Which expression gives the length of the transverse axis of the hyperbola
shown below?
Answers
Explanation:
Length of transverse axis of hyperbola means distance between both the vertices of hyperbola which is constant given by 2a.
As definition of hyperbola:
Difference in distance of any point (x,y) from both focus is a positive constant equals to length of transverse axis.
So, distance of (x,y) from foci 1)-( distance of (x,y) from foci 2)=2a
x-y=2a
Length of transverse axis is x-y.
hope it helps....
Good luck on your assignment
The length of the transverse axis is x - y if point (x, y) is separated from either focus by a positive constant equal to the transverse axis' length option (C) x - y is correct.
What is hyperbola?It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
We have given a hyperbola shown in the picture.
The green line indicates the transverse axis of the hyperbola.
As we know,
The distance between the two vertices of the hyperbola, which is always given by 2a, is referred to as the length of the transverse axis.
Any point (x, y) is separated from either focus by a positive constant equal to the transverse axis' length.
x-y=2a
The length of the transverse axis = x - y
Thus, the length of the transverse axis is x - y if point (x, y) is separated from either focus by a positive constant equal to the transverse axis' length option (C) x - y is correct.
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Related Questions
Please help
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If the intercepts of a line are (a, 0) and (0, b), what is the slope of the line?
Answers
Answer:
a−b=aa=1
Step-by-step explanation:
Since the graph of the linear function f has intercepts (a,0) and (0,b), the two points satisfy the function. Therefore, the slope becomes a−b=aa=1, which is positive.
If Tim Cook, CEO of Apple wants to make a list of the employees who are above 40, what process he will use? Option: 1.Data query 2.data sorting 3.data compiling
Answers
What is the solution to the equation 7(a – 10) = 13 – 2(2a + 3)?
a = StartFraction 26 Over 11 EndFraction
a = 7
a = StartFraction 89 Over 11 EndFraction
a = 621
Answers
Answer:
a=7
Step-by-step explanation:
7(a – 10) = 13 – 2(2a + 3)
Open the bracket
7a-70=13-4a-6
Collect like terms
7a+4a=13-6+70
11a=77
divide both sides by 11
11a/11=77/11
a=77/11
a=7
n
Which expression has twice the value of 2-2.2-2.2?
Answers
Answer:
2^5
explanation:
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Answers
Answer:
The second one
Step-by-step explanation:
Please I need help with this tooo.....will give 5 start and brainlist....
Answers
Which of the following relations is a function? A.{(0,2),(1,2),(2,2),(3,2)} B.{(2,0),(2,1),(2,2),(2,3)} C.{(3,5) ,(4,7),(5,9),(5,11)} D. {(4,5),(6,7),(8,9),(8,11)}
Answers
Answer:
the answer is A
Step-by-step explanation:
If b = the number of baseballs which algebraic expression represents the phrase below the number of baseballs minus 3 lost during practice
Answers
Answer: B
Explanation: Baseballs(b) minus 3 which is b-3
A girl is on a train that is headed East at 100 miles per hour. The girl is walking at 5 miles per hour
toward the back of the train.
1.
What is the speed and direction of the train if the girls is the frame of reference?
Answers
Answer: The speed is 105 miles/ hr and the direction of the train would be East if the girl is the frame of reference.
Step-by-step explanation:
Since we have given that
Speed of train = 100 miles per hour
Speed of girl = 5 miles per hour
Since the girl is moving towards the back of train.
So,it means train and girl are moving in opposite direction.
So, Relative speed would be
[tex]100+5=105\ miles/hr[/tex]
Hence, the speed is 105 miles/ hr and the direction of the train would be East if the girl is the frame of reference.
I will give brainliest answer
Answers
Answer:
≈ 93.06 cm²
Step-by-step explanation:
Subtract the area of the rectangle from the area of the circle
area of circle = πr² = π × 8² = 64π cm²
area of rectangle = 12 × 8 = 108 cm²
Thus
shaded area = 64π - 108 = 201.062 - 108 ≈ 93.05 cm² ( nearest hundredth )
Answer:
The area of the shaded region = area of the circle - area of the rectangle
area of circle = πr² = π × 8² = 201.14 cm²
area of rectangle = 12 × 2 = 24 cm²
shaded area = 201.14 - 24 ≈ 177.14 cm²
A ship is sailing due west …
Plz answer !!
Answers
Answer:
8.75° south of west
26.3 mph
Step-by-step explanation:
Let's say that east is +x and north is +y.
The sailor's horizontal velocity is -26 mph. The vertical velocity is -4 mph. So the velocity vector is in the 3rd quadrant. The direction is:
θ = tan⁻¹(-4 / -26)
θ = 188.75°, or 8.75° south of west.
The magnitude of the speed is:
v = √((-4)² + (-26)²)
v = 26.3 mph
Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answers
Answer:
(40/3)*pi
Step-by-step explanation:
lets first find the area of the little circle
A=pi*r^2
A=pi*3^2
A=9pi
Now, lets find the area of the big circle
A=pi*r^2
A=pi*(3+4)^2
A=pi*7^2
A=49pi
now lets subtract the area of the little circle from the area of the big circle
49pi-9pi=40pi, now we found the area of the "bagel)
lets find what portion of the bagel is the shaded region
120/360=1/3
now lets multiply the bagel area by the fraction
40pi*(1/3)=
(40/3)*pi or (40*pi)/3
Area of the shaded regions is equal to 7π/3
What is the area and circumference of a circle?The circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Where r is the radius of the circle. The circumference of the circle or the perimeter of the circle is the measurement of the boundary of the circle. Whereas the area of the circle defines the region occupied by the circle.
Given here: radius of the smaller circle= 3 and larger circle =4 cm
Now A = (θ/360°) × πr2
θ is the sector angle subtended by the arcs at the center (in degrees), r is the radius of the circle. If the subtended angle θ is in radians, the area is given by, A = 1/2 × r² × θ.
Thus we have Area ADBC= 1/2 × 16×2π/3 -1/2×9×2π/3
=16π/3 -3π
=7π/3
Hence, Area of the shaded regions is equal to 7π/3
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Given:
AC – AR
<1 = <2
Prove:
<3 =<4
Answers
Answer:
ΔCTA ≅ ΔDRA
Step-by-step explanation:
Triangles CTA and DRA are congruent by ASA postulate. This is because:
∠1 ≅ ∠2 (given)AC ≅ AR (given)∠A is the same for both triangles (they are opposite angles)Then, correspondent angles and sides are congruent, for example, ∠3 ≅ ∠4
What is the slope of -2x+ 5y = 10?
Answers
Answer:
the rise is 2 and the run is 5
Step-by-step explanation:
2/5
Answer:
Step-by-step explanation:
the slope is = 2/5
the y-intercept = 2
1) A microbiologist measures the length of a bacterium of 0.000163 m and the
length of yeast as 0.0087 mm.
a) Which is longest? (Hint: Both must be the same units)
b) How much longer is the longer specimen than the shorter specimen?
Answers
Answer:
a) The bacterium is longer;
b) The bacterium is 0.1543 mm longer than the yeast.
Step-by-step explanation:
In order to compare the length of the two beings we need to convert them to the same unit. We can do it either way, but we'll choose to convert from meters to milimetres, since we're dealing with small numbers. To do that we need to multiply the length that is in "m" by 1000.
[tex]length_{bac} = 0.000163*1000 = 0.163 \text{ mm}[/tex]
a) The bacteria is longer than the yeast.
b) We need to subtract their length in order to find this answer:
[tex]\text{dif} = length_{bac} - length_{yeast}\\\text{dif} = 0.163 - 0.0087 = 0.1543 \text{ mm}[/tex]
Phone’s Plus charges a connection fee of 35 cents and 3 cents per minute. Fabulous Phones charges a connection fee of 45 cents and 2 cents per minute. Which equation could be used to determine the number of minutes, x, when a phone call would cost the same at both companies?
0.35+0.3x=0.45+0.2x
0.35+0.03x=0.45+0.02x
35+0.03x=45+0.2x
35+0.03x=45+0.02x
Answers
PLEASE HELP ME!! I WILL MARK BRAINLIEST, PLEASE ANSWER ALL 4 QUESTIONS BELOW ABOUT THE MATHEMATICAL EQUATION!
y = 595(1.075)x
1. What is the starting amount?
2. What is the growth factor?
3. What is the growth rate?
4. How many factors are in the equation?
Answers
Step-by-step explanation:
The starting amount is the coefficient of the exponent which is 595.
The growth factor is 1.075 and the growth rate would be 7.5%.
There are 2 factors in the equation.
I NEED HELP QUICK! PLEASE
Answers
Answer:
(a, 0), (0, b), (-a, 0), (0, - b)
Step-by-step explanation:
Since, all vertices of the rhombus lie in the x and y axes.
x - axis is given by a and y - axis is given by b.
Therefore, coordinates of vertices lying on x - axes will be (a, 0) & (-a, 0) and coordinates of vertices lying on y - axes will be (0, b) & (0, - b).
If a vendor sells an item he bought for Rs. 500 such that he earns a profit of 20%, determine the selling price of the item.
Answers
Hope this helps ya
HELP PLEASE I NEED HELPPPP
What is the sign of....
a x (-b/b)
when a =0 and b<0
A. positive
B. negative
C. zero
THIS IS ON KHAN ACADEMY AND I DONT GET IT IF U ANSWER ILL GIVE YOU BRANLIEST AND 100 points PLEASE JUST HELP MEH
Answers
Answer:
C. zero
Step-by-step explanation:
a * (-b/b)
-b/b = -1
a* -1
If a = 0 then
0 * -1 = 0
Answer:
0
Step-by-step explanation:
pls give brainliest
Which ordered pair is the solution to the system of equations? {x+2y=−8y=12x−2
Answers
Answer:
[tex]\left( -\dfrac{4}{25}, -\dfrac{98}{25} \right)[/tex]
Step-by-step explanation:
[tex]x+2y=-8 \\\\y=12x-2[/tex]
Substitute:
[tex]x+2(12x-2)=-8[/tex]
Expand:
[tex]x+24x-4=-8[/tex]
Simplify:
[tex]25x=-4[/tex]
Divide both sides by 25:
[tex]x=-\dfrac{4}{25}[/tex]
Plug this back into one of the original equations to find y:
[tex]-\dfrac{4}{25}+2y=-8 \\\\\\2y=-7 \dfrac{21}{25}=-\dfrac{196}{25} \\\\\\y=-\dfrac{98}{25}[/tex]
The ordered pair that represents this solution is therefore:
[tex]\left( -\dfrac{4}{25}, -\dfrac{98}{25} \right)[/tex]
Hope this helps!
A grocery store has 45% of its carts being used. Which ratio compares the used carts with all the carts that the store has? A. 10:100 B. 45:55 C. 55:100 D. 9:20
Answers
Answer:
D
Step-by-step explanation:
45%=[tex]\frac{45}{100}[/tex]
[tex]\frac{45}{100}[/tex] is equal to [tex]\frac{9}{20}[/tex]
so D
HOPE THIS HELPS
Answer: 9:20
Step-by-step explanation:
45% if carts used from the 100%
Ratio will be 45:100 = 9:20
1. If u were to draw a tree diagram showing all the possible outcomes for rolling a six sided die twice, how many total outcomes would there be
1. 6
2. 12
3. 36
2. Rick is deciding what to wear to school. He has two different shirts, two different pants, and two different pairs of shoes to choose from. How many different outfit combinations does Rick have to choose from
1. 6
2. 8
3. 16
Answers
CAN SOMEONE HELP OVER HERE LOL PLEASE HELPPPPP Solve the inequality. -3/4y less than 9. The solution set is ?
Answers
Answer: y<-12
Step-by-step explanation:
[tex]-\frac{3}{4}y>9[/tex] is our einequality we are given. To solve, we want to get x alone. We would have to multiply both sides by -4/3.
[tex]y>-12[/tex]
You may thing this is the answer, but it is very close. When you multiply or divide by a negative number, you flip the sign. Therefore, the answer is [tex]y<-12[/tex].
a bus travels at a speed of 80km per hour . what is the distance it travels by 15 mins.
Answers
Answer:
The bus will travel 20km within 15 minutes
Step-by-step explanation:
Answer: 20 km
Step-by-step explanation:
Distance = speed / time
у – бх — 11
— 2x — Зу = -7
Answers
Answer: -2y -8x = 4
Step-by-step explanation:
y - 6x - 11 - 2x - 3y = -7
y -3y -6x -2x = -7 +11
-2y -8x = 4
this table shows values that represent an exponential function.what is the average rate of change for this function for the interval from x=1 to x=3
Answers
Answer: -4
Step-by-step explanation:
Solve for y: 4y + 4 = -8
Answers
Answer: YOUR ANSWER IS -3
Step-by-step explanation:
4y + 4 = -8
-4 -4
___________
4y = -12
Divide -12 by 4
Y = -3
Which point best approximates √3?
A
B
C
D
Answers
Answer:
B
Step-by-step explanation:
Square root of 3 is between 1 and 2
1^2 =1
(sqrt(3)) ^2 =3
2^2 = 4
So it must be point B
Answer:
B
Step-by-step explanation:
What are the coordinates of the center of the hyperbola with equation (x-2)^2/4^2-(y+3)^2/5^2=1
Answers
Answer: (6, -3)
(x^2-4x+4)/16-(y^2+6y+9)/25 = 1
x = 6
y = -3
6^2 = 36
4 * 6 = 24
36 - 24 = 12
12 + 4 = 16
16/16 = 1
-3^2 = 9
6 * -3 = -18
9 - 18 = -9
-9 + 9 = 0
0/25 = 0
1 - 0 = 1
I really hope this helped, at least a little bit.
The coordinates of the center of the hyperbola is (6,-3).
What is hyperbola?
Hyperbola is a type of "smooth curve, lying in the plane defined by its geometric properties or by the equation for which it is in solution set".
According to the question,
[tex]\frac{(x-2)^2}{4^2}[/tex] - [tex]\frac{(y+3)^2}{5^2}[/tex] = 1
Standard form of hyperbola = [tex]\frac{(x-k)^2}{a^2}[/tex] - [tex]\frac{(y-h)^2}{b^2}[/tex] = 1.
The expression 'y' is positive leading coefficient so the hyperbola so the hyperbola is open upward and downward . Comparing with standard equation we get center of hyperbola (2,-3) and 'a' point the hyperbola is 4 and the 'b' point of hyperbola is 5 and mark point 5 unit right as well as left on x-axis and 4 unit up and down on y-axis.
From above discussion we get clearly the coordinate of hyperbola is
(6-3).
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