Write the equation of a hyperbola with vertices (3, -1) and (3, -9) and co-vertices (-6. -5) and (12, -5).

Answers

Answer 1

the answer:
the main formula of hyperbola is

(x-h)² / a² - (y-k)² / b² = 1, where the center is C (h,k)
and the vertex formmula is

(h+-a, k) and the covertex is (h, k+-b)

in our case vertices are already given:
(3, -1) and (3, -9) so h+a =3 or h - a =3 and k= -1, or k= -9
and co-vertices (-6. -5) and (12, -5)
h= -6 or h= 12, and k+ b=-5, or k- b = -5
for example h= -6, h+a =3, a=3+6=9, k= -1, k+ b=-5 , we can get b= - 5 + 1 = - 4, so a=9, b=-4, h=-6, k= -1
the equation is
(x+6)² / 81 - (y+1)² / 16 = 1, if the center is C(-6, -1)

the same method can be applied with the other choices of h and k.

Related Questions

Plato-Match each set of conditions with the corresponding relationship between ∆ABC and ∆XYZ and the criterion (if any) that proves the relationship.

Answers

The first box on the left would be matched with the third box on the right, because the left one is saying that two of the sides are equal, and one angle is equal, therefore, SSA, or SAS.

The second one on the left is matched with the last one on the right, because it says that two of the angles are equal, and one side is equal, hence, AAS, or ASA.

The last one on the left is matched with the first one on the right, because it says all three sides are equal, therefore, SSS.

The third one on the left is matched with the second one on the left. I'll be honest, I'm not sure why this is, (geometry isn't my best subject either Dx) but by the process of elimination, this is it.

what can 4 and 22 divided into equally the answer is smaller than 88

Answers

The answer would be 44...
11x4
22x2

What is the initial value of the function represented by this graph?

A coordinate grid is shown with x and y axes labeled from 0 to 7 at increments of 1. A straight line joins the ordered pair 0, 2 with the ordered pair 7, 5.
0
1
2
5

Answers

The initial value of a function is the value of the function when x = 0

o when x = 0, y = 2 so the initial value is 2

Answer:

Step-by-step explanation:

The initial value is what you start off with, so it is 2! :)

When $n$ is divided by 10, the remainder is $a$. when $n$ is divided by 13, the remainder is $b$. what is $n$ modulo 130, in terms of $a$ and $b$?

Answers

N = a (mod 10)

N = b (mod 13)

gcd(10,13) = 1

then

N = 10 bx + 13 ay (mod 130)

Where

10x + 13y = 1

-> (10x + 13) (mod 2) = 1 (mod 2)

-> y (mod 2) = 1

y = -3, x = 4

-> N = 40b – 39a (mod 130)

It is given that ra + sb should be non-negative:

N = 40b – 39a (mod 130)

N = 40b + (130 – 39)a (mod 130)

N = 40b + 91a (mod 130)

Therefore, N modulo 130, in terms of a and b is: N = 40b + 91a (mod 130).

Final answer:

To find the value of n modulo 130 in terms of a and b, one must solve two congruences using the Chinese Remainder Theorem. The solution would require computations beyond the scope of this response and would result in n expressed as a linear combination of a and b modulo 130.

Explanation:

To solve for the values of n modulo 130, given that when n is divided by 10, the remainder is a, and when n is divided by 13, the remainder is b, we can express n in the following forms:

n = 10k + a, where k is some integer

n = 13l + b, where l is some integer

Since 10 and 13 are coprime, Chinese Remainder Theorem tells us that there is a unique solution for n modulo 130 that satisfies both of these congruences. To find n in terms of a and b, we must find k and l such that these two equations give the same n for a particular value of n between 0 and 129 inclusive. This can be done through careful calculations or using a method designed for solving simultaneous congruences.

Once the suitable k and l values are found, the value of n modulo 130 can be stated. Since the exact solution requires more context or computational techniques, we can't provide the specific number in this case, but the final answer will be in the form: n ≡ (something involving a and b) (mod 130).

Evaluate the following expression using the values given:

Find 3x2 − y3 − y3 − z if x = 3, y = −2, and z = −5.

Answers

is the 3x2 an exponent?

the questionnnnnnnn issssssssss

Answers

arc length of a circle=Ф/360º(2πr)
Ф=angle of the arc
r=radius

Data:
Ф=140º
r=diameter/2=(100 m)/2=50 m
π=3.14

arc length=(140º/360º)(2)(3.14)(50 m)=122.1111...m=122.1 m

Answer: A) 122.1 m

A party rental company has chairs and tables for rent. The total cost to rent 3 chars and 2 tables is $20. The total cost to rent 8 chairs and 4 tables is $45. What is the cost to rent each chair and each table?

Answers

Equations:
8c + 4t = 45
3c + 2t = 20

Modify for elimination: ( multiply 2nd eq by -2)
8c + 4t = 45
-6c + -4t = -40

Subtract and solve for "c":
2c = 5
c = $2.50 (cost of one chair)

Solve for "t":
3c + 2t = 20
3(2.50) + 2t = 20
7.50 + 2t =20

2t=12.50

T= 12.50/2 =6.25
t = $ 6.25 (cost of one table)

Table = 6.25 each

Chair = 2.50 each

Check:

3(2.50) + 2(6.25) =

7.50 +12.50 = 20

8(2.50) + 4(6.25) =

20.00 + 25.00 = 45.00

Sam picked a card from a standard deck. What is the probability that Sam picked a heart or a king?

A. 1/13
B. 16/52
C. 17/52
D. 16/53

Answers

P(H or K)=(H+3K)/52 (there are thirteen hearts and three other kings)

P(HorK)=16/52

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

Number of cards in a deck = 52

Number of heart = 13

Number of king = 4

But we know that heart contains one king too.

So, to avoid double counting we have to subtract 1 from it.

so, Number of king = 3

So, Probability that Sam picked a heart or a king is given by

[tex]\frac{13}{52}+\frac{3}{52}\\\\=\frac{16}{52}\\\\[/tex]

Hence, Option 'B' is correct.

The variable Z is directly proportional to X. When X is 15, Z has the value 45.
What is the value of Z when X = 23

Answers

Hello!

If variable Z is directly proportional to X, this means that the value of X increases a certain amount when Z increases. The same will apply to decreasing of either variable.

If Z = 45, X = 15. This means Z is 3 times as much as X.
X is currently 23. We can now figure out for Z.

Since Z is 3 times as much as X, multiply 23 by 3.
23 * 3 = 69

The value of Z is 69 when X is 23.

I hope this helps!

Write the number in the form a +bi

Answers

[tex]\bf \sqrt{-9}+10\implies \sqrt{-1\cdot 9}+10\implies \sqrt{-1}\cdot \sqrt{9}+10 \\\\\\ \sqrt{-1}\cdot \sqrt{3^2}+10\implies i\cdot 3+10\implies 3i+10\implies \boxed{10+3i}[/tex]

What is the measure of RST?

Answers

Answer:

∠TSR = 93°

Step-by-step explanation:

In the figure attached as we know ∠S = [tex]\frac{mQR+mPT}{2}[/tex] [ By the theorem of angles of the intersecting secants in a circle]

∠S = [tex]\frac{131+43}{2}[/tex]

= [tex]\frac{174}{2}[/tex]

= 87°

Now we have to find the measure of ∠RST

Since ∠QSR + ∠TSR = 180° [ supplementary angles]

87° + ∠TSR = 180°

∠TSR = 180 - 87 = 93°

Therefore, m∠TSR = 93° is the answer.

Solve for z: 3z -5 +2z=25 -5z

Answers

To answer this question you will have to combine like terms.

3z-5+2z=25-5z

Combine 3z and 2z first because they have z in common and are on the same side: 3z+2z=5z

Now you have -5+5z=25-5z

Now you will go ahead and distribute since you can't combine anymore on certain sides.

You can add 5 to 25 on the other side: 25+5=30

Then add 5z to 5z on the other side: 5z+5z=10z

So now your equation should look like this: 10z=30

From here you will have to divide both sides by 10: 10/10=1(since it came to 1 it will just stay as z instead of 1z) 30/10=3

So your solution should come to: z=3

Which expression is equivalent to r^9/r^3

Answers

[tex] \cfrac{r^9}{r^3} =r^{9-3}=r^6[/tex]

Answer:

The correct option is B.

Step-by-step explanation:

The given expression is

[tex]\frac{r^9}{r^3}[/tex]

According to the property of exponent,

[tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

Using this property of exponent, we get

[tex]\frac{r^9}{r^3}=r^{9-3}[/tex]

[tex]\frac{r^9}{r^3}=r^{6}[/tex]

The expression [tex]r^{6}[/tex] is equivalent to the given expression.

Therefore the correct option is B.

The following is an incomplete paragraph proving that ∠WRS ≅ ∠VQT, given the information in the figure where segment UV is parallel to segment WZ.:

Segments UV and WZ are parallel with line ST intersecting both at points Q and R respectively

According to the given information, segment UV is parallel to segment WZ while angles SQU and VQT are vertical angles. Angle VQT is congruent to angle SQU by the Vertical Angles Theorem. Because angles SQU and WRS are corresponding angles, they are congruent according to the Corresponding Angles Postulate. Finally, angle VQT is congruent to angle WRS by the _____________________.

Which Property of Equality accurately completes the proof?

Reflexive
Substitution
Subtraction
Transitive

Answers

Answer: Transitive Property of Equality
The Subtraction Property does not apply here, and the Reflexive Property is used to show something is equal to itself (a = a).

Given that ∠VQT is congruent to ∠SQU by the Vertical Angles Theorem and ∠SQU is congruent to ∠WRS by the Corresponding Angles Postulate, ∠VQT is congruent to ∠WRS because of the Transitive Property of Equality.

Basically, Angle 1 = Angle 2, Angle 2 = Angle 3, therefore Angle 1 should also equal Angle 3.

Answer:

Transitive

Step-by-step explanation:

Just took the test

Hope it helps :)

What is the range of this set of heights in centimeters?

{140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}

38
41
46
50

(If you can help me with this maybe you can help me with my last posted question? It hasn't been answered and I need help!)

Answers

First, arrange your data from least (smallest number) to greatest (biggest number): {132,140, 142, 147, 149, 152, 158, 163, 165, 166, 168, 171, 173, 177, 178, 180, 180, 181, 182}
Second, subtract your greatest number from your smallest number: 182-132 = 50
Therefore, your answer is: 50

Final answer:

The range of the given set of heights is 50 cm, which is determined by subtracting the smallest height (132 cm) from the largest height (182 cm) in the set.

Explanation:

The range of a set of numbers is the difference between the largest and the smallest numbers in the set. To find the range of the given heights in centimeters, you first identify the largest and smallest numbers in the set {140, 166, 132, 165, 152, 168, 181, 158, 173, 171, 180, 182, 163, 177, 180, 142, 147, 149, 178}. The smallest height is 132 cm, and the largest is 182 cm.

Now, subtract the smallest value from the largest value to determine the range:

Range = Largest value – Smallest value

Range = 182 cm – 132 cm

Range = 50 cm

Therefore, the range of the given set of heights is 50 cm.

How do you graph y^2=x^3?

Answers

Below I have attached a graph that would show how to graph this.

To graph these types of equations, we need to remember our rules about graphing squared values and cubed values. A squared function will create a parabola, while a cubed function will create a curvy line over the y-axis.

A baby wriggled so much that weighing him at the clinic was a problem. So the doctor held the baby and stood on a scale. Then the nurse held the baby and stood on the scale. Then the doctor held the nurse who held the baby and stood on the scale. the three results were 78 kg, 69 kg and 142 kg respectively. What was the weight of the baby.
Long question but help me out ( it was 69 kg I mean)

Answers

x = weight of the baby.
y = weight of the doctor.
z = weight of the nurse.

x + y = 78 so y = 78 - x
x + z = 69 so z = 69 - x
x + y + z = 142

substitute y = 78 - x and z = 69 - x into x + y + z = 142

x + y + z = 142
x +78 - x + 69 - x = 142
-x + 147 = 142
-x = - 5
x = 5

answer

the weight of the baby was 5 kg

Let the weight of the baby be B
weight of the Nurse be N
weight of the Doctor be D

Now if we fit those into equations we have:

1. B+D= 78
2. B+N= 69
3. B+D+N= 142

Now take 1 and 3:

B+D= 78 so substitute 78 in the thrid equation were B+D is
78+N= 142 ( what plus 78 will get you 142)
78+64= 142

The nurse's weight is 64 kg

Now that we have the nurses weight. You take the combined weight of the baby and nurse and subtract 64

The baby weighs 5kg

now take the doctors and babies combine weight and subtract 4

The Doctor weighs 73 kg

ANSWER:

The baby weighs 5kg, the nurse weighs 64, and the doctor weighs 74.

Sorry for the long answer but hope this helps.

1 + 4 + 7 + 10 ... what is last number that makes sum go over 1 million.

Answers

The sum can be expressed as

[tex]\displaystyle\sum_{k=0}^n(3k+1)=n+1+3\sum_{k=1}^nk=n+1+\dfrac{3n(n+1)}2[/tex]
[tex]=\dfrac32n^2+\dfrac52n+1[/tex]

The sum will exceed 1 million for [tex]n[/tex] satisfying

[tex]\dfrac32n^2+\dfrac52n+1>1000000[/tex]
[tex]3n^2+5n+2>2000000[/tex]
[tex]3n^2+5n-1999998>0[/tex]

The least integer that satisfies this is [tex]n=816[/tex].

Need help with this question! Will attach pic! A satellite is to be put into an elliptical orbit around a moon as shown below.The moon is a sphere with radius of 1000 km. Determine an equation for the ellipse if the distance of the satellite from the surface of the moon varies from 953 km to 466 km

Answers

An equation for the ellipse ( standard form ):
x²/a² + y²/b² = 1
Here is: a - semi-major axis and b - semi-minor axis.
Radius of the moon is 1,000 km and the distance from the surface of the moon to the satellite varies from 953 km to 466 km.
a = 1,000 + 953 = 1,953 km
b = 1,000 + 466 = 1,466 km
Answer:
The equation is x² / 1,953² + y² / 1,466² = 1
or: x²/3,814,209 + y²/2,149,156 = 1

Find the limit of the function algebraically. limit as x approaches negative nine of quantity x squared minus eighty one divided by quantity x plus nine.

Answers

Let me express the equation clearly:

lim x→-9 (x²-81)/(x+9)

Initially, we solve this by substituting x=-9 to the equation.

((-9)²-81)/(-9+9) = 0/0

The term 0/0 is undefined. This means that the solution is not see on the number line because it is imaginary. Other undefined terms are N/0 (where N is any number), 0⁰, 0×∞, ∞-∞, 1^∞ and ∞/∞. One way to solve this is by applying L'Hopitals Rule. This can be done by differentiating the numerator and denominator of the fraction independently. Then, you can already substitute the x=-9.

(2x-0)/(1+0) = 2x = 2(-9) = -18

The other easy way is to substitute x=-8.999 to the original equation. Note that the term x→-9 means that x only approaches to -9. Thus, you substitute a number that is very close to -9. Substituting x=-8.999

((-8.999)²-81)/(-8.999+9) = -18

How many cookies will Tanya have if she bakes 6batches more than the maximum number of batches in the table

Answers

The number of cookies increases at a constant rate for each batch. The increase is 16 cookies every time. This constant increase represents a linear relationship.

We can form an equation for this linear relationship.
The relationship is in the form [tex]y=ax+b[/tex] where

y = number of cookies of 'x' batches
x = number of batches
a = changing rate = 16
b = the number of cookies when the batch is 0

We need to find the value of 'b' and we can achieve this by keep subtracting 16 from 165, which is batch 5 until we get to batch 0.

Batch 5 = 165
Batch 4 = 165 - 16 = 149
Batch 3 = 149 - 16 = 133
Batch 2 = 133 - 16 = 117
Batch 1 = 117 - 16 = 101
Batch 0 = 101 - 16 = 85 ⇒ this is the value of 'b'

So the equation is [tex]y=16x+85[/tex]

We will use this equation to work out the number of cookies if we cook another 6 batches.

6 batches more than batch 9 will give us batch number 15

We have: x=15, a=16, b=85

y = 16(15) + 85 = 325 cookies

Answer:

325 cookies

Step-by-step explanation: I just took the test and got it right.

What is the solution of the equation 6x - 8 = 4x? X=

Answers

x=4

hope this helps you

The solution to the equation is X=4

can someone pls help me

Answers

3*circle= 12
circle=4 <=======

Plug circle value in
diamond+2= 5*(4)
diamond+2=20
diamond=18 <=====

Plug circle and diamond value in
2(4)=18+2*triangle
8=18+2*triangle
-10=2*triangle
-5= triangle <=======

Below are the steps to solve an equation: Step 1: |x − 5| + 2 = 5 Step 2: |x − 5| = 5 − 2 Step 3: |x − 5| = 3 Which of the following is a correct next step to solve the equation?

Answers

The next correct step would be to open the absolute value signs. To do so, the equation would need to be put equal to two values wich both need to be solved to find the correct answers.

Equation 1: x-5=3
Equation 2: x-5=-3

The answers would be x=8 and x=2.

Answer: [tex]x-5=\pm 3[/tex] will be the next step of the given expression.

Step-by-step explanation:

Since, Given expression is |x-5|+2=5

On solving the above expression,

Step 1. [tex]|x-5|+2=5[/tex]

step 2. [tex]|x-5| = 5-2[/tex]

Step 3. [tex]|x-5| = 3[/tex]

Step 4. [tex]x-5=\pm 3[/tex] (because mode takes both positive and negative values)

Your job pays $8 per hour. (a) Write an algebraic expression for your pay in dollars for working h hours. (b) What is your pay if you work 36 hours?

Answers

P = 8h.....where P stands for pay

if u work 36 hrs...
P = 8(36)
P = 288 <==

a. 8h
b. Plug in 36 for h
8*36
288

Final answer: $288

How do I solve this? (Geometry)

Answers

7x4 = 28

5 x z = 28

z = 28/5 = 5.6

Write | √3 - 2i | in a + bi form.

Answers

keeping in mind that, an absolute value expression is in effect a piece-wise, then

[tex]\bf |\sqrt{3}-2i|\implies \begin{cases} +(\sqrt{3}-2i)\\ -(\sqrt{3}-2i) \end{cases}\implies \begin{cases} \sqrt{3}-2i\\ -\sqrt{3}+2i \end{cases}[/tex]

Which statements are true for solving the equation 0.5 – |x – 12| = –0.25? Check all that apply.

The equation will have no solutions.

A good first step for solving the equation is to subtract 0.5 from both sides of the equation.

A good first step for solving the equation is to split it into a positive case and a negative case.

The positive case of this equation is 0.5 – |x – 12| = 0.25.

The negative case of this equation is x – 12 = –0.75.

The equation will have only 1 solution

Answers

we have

[tex]0.5-\left|x-12\right|=-0.25[/tex]

we know that

The absolute value has two solutions

Subtract [tex]0.5[/tex] both sides

[tex]-\left|x-12\right|=-0.25-0.5[/tex]

[tex]-\left|x-12\right|=-0.75[/tex]

Step 1

Find the first solution (Case positive)

[tex]-[+(x-12)]=-0.75[/tex]

[tex]-x+12=-0.75[/tex]

Subtract [tex]12[/tex] both sides

[tex]-x+12-12=-0.75-12[/tex]

[tex]-x=-12.75[/tex]

Multiply by [tex]-1[/tex] both sides

[tex]x=12.75[/tex]

Step 2

Find the second solution (Case negative)

[tex]-[-(x-12)]=-0.75[/tex]

[tex]x-12=-0.75[/tex]

Adds [tex]12[/tex] both sides

[tex]x=-0.75+12[/tex]

[tex]x=11.25[/tex]

Statements

case A) The equation will have no solutions

The statement is False

Because the equation has two solutions------> See the procedure

case B) A good first step for solving the equation is to subtract 0.5 from both sides of the equation

The statement is True -----> See the procedure

case C) A good first step for solving the equation is to split it into a positive case and a negative case

The statement is False -----> See the procedure

case D) The positive case of this equation is 0.5 – |x – 12| = 0.25

The statement is False

Because the positive case is [tex]0.5-(x-12)=-0.25[/tex] -----> see the procedure

case E) The negative case of this equation is x – 12 = –0.75

The statement is True -----> see the procedure

case F) The equation will have only 1 solution

The statement is False

Because The equation has two solutions------> See the procedure

Final answer:

The equation 0.5 - |x - 12| = -0.25 has no solutions because an absolute value cannot be negative. Attempting to split the equation into positive and negative cases or solving for x is fruitless because the left side of the equation will always be at least 0.5.

Explanation:

When solving the equation 0.5 - |x - 12| = -0.25, we can immediately notice that it will have no solutions because the absolute value is always non-negative, and therefore the left-hand side cannot be less than 0.5. Hence, subtracting 0.5 from both sides is not a good first step. Instead, you would typically isolate the absolute value on one side, but given that the equation equals a negative number, we know it has no solutions without additional steps.

Additionally, splitting the equation into a positive case and a negative case isn't useful here, because no matter what's inside the absolute value, the output cannot lead to a negative result, thus making both cases moot.

The statements that say "The positive case of this equation is 0.5 - |x - 12| = 0.25" and "The negative case of this equation is x - 12 = -0.75" are incorrect as they misinterpret how the absolute value works. Lastly, the equation does not have any solution, so it cannot have only one solution.

Learn more about Absolute Value Equations here:

https://brainly.com/question/35209059

#SPJ3

Jessica plans to purchase a car in one year at a cost of $30,000. how much should be invested in an account paying 10% compounded semiannually to have the funds needed?

Answers

The formula is
A=p (1+r/k)^kt
A fund needed 30000
p Amount invested?
R interest rate 0.1
K compounded semiannual 2
T time 1 year
Solve the formula for p to get
P=A÷(1+r/k)^kt
P=30,000÷(1+0.1÷2)^(2×1)
P=27,210.88

Hans the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 6 clients who did Plan A and 5 who did Plan B. On Tuesday there were 2 clients who did Plan A and 3 who did Plan B. Hans trained his Monday clients for a total of 7 hours and his Tuesday clients for a total of 3 hours. How long does each of the workout plans last?

Answers

A = hours for plan A
B = hours for plan B

Monday: 6A + 5B = 7
Tuesday: 2A + 3B = 3

use elimination by multiplying the 2nd equation by 3.

Doing that we get 3(2A + 3B = 3) = 6A + 9B = 9

So the two equations are now:
6A + 9B = 9

6A + 5B = 7

Subtract and we have 4B = 2

B = 2/4 = 1/2 of an hour

Now put 1/2 back into either equation to solve for A

6A + 5(1/2) = 7
6A + 5/2 = 7
6A = 14/2 -5/2
6A = 9/2
divide by 6 to get A = 9/12 = ¾ hours

Plan A = 3/4 hour

Plan B = 1/2 hour

Final answer:

By setting up and solving a system of equations, we find that Plan A lasts for 45 minutes per session and Plan B lasts for 30 minutes per session.

Explanation:

Solving for the Duration of Workout Plans

We have information regarding the total duration of workouts and the number of clients for two consecutive days. To find the duration of each workout plan, we use a system of equations. Let A represent the duration of Plan A and B represent the duration of Plan B. The equations based on the given information are:

6A + 5B = 420 minutes (7 hours on Monday)

2A + 3B = 180 minutes (3 hours on Tuesday)

Multiplying the second equation by 3 gives us:

6A + 9B = 540

Subtracting the first equation from this result gives us:

4B = 120 minutes, therefore, B = 30 minutes

Now we substitute B = 30 in the first equation:

6A + 150 = 420, which simplifies to 6A = 270, hence A = 45 minutes

Thus, Plan A lasts for 45 minutes and Plan B lasts for 30 minutes.

Other Questions

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