The foci and the vertices of the hyperbola are labeled.
Which equation represents the hyperbola shown in the graph?
Answer is B
Answers
The answer is B and pls mark me brainiest
The equation of the hyperbola is:
(x - 3)² / 9 - (y - 2)² / 16 = 1.
To find the equation of the hyperbola with the given foci and vertices, we need to determine the center, semi-major axis (a), and semi-minor axis (b) of the hyperbola.
The center of the hyperbola is the midpoint between the two vertices:
Center = ((3 + 3) / 2, (5 + (-1)) / 2) = (3, 2).
The distance between the center and one of the vertices gives us the semi-major axis (a):
a = distance between center and vertex = 5 - 2 = 3.
The distance between the center and one of the foci gives us the distance c (the distance from the center to the focus):
c = distance between center and focus = 7 - 2 = 5.
Now, we can find the value of b (the semi-minor axis) using the relationship between a, b, and c in a hyperbola:
c² = a² + b²
5² = 3² + b²
25 = 9 + b²
b² = 25 - 9
b² = 16
b = 4.
Now that we have the center (h, k) = (3, 2), the semi-major axis (a) = 3, and the semi-minor axis (b) = 4, we can write the equation of the hyperbola in standard form:
For a hyperbola (center at (h, k)), the equation is:
(x - h)² / a² - (y - k)² / b² = 1.
Plugging in the values:
(x - 3)² / 3² - (y - 2)² / 4² = 1.
The equation of the hyperbola is:
(x - 3)² / 9 - (y - 2)² / 16 = 1.
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Related Questions
A city library just received a grant that it can use to increase its book collection. If it currently has 1.3 million books and the grant will increase the book collection by 2%, how many books will it have in its collection?
Answers
Answer:
1,326,000 books
Step-by-step explanation:
2% of 1.3 million is 26,000
1,300,000 + 26,000 = 1,326,000
Find the surface area of the cylinder. Type an exact answer in terms of pi.
Answers
Answer:
=150.79644...cm²
~150cm²
Step-by-step explanation:
cylinder surface area = 2 pi r h + 2 pi r²
Answer:
24π cm²
Step-by-step explanation:
Radius (r) = 3 cm
Height (h) = 5 cm
Surface area of cylinder
= 2πr (h + r)
= 2 × π × 3 (5 + 3)
= π × 3 (8)
= π × 24
= 24π cm²
______
#Rosé
Hope it helps ⚜
Using the numbers 1 to 9 (inclusive), without repeating any numbers, fill in the boxes to write two equivalent equations. The top equation is written in slope-intercept form. The bottom equation is written in standard form.
Answers
1The two equivalent equations will be
1. [tex]y=\dfrac{-6}{4}x+10[/tex]
2. [tex]3x+2y=5[/tex]
What is linear equation?An equation between two variables that gives a straight line when plotted on a graph.
The required two equivalent equations are
[tex]y=\dfrac{-6}{4}x+10[/tex]
[tex]3x+2y=5[/tex]
The above equation has no repeating numbers and fulfill the criteria.
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Which best describes word choice in an academic paper? it’s the internal structure, sequence of ideas, and unity of paragraphs. it’s the transitions that connect one body paragraph to another. it’s the rhythm and flow of the language, aided by sentence variation. it’s the use of precise, rich, and colorful language to convey ideas.
Answers
The term word choice in an academic paper refers to the use of precise, rich, and colorful language to convey ideas.
What is an academic paper?
An academic paper is a research work that aims at conveying ideas to a limited group of experts in a given field. As a result of that, the structure of the paper must be such that it could be recieved by a professional auidience.
The term word choice in an academic paper refers to the use of precise, rich, and colorful language to convey ideas.
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Answer: D
Step-by-step explanation: On EDG
this is what i need help with
Answers
Answer:
It's B
Step-by-step explanation:
All you're doing is adding 1.5 each time
Hope this helps :)
What is 24/10 simplified
Answers
Answer:
2.4
Step-by-step explanation:
24 divided by 10 is equal to 2.4
Answer:
Do you want it in decimal or fraction cause heres fraction ~12/5~ and as a decimal its ~2.4~
Step-by-step explanation:
find the measure of angle R
i need help asap!
Answers
Answer: 68 degrees
Step-by-step explanation:
giving brainliest to whoever can give me the right answers :)
Answers
Answer:
The First problem is empty
The second is (-oo,3) U [6,oo)
Step-by-step explanation:
Set C is defined for all reals less than or equal to. 3.
Set D is defined for all reals greater than or equal to 6.
The First cardinal want us to find when the two Set intersects. They never intersect so that the Set is empty.
The next cardinal want us to find when the Set contains both of their subsets.
Set C can be from any negative number up to 3 inclusive.
Set D start at 6, exclusively and continues forever to thr positve. So
the Set C And Set D will be
(-oo, 3) U [6,oo)
Which Is Most Likely To Weigh 4 Tons?
A A Watermelon
B A Man
C A Clothes Dryer
D A Helicopter
(30 points)
Answers
The most likely object to weigh 4 tons will be Helicopter
The correct option is (D) Helicopter
What is ton in kg?1 ton = 1000 Kg
First, a watermelon weigh= 0.001 to 0.003 tons(i.e., 1-3 Kg)
then, A man weigh= 0.09 to 0.1 tons (i.e., 90 - 100kg)
A clothes dryer weigh= 0.07 to 0.09 tons (i.e., 70- 90 Kg)
lastly, a Helicopter weigh= 0.275- 56 tons (i.e., 275 - 56,000 Kg)
The closest is Helicopter weight 0.275- 56 tons
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Triangle 1 and Triangle 2, shown below, are similar triangles.
Which proportion can be used to find side x in Triangle 1?
A. 6/9 = x/6
B.4/6 = x/10.5
C.4/6 = 10.5/x
D. 9/4 = 6/x
Answers
Answer:
option c is the correct answer of given statement
Answer: it c
Step-by-step explanation:
what is 10 = 0.860(7) + 3.302
Answers
Hey there!
0.860(17) + 3.302 = 10
= 0.86(17) + 3.302
= 14.62 + 3.302
= 17.922
Thus, your answer is: FALSE because
17.922 ≠ 10
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Answer:
this is false btw
Step-by-step explanation:
u should give e brainiest, pls
The probability of flipping heads or tails on
2 fair coins would be considered:
Certain
Equally likely
Likely
Unlikely
Answers
Answer:
b
Step-by-step explanation:
Help pls
I need help on this
Answers
Answer:
Slope < 0 : 1 slope between 0 and1 :3
slope greater than 1 : 2 #4 has 'undefined' slope
Step-by-step explanation:
1. What is( - 1/2 + 2)
2. 4( 1/2+5/4) + (-5)
(please answer, I will mark brainliest)
:)
Answers
1)
[tex]\longrightarrow (-\dfrac{1}{2} +2)[/tex]
[tex]\longrightarrow (-\dfrac{1}{2} +\dfrac{4}{2} )[/tex]
[tex]\longrightarrow \dfrac{-1+4}{2}[/tex]
[tex]\longrightarrow \dfrac{3}{2}[/tex]
[tex]\sf \bold{\longrightarrow 1\dfrac{1}{2}}[/tex] (final answer)
2)
[tex]\longrightarrow \sf 4(\dfrac{1}{2} +\dfrac{5}{4} ) + (-5)[/tex]
[tex]\longrightarrow \sf 4(\dfrac{2}{4} +\dfrac{5}{4} ) + (-5)[/tex]
[tex]\longrightarrow \sf 4(\dfrac{7}{4} ) + (-5)[/tex]
[tex]\longrightarrow \sf 7-5[/tex]
[tex]\longrightarrow \bold{\sf 2}[/tex] (final answer)
What is the Volume of the square pyramid? (Round to the nearest tenth as needed)
Answers
base= 25 mm
height= 28 mm
to find:the volume of the square pyramid.
solution:[tex]volume = {a}^{2} \frac{h}{3} [/tex]
[tex]v = {25}^{2} \frac{28}{3} [/tex]
[tex]v = 5833.33333 {mm}^{3} [/tex]
[tex]v = 5833.3 {mm}^{3} [/tex]
translate the triangle then enter the new coordinates
Answers
Answer:
1,(8)
Step-by-step explanation:
x = 3-2=1
y = 4+4=8
Therefore, 1,8
Ally surveyed 5 classrooms. She wanted to know the number of students in each class who love painting. The data she collected from the 5 classrooms is below.
10, 7, 9, 11, 8
The value that could be the best measure of the center of this data is__.
Answers
Answer:
45 im not to shur
Step-by-step explanation:
10 + 7 + 9 + 11 + 8 = ?
? = 45
find the area of the shaded figure
Answers
At Shannon's Pancake House there are 228 dirty coffee mugs and 247 clean coffee mugs. What percentage of the coffee mugs at the pancake house are dirty? Write your answer using a percent sign
Answers
Answer:
48%
Step-by-step explanation:
First, we need to add the amounts together to be able to see what percent of all the cups are dirty. (228 + 247 = 475). Now we can find one percent of 475 we can do this by moving the decimal point two to the left. (4.75). so If 4.75 is 1% we can multiply 4.75 until we get 228.
4.75 x 20 = 95.
4.75 x 40 = 190
4.75 x 45 = 213.75
4.75 x 50 = 237.5
4.75 x 48 = 228
Since every time we multiplied by 1 more we went up 1%. We multiplied by 48 so 48%.
A rectangle has an area of 48 square feet and a length of 12 feet
Which answer choice shows the correct way to find w the width of the rectangle?
Answers
Answer:12 x w = 48
Step-by-step explanation:
the width is 4
Answer:
w=4
Step-by-step explanation:
length is 12
area is 48
:) don't know how to explain so i'll just put the formula thing
w=a/1=48/12=4 also /=fraction
Which statement correctly describes the function?
f(x)=
[6x-5, ifx>0
2x-10, ifx≤0
OA. It is continuous.
OB. It is discontinuous because there is a value for a for which f(a) is not defined.
OC. It is discontinuous because there is a value of a such that lim f(x) = f(a).
X-a
OD. It is discontinuous because there is a value for a such that lim f(x) does not exist.
Answers
Answer:
D) It is discontinuous because there is a value for a such that [tex]\lim_{x \to \\a } f(x)[/tex] does not exist.
Step-by-step explanation:
Just did the practice.
what is 3.486 round to the nearest hundred
Answers
Answer:
3.49
Step-by-step explanation:
Answer:
3.5
Step-by-step explanation:
because the number is 3.486 and 8 is more close to the next number which is 50 so is 3.50 or 3.5
If I get a 100 on one assingment and a 57 on the other, what is my average of the assignments?
Answers
Answer:
78.5
Step-by-step explanation:
Add the two scores, and then divide this sum by 2 to obtain the average score:
[tex] \frac{100 + 57}{2} = \frac{157}{2} = 78.5[/tex]
Answer:
78.5
Step-by-step explanation:
To calculate the average of the assignments, you must find the mean of the assignments.
Mean = sum of the items divided by the number of items
[tex]\frac{100+57}{2}[/tex]
[tex]=\frac{157}{2}[/tex]
[tex]=78.5[/tex]
help plese will markbrainliest
Answers
Your answer is 53
Yw :D
What is the area of the following circle?
Answers
Answer:
78.5 or 78 1/2 units
Step-by-step explanation:
The formula for the area of a circle using diameter is 1/4*pi.*d to the second power. Plug it in, and you get 78.5 or 78 1/2 units.
A student solved the equation x2=132 to find the length of the diagonal of a square in centimeters which measurement is closer to x,the length of the diagonal of this square in centimeters.
Answers
The length 11 cm is closer to the length of the diagonal of this square in centimeters.
How to determine the value of x?The equation is given as:
x^2 = 132
Take the square root of both sides
x = √132
Evaluate the square root
x = 11.49
Approximate
x = 11
This means that 11 is closer to the length of the diagonal of this square in centimeters.
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A Type II error is committed if we make A. an incorrect decision when the null hypothesis is false B. a correct decision when the null hypothesis is false C. a correct decision when the null hypothesis is true D. an incorrect decision when the null hypothesis is true
Answers
Answer: A. an incorrect decision when the null hypothesis is false
Explanation:
A type I error is when we reject the null, but the null was true.
A type II error is when we fail to reject the null, but the alternative was true.
Refer to the chart below to help organize things.
Cant find the answer
Answers
Answer:
Carter family = 25 hours
Davis family = 31 hours
Step-by-step explanation:
Let's say the number of hours the Carter family used their sprinkler is x and the number of hours the Davis family used their sprinkler for is y.
So combined:
x + y = 45 hours
and we are also told that:
40x + 15y = 1300 L
So we can do simultaneous equations to solve the problem.
With some rearranging, we can figure out that:
y= 45 - x
and by substituting that into the second equation:
40x + 15 (45 -x) = 40x + 675 - 15x = 1300L
25x = 1300 - 675
25x = 625
x = 25 = hours that the Carter family used their sprinkler
and we can substitute that back into the original equation to find how many hours the Davis family used their sprinkler so:
25 + y = 56
y = 31
The Davis family used their sprinkler for 31 hours whilst the Carter family used their sprinkler for 25 hours.
The image shows a circle with center (4,6) and radius 10 units.
Answers
A circle is a curve sketched out by a point moving in a plane. The point that lies on the circle is (-4, 12), (-6, 6), and (4, 16).
What is a circle?A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The simple way to do such questions is to make the given circle and plot the points on the graph. As shown below.
The other way to do the question is to find the distance between the centre point of the circle and the point if it is equal to the radius of the circle, the point will lie on the circle, otherwise not.
The formula to find the distance between the two points on a graph is,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Hence, the point that lies on the circle is (-4, 12), (-6, 6), and (4, 16).
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Look at the picture down below to answer the question
options:
$12
Graph doesn't show me that information
$10.15
$11.10
Answers
Answer:
11.10
Step-by-step explanation:
you just have to look at where 5 years stops on the line
Answer:
$11.10
Step-by-step explanation:
made a line on snip tool, it went well above 11