PLEASE HELP ASAP
What are the equations of the asymptotes of the hyperbola?

(x+1)^2/25−(y−3)^2/16=1

Answers

Answer 1

The horizontal and vertical asymptotes of the hyperbola equation (x + 1)² / 25 - (y - 3)² / 16 = 1 are y = 4x / 5 + 19 / 5 and y = -4x / 5 + 11/5 respectively

Equation of Asymptotes

An asymptote of the curve y = f(x) or in the implicit form: f(x,y) = 0 is a straight line such that the distance between the curve and the straight line lends to zero when the points on the curve approach infinity. This can be said to be a line that a curve approaches but never touches.

Basically, we have three types of asymptotes which are horizontal asymptotes, vertical asymptotes and oblique asymptotes.

In the hyperbola equation given

(x + 1)² / 25 - (y - 3)² / 16 = 1

The equation of asymptotes are;

Horizontal asymptotes : y = 4x / 5 + 19 / 5

Vertical asymptotes : y = -4x / 5 + 11/5

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Related Questions

14. A zip wire is shown as the dashed line AC in the diagram.
The zip wire is supported by two vertical posts AB and CD standing on horizontal ground.
CD=2.6 BD=12
The zip wire makes an angle x with the horizontal, as shown in the diagram. The design of the zip wire requires the angle x to be at least 5⁰.
Work out the least possible height of the post $A B$ Give your answer correct to 3 significant figures.

Answers

The least possible height of AB is 3.650 m.

What is a word problem?

A word problem is described as a few phrases outlining a "real-life" situation where a problem needs to be solved using mathematics.

For everything from counting pennies to calculating a tip, we can employ the three primary sorts of word problems: part-part whole, separate and join, and multiply and divide.

Given, CD=2.6 m, BD=12 m

From the figure,

or, tan x = [tex]\frac{AB - 2.6}{12}[/tex]

or, tan 5 [tex]\leq \frac{AB - 2.6}{12}[/tex]

When AB be least, then

[tex]\frac{AB - 2.6}{12}[/tex] = tan 5

or, AB = (12*tan 5) + 2.6

or, AB = 3.650 m

Hence, the least possible height of the AB is 3.650 m.

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4 2/3 - 3 3/8 + 4 3/5

Answers

Answer:

18.475?

Step-by-step explanation:

If you make $31.65 in 8 hours, how much in total?

Answers

Answer:

$253.20

Step-by-step explanation:

A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t3 + 8t2 + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million. According to the graph of the function, what other quantity of product would result in the same profit?

Answers

The required value of the production at which the company attained the same profit is 4 thousand skin care items.

Given that,

A certain skincare company's profit in millions of dollars, P(t), can be modeled by the polynomial function P(t) = –2t³ + 8t² + 2t, where t represents the number of skincare items produced, in thousands. Today, the company produces 1 thousand products for a profit of $8 million.

Here,
Plotting the graph of the polynomial equation,

P(t) = –2t³ + 8t² + 2t,
From the graph at x = 4,
The polynomial gives the same value as it gave at x = 1,

Thus, the required value of the production at which the company attained the same profit is 4 thousand skin care items.

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A certain vending machine offers 20-ounce bottles of soda for $1.50. The number of bottles X bought from the machine on any day is a random variable with mean 50 and standard deviation 15. Let the random variable Y equal the total revenue from this machine on a given day. Assume that the machine works properly and that no sodas are stolen from the machine. What are the mean and standard deviation of Y?

Answers

The mean and standard deviation of a random variable can be used to describe the distribution of its possible values. In this case, the mean of the random variable X represents the average number of bottles of soda that are bought from the vending machine on a given day, and the standard deviation represents the amount of variation in the number of bottles bought from one day to the next.

To find the mean and standard deviation of the random variable Y, which represents the total revenue from the vending machine on a given day, you will need to use the mean and standard deviation of X and the price per bottle of soda.

The mean of Y can be calculated using the formula:

mean of Y = mean of X * price per bottle

Plugging in the given values, we get:

mean of Y = 50 * $1.50 = $75

So the mean of the random variable Y, which represents the total revenue from the vending machine on a given day, is $75.

The standard deviation of Y can be calculated using the formula:

standard deviation of Y = standard deviation of X * price per bottle

Plugging in the given values, we get:

standard deviation of Y = 15 * $1.50 = $22.50

So the standard deviation of the random variable Y, which represents the total revenue from the vending machine on a given day, is $22.50.

Therefore, the mean and standard deviation of Y, the total revenue from the vending machine on a given day, are $75 and $22.50, respectively.

Write an equation in slope-intercept form of the line that passes through (-2,-7) and (-1,6)

Answers

y = 13x + 18
1. Find the slope of the two points. 6-(-7) is 13 and -1 -(-2) is 1, so the slope is 13/1.

2. Write the equation in point slope form.
y - y1 = m(x - x1)
y - 6 = 13(x -(-1)

3. Use distributive property.
y - 6 = 13x + 13

4. Add 6 to both sides.
y = 13x + 18

Hope this helps

If BD bisects AC and AC bisects BD, is AABE^ ACDE? Explain.
Yes; the triangles are congruent by SSS.
Yes; the triangles are congruent by ASA.
Yes; the triangles are congruent by SAS
NO; the triangles are not congruent.

Answers

Yes; the triangles are congruent by SAS.

What is triangle ?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.

AC and BD bisects one another

AE = CE --- Side

and

BE = DE --- Side

When both lines bisect one another, they form a pair of vertical angles and

When we apply the theorem of vertical angles to this, we have that:

∠AEB = ∠CED --- Angle

At this point, we have established:

Two sides of ABE and CDE are congruent and One angle in each of ABE and CDE are also congruent

Hence, the triangles are congruent by SAS.

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Use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) squareroot of (9 + 49^x2) dx

Answers

The indefinite integral of given integral ∫√(9+49x^2)dx is ∫√(9+49x^2)dx = [tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex].

In the given question we have to find the indefinite integral.

The given integral is

∫√(9+49x^2)dx

Now finding the indefinite integral using the C for the constant of integration.

An integral is regarded to be indefinite if it has no lower or upper bounds. In mathematics, the most generic antiderivative of f(x) is known as an indefinite integral and expressed by the expression f(x) dx = F(x) + C.

We can write it as:

[tex]\int\sqrt{(9+49x^2)}dx = \int\sqrt{[(3)^2+(7x)^2]}dx[/tex]

Taking common 7^2

[tex]\int\sqrt{(9+49x^2)}dx = 7\int\sqrt{[(3/7)^2+(x)^2]}dx[/tex]

Using the formula

[tex]\int\sqrt{(a^2+x^2)}dx = \frac{1}{2}\times\sqrt{a^2+x^2} + \frac{1}{2}\cdot a^2In|x+\sqrt{a^2+x^2}|+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{(3/7)^2+x^2}+\frac{1}{2}\cdot(\frac{3}{7})^2In|x+\sqrt{(3/7)^2+x^2}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\sqrt{9/49+x^2}+1/2\cdot(9/49)In|x+\sqrt{(9/49)+x^2}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+1/2\cdot(9/49)In|x+\frac{\sqrt{9+49x^2}}{7}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 7[x\cdot\frac{\sqrt{9+49x^2}}{7}+(9/98)In|\frac{7x+\sqrt{9+49x^2}}{7}|]+C[/tex]

[tex]\int\sqrt{(9+49x^2)}dx = 1/98[98x\sqrt{9+49x^2}+9In|7x+\sqrt{9+49x^2}}|]+C[/tex]

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Write the following as an inequality.
−8 is less than or equal to w, and 3 is greater than or equal to w
Use w only once in your inequality.

Answers

Answer:

Step-by-step explanation:

If -8 is less than or equal to w, and 3 is greater than or equal to w, then we can combine these two inequalities into a single inequality by combining the left and right sides:

-8 ≤ w ≤ 3

This inequality can be read as "w is greater than or equal to -8 and less than or equal to 3." It represents all values of w that are greater than or equal to -8 and less than or equal to 3, including -8 and 3.

I hope this helps! Let me know if you have any questions.

-8w hope this answer helps u a lot!

HELPME Mike has $25.00 to rent paddleboards for himself and a friend for 3 hours. Each paddleboard rental costs $3.75 per hour.

Answers

He’ll pay 22.5 for the both of them and will have 2.5 dollars left

Explanation: 3 times 3.75= 11.25

11.25 times 2= 22.5

The length and width of two sides of a rectangle are consecutive odd integers. The area of the rectangle is 143 square units.

Find the dimensions of the rectangle.

The width of the rectangle is blank and length is blank

Answers

The dimensions of the rectangle are 70.5 by 72.5 units.

What is a dimension?

A length measurement that only goes one way. Dimensions include things like width, depth, and height. One dimension is that of a line, two dimensions are found in a square, three dimensions are found in a cube, and one dimension is that of something's height, length, or width. For instance, the room is 26 feet by 15 feet in size.

Solution Explained:
Given,

Area = 143 unit^2

A/Q,

Let length be x and width be x + 2.

So, Area = l X w

143 = x + x + 2

143 = 2x + 2

x = (143 - 2)/2

x = 70.5

So width = x + 2 = 70.5 + 2 = 72.5

So, the dimensions are 70.5 by 72.5

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help please very easy proportional relationship due hurry please than u!

Answers

1) h=1/5 k

(10/2 = 1/5, 20/4 = 1/5... etc)

2) k=5/4 h

(5/4 = 5/4, 10/8=5/4... etc)

3) h=5/1 k

(25/5 = 5/1, 30/6 = 5/1 ... etc)

Hope this helps!

Complete the ratio 4:16 = 1:?

Answers

Answer:

1:4

Step-by-step explanation:

4:16 = 1:?

4/4 = 1

16/4 = 4

= 1:4

write an expression that is equivalent to 2/3 (4x + 9)

Answers

Hello,

I hope you and your family are doing well!

To write an expression that is equivalent to 2/3 (4x + 9), you can simply distribute the 2/3 over the parentheses:

2/3 (4x + 9) = (2/3 * 4x) + (2/3 * 9)

This simplifies to:

2/3 (4x + 9) = (8/3)x + (18/3)

Therefore, an expression that is equivalent to 2/3 (4x + 9) is (8/3)x + (18/3).

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Happy Holidays & New Year!

Answer: 2 2/3x + 6

Step-by-step explanation: 1 of 3 ways to find how to make the equivalent is to use the distributive property. So, that means we need to multiply or distribute 2/3 to both 4x and 9. So, 2/3 x 4 is roughly 2 2/3. Also, 2/3 x 9 = 6. So, I combined the like terms to get 2 2/3x + 6 as my equivalent expression. I hope this helps.

a plumber cuts 2 3/4 feet from pipe. The pipe is now 13 1/4 feet long. Write and solve an equation of to determine the original length if the pipe

Answers

2=3/4,13=1/4,2-3/4=0,13-1/4=0,2-3/4=0*13,13-1/4=0*2

Kaitlin the trainer has two solo workout plans that she offers her clients: plan A and plan B each client does either one or the other (not both) on Friday there were 3 clients who did plan A and 8 who did plan b on Saturday there were 5 clients who did plan A and 2 who did plan b Kaitlin trained her friday clients for a total of 7 hours and her Saturday clients for a total of 6 hours how long does each of the workout plans last

Answers

To find the length of each workout plan, we can use the total number of hours that Kaitlin spent training her clients on Friday and Saturday and the number of clients who did each plan on those days.

Let A be the length of plan A in hours and B be the length of plan B in hours. We can set up the following system of equations to represent the given information:

3A + 8B = 7
5A + 2B = 6

Solving this system of equations using elimination, we find that A = 0.6 hours and B = 0.4 hours.

Therefore, plan A lasts 0.6 hours and plan B lasts 0.4 hours.

1.6y+y-4/15y+1 1/6y=2 1/3 pls help

Answers

The simplification of the given equation is -630y² + 81y + (+2.6y) * 90y² = 0.

What is the domain of the function?

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

We have,

1.6y+y-4/15y+7/6y=21/3

Move all terms to the left:

1.6y+y-4/15y+7/6y-(21/3)=0

Domain of the equation: 15y!=0

y!=0/15

y!=0

y∈R

Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R