The equation of the hyperbola is,
(x/12)² - 4y²/(527) = 1
The standard equation of the hyperbola is
(x/a)² - (y/b)² = 1
Here (a, 0) and (-a, 0) are vertices and asymptotes y = ± √(b/a)x
Foci are (c, 0) & (-c, 0)
Then a² + b² = c²
Here we have to give that.,
2a = 24
a = 12
And 2c = 7
c = 7/2
Therefore a = 12 and c = 3.5
Substituting a and c in Pythagorean identity;
b² = 527/4
Then, the equation of the hyperbola is
(x/12)² - 4y²/(527) = 1
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We have b = 0, which implies that the foci coincide with the vertices, making the hyperbola a degenerate case. In this scenario, the equation of the border would be a vertical line passing through the vertices/foci, given by the equation x = ±a.
To find the equation of the hyperbolic border created by the shadow on the wall, we can start by understanding the properties of a hyperbola. A hyperbola is defined as the set of all points such that the difference of the distances from any point on the hyperbola to two fixed points, called the foci, is constant.
Let's label the vertices of the hyperbola as A and B, and the foci as F1 and F2. The distance between the vertices is given as 2a inches, and the foci are located at a distance c inches from the vertices.
Using the given information, we can find the value of a and c. Since the center of the hyperbola is at the origin, the coordinates of the vertices are (±a, 0), and the coordinates of the foci are (±c, 0).
The distance between the foci is given by the equation:
c = √(a^2 + b^2)
We know that the distance between the foci is given as 2c inches, so:
2c = 2√(a^2 + b^2)
Since c is given as a distance from the vertices, we can substitute c = a - b to simplify the equation:
2(a - b) = 2√(a^2 + b^2)
Squaring both sides to eliminate the square root:
4(a - b)^2 = 4(a^2 + b^2)
Expanding the equation:
4(a^2 - 2ab + b^2) = 4a^2 + 4b^2
Simplifying the equation:
4a^2 - 8ab + 4b^2 = 4a^2 + 4b^2
Canceling out the common terms:
-8ab = 0
Dividing by -8:
ab = 0
This implies that either a = 0 or b = 0. However, since a represents the distance between the vertices and b represents the distance between the foci and vertices, we can rule out a = 0 as it would result in a degenerate hyperbola.
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Step by step please help answer.
The diameter of a circular reservoir is 840 feet. To walk around the reservoir, you would walk approximately how far? (Use tt = 22/7.)
(1) 267 ft
(2) 2,640 ft
(3) 2,800 ft
(4) 18,480 ft
(5) Not enough information is given.
Answer:
(2) 2,640 ft
Step-by-step explanation:
I'm going to assume that in this question, you are walking 1 full circle around the reservoir. That would mean you need to calculate the circumference of the circular reservoir.
The circumference formula is:
C = ⫪d
C stands for Circumference
d stands for diameter
I will use 22/7 instead of pi, so the formula looks more like this:
C = (22/7)(d)
The diameter is 840 feet, so we will substitute the variable d with 840:
C = (22/7)(840)
You can plug this part into the calculator, but by hand, it'll look something like this:
(22/7)*840 = (22*840)/7
18,480/7 = 2.640
Hope it helps (●'◡'●)
What is each of the four sections created by the intersecting lines called?
Answer:
Quadrants
Step-by-step explanation:
When two lines intersect such that they are perpendicular to each other, then quadrants are said to be formed. So that a given space would be divided into four quadrants when two perpendicular lines are drawn on it.
Each section which is called quadrant is at right angle to one another. So that the addition of their angles at the meeting point is the sum of four right angles i.e [tex]360^{o}[/tex]. Thus each of the four sections created by the intersecting lines is called a quadrant.
The following data was obtained from 32 people aged 25-29 who were asked how many hours of TV they watched per week.
4,2,8,9,4,5,10,11,7,8,3,4,10,3,8,5,1,7,0,4,3,2,2,1,1,0,2,3,5,2,1,1.
Group the data in intervals and record the frequency of each interval as well as the cumulative frequency and relative frequency. Make a table showing this information.
Graph the data using frequency histogram.
Graph the data using a cumulative frequency chart.
5/4 hour = __ minutes
Answer:
hour= 1.25
MINUTES ANSWER= 75 minutes
Step-by-step explanation:
hope that helps>3
Answer:
5/4 hour= 75 minutes
--------------------------------
[tex]\textbf{HOPE IT HELPS}[/tex]
[tex]\textbf{HAVE A GREAT DAY!!}[/tex]
1. What is the area of the figure below? (1 point)
5 in.
3 in.
12 in
O 18 in.2
O 30 in.2
O 36 in.2
O 60 in.2
Answer: 36in2
Step-by-step explanation:
A= base *height
=12*3
=36
The Area of the figure is 36 in².
What is Area of parallelogram?The area of a parallelogram refers to the total number of unit squares that can fit into it and it is measured in square units (like cm2, m2, in2, etc). It is the region enclosed or encompassed by a parallelogram in two-dimensional space.
two equal, opposite sides,two intersecting and non-equal diagonals, andopposite angles that are equalThe area of a parallelogram can be calculated by multiplying its base with the altitude. The base and altitude of a parallelogram are perpendicular to each other. The formula to calculate the area of a parallelogram can thus be given as,
Area of parallelogram = b × h square units
where,
b is the length of the base
h is the height or altitude
Given:
base= 12 in
height= 3 in
Area of parallelogram,
= base * height
=12* 3
= 36 in²
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Jimmy thought he had purchased 7 folders, but purchased 6. What was his percent error?
Answer:
Step-by-step explanation:
Percent Error = | Actual Yield-Theoretical/ Theoretical Yield | *100%
Error= |-1/7|*100%= 14.29%
Identify the dependent and independent variable in y = 12x - 30.
Step-by-step explanation:
guess
Dependent variable: y and Independent variable: x
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The graphs below have the same shape. Complete the equation of the blue
graph. Enter exponents using the caret (-); for example, enter y as x^3. Do
not include "G(x) =" in your answer.
Answer:
The graphs below have the same shape. What is the equation of the blue graph? A. G(x) = (x + 3)^3 B. G(x) = x^3 + 3 C. G(x) = x^3 - 3 D. G(x) = (x - 3)^3
The blue graph is a horizontal shift to the left by 3 units of F(x) = x³.
G(x) = (x + 3)³.
What is translation?In mathematics, translation is the process of moving an object from one position to another without changing its shape, size, or orientation.
It involves sliding the object in a particular direction by a certain distance.
We have,
From the graph, the blue graph is G(x) = (x + 3)³.
The function f(x) = (x + 3)³ is a transformation of the function f(x) = x³.
Specifically, it is a horizontal shift to the left by 3 units.
To see why,
Let's consider the effect of replacing x with x + 3 in the original function f(x) = x³.
f(x + 3) = (x + 3)³
Notice that f(x + 3) is equal to f(x) translated horizontally to the left by 3 units.
For example, when x = 0, we have:
f(0) = 0³ = 0
f(0 + 3) = 3³ = 27
So the point (0, 0) on the graph of f(x) = x³ is transformed to the point
(-3, 27) on the graph of f(x) = (x + 3)³.
Similarly, we can see that every point on the graph of f(x) = x³ is shifted horizontally to the left by 3 units to obtain the graph of f(x) = (x + 3)³.
Therefore,
The blue graph is G(x) = (x + 3)³.
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rewrite 1/6 and 2/11 so they have a common denominator then use <, =, or > to order
Answer:
1/6 < 2/11
Step-by-step explanation:
1/6 = 2/12
2/11 >2/12
So that means 1/6 < 2/11
Answer: 1/6 < 2/11
This is the same as saying 11/66 < 12/66
===========================================================
Explanation:
1/6 is the same as 11/66 when multiplying top and bottom by 11.
2/11 is the same as 12/66 when multiplying top and bottom by 6.
The 6 and 11 multipliers are from the original denominators (just swapped).
We can see that 11/66 is smaller than 12/66, simply because 11 < 12, so that means 1/6 is smaller than 2/11
-----------------
Here's one way you could list out the steps
11 < 12
11/66 < 12/66
1/6 < 2/11
------------------
Here's another way to list out the steps. First assume that 1/6 and 2/11 are equal. Cross multiplication then leads to
1/6 = 2/11
1*11 = 6*2
11 = 12
Which is false. But we can fix this by replacing every equal sign with a less than sign
1/6 < 2/11
1*11 < 6*2
11 < 12
---------------------
Yet another way to see which is smaller is to use your calculator or long division to find the decimal form of each value
1/6 = 0.1667 approximately
2/11 = 0.1818 approximately
We see that 0.1667 is smaller than 0.1818, which must mean 1/6 is smaller than 2/11.
The sum of two numbers is 44 . One number is 3 times as large as the other. What are the numbers?
Answer:
11 and 33
Step-by-step explanation:
The the smaller number be [tex]x[/tex]. Since the other number is 3 times as large as the other, we can represent the large number as [tex]3x[/tex]. Because they add up to 44, we have the following equation:
[tex]x+3x=44[/tex]
Combine like terms:
[tex]4x=44[/tex]
Divide both sides by 4:
[tex]x=\frac{44}{4}=\boxed{11}[/tex]
Substitute [tex]x=11[/tex] into [tex]3x[/tex] to find the larger number:
[tex]11\cdot 3=\boxed{33}[/tex]
Therefore, the two numbers are 11 and 33.
Researchers study the relationship between interpersonal violence and health in college age women. The selected an alpha of 0.05. The researchers examined the average score on a psychological distress scale and compared the score for abused versus non abused women. A p value of 0.016 is reported. Based on this information, you know:
Answer:
There exists a relationship between interpersonal violence and health.
Step-by-step explanation:
The relationship between interpersonal violence and health :
The null hypothesis will be ; the is no relationship between interpersonal violence and health while the alternative will negate the Null ;
If no relationship exists, correlation Coefficient = 0 and if a relationship exists, then correlation Coefficient is not = 0
H0 : ρ = 0
H1 : ρ ≠ 0
α = 0.05
Reported Pvalue = 0.016
Decison region :
Reject H0 ; If Pvalue < α
Therefore, Since Pvalue < α ; we reject H0 and conclude that there exists a relationship between interpersonal violence and health.
You may recall that the area of a rectangle is A=L⋅W, where W is the width and L is the length.
Suppose that the length of a rectangle is 3 times the width. If the area is 300 square feet, then what is the width of the rectangle, in feet?
Do not type the units in your answer.
Answer:
The width is 10 feet.
Step-by-step explanation:
We know that the area of a rectangle is given by the formula:
[tex]\displaystyle A=L\cdot W[/tex]
Where L is the length and W is the width.
We are given that the length of the rectangle is three times the width. In other words:
[tex]L=3W[/tex]
The total area is 300 square feet. And we want to determine the width of the rectangle.
So, substitute 300 for A and 3W for L:
[tex](300)=(3W)\cdot W[/tex]
Multiply:
[tex]300=3W^2[/tex]
Divide both sides by three:
[tex]W^2=100[/tex]
And take the principal square root of both sides. So:
[tex]W=10[/tex]
Thus, the width of the rectangle is 10 feet.
what graph shows the solution to the equation below log3(x+2)=1
Answer:
The solution to the equation log3(x+2)=1 is given by x=1
Step-by-step explanation:
We are given that
[tex]log_3(x+2)=1[/tex]
We have to find the graph which shows the solution to the equation log3(x+2)=1.
[tex]log_3(x+2)=1[/tex]
[tex]x+2=3^1[/tex]
Using the formula
[tex]lnx=y\implies x=e^y[/tex]
[tex]x+2=3[/tex]
[tex]x=3-2[/tex]
[tex]x=1[/tex]
The domain of the function f(x)=-x3+4
Answer:
Domain= {x:x £|R}
|R=any real number
A board is 87 cm in length and must be cut so that one piece is 21 cm longer than the other piece. Find the length of each piece. Round your answers to the nearest centimeter, if necessary. * + 21?
Thank you for answer Yey can I answer in my subject
Plzz prove this tomorrow is my test plzz help me
Step-by-step explanation:
this is the correct answer for the question
find the value of...
Answer:
1
Step-by-step explanation:
tan(1)tan(2)....tan(89)=?
Recall tan(90-x)=cot(x) and cot(x)tan(x)=1.
tan(89)=tan(90-1)=cot(1)
tan(88)=tan(90-2)=cot(2)
tan(87)=tan(90-3)=cot(3)
...
tan(46)=tan(90-44)=cot(44)
tan(45)=tan(90-45)=cot(45)
So we can replace the last half of the factors with cotangent of the angles in the first half.
The only one that doesn't get a partner is the exact middle factor which is tan(45).
So this is whar we have:
tan(1)tan(2)tan(3)....tan(45)....cot(3)cot(2)cot(1)
So you should see that cot(1)tan(1)=1 and cot(2)tan(2)=1 and so on....
So the product equals tan(45) and tan(45)=1 using unit circle.
Indicate the method you would use to prove the triangles congruent. If no
method applies, enter "none."
O SSS
k O SAS
O ASA
© None
Step-by-step explanation:
I suspect we don't see the full information for the problem here.
all listed 3 methods are typically used to prove that triangles are congruent (= when turned to have the same orientation, they would simply cover each other completely - no overhanging parts from either triangle).
I guess there is a diagram with 2 triangles and what is known about them.
and since we cannot see them, we cannot tell you which method would apply here.
just remember
SSS means all 3 sides of one triangle are exactly the same as the 3 sides of the other triangle. if you know the lengths of all 3 sides, there is only one triangle you can create. you can only orient it differently.
SAS means two sides and the enclosed angle are the same. again, only one triangle can be created with that information.
ASA means one side and the 2 angles at the end points of that side are known. again, only one triangle can be created with that information.
Suppose X has a normal distribution with mean 10.0 and standard deviation 5.0 what is the P(2.0
Answer:
what r u answers picks
Step-by-step explanation:
cant answer with out of t
Lisa, an experienced shipping clerk, can fill a certain order in 9 hours. Felipe, a new clerk, needs 10 hours to do the same job. Working together, how long will it take them to fill the order?
Answer:
9.5hrs
Step-by-step explanation:
since they are working together you have to take the average time since is the same order
PLZZZ HELPP EVEN IF I HAVE TO WASTE MY POINTS JUST HELP ME
Answer:
soln,
x=63°
Step-by-step explanation:
yea , 63° is the answer you asked
At what x value does the function given below have a hole?
f(x)=x+3/x2−9
Answer:
hole at x=-3
Step-by-step explanation:
The hole is the discontinuity that exists after the fraction reduces. (Still doesn't exist for original of course)
The discontinuities for this expression is when the bottom is 0. x^2-9=0 when x=3 or x=-3 since squaring either and then subtracting 9 would lead to 0.
So anyways we have (x+3)/(x^2-9)
= (x+3)/((x-3)(x+3))
Now this equals 1/(x-3) with a hole at x=-3 since the x+3 factor was "cancelled" from the denominator.
The distribution of the number of apples trees a farmer can plant each day is bell-shaped and has a mean of 62 and a standard deviation of 8. Use the empirical rule to help you answer the following. What is the approximate percentage of trees planted between 38 and 68
Answer:
The empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 62, standard deviation of 8.
What is the approximate percentage of trees planted between 38 and 86?
38 = 62 - 3*8
86 = 62 + 3*8
So within 3 standard deviations of the mean, which, by the empirical rule, the approximate percentage of trees planted between 38 and 68 is 99.7%.
How many boxes could you stack safely on a pallet if the pallet is 5 feet deep, five feet across, every box is 1 x 1 and the maximum safe stacking height is 5 boxes? *
Answer:
125 boxes
Step-by-step explanation:
5*5*5
The graph of y=x^3 is transformed as shown in the graph below. Which equation represents the transformed function?
y = x cubed minus 4
y = (x minus 4) cubed
y = (negative x minus 4) cubed
y = (negative x) cubed minus 4
Answer:
y = (-x)^3 - 4
Step-by-step explanation:
Ok, for the function:
y = x^3
When x = 0, we have:
y = 0^3 = 0
So the original graph passes through the point (0, 0)
If we look at the given graph, we can see that the y-intercept (the value of y when x = 0) is:
y = -4
So, this is the graph of y = x^3 moved down 4 units.
You can also see that the graph goes downward as x increases (and up as x decreases) while for the function:
y = x^3
as x increases, we should see that y also increases.
Then we have a reflection across the x-axis.
Ok, now let's describe a vertical shift.
For a general function f(x), a vertical shift of N units is written as:
g(x) = f(x) + N
if N is positive, the shift is upwards
if N is negative, the shift is downwards.
And for a function f(x), a reflection across the x-axis is written as:
g(x) = - f(x)
Here we first apply the reflection across the x-axis, so we get:
g(x) = -f(x)
now we apply the shift 4 units downwards
g(x) = - f(x) - 4
replacing f(x) by our function, x^3
we get:
g(x) = -x^3 - 4
And because of the odd power, we can write:
-x^3 = (-x)^3
Then the function is:
g(x) = (-x)^3 - 4
The correct option is the last one.
y = (-x)^3 - 4
When two parallel lines are cut by a transversal, argles A and B are alternate Interior angles that each measure 105°. What is the measure of
each of the other alternate interior angles
Answer:
The angle for the other interior angel is 75°, all you have to do is subtract 180, from the 105
Step-by-step explanation:
DE is tangent to Circle C at point D.
What is the measure of
Enter your answer in the box.
Answer:
39°
Step-by-step explanation:
A radius of a circle (segment CD) drawn to the point of tangency (D) intersects the tangent (line DE) at a 90-deg angle.
That makes m<D = 90.
m<D + m<C + m<E = 180
90 + 51 + m<E = 180
m<E = 39
please help me i begging.
Answer:
The two equivalent expressions are 6(x − y) and 6x − 6y.
Step-by-step explanation:
Solve using suitable arrangement and properties.
a) 417×1002
b) 4×573×25
c) 8312+284+788+716
d) 125×44+56×125
Answer:
Step-by-step explanation:
A- 417 × 1002
= 417 × (1000+2)
= 417× 1000+ 417×2
= 417000+ 834
= 417834
B- 4× 573×25
= 4× 25+ 573
= 100+ 573
= 57300
C- 8312+284+788+716
= (8312+284) + (788+716)
= 8596+ 1504
= 10,100
D- 125×44+56×125
= 125× (44+56)
= 125× 100
= 12500
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It took me alot of time to type sorry for that...
Bob had 10 more cars than Paul. Paul had 15 cars.
Answer:
Bob had 25 cars
Step-by-step explanation:
10+15=25
