Answers
Step-by-step explanation:
Use these equations.
Equation of a Hyperbola, centered at orgin
[tex] \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
where a is the major axis
B is the minor axis.
Since a and X are first, the x axis is the major.
This also means the x axis contains the vertices and foci as well.
The equation of vertices when x is major axis is
[tex](x ±a)[/tex]
Since the vertices are (±1,0), and the orgin is (0,0). The length of a is 1.
So a=1.
The equation of foci is
[tex](x±c)[/tex]
Where c is formed by
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
We know that c is 2 since the distance from the foci and center is 2. A is 1, so let find b.
[tex] {2}^{2} = {1}^{2} + {b}^{2} [/tex]
[tex]4 = 1 + {b}^{2} [/tex]
[tex]3 = {b}^{2} [/tex]
[tex] \sqrt{3} = {b}[/tex]
So our equation is
[tex] \frac{ {x}^{2} }{1 {}^{2} } - \frac{ {y}^{2} }{ (\sqrt{3}) {}^{2} } = 1[/tex]
[tex] \frac{ {x}^{2} }{1} - \frac{ {y}^{2} }{3} = 1[/tex]
Related Questions
What is the surface area of the net?
Answers
Answer:
150.66
Step-by-step explanation:
Scupper Molly invested $1,800 semiannually for 23 years at 8% interest compounded semiannually. What is the value of this annuity
due? (Please use the following provided Table.) (Round your answer to the nearest cent.)
Annuity due
Answers
Answer:
the amount of a $3,000.00 annuity due at 12 percent compounded semiannually for 3 years. A. $334,321.00 B. $43,068.93 C. $22,180.50 D. $41,814.50
The amount of the annuity due in 23 years with 8% of interest compounded semiannually is $62053.35.
What is compound interest?Compound interest is the interest on a loan or deposit calculated based on the initial principal and the accumulated interest from the previous period.
Scupper Molly invested $1,800 semiannually for 23 years at 8% interest compounded semiannually.
Then the amount of the annuity due will be
[tex]\rm A = 1800 (1 + 0.08)^{2\times 23}\\\\A = 1800 (1.08)^{46}\\\\A = 1800 \times 34.474\\\\A = 62053.35[/tex]
More about the compound interest link is given below.
https://brainly.com/question/25857212
if you take Yola's age and subtract Zed's age you get 23. If you double Zeds age and then add Yolas age you get 80. Find both ages
Answers
Answer:
Yola is 42, Zed is 19
Step-by-step explanation:
I used a system of equations:
y - z = 23
2z + y = 80
Then I graphed them.
6849 rounded to the nearest 100
Answers
Hope this helps!
g(t)=-3t^2+2t-5 and h(t)=4t+3
Find:
h(t)-g(t) , g(3)+h(3) , (g-h)(2) , g(-1)-h(2) , (g•h)(3) , g(2)+h(4) , g(1)•h(-1)
Answers
Answer:
If this is the problem
g(t) = t2 - 3t and h(t) = 3t - 4
g[ h(t) ] = (3t-4)2 - 3 (3t-4)
g[ h(t) ] = 9t2 - 24t + 16 - 9t + 12
g[ h(t) ] = 9t2 - 33t + 28
In a survey of 2500 registered voters, 1900 of them said that they plan to vote in the next presidential election. Let p denote the proportion of all registered voters who plan to vote. Find the 95% confidence interval for p.
Answers
This can alternatively be written as 0.74 < p < 0.78
========================================================
Explanation:
n = 2500 = sample size
x = 1900 = number of successes = number who plan to vote
phat = x/n = 1900/2500 = 0.76
phat is the sample proportion that estimates the population proportion p.
At 95% confidence, the z critical value is roughly z = 1.96 which you use a table or calculator to find this value (or it's something you memorize).
E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 1.96*sqrt(0.76*(1-0.76)/2500)
E = 0.016742 approximately
The lower bound (L) of the confidence interval is
L = phat - E
L = 0.76 - 0.016742
L = 0.743258
L = 0.74
The upper bound (U) of the confidence interval is
U = phat + E
U = 0.76 + 0.016742
U = 0.776742
U = 0.78
The values of L and U are approximate.
The confidence interval in the format (L, U) would be (0.74, 0.78) approximately.
Another way to write the confidence interval is to say 0.74 < p < 0.78 as it's in the form L < p < U; showing that we're 95% confident that p is somewhere between 0.74 and 0.78
In other words, we're 95% confident that between 74% and 78% of the population would plan to vote in the next presidential election.
Nonsense will be reported!!
With solution.
Answers
Hopefully, I have read the problems right. The small writing is slightly blurry.
[1] Both 1 and 2 are equal to 70°
Angle 1 and Angle 2 will be equal to each other because they are vertical angles.
A straight line is 180°, so 180° - 110° = 70°
[2] Both 3 and 4 are equal to 99°
Again, Angle 3 and Angle 4 will be equal to each other because they are vertical angles.
We can solve for the other two angles by putting them equal to each other since they are also vertical angles.
3x - 15° = 2x + 17°
3x = 2x + 32°
x = 32°
-
2x + 17°
2(32)° + 17°
64° + 17°
81°
Also again, a straight line is 180°. 180° - 81° = 99°
[3] This one has too many subparts for Brainly.
As a hint, you will use the same methods above. Find vertical angles and use the degree of a straight line.
Find the perimeter of the semicircle. Let ≈ 3.14. r=17
Answers
Answer:
53.38
Step-by-step explanation:
First, find the circumference of the whole circle.
C=2pir
C=2(3.14)(17)
C=106.76
Then, divide by 2 because a semi-circle is half of a circle.
106.76/2 = 53.38
Therefore, the circumference, or the perimeter, of the semicircle is 53.38
-4 and a y intercept at 3
Answers
Answer:
f(x)=-4x+3
Step-by-step explanation:
Assuming you're talking about f(x)=mx+b. b is y intercept. So f(x)=mx+3. You substitute m for -4, as you said, and we get f(x)=-4x+3
Most dogs fail to become service dogs. In a recent training class, only 4 of 15 were certified as service dogs. What percent of dogs, rounded to the nearest whole number, became certified service dogs?
Answers
Answer:
27
Step-by-step explanation:
4/15×100 =80/3 =26.6
Rounded to the nearest whole number is 27
Explain how the Multiplication Property of Equality can be used to solve the equation
x ÷ 6 = 7.
Answers
Step-by-step explanation:
Multiplication property of equality is when you multiply the same number on both sides of an equation, the equation will still hold true.
In order to have x by itself, you need to multiply by 6. The property states that you can multiply 6 on both sides and the equation will still hold true.
Nonsense will be reported!!
Plss I need solution Ty!!.
Answers
[tex]\\ \rm\Rrightarrow \sqrt{36x^{21}y^{64}}=6y^8x^{10.5}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt[15]{7^{10}a^{25}b^{-35}}=7^{2/3}a^5b^{-7}{3}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt[3]{648(3m-2n)^{64}}=648^{1/3}(3m-2n)^4[/tex]
[tex]\\ \rm\Rrightarrow \sqrt[4]{(a^2-2a+1)^{29}(a^2-1)^7}=(a^2-a+1)^{29/4}(a^2-1)^{7/4}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{3a^2b}{\sqrt[3]{18a^{21}b^{17}}}=\dfrac{3a^2b}{18^{1/3}a^7b^{17/3}}=\dfrac{3a^{-5}b^{-14/3}}{18^{1/3}}=\dfrac{3}{18^{1/3}a^5b^{14/3}}[/tex]
Mark is 8 years older than half Jon's age. If Jon is 20, how old is Mark?
Answers
Answer:
18 years old
Step-by-step explanation:
20÷2=10
10+8=18 years old
(75*100) / 250 with steps please
Answers
Answer:
30
Step-by-step explanation:
solution
= (75*100)/250
= (7500)/250
= 7500/250
=30
Mamady is planning a trip. He will stay six nights at a hotel that charges $51.25 a night. What is a good estimate of the total amount he will pay for the hotel? 250, 300, 360, 50.
Answers
Answer:
Answer is 300
Step-by-step explanation:
because 51.25x6=307.5 and the closest estimate is 300.
Find the slope and the y-intercept of the graph of the linear equation.
y = -3x+2
The slope is (Answer here)
and the y -intercept is (Answer here)
Answers
Answer:
-3 is the slope
2 is the y intercept
Step-by-step explanation:
always
Linda bought 2 sets of 8 apples and each set costs $5.6 how much money does Linda need to pay to the cashier?(giving brainliest!)
Answers
Explanation: If she bought 2 sets of 8 apples then it’s 8 x 2 which is 16 and then 16 x 5.6 is 89.6
Paul needs to pay two separate bills each month for one ear. He uses the expression 12(4 + 7) to represent this situation. Which
expression also represents Pauls monthly bills for one year? Pls help
Answers
Which graph represents the function y = log x + 4?
Answers
Answer:
see attached
Step-by-step explanation:
We assume you are looking for the graph of ...
y = log(x) +4
This represents a vertical translation 4 units upward of the graph of log(x). That is, the point (1, 0) that appears on a graph of a log function will be translated to (1, 4).
The only graph shown that goes through the point (1, 4) is the last one, attached.
__
If you are actually looking for the graph of ...
y = log(x +4)
it will be a graph of the log function shifted 4 units to the left. The 2nd offered choice is that graph. The point (-3, 0) will be on that graph.
_____
Additional comment
For a function y = f(x), the transformation ...
y = f(x -h) +k
represents a horizontal shift of h units to the right, and a vertical shift of k units upward. Here, the argument of the log function is not clearly shown, so we cannot tell if the intended shift is to the left or upward.
1/2 + p = -3
PLEASE HELP I DONT UNDERSTAND HOW TO DO THIS
Answers
Answer:
p=3.5
Step-by-step explanation:
So minus 1/2 on both sides. p= 3.5
Please answer quick 15 points this is urgent
Answers
Answer:
x = 26
Step-by-step explanation:
180 = (5x-10) + (3x-18)
180 = 8x -28
180 + 28 = 8x
208 = 8x
x = 26
Select the correct answer.
Adam constructed quadrilateral PQRS inscribed in circle O. How can he prove PQRS is a square?
A.
He needs to show only that the diagonals are perpendicular.
B.
He needs to show only that the diagonals are perpendicular and congruent.
C.
He needs to show only that the diagonals are perpendicular and bisect each other.
D.
He needs to show that the diagonals are perpendicular, congruent, and bisect each other.
Answers
Answer: D
Step-by-step explanation:
You need to prove that the diagonals bisect each other to prove it's a parallelogram.
Now, to prove it's a square, you need to prove it's both a rectangle and a rhombus.
To prove it's a rectangle, you need to prove the diagonals are congruent.To prove it's a rhombus, you need to prove the diagonals are perpendicular.Area + circumference of circle
Answers
Answer:
153.86 cm² and 43.96
Step-by-step explanation:
The formula to find the area of a circle is A = πr²
A = 3.14(7)²
A = 3.14(49)
A = 153.86
To find the circumference, use the formula C = π2r
C = 3.14*2*7
C = 43.96
The area of the circle is 153.86 cm² and the circumference of the circle is 43.96.
Hope this helps :)
gina wilson unit 7 homework 3 second page document
Answers
Answer:
4) 14.5
6) 11.4
Step-by-step explanation:
4) Area = 20 * 21/2 = 29 * x/2
so x = 20 * 21/29 = 14.5
6) Area = 22.4 * 13.2/2 = 26 * x/2
so x = 22.4 * 13.2/26 = 11.4
Round 822,119 to the nearest ten thousand.
Answers
Answer:
820,000
Step-by-step explanation:
2 is lower than 5 so round down to 20
Pls Brainliest If Helps
Answer:
820,000
Step-by-step explanation:
The 10,000 digit is the 2 on the left.
All digits to the right of the left 2 become zero.
820,000
The first digit that is dropped is the right 2.
Since it is not 5 or more, the 2 that is kept does not go up to 3.
Answer: 820,000
Which method would be the best to solve the following system of equations? y=1/2x+6 -2x+4y=24
A. None of these methods will work.
B. Elimination
C. Substitution
D. Graphing
Answers
Answer:
C. Substitution
But gives you infinity solitions
Solving steps:
Step: Solvey=1/2
x+6for y:
y=1/2x+6
Step: Substitute
1/2
x+6foryin−2x+4y=24:
−2x+4y=24
−2x+4(1/2x+6)=24
24=24(Simplify both sides of the equation)
24+−24=24+−24(Add -24 to both sides)
0=0
ACTUALLY GUVW ME THE ANSWERS I NEED!!!!
A diver is standing on a platform 24 ft above a pool. He jumps from the platform with an initial
upward velocity of 8 ft/s. Using the formula, h(t) = -16t2 + vt + s, where h is his height
above the water, t is the time, v is his starting upward velocity, and s is his starting height.
A) After how long will the diver reach its maximum height?
B) What is the maximum height the diver will reach?
Answers
Answer:
A) t = 0.25 s
B) h = 25 m
Step-by-step explanation:
Given equation: [tex]h(t) = -16t^2 + vt + s[/tex]
where:
h = height above water (in feet)t = time (in seconds)v = initial upwards velocity = 8 ft/ss = initial height = 24 ftA) To find the value of t when h is at its maximum, differentiate the equation with respect to t:
[tex]\implies h'(t)=-32t+v[/tex]
Substitute given value of v:
[tex]\implies h'(t)=-32t+8[/tex]
Set to zero and solve for t:
[tex]\implies -32t+8=0[/tex]
[tex]\implies t=0.25 \textsf{s}[/tex]
B) Substitute the found value for t into the equation and solve for h:
[tex]\implies h(0.25) = -16(0.25)^2 + 8(0.25) + 24[/tex]
[tex]\implies h(0.25) = -1 + 2 + 24[/tex]
[tex]\implies h(0.25) =25 \textsf{ m}[/tex]
NO LINKS!!
Finding the Width of a Gorge: Find the distance from A to C across the gorge illustrated in the figure.
Answers
Answer:
70.02ft≈70ft
Step-by-step explanation:
Here,
∠ABC=35°
BC=100ft
AC=?
Now,
[tex]tanB=\frac{AC}{BC} \\\\[/tex][tex]tanB=\frac{AC}{BC} \\\\tan35=\frac{AC}{100ft} \\\\0.7002=\frac{AC}{100ft} \\\\100ft*0.7002=AC\\\\AC=70.02ft[/tex]
Because tan=p/b
[tex]\\ \rm\rightarrowtail cot35=\dfrac{Base}{Perpendicular}[/tex]
[tex]\\ \rm\rightarrowtail cot35=\dfrac{BC}{AC}[/tex]
[tex]\\ \rm\rightarrowtail cot35=\dfrac{100}{AC}[/tex]
[tex]\\ \rm\rightarrowtail AC=\dfrac{100}{1.43}[/tex]
[tex]\\ \rm\rightarrowtail AC=69.93ft[/tex]
Find the missing side lengths. Answers are in simplest radical form with the
denominator rationalized.
Answers
Step-by-step explanation:
Given is the 30°x60°x90° right triangle.
The ratio of its sides is:
1 : √3 : 2Find the missing sides using the ratio above:
x = 2*2√6 = 4√6y = 2√6*√3 = 2*3√2 = 6√2Answer:
[tex]\sf x = 4\sqrt{6}[/tex] and [tex]\sf y = 6\sqrt{2}[/tex]
step-by-step explanation:
given:
opposite length: yadjacent length: 2√6hypotenuse length: xusing tan rule:
[tex]\sf tan(x)= \dfrac{opposite}{adjacent}[/tex]
[tex]\sf tan(60)= \dfrac{y}{2\sqrt{6} }[/tex]
[tex]\sf tan(60)*{2\sqrt{6}= y[/tex]
[tex]\sf y = 6\sqrt{2}[/tex]
using cosine rule:
[tex]\sf cos(x)= \dfrac{adjacent}{hypotensue}[/tex]
[tex]\sf cos(60)= \dfrac{2\sqrt{6} }{x}[/tex]
[tex]\sf x= \dfrac{2\sqrt{6} }{cos(60)}[/tex]
[tex]\sf x = 4\sqrt{6}[/tex]
a butterfly can fly 82 feet in four seconds and a dragonfly 50 in two seconds. which is faster
Answers
Answer:
The dragonfly is 4.5 feet per second faster.
Step-by-step explanation: