The equation of the hyperbola with and vertices (1, 6) and (1, -12) and
asymptotes y = 3x - 6 and y=-3x is [tex]$\frac{(y+3)^2}{9}-\frac{(x-1)^2}{81}=1$[/tex]
The answer provided below has been developed in a clear step by step manner.
Given asymptotes [tex]$\mathrm{y}=3 \mathrm{x}-6$[/tex] and [tex]$\mathrm{y}=-3 \mathrm{x}$[/tex] and
vertices (1,6) and (1,-12)
What is hyperbola ?
Standard hyperbola through origin when values of x for the vertices are equal. [tex]$\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$[/tex]
Now solve the asymptotes [tex]$\mathrm{y}=3 \mathrm{x}-6$[/tex] and [tex]$\mathrm{y}=-3 \mathrm{x}$[/tex]
After solving we get [tex]$\mathrm{x}=1 \quad$[/tex]and [tex]$\quad \mathrm{y}=-3$[/tex]centre =(1,-3)
translation in form of [tex]$\mathrm{x}_1$[/tex] and [tex]$\mathrm{y}_1$[/tex]
[tex]$\mathrm{x}_1=\mathrm{x}-1 \quad$[/tex] and [tex]$\quad \mathrm{y}_1=\mathrm{y}+3$[/tex]
Distance from vertices (1,6) and (1,-12) to centre (1,-3) is [tex]$9=\mathrm{a}$[/tex]vertical symmetry the asymptotes have a slope [tex]$=\pm 3=a / b$[/tex] so [tex]$\mathrm{b}=\frac{9}{3} \Rightarrow \mathrm{b}^2=9$[/tex]
Put all the values of a and b into original equation
[tex]$$\begin{aligned}& x_1=x-1 \quad \text { and } \quad y_1=y+3 \\& \Rightarrow \frac{(y+3)^2}{3^2}-\frac{(x-1)^2}{9^2}=1 \\& \Rightarrow \frac{(y+3)^2}{9}-\frac{(x-1)^2}{81}=1\end{aligned}$$[/tex]
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function rule to find f(11).
the next question is more point go check it out after you answer this question!!!!!
The solution for f(11) in the function when the function f(x) = 12|x + 8| is 228
How to determine the solution for f(x) in the function?From the question, we have the following equation that can be used in our computation:
f(x) = 12|x + 8|
The above equation is an absolute value equation
An absolute value equation has the following representation
f(x) = a|x - h| + k
So, we have the following representation
f(x) = 12|x + 8|
Also from the question, we have
f(11)
This means that the value of x is 11, and we calculate f(x) when x = 11
Substitute the known values in the above equation, so, we have the following representation
f(11) = 12|x + 8|
So, we have the following equation
f(11) = 12|11 + 8|
There are constants to add or subtract to both sides of the equation
Also, there are factors to multiply or divide from both sides of the equation
So, we have the following representation
f(11) = 12|19|
Solving further, we have
f(11) = 12 * 19
Evaluate the products
f(11) = 228
Hence, the solution is 228
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Two fair number cubes have faces labeled with the numbers 1 through 6. The two cubes will be rolled simultaneously. What is the probability that at least one of the cubes will have the face labeled 5 showing and that the sum of the showing faces will be greater than 8 ?.
The probability that at least one of the cubes will have the face labeled 5 showing and that the sum of the showing faces will be greater than 8 is 5/36.
What is the probability?A probability is a numerical representation of the possibility or chance that a specific event will take place. Probabilities can be written as percentage between 0 and 1.
Number of sample spaces that are labeled 5 and display a sum more than 8 / total sample space gives the likelihood that at least one of the cubes will have the face labeled 5 showing and that the sum of the faces showing will be greater than 8.
When two cubes are rolled, the total sample space is 36.
The sample space that is labelled 5 and has a sum greater than 5 are: (4,5) , (5, 4) , (5, 5), (5, 6) , (6,5) = 5
The probability = 5/36
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In Michael’s closet he can choose from a yellow, green, or orange shirt, navy or gray shorts, and tennis shoes or sandals. Create a table to represent the various clothing options.
The table is attached below.
What are table entries?
Entities are gathered at tables. A group of properties makes up an entity. Each object may contain up to 252 name-value pairs for its properties.
From the information given, we can make a table to display all the options available for Michael to choose clothing options.
The table is attached as follows:
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There are 12 clothing options for Michael to choose from in his closet. By the fundamental principle of counting, the possible number of options is calculated.
What is the fundamental principle of counting?The fundamental principle of counting states that an operation/event can be performed in 'm' ways and a second operation/event can be performed in 'n' ways. Then there are (m × n) ways for the two operations to be performed together.
Calculation:It is given that,
Michael is having three shirts - yellow, green, and orange; two pairs of shorts: navy, gray and two footwear: tennis shoes and sandals.
So, we can write
the number of shirts = 3
the number of shorts = 2
the number of footwear = 2
Then, according to the fundamental principle of counting, all these are multiplied to get the total number of ways that he can wear them together.
I.e., 3 × 2 × 2 = 12
Therefore, there are 12 combinations for him to choose one among these.
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Aaliyah is going to invest in an account paying an interest rate of 5% compounded continuously. How much would Aaliyah need to invest, to the nearest hundred dollars, for the value of the account to reach $181,000 in 19 years?
Based on the given parameters, the value of the money to invest initially is $99341.383
How to determine the amount of investment?The given parameters about the compound interest are
Amount, A = $181000
Interest Rate, R = 5%
Time, t = 19 years
Number of times, n = 365 i.e. continuously
To calculate the amount, we have:
A = P + CI
Where
C = P(1 + R)^t
So, we have
A = P(1 + R)^t
This can be rewritten as
A = P(1 + R/n)^nt
Substitute the known values in the above equation
181000 = A * (1 + 5%/365)^(12*365)
So, we have
A = 181000 /[(1 + 5%/365)^(12*365)]
Evaluate the expression
A = 99341.383
Hence, the amount of the investment is $99341.383
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Rotate triangle P 90° clockwise about the point (2, -1).
54
3
2
1
-5 -4 -3 -2 -1 0
-1
2345
-4
1 2 3 4 5
P
Answer:
p=12345
Step-by-step explanation:
Answer:
see attached
Step-by-step explanation:
You want the graphed triangle rotated 90° CW about the point (2, -1).
RotationAfter rotation 90° CW, points will be as far to the south and west of the center of rotation as they are east and south in the original image. This is shown by the blue triangle in the attachment.
i need help with this question
Answer: it’s B
Step-by-step explanation: Look at the graph clearly
and you will see the value of x and y
Sam tries to draw lines of reflection through a rectangle so that the rectangle can be reflected onto itself. How many lines of reflection can sam draw? enter the answer in the box.
Therefore the solution of this question is Sam can draw 2 lines of reflection.
What is line of reflection?If a figure is reflected in a line or a point, the image and preimage are consistent. A reflection converts each point in a figure into an image along a predetermined line. Line of Reflection refers to the fixed line.
To determine the quantity of lines that will reflect a rectangle back onto itself.
Due to the fact that the line of reflection is the perpendicular bisector of the segment connecting a point with its image. The perpendicular bisector of a side must be the line of reflection if one side of the rectangle is to map to itself.
A rectangle has two distinct perpendicular bisectors of its sides, leading to two lines of reflection that map a rectangle to itself.
Therefore Sam can draw 2 lines of reflection.
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Consider the system of equations
5x+3y=30
−5x−2y=−25
Part A: Solve the system. Show your work.
_______
Part B: Use the solution to your equation to find the value of x – y. Show your work.
x−y = _____
By solving the two equations, the values of x , y and x-y are found to be 1, 25/3 and -22/3 respectively.
Given two equations are;
5x+3y=30..........(1)
−5x−2y=−25.........(2)
Now , from (2)
−5x−2y=−25
⇒ 5x +2y = 25 (multiply both sides with '-' sign)
⇒ y = [tex]\frac{(25 -5x)}{2}[/tex]
Solving the system;
substitute the above vale of y in eq (1)
5x + 3y = 30
⇒ 5x + 3 ( [tex]\frac{(25 -5x)}{2}[/tex]) = 30
⇒ 5x + ([tex]\frac{(75 - 15x)}{2}[/tex]) = 30
⇒ [tex]\frac{10x+75-15x}{2}[/tex] = 30
⇒ -5x + 75 = 60
⇒ -5x = -5
⇒ x = 1
∴ x = 1
Now substitute the value of x in (1)
5x + 3y = 30
⇒ 5 × 1 + 3y = 30
⇒ 3y = 25
⇒ y = 25/3
∴ y = 25/3
Now using the value of x and y , we can find the value of x - y
x - y = 1 -25/3 = (3 - 25)/ 3 = -22/3
∴ x - y = -22/3
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Which equation models the relationship between the two variables in the table below?
2343H
5
-7
-10
-13
y=-2z
y=-3z+2
1=-3z
IN
y=-2z-3
Answer:
2nd equation
Step-by-step explaination:
1st. -7≠-2(3)
2nd. Sastifies all
3rd. -10≠-3(4)
4th. -4≠-2(2)-3
Write an equation in slope-intercept form of the line that is parallel to the one given and passes through the given point
(1,3); y=7x+5
What is the equation for the line in slope-intercept form?
Answer:
y = -2x - 4
Step-by-step explanation:
y = mx +b is the slope intercept form of a line. The m is the slope and the b is the y intercept.
The y intercept is where the line crosses the y axis. It crosses at the point (0,-4). The -4 is where the line crosses the y axis. It is the b.
The slope is the change in y over the change in x. To go from point (0,-4) to the point (-2,0) You go up 4 units and the left 2 units. Up is positive and left is negative. 4/-2 which simplifies to -2. This is your m.
please help me i’ve got midterms and i’ve been stuck on this for like 45 minutes Dx
Answer:
f(x) = ³√(x–1) + 4
f-¹(x) = (x + 1)³ + 4
Step-by-step explanation:
i hope this helped
A polygon has vertices at (-5, 3), (-1, 3), (1, 0), and (-3, 0). Which represents a geometric translation of the give
polygon 4 units to the right and 5 units down?
Answer:
(-1, 3), (3, 3), (5, 3), (1, 0)
Step-by-step explanation:
A translation of 4 units to the right means adding 4 to every x-coordinate.
The new coordinates are:
(-1, 3), (3, 3), (5, 3), (1, 0)
can anyone help its 7th grade math
Answer:
first and second, which are the same number line
Step-by-step explanation:
250x + 300 ≥ 1,550 ( subtract 300 from both sides )
250x ≥ 1,250 ( divide both sides by 250 )
x ≥ 5
since x is greater than or equal to the number line will have a solid circle at 5, indicating x can be equal to 5.
the arrow will point to the right, indicating the values x can be greater than 5.
this solution is represented on both graph 1 and graph 2
I need help !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
a) 15
b) 270
Step-by-step explanation:
a)
(√5)² = 5
(√3)² = 3
This is due to the square root and to the power of 2 cancelling each other out if that makes sense. It's the same with (√3)²
So all you're actually doing is 5 × 3 which is 15
b)
It's basically the same except (³√9)³ is cube(d) root and to the power of 3
(³√9)³ = 9
(√30)² = 30
So you do 9 × 30 = 270
:)
Mr. Reynolds, the gym teacher, divided a class of 16 students into 2 equal teams. How many students were on the team?
Answer:
8
Step-by-step explanation:
16 divided by 2 is 8.
Answer: 8 students
Step-by-step explanation: 16/2=8
Which best describes Nosaira’s work and answer?
Her work is correct, but there is one solution rather than no solution.
Her work is correct and her interpretation of the answer is correct.
Her work is incorrect. She distributed incorrectly.
Her work is incorrect. She moved terms across the equals sign incorrectly.
Answer: A
Step-by-step explanation:
J53)
a) what i the x-coordinate of every point along thi line?
b) ue your anwer to ue part a) to write the equation of the line
The abscissa or x-coordinate of any point on Y-axis is zero.
Which line is the x-coordinate?
Two parallel lines, known as axes (pronounced AX-eez), that are perpendicular to each other make up a coordinate grid. Typically, the term "x-axis" refers to the horizontal axis. The y-axis is the common name for the vertical axis.
The ordinate and abscissa are other names for the x-axis and y-axis, respectively. These two axes can be used to find or represent any point on the coordinate plane as an ordered pair of the form (x,y).
The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.
In order to represent the equation in y-intercept (y=mx+b) form, the slope and y-intercept must be included. The slope is the ratio of the y-to-x change. Draw a sloping triangle connecting the two spots you find on the line.
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The points L(5,0) , M(-4,0) and N(5,-4) form a triangle find the perimeter of the triangle . Round your answer to the nearest tenth if necessary .
Answer:
9.1 units
Step-by-step explanation:
See diagram below ....using pythagorean theorem
James earned a total of $68 last week. He earned $48 washing cars and won x dollars in an art contest. Which equation can be used to find the number of dollars James won in the art contest?
Answer:
Step-by-step explanation:
since $68 is your total, let's use the example z=y+x
z is our total, and we know that he made a total of $68, therefore z is the number 68.
We also know that James made a total of $48 washing cars, which gives us the answer 48 as y. So in order to find x, we would need to subtract 68 and 48, which is called using the communtative property. Thsi answer would give us the remaining amount of money we do not yet know.
So 68-48= 20. therefore James made $20 at the art contest.
I need help with this geometry please i don’t understand. Just #1 please
Answer:
a) CE=PR
b) TR=FE
c) <F=<T
d) <P=<C
e) RPT=ECF
Step-by-step explanation:
in 2016, a 1952 Willie Mays rookie card from Topps sold for $478,000! Currently, a toaster may cost $25. How many toasters could you buy with the money spent on the willie Mays rookie card?
Answer: 19120 Toaster
Step-by-step explanation: We just need to take $478000 divided by 25, equal to 19120 Toaster!
find the slope of the line through (1,-1) and (6,2
Answer:3/5
Step-by-step explanation:
(y2-y1)/(x2-x1)
(2-(-1))/(6-1)=3/5
suppose the continuous random variable, x, is uniformly distributed between 2 and 10. what is the probability that x is either less than 3 or greater than 8?
The probability that x is either less than 3 or greater than 8 is 0.375 .
In the question ,
it is given that ,
a continuous random variable X , is uniformly distributed between 2 and 10 ,
So , alpha(α) = 2 and beta(β) = 10 .
the probability that x is either less than 3 or greater than 8 can be calculated by :
P(X < 3 or X > 8) = 1 - (8 - 3)/(β - α)
= 1 - (8 - 3)/(10 - 2)
= 1 - 5/8
On simplifying further ,
we get ,
= 0.375
Therefore , the probability P(X < 3 or X > 8) is = 0.375 .
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What is the radius of 6 inches
Answer:
28.27 sq. units or 9π sq.
Step-by-step explanation:
a. Prove ABD is congruent to CBD.
b. Determine whether all four triangles in the diagram are congruent.
c. Explain your reasoning.
Answer:
a. The proof is in your picture
b. Yes
c. All four triangles are congruent by the HL theorem
Step-by-step explanation:
Given AB≅CB in ∆ABC with BD⊥AC, you want to show ∆ABD≅∆CBD, and you want to know if these are congruent to ∆CEG and ∆FEG.
a. Left trianglesYour picture correctly shows a proof that ∆ABD≅∆CBD by the HL postulate.
b. Right trianglesSides CE and FE are marked congruent to each other and sides AB and CB. The altitudes BD and EG of these isosceles triangles are marked as congruent. Hence all four triangles, ∆ABD, ∆CBD, ∆CEG, and ∆FEG are congruent by the HL theorem.
c. All trianglesThe same HL theorem reasoning applies to all of the triangles.
__
Additional comment
The distance from the light to the stage is said to be the same for both lights. That would be measured perpendicular to the stage, and is the shortest such distance. We are assuming that BD and EG are those perpendicular distances, as we see no markings on the diagram indicating right angles.
help me pleaseeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!
Answer: omg never seen somthing dat complex :O
Step-by-step explanation:
Answer the question and help a brother out
Answer:
25
Step-by-step explanation:
first add the degrees: 50+30+25=105, then 180-105 is 75, 75=3s, s is 25
(im not sure completely im only in 7th grade)
is 0.04x=y proportional
i’m so lost and i really need help :’). this is 9th grade algebra
Answer:
1 and 2 are functions, 3 is not a function.
Step-by-step explanation:
One x-value can lead to one y-value. If the x-value leads to more than one y-value like #3, then the relation is not a function.
If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.