Answer:
72
Step-by-step explanation:
Which is the equation of a hyperbola centered at the origin with focus (-3,0) and vertex (-2,0)
Main answer:[tex]x^{2}[/tex]/4 - [tex]y^{2}[/tex]/5=1
Definition of Hyperbola=a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.
Formula=[tex](x-x1)^{2}[/tex]/[tex]a^{2}[/tex] - [tex](y-y1)^{2}[/tex]/[tex]b^{2}[/tex]=1
Given,
origin o(0,0) , focus s(-3,0) , vertex v(-2,0)
and , x1=0, y1=0
then, equation of hyperbola becomes= [tex]x^{2}[/tex]/[tex]a^{2}[/tex]-[tex]y^{2}[/tex]/[tex]b^{2}[/tex]=1
a is the distance between center and the vertex,
distance between o and v = 2
c is the distance between center and the focus,
distance between o and s =3
[tex]a^{2}[/tex]+[tex]b^{2}[/tex]=[tex]c^{2}[/tex]
4+[tex]b^{2}[/tex]=9
[tex]b^{2}[/tex]=5
Then the equation of hyperbola becomes=[tex]x^{2}[/tex]/4 -[tex]y{2}[/tex]/5=1
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y=1,5 sin(x - 2п/3) + 2
Hence , the graph of the equation is y = 1.5 sin(x - 2π/3) + 3 is given below .
In math, a graph may be outlined as a representation or a diagram that represents knowledge or values in associate degree organized manner.The points on the graph usually represent the connection between 2 or additional things.The general form of a sine function is of the form:
y = a×sin(bx − c) + d,
here the amplitude is a,
the period is 2π/|b|,
the phase shift is c/b, and
the vertical shift is d.
From the given equation we have,
The amplitude, a = 1.5
The period, = 2π/|1| = 2π
The phase shift = (2π/3)/1 = 2π/3
And the vertical shift is d = 2
The given equation can be graphed using the amplitude, period, phase shift, vertical shift, and points.
Refer to the attached image(table) for the points to plot the graph.
Refer to the attached image(sine_graph) for the graph of this equation.
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Disclaimer:
The question is not complete.
Assume the following to answer this question.
Graph of the equation: y = 1.5 sin(x - 2π/3) + 3
Let q = a / b and r = c / d be two rational numbers written in lowest terms. Let s = q + r and s = e / f be written in lowest terms. Assume that is not 0. Prove or disprove the following two statements. A.) If b and d are odd, then f is odd. B.) If b and d are even, then f is even.
Both the statements are true.
q = a/b and r = c/d.s = q + rs = a/b + c/ds = (ad + bc)/bde/f = (ad + bc)/bde = ad + bc and f = bda) If b and d are odd, we know that the product of two odd numbers is always odd, so f = b*d is odd.We can prove this because b*d = b*(d-1+1)b*(d-1+1) = b*(d-1) + bSince d is odd, d-1 is even, and therefore b*(d-1) is even. Since b is odd and the sum of an odd number and an even number is always odd, the above product is odd.b) If b and d are even, we know that the product of two even numbers is even, and therefore f = b*d is even.To learn more about numbers, visit :
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how do you find the perimeter on a coordinate plane
Answer: You draw the shape on the coordinate plan and then you can count the number of unit squares
Step-by-step explanation:
Please answer question 1 in the picture, I will mark brainliest
Answer:
B,
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
What can you multiply 4 by to get 120?
Answer:30
Step-by-step explanation:
30+30+30+30 just do 120/4
15. Isabel made the following graph to show
the daily share price for Company XYZ.
What was the change in the price from
Monday to Friday?
The change in the price from Monday to Friday is $0.75
How to determine what was the change in the price from Monday to Friday?The graph that completes the question is added as an attachment
From the attachment, we have:
Monday = $0.75
Friday = $1.50
There are 5 days between Monday and Friday
So, we have the change in the price from Monday to Friday to be
Change = Friday - Monday
This gives
Change = $1.50 - $0.75
Evaluate
Change = $0.75
Hence, the change in the price from Monday to Friday is $0.75
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A test consists of 100 multiple choice questions, each with five possible
answers, only one of which is correct. A student randomly guesses at all
100 questions.
Use the Mean And Standard deviation to determine how many questions correct we could usually expect from a student who randomly guesses at all 100 questions.
Mean = 20; standard deviation = 4;
Let x be the success of receiving the right response.
The total number of trials in this case is 100.
The likelihood of receiving the right response is p = 1/5.
In light of the average number of correct answer;
μₓ = np
μₓ = 100 * (1/5);
μₓ = 20;
The standard deviation is now; σ = √(n)(p)(1 - p)
σ = √(100)(1/5)(4/5)
σ = 4
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12. A summer soccer camp ordered a total of 84 soccer balls and t-shirts for the season. Soccer balls cost $25 each and t-shirts cost $9.50 each. If they payed $1,046 total for the purchase, how many of each item was ordered?
Answer:
16 Soccer balls
68 T-shirts
Step-by-step explanation:
Given information:
Total order = 84 itemsCost of a soccer ball = $25Cost of a t-shirt = $9.50Total bill = $1,046Define the variables:
Let x = the number of soccer balls ordered.Let y = the number of t-shirts ordered.Create two equations from the given information:
[tex]\textsf{Equation 1}: \quad x + y = 84[/tex]
[tex]\textsf{Equation 2}: \quad 25x+9.5y=1046[/tex]
Rewrite Equation 1 to make y the subject:
[tex]\implies y=84-x[/tex]
Substitute this into Equation 2 and solve for x:
[tex]\implies 25x+9.5(84-x)=1046[/tex]
[tex]\implies 25x+798-9.5x=1046[/tex]
[tex]\implies 15.5x+798=1046[/tex]
[tex]\implies 15.5x=248[/tex]
[tex]\implies x=16[/tex]
Substitute the found value of x into the rewritten form of Equation 1 and solve for y:
[tex]\implies y=84-16[/tex]
[tex]\implies y=68[/tex]
Solution
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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an (x, y) point. y ==2x² - 24r – 56
The solution of the given equation y ==2x² - 24r – 56 :
(6 , -128)
What is graphing technology?Graph technology aids in the discovery of unknown links in data that cannot be detected or examined using traditional methods. When the broad term graph is introduced as both a topic, it frequently blurs three distinct topics: graph theory, graph analytics, and graph data management.
Why is graphing useful?Graphs and charts are useful visual tools because they deliver information quickly and readily. It is hardly surprising, then, that graphs are widely utilized in print and electronic media. Data can be easier understood when displayed as a graph rather than a table since the graph can illustrate a pattern or comparison.
According to the given equation:y =2x² - 24x – 56
Solving for :
Parabola equation in polynomial form
ax² + bx + c for x = -b/(2a)
a = 2
b = -24
c = -56.
on solving we get
= -(- 24)/2* 2
= 6
The value of x = 6
putting the value of x to get y:
2x² - 24x – 56
2(6)² - 24(6) – 56
-128
the value of y = -128.
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Evaluate [tex]8^{10/}[/tex][tex]8^{2}[/tex] using the quotient of exponents property.
Answer:
16777216
Step-by-step explanation:
1) [tex]\frac{8^{10} }{8^2} = 8^{10-2}[/tex]
2) [tex]8^{10-2} = 8^8[/tex]
3) [tex]8^8[/tex] = 16777216
Find the value of X NEED HELP YRGENTLY
Answer:
x = 11°
Step-by-step explanation:
You want to know the value of x given a triangle with exterior angles 147°, 4x, and an interior angle of x at the third vertex.
SetupThe exterior angle of the triangle at B is the supplement of x: 180°-x. The sum of the exterior angles of a polygon is 360°, so we have ...
147° +4x +180° -x = 360°
SolutionCollecting terms, we have ...
327° +3x = 360°
3x = 33° . . . . . . . . . subtract 327°
x = 11° . . . . . . . . . . divide by x
The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x=3.
x=5, y=-4
an equation is y=___
When x=3, y=___
Show work
The equation is y = ₋20/x and when x = 3 then y = ₋ 6.6 .
Given x and y vary inversely.
The relationships between variables that are expressed as y = k/x, where x and y are two variables and k is a constant value, are known as inverse variation. According to this statement, if the value of one item rises, the value of the other quantity falls.
the value of x is = 3, we need to find the value of y.
then when x = 5 and y = ₋4
If y varies inversely as x then:
x × y = k (for some constant c)
If (x,y) = (5,₋4) then:
5 × ₋4 = k
₋20 = k
Therefore, xy = ₋20
then, y = ₋20/x ; is the equation of y.
when x = 3, then:
y = ₋20/3 or y = 6.6
Hence we get the required equation of y and the value of when x = 3 as y=₋20/x and y = ₋20/3 or y = 6.6
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A state park has an area of 112 acres. The table shows the estimated park populations for several animals. Find the population density in animals per acre for each animal?
Animal-Population
otter-35
raccoon-186
fox-9
bobcat-3
The population density of otter, raccoon, fox and bobcat is 0.3125, 1.66, 0.0803 and 0.0267 per acre
Total park area of the state park = 112 acres
Number of Otter = 35
Number of Raccoon = 186
Number of Fox = 9
Number of Bobcat = 3
The formula of population density is given by:
Population Density = Number of animals/Area of land
Population density of Otter in the park = 35/112 = 0.3125 Otter per acre
Population density of raccoon in the park = 186/112 = 1.66 Raccoon per acre
Population density of fox in the park = 9/112 = 0.0803 Fox per acre
Population density of bobcat in the park= 3/112 = 0.0267 bobcat per acre
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What happens to matter when it is an closed system.
Answer:
In thermodynamics, a closed system can exchange energy (as heat or work) but not matter, with its surroundings. An isolated system cannot exchange any heat, work, or matter with the surroundings, while an open system can exchange energy and matter.
Select the expression that are equivalent to -3(g+2)
Answer:
Step-by-step explanation:
-3g-6
- 4/7 + 2/7x - 14 + 4/7
Answer: 2x/7 -14
Step-by-step explanation:
- 4/7 + 2/7x - 14 + 4/7=
2/7x - 14 + 4/7 - 4/7=
2/7x - 14 = 2x/7 - 14
If T is the midpoint of SU what are ST, TU, and SU?
Answer:
Step-by-step explanation:
ST=SU
5x=3x+32
5x-3x=32
2x=32
x=32/2=16
ST=5×16=80
TU=80
SU=2×80=160
A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The
function f(x)-- 5 represents the remaining time in minutes needed to fill the tank. How is the graph of the pare
100
-
X
function f(x)-
-
100
transformed to create the graph of the function f(x)-- X
-5?
The function f(x)-- 5 represents the remaining time in minutes needed to fill the tank in the graph of the pare
Answer:
- Vertically stretching the parent function [tex]f(x) = \frac{1}{x}[/tex] .- A 5 unit right shift of the parent function [tex]f(x) = \frac{100}{x-5}[/tex] .Here are some function transformations:
1. The function is moved up by "k" units if [tex]f(x) + k[/tex].
2. The function is moved down "k" units if [tex]f(x) - k[/tex].
3. The function is moved "k" units to the right if [tex]f(x) - k\\[/tex] .
4. If [tex]f(x) + k[/tex], the function is "k" units to the left.
5. If [tex]bf(x)[/tex] and b>1, the function is b times more vertically stretched.
6. In the event that [tex]bf(x)[/tex] and 0<b<1 the function is vertically compressed by a factor of "b".
The following parent function is provided by the question:
[tex]f(x) = \frac{1}{x}[/tex] .We also know that the transformed function, which denotes the number of minutes still required to fill the tank, is:
[tex]f(x) = \frac{100}{x-5}[/tex] .Therefore, based on the transformations previously described, we can determine that the following produces the graph of the transformed function:
Answer:
- Vertically stretching the parent function [tex]f(x) = \frac{1}{x}[/tex] .- A 5 unit right shift of the parent function [tex]f(x) = \frac{100}{x-5}[/tex] .To learn more about graph please click on the link:
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The complete exercise is: " A 100 gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The function [tex]f(x) = \frac{100}{x-5}[/tex] represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function [tex]f(x) = \frac{1}{x}[/tex] transformed to create the graph of [tex]f(x) = \frac{100}{x-5}[/tex] ?"
Round 249798.828806 to the nearest ten
Answer:
249798.8
Hope this helps! <3
will mark u brainliest
Find the difference between 8.72 and 0.872
Answer:
Step-by-step explanation:
Find the difference between 8.72 and 0.872. This just means to subtract 0.872 from 8.72. [tex]8.72-0.872=7.848[/tex]
e table shows ordered pairs of the function . What is the value of y when ? A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 1, 1, 4, 8, 10. The second column is labeled y with entries 14, 10, 6, 0, question mark, negative 12. –20 –8 8 48
y = -8.
An ordered pair is a composition of the x coordinate and the y coordinate, having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension.
Ordered pairs are often used to represent two variables. When we write (x, y) = (7, - 2), we mean x = 7 and y = - 2. The number which corresponds to the value of x is called the x-coordinate and the number which corresponds to the value of y is called the y-coordinate.
see attachment for the table
we observe from the given table that
As x increases by 2, y decreases by 4
As x decreases by 2, y increases by 4
for example x = 10, y = -12
when x decreases by 2 (to 8), the value of y will increase by 4 (to -8).
Hence, the value of y when x = 8 is -8
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How to set up equation
Answer:
To set up an equation, you must first see what the question is looking for.
Hope this helps :)
Answer:
Basic Steps to Setting Up EquationsDetermine what the question is asking. Write down the relevant information in simple statements. Assign symbols to unknown values that need to be found. Determine how the statements relate to each other mathematically.
Step-by-step explanation:
if right mark as brainliest5/6 divided by 3/5 =
A. 18/25
B. -25/18
C. 25/18
D. -18/25
Answer:
5/6*5/3
25/18
so the answer is 25/18
Find the inverse of the linear function
Answer:
D [tex]y = - \frac{1}{4} x - \frac{1}{4} [/tex]
Step-by-step explanation:
See attached image for explanationdoes anyone know how to solve this pre cal question Im super confused
Answer:
f(-3) = 3*-3 + 4 = -9 + 4 = -5
f(3) = 2*3 - 2 = 6 - 2 = 4
f(0) = 2*0 - 2 = 0 - 2 = -2
Not sure how to solve this problem
Answer:
98
Step-by-step explanation:
For every 1 true or false question, there are 2 answers
so that means, it would mean you could do
7 x 7 = 49
then do 49 x 2 =
98
the reason you would do this is that you want to find all the possible answers chances.
Suppose the geographic area of Los Angeles County is 4,751 square miles. If the state of California has an
area of 1.637 x 105 square miles, that means that it would take approximately 35 Los Angeles Counties
to make up the state of California. As of 2013, the population of Los Angeles County was 1 x 107 people.
If the population were proportional to area, what would be the population of the state of California?
Answer:
go get smart and stop cheating on online websites
Step-by-step explanation:
Sherman has 3 cats and 2 dogs. He wants to buy a toy for eeach of his pets. Sherman has $22 dollars to spend on pet toys. How much can he spend on each pet? Write your answer as a fraction and as amount in dollars and cents.
Answer:
22/5
4 2/5
$4.40
Step-by-step explanation:
Answer:
4 4/10
Step-by-step explanation:
He has 5 pets in all (3 cats, 2 dogs)
Divide 22 with 5
22/5 = 4.4
He can spend $4.40, or in fraction form:
4 4/10 (Mixed fraction)