Mathematics High School

A hyperbola centered at the origin has a vertex at (9, 0) and a focus at (−15, 0).
Which are the equations of the asymptotes?

Answers

Answer 1
Hyperbola equation opening horizontally:
[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]
Asymptotes:
[tex]y = \pm \frac{b}{a} x[/tex]

'a' is distance vertex is from center --> a = 9
'c' is distance focus is from center  --> c = 15
[tex]a^2 + b^2 = c^2 \\ \\ b^2 = 15^2 - 9^2 = 144 \\ \\ b = 12[/tex]

Asymptotes are:
[tex]y = \pm \frac{12}{9} x = \pm \frac{4}{3} x[/tex]
Answer 2

Answer:

C

Step-by-step explanation:

Related Questions

What is the domain of the function

Answers

5. D (the number under the square root symbol must be greater than or equal to 0. 


Answer:

The domain of the function is x>=-7

Step-by-step explanation:

The domain is all the values that x can take so the function is defined, that means we can find a value of y

The sqrt is defined only for positive values and zero. So the expression in the sqrt must  satisfy that

6x + 42 >=0

We only have to find x

6x >=-42

x>=-42/6

x>=-7

So the answer is D x>=-7

Claudia is on a motorcycle trip. She checked the odometer at the beginning of the trip, and it showed 16,789 miles. After 15 days it showed 22,189 miles. If Claudia rode the same number of miles each day how many miles did she ride in a day?
A.360 miles
B 540 miles.
C.771 miles
D.1,479 miles
please help me

Answers

22,189 - 16,789 = 5,400

Total miles = 5,400
Days = 15

Divide total by how many days:

5,400 ÷ 15 =  360

Answer = A.360

Hope this helped :)

22,189 - 16,789 = 5,400

5,400 / 15 = 360

360 miles a day

Solve a(x - b) - 2k = l for k

Answers

a(x - b) - 2k = l 
ax - ab - 2k = l

Subtract ax, add ab to both sides

- 2k = l - ax + ab

Divide by - 2 to isolate variable K

k = (l - ax + ab) / - 2 or [tex]k = \frac{l - ax + ab}{-2} [/tex]

find the volume of the specificed cone. Use 3.14 for pie, and round your answer to the nearest whole number.
Radius=9 in., Height=8 in.
a. 1017 cu. in.
b. 151 cu. in.
c. 678 cu. in.
d. 1356 cu. in.

Answers

The answer is C.678 cu. in. :D

Assume that lines that appear to be tangent are tangent. O is the center of the circle. Find the value of x.
m<O = 135
(See picture down below)

a) 45

b) 315

c) 270

d) 67.5

Answers

Draw an imaginary line from the vertex of angle x to the center of the circle.
This divides the 4-sided polygon into two right triangles.  For example, the upper right triangle has an acute angle whose measure is 135 degrees / 2, or 67.5 degrees, and the another acute angle whose measure is x/2.

x/2 and 67.5 degrees are complementary angles, so x/2 + 67.5 deg = 90 deg.  Thus, x/2 = 22.5 deg, and so x = 45 deg.  (answer)

Roger goose had a 500-yard head start on willa. if willa's speed was 40 yards per second and roger's speed was only 20 yards per second, how long did it take willa to catch up

Answers

For this case what we should do is write the equation of movement for each person.
 We have then:
 For Roger:
 r = 20 * t + 500
 For Willa:
 r = 40 * t
 Equating the equations:
 20 * t + 500 = 40 * t
 We cleared t:
 40 * t - 20 * t = 500
 20 * t = 500
 t = 500/20
 t = 25 s
 Answer:
 it did take willa 25 s to catch up Roger.

Which equation represents a parabola with a focus at (0,-2) and a directrix of y=6?

Answers

Hey there!!

First, let's learn the parabola formula when the focus and the directrix is given.

Formula :

[tex]y = \frac{( x - a ) ^{2} }{ 2 ( b - k ) } + \frac{( b + k ) }{2}[/tex]

We have ,

Focus : ( 0 , -2 )

Hence, a = 0 and b = -2

And k = 6

Now, we will just have to plug in the values and find out the equation.

[tex]y = \frac{( x - 0 )^{2} }{2 ( - 2 - 6 )} + \frac{( - 2 + 6 ) }{2}[/tex]

[tex]y = \frac{x^{2} }{-16}+ 2[/tex]

The final equation would be :

[tex]y = \frac{-x^{2} }{16} + 2[/tex]

Hope my answer helps!!

Carlos swam the perimeter of a rectangular pool seven times. If the length of the pool is 21 ft and the width of the pool is 9 ft, how many feet did Carlos swim?

Answers

21+9+21+9=Perimeter of the pool = 60
And Carlos did this 7 times (x)...60 x 7 = 420



The total length did Carlos swim is 420 feet.

To find the perimeter.

What is rectangle?

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.

Given that:

Let the perimeter of rectangular swimming pool be x metres.

Then, its length =21 feet.

The width of the pool = 9 feet

The Perimeter of a rectangle =2(Length+Breadth)

According to the given condition, we have

Perimeter of a rectangle =2(Length+Breadth)

Perimeter of a rectangle=2(21+9)

Perimeter of a rectangle=2*30

Perimeter of a rectangle=60 feet

But, ​carlos swam the perimeter of a rectangular pool seven times.

Old perimeter=7*60=420  feet

Thus ,the total length did Carlos swim is 420 feet.

Learn more about rectangle here:

https://brainly.com/question/10064327

#SPJ2

Greg wants to move out of his dormitory and into an apartment near his college. His parents agreed, on the condition that the rent is no more than 25% of the cost of dorm living. To get an idea of rent amounts for one-bedroom apartments, Greg looks at listings in a local newspaper and on an Internet site.

Which answer best describes the sample and population?




A. Sample: listings in a local newspaper and on an Internet site
Population: all available apartments near the college


B. Sample: all available apartments near the college
Population: all available dormitories near the college


C. Sample: all available dormitories near the college
Population: all available apartments near the college


D. Sample: all available apartments near the college
Population: listings in a local newspaper and on an Internet site

Answers

the sample would be where Greg searched so the sample is the local newspaper and the internet site
 the population would be all available apartments
 the answer would be 

A. Sample: listings in a local newspaper and on an Internet site
Population: all available apartments near the college

The average of paula's two test scores must be 80 or more for her to get at least a b in the class. she got a 72 on here first test. what grades can she get on the second test to make at least a b in the class

Answers

She would have to make an 88 or higher to average a B.

please help asap 50 pts

Answers

I believe the answer is C. If you were to plug in 1 for t, you would get h=22. Thus, the max height is 22 feet, and the time it took to get there was 1 second.

I tried plugging in all the answers, and found that C works the best. Hope that helps.

Good luck!

-RxL

Give an exact answer in simplified form. 5y+3 > -7y + 13 5y+3>−7y+13 (see pic

Answers

Th answer to the inequality will be evaluated as follows:
5y+3>-7y+3
putting like terms together we obtain:
5y+7y>3-3
2y>0
dividing both sides by 2 we get:
(2y)/2>0/2
thus
y>0

Answer: y>0

Th answer to the inequality will be evaluated as follows:

5y+3>-7y+3

putting like terms together we obtain:

5y+7y>3-3

2y>0

dividing both sides by 2 we get:

(2y)/2>0/2

thus

y>0

I am posting my work for an application of integrals problem. I would love to know if anyone else agrees with my work!

Answers

Your work appears to be correct.

The results from a graphing calculator are in agreement.

ANSWER TRUTHFULLY WILL NAME YOU BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!
The ordered pairs (1,5) (2,25) (3,125) (4,625) and (5,3125) represent the function y=5^x. How does this rule represent the function?

A) y=x5
B) y=5x
C) y=5^5=x
D) y=x+5

Answers

For each answer, we can plug in the given points:

A) is technically the same as B), but B) expresses correct function notation.

B) 5 = 5(1) ⇒ 5 = 5
     25 = 5(2) ⇒ 25 ≠ 10
     B) is incorrect.

C) I'm not sure what you mean y=5^5=x, but I'm going to use [tex]y=5^{x} [/tex] because it's close to what you wrote:
[tex]5=5^{1} =\ \textgreater \ 5=5 \\ 25=5^{2} =\ \textgreater \ 25=25 \\ 125=5^{3} =\ \textgreater \ 125 = 125 \\ 625=5^{4}=\ \textgreater \ 625=625 \\ 3125=5^{5}=\ \textgreater \ 3125=3125[/tex]
The function [tex]y=5^{x} [/tex] works for the points given.

D) 5 = 1 + 5 ⇒ 5 ≠ 6
     D) is not correct.

Please check your functions; I'm not sure that C) is a function.  In any case, the answer is C) because all the other answers are wrong.

The length of a rectangle is 7 cm less than twice its width. if the area of the rectangle is 39 cm2​, find the dimensions of the rectangle.

Answers

Use the equation 2n+2(n-7)=39 to find the answer :)

Mrs. Cantonwine teaches 2 math classes. There are 28 students in 6A and 21 students in 6B. She divided both classes into groups of equal size. How many students are in a group?

Answers

Hi there!

In order to figure out how many students are in each group, we'll need to find the greatest common factor of the two class sizes. The greatest common factor is 7. This means that 7 students are in each group.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

Melissa pulls the pep club to see which sport they like. She finds that 45 students like soccer only, 35 students like football only, and 15 students like soccer and football. There is no one who doesn't like at least one of the two sports mentioned. Which venn diagram would be an appropriate model for the data melissa collected

Answers

The one that looks like this.

Someone please help

Answers

D is the  right answer!
 

please help!!!

Write an expression for the volume of a cylinder with a height 7in. greater than the radius.

Answers

Answer: 7 π r² + π r³

Explanation:

1) The general formula for the volumen, V, of a cylinder with radius r and height h is:

V = π r² h

2) Now you have the condition that the height is 7 inches greater than the radius, that is:

h = 7 + r

3) Replace h with its expression

V = π r² (7 + r)

4) Expand the product (use distributive property):

V = π (7r²) + π r³ = 7 π r² + π r³

Answer: 7 π r² + π r³

What is the surface area of a sphere with the given dimension? Express your answer to nearest hundredth. Use 3.14 for pi. Radius = 5cm.

Answers

Okay. The equation for a sphere's surface area is A = 4 * pi * r^2. Let's plug 5 in for r. 
[tex]4 \pi (5^2) = 4(3.14)*25 = 100 * 3.14 = 314[/tex]
I got 314 cm^2 is the surface area, but it always helps to double check work! Hope this helps!
Surface area of a sphere can be calculated as:

Surface Area = 4πr²

r = 5cm
π = 3.14

Using the values we get:

Surface Area = 4(3.14)(5²) = 314 cm²

Thus, the surface area of the sphere is 314 cm²

The length of a rectangle is 4 inches less than twice its width. If the area of the rectangle is 70 square inches, what are its demensions

Answers

By definition, the area of a rectangle is given by:
 A = w * l
 Where,
 w: width
 l: long
 Substituting values we have:
 70 = w * (2w-4)
 Rewriting we have:
 70 = 2w ^ 2-4w
 2w ^ 2 - 4w - 70 = 0
 Solving the polynomial we have:
 w1 = -5
 w2 = 7
 We take the positive root because it is a dimension.
 w = 7 inches
 Then, the length will be:
 l = 2w-4
 l = 2 (7) -4
 l = 14-4
 l = 10 inches
 Answer:
 its demensions are:
 w = 7 inches
 l = 10 inches
let
x-----------> the length side of rectangle
y----------> the width side of rectangle

we know that
70=x*y--------> x=70/y-----------> equation 1
x-4=2y--------> equation 2
substitute equation 1 in equation 2

[70/y]-4=2y--------> multiply by y------> 70-4y=2y²----> 2y²+4y-70=0

using a graph tool ----> to resolve the second order equation
see the attached figure

the solution is 
y=5
x=70/y--------> x=70/5=14

the answer is
the dimensions are
length=14 in
width=5 in

for the function f(x)= -(x + 1)^2 + 4 identify the vertex, domain, and range

Answers

Vertex (-1, 4)

Domain = All real numbers

Range = All y values such that y ≤ 4

Answer:

Vertex = (-1, 4)

Domain = All real numbers i.e. R

Range = (-∞, 4)

Step-by-step explanation:

The vertex of the quadratic equation:

f(x) = a(x - h)² + k

Here, Vertex = (h,k)

Thus, Vertex = (-1, 4)

Domain = All real numbers i.e. R

Range = All real numbers less than or equal to 4 i.e. (-∞, 4) or f = ≤ 4.

Further, the possible values of x are called Domain.

And, the possible output we get as y is called Range.

The equation of a parabola is given. y=−16x2+7x−80 What is the equation of the directrix of the parabola?

Answers

we have that
y=−16x²+7x−80

see the answer in the attached figure
y=-1/6x^2+7x-80
the answer is y=-5 

What is the focus of the parabola? y=−1/4x^2−x+3
Enter your answer in the boxes.
(__ ,__ )

Answers

we know that
the equation of the parabola is of the form
y=ax²+bx+c

in this problem
y=−1/4x²−x+3
where
a=-1/4
b=-1
c=3

 the coordinates of the focus are

(-b/2a,(1-D)/4a)
where
D is the discriminant b²-4ac
D=(-1)²-4*(-1/4)*3-----> D=1+3---> D=4
therefore
x coordinate of the focus
-b/2a----> 1/[2*(-1/4)]----> -2

y coordinate of the focus
(1-D)/4a------> (1-4)/(-4/4)---> 3

the coordinates of the focus are
(-2,3)

(08.05 HC) The work of a student to solve a set of equations is shown: Equation A: y = 15 − 2z Equation B: 3y = 3 − 4z Step 1: −3(y) = −3(15 − 2z) [Equation A is multiplied by −3.] 3y = 3 − 4z [Equation B] Step 2: −3y = 15 − 2z [Equation A in Step 1 is simplified.] 3y = 3 − 4z [Equation B] Step 3: 0 = 18 − 6z [Equations in Step 2 are added.] Step 4: 6z = 18 Step 5: z = 3 In which step did the student first make an error?

Answers

The error appears to be in Step 2.

Simplifying
  -3(y) = -3(15 -2z)
should yield
  -3y = -45 +6z
not
  -3y = 15 -2z

Answer:

STEP 2

Step-by-step explanation:Simplifying

 -3(y) = -3(15 -2z)

should yield

 -3y = -45 +6z

What is the length of the unknown side of the right triangle? (1 point) A right triangle with hypotenuse x and legs 5 and 12 13 17 25 60

Answers

If the legs are...

5,12 --> 13

Why? Pythagorean theorem. 

5 squared plus 12 squared equals 169. The square root of that is 13.
Answer is 13;
[tex] \sqrt{{(12)}^{2} + {(5)}^{2}} = 13[/tex]

Which of the following best describes the following set of numbers? 6 + 8 + 10 + 12 + ... + (4 + 2n) + ...

answers:
Arithmetic SequenceGeometric SeriesGeometric SequenceArithmetic Series

Answers

From the series given:
6+8+10+12+.....+(4+2n)+
the common difference is:
8-6=10-8=12-10=2
since the series has a common difference then it is known as:
Arithmetic series.

Answer:

The term that best describes the given set of numbers is:

                                Arithmetic Series.

Step-by-step explanation:

We are given a series of numbers as:

6 + 8 + 10 + 12 + ... + (4 + 2n) + ...

Clearly as wee could see that each term in the given expression is separated by a plus sign, Hence, the given expression is a series and not a sequence.

Also as we could see that each in the series is more than the preceding term by 2 i.e. the common difference of the term is 2.

( Since, the set of numbers is given as:

[tex]a_0+a_1+a_2+a_3+....[/tex]

where,

[tex]a_n=2n+4[/tex]

[tex]when,n=0\\\\a_1=4\\\\when,n=1\\\\a_1=6\\\\and\ so\ on[/tex]

Also,

[tex]a_0-a_1=2\\\\Simialrly\\a_2-a_1=2\\\\and\ so\ on[/tex]

Hence, the common difference is 2. )

Hence, the given series is an Arithmetic series.

Find the derivative of f(x) = negative 10 divided by x at x = -12.

Answers

[tex]f(x)=\dfrac{10}{x};\ D:x\neq0\\\\f'(x)=-\dfrac{10}{x^2}\\\\x=-12\to f'(-12)=\dfrac{-10}{(-12)^2}=\dfrac{-10}{144}=-\dfrac{5}{72}[/tex]

A box is 10 cm long, 5 cm wide, and 2 cm high. What is the surface area of the box? (S.A. = 2lw + 2lh + 2wh)

Answers

your answer is 160 cm2 all you need to do is look up a calculator online i use calculator soup

Answer:

your answer is 160 cm2

Step-by-step explanation:

ez

I don't understand this question. Could anyone excplain to me what it wants me to do and what the answer is?

What is the diameter of a sphere that has a surface area of 1041 square inches?

A) 9.1

B) 22.5

C) 40.3

D) 18.2

Answers

The answer is 18.2
I got the answer by solving it
1st you need equation for the surface area of a sphere which is:
A=4*π*r^2
Where r=radius
r = diameter/2 or d/2

So
area of a sphere = 4*π*(d/2)^2

Plug in the area given
1041 = 4*π*(d/2)^2

Solve for d
1041/(4* π)=82.84

82.84 = (d/2)^2

Sqrt(82.84)=d/2

9.10=d/2

9.10*2= d

18.2=d
So the answer is 18.2 in





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