, is no more than three times the number of elm trees, y. This is the relationship between the two types of trees.

Therefore, the system represents the maximum amount of money that the parks department can spend on trees and the relationship between the number of oak trees, x, and elm trees, y.

Answer:

hi :)

Step-by-step explanation:

Answer:

D year 15

Step-by-step explanation:

Given:

y= 8x^2-40x+6

year is the best prediction for when 1206

Finding value of x for y=1206

8x^2-40x+6= 1206

8x^2-40x+6-1206=0

8x^2-40x-1200=0

Solving the above by quadratic formula:

x= [tex]\frac{-b\sqrt{b^{2}-4ac } }{2a}[/tex]

 = [tex]\frac{40\sqrt{40^{2}-4(8)(-1200) } }{2(8)}[/tex]

x= 15 and x= -10

As year can not be negative, hence correct answer is

D: year 15!

Very true. Answer is choice A.

Geometry is a branch of mathematics that deals with the study of shapes and their properties. It involves concepts like points, lines, angles, and curves. Geometry is important in various fields and helps develop problem-solving skills.

Geometry is a branch of mathematics that deals with the study of shapes, sizes, and properties of figures and spaces. It involves concepts like points, lines, angles, and curves, and explores their relationships and measurements. One important aspect of geometry is the study of geometric proofs, which are logical arguments that demonstrate the truth of mathematical statements.

For example, in a triangle, the sum of the three interior angles is always 180 degrees. This can be proven using the properties of parallel lines and transversals, and the fact that the angles in a straight line add up to 180 degrees.

Geometry is an essential part of mathematics education and is used in various fields such as architecture, engineering, and physics. It helps us understand and analyze the physical world around us, as well as develop critical thinking and problem-solving skills.

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Final answer:

Cathy's commission rate is calculated by subtracting her base salary from her gross earnings and then dividing the commission amount by her sales exceeding the quota, resulting in a rate of 4.25%.

Explanation:

To calculate Cathy's commission rate, we need to determine how much she earned from sales that exceeded her quota. Cathy's sales were $6560, and her quota is $5000, meaning she exceeded her quota by $1560 ($6560 - $5000).

As her gross earnings were $441.30, we also need to account for her base salary of $375, which leaves $66.30 ($441.30 - $375) as the amount earned from commission.

Finally, to find the commission rate, we divide the commission amount by the sales that exceeded the quota, which is $66.30 / $1560.

Therefore, Cathy's commission rate is 4.25% (rounded to two decimal places).

Answer:

q = -13

Step-by-step explanation:

The given equation is:

[tex]2x^{2}-8x=5[/tex]

Taking 2 as common from left hand side, we get:

[tex]2(x^{2}-4x)=5\\\\2[x^{2} - 2(x)(2)]=5[/tex]

The square of difference is written as:

[tex](a-b)^{2}=a^2 - 2ab + b^{2}[/tex]                            Equation 1

If we compare the given equation from previous step to formula in Equation 1, we note that we have square of first term(x), twice the product of 1st term(x) and second term(2) and the square of second term(2) is missing. So in order to complete the square we need to add and subtract square of 2 to right hand side. i.e.

[tex]2[x^{2}-2(x)(2)+(2)^2-(2)^{2}]=5\\\\ 2[x^{2}-2(x)(2)+(2)^2]-2(2)^{2}=5\\\\ 2(x-2)^{2}-2(4)=5\\\\ 2(x-2)^2-8=5\\\\ 2(x-2)^{2}-8-5=0\\\\ 2(x-2)^{2}-13=0[/tex]

Comparing the above equation with the given equation:

[tex]2(x-p)^{2}+q=0[/tex], we can say:

p = 2 and q= -13

Answer:

Increasing on it's domain [tex](-\infty,\infty)[/tex] because the slope is positive.

The domain and range are both all real numbers, also known as

[tex](-\infty,\infty)[/tex].

Step-by-step explanation:

All domain really means is what numbers can you plug in and you get number back from your function.

I should be able to plug in any number into 3x+2 and result in a number. There are no restrictions for x on 3x+2.

The domain is all real numbers.

In interval notation that is [tex](-\infty,\infty)[/tex].

Now the range is the set of numbers that get hit by y=3x+2.

Well y=3x+2 is a linear function that is increasing.  I know it is increasing because the slope is positive 3. I wrote out the positive part because that is the item you focus on in a linear equation to determine if is increasing or decreasing.

If slope is positive, then the line is increasing.

If slope is negative, then the line is decreasing.

So y=3x+2 hits all values of y because it is increasing forever.  The range is all real numbers. In interval notation that is [tex](-\infty,\infty)[/tex].

Answer: C. [tex]126\pi \text{units}^2[/tex]

Step-by-step explanation:

The surface area of right cylinder is given by :-

[tex]S.A.=2\pi r(r+h)[/tex]

Given : Height : h=2 units

Radius : r= 7 units

The the surface area of the given right cylinder will be :-

[tex]S.A.=2(\pi) (7)(2+7)\ \ \ \text{Put }\pi=3.14[/tex]

i.e. [tex]S.A.=126\pi \text{units}^2[/tex]

Hence, the surface area of the right cylinder = [tex]126\pi \text{units}^2[/tex]

Answer:

C

Step-by-step explanation:

Answer:

=48.0

Step-by-step explanation:

In this problem we can use the cosine formula to find b.

b²=a²+c²-2acCosB

Where a, b and c are the sides of the triangle.

Substituting with the values from the question gives:

b²=28²+28²-2×38×28×Cos 92

b²=2302.26

b=√2302.26

=47.98

The side b=48.0 to the nearest tenth.

Answer:

6.

Step-by-step explanation:

We have that the regular hexagon has 6 reflection axis that after the reflection the hexagon doesn't change its position. 3 axis are in the vertex that cuts the hexagon in two equal parts and the other 3 in the middle point of each side that also cuts the hexagon in two equal parts.

Answer:

6

Step-by-step explanation:

Answer:

8 dogs

Step-by-step explanation:

1.  Divide.

40/5 = 8

2. Answer.

x = 8

Answer:

Step-by-step explanation:

[tex](8+6i)(8-6i)\qquad\text{use}\ (a+b)(a-b)=a^2-b^2\\\\=8^2-(6i)^2\qquad\text{use}\ (ab)^n=a^nb^n\\\\=64-6^2i^2\qquad\text{use}\ i^2=-1\\\\=64-(36)(-1)\\\\=64+36\\\\=100[/tex]

The expression (8 + 6i)(8 - 6i) = 100.

= (8+6i) (8-6i)

=8^2 - (6i)^2

=64 - 6^2i^2

=64 - (36)(-1)

=64+36

=100

(8 + 6i)(8 - 6i) = 100.

An expression is a set of two or more numbers or variables and one or more mathematical operations. This math operation is addition, subtraction, multiplication, or division. The structure of the expression is as follows: The expression is (number/variable, math operator, number/variable)

. In mathematics, an expression is defined as a clause that contains numbers, variables, and operators used to indicate values. In mathematics, an equation is defined as a mathematical statement in which two terms are equal to each other.

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Answer:

C. Amplitude = 3 feet; period = 8 hours; midline: y = 4

Step-by-step explanation:

The midline is halfway between the lowest point and the highest point.

y = (1 + 7) / 2

y = 4

The period is the time it takes for a full cycle.  So the period is 8 hours.

The amplitude is the distance from the midline to the lowest or highest point.

a = 4 − 1 = 3, or a = 7 − 4 = 3

It's also half the distance between the lowest and highest points.

a = (7 − 1) / 2

a = 3

Answer:

B. Amplitude= 6 feet; period = 4 hours; midline: y =3

Step-by-step explanation:

If the Bay is 1 foot and 7 feet, and the tide is at its lowest at 0 and completes a full cycle every 8 hours. If every 8 hours is a new cycle the divide that by 2 to get the midline of 4 because for is the half way point for the full 8 hours

Hope this helped! :3

Answer:

                       *                                                   *          *

|-4|___|-3|___|-2|___|-1|___|0|___|1|___|2|___|3|___|4|___|5|___|6|

Step-by-step explanation:

You are looking for a dot over -2 (that is 2 units to the left of 0).

You are looking for a dot over 3 (that is 3 units to the right of 0).

You are looking for a dot over 4 (that is 4 units to the right of 0).

If you find one of the graphs matches this, then you should select.

The graph would look like this:

                       *                                                   *          *

|-4|___|-3|___|-2|___|-1|___|0|___|1|___|2|___|3|___|4|___|5|___|6|

Answer:

the last one (D.)

Step-by-step explanation:

Answer:

1/5525 ≈ 0.018%

Step-by-step explanation:

There are 4 kings in a standard deck of 52 cards.

The probability that the first card is a king is 4/52.

The probability that the second card is also a king is 3/51 (the first king isn't replaced, so there's one less king and one less card in the deck).

The probability that the third card is a king is 2/50.

The probability of choosing 3 king cards is therefore:

P = (4/52) (3/51) (2/50)

P = (1/13) (1/17) (1/25)

P = 1/5525

P ≈ 0.018%

Answer:

sometimes HAVE A NICE DAY

Step-by-step explanation:

A plane in geometry extends infinitely in all directions and can contain an infinite number of points. It takes at least three non-collinear points to define a plane, but a plane is never limited to just those three points. Thus, the statement that a plane contains only three points is never true.

When the question asks if a plane contains only three points always, sometimes, or never, it refers to the concept in geometry where a plane is a flat, two-dimensional surface that extends infinitely in all directions.

In geometrical terms, a plane can contain an infinite number of points. However, it is often said in geometry that it takes a minimum of three non-collinear points to define a plane. This means that while a plane can be uniquely determined by three non-collinear points, the phrase 'a plane contains only three points' is never true because a plane can contain an infinite number of points, not just three. When three points do determine a plane, they can be considered as forming a triangle on that plane, with each point corresponding to a vertex of the triangle.