The equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.
What is the equation of hyperbola?The equation of the hyperbola is the equation which is used to represent the hyperbola in the algebraic equation form, with the value of center point in the coordinate plane and foci.
The standard form of the equation of the hyperbola can be given as,
[tex]\dfrac{(y-k)^2}{b^2}-\dfrac{(x-h)^2}{a^2}=r^2[/tex]
Here (h,k) is the center of the hyperbola, (b) is the transverse axis, and (a) is the conjugate axis.
The foci of the hyperbola is,
[tex](h,k\pm c)[/tex]
The directrix is,
[tex]y=k\pm \dfrac{a^2}{c}[/tex]
A hyperbola is given with directrices at x = ±2 and foci at (6, 0) and (−6, 0). Thus, the directrix is,
[tex]y=k\pm \dfrac{a^2}{c}\\\pm 2=k\pm \dfrac{a^2}{c}\\\dfrac{a^2}{6}=2\\a^2=12\\[/tex]
It is known that,
[tex]a^2+b^2=c^2\\[/tex]
Put the value of a and c,
[tex](12)+b^2=6^2\\b^2=36-12\\b^2=24[/tex]
The value of center is (0,0). Thus, the equation of hyperbola is,
[tex]\dfrac{(y-0)^2}{24^2}-\dfrac{(x-0)^2}{12^2}=1\\\dfrac{y^2}{24^2}-\dfrac{x^2}{12^2}=1[/tex]
Thus, the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0) is y squared over 48 minus x squared over 12 equals 1.
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Please help me solve math problems
VW = 6
hope it helps...!!!
Find f(g(x)) simplify completely f(x)= x^2+5x+2 g(x)=3x
Answer:
f(g(x)) = 9x² + 15x + 2
Step-by-step explanation:
f(x) = x² + 5x + 2g(x) = 3xSolving f(g(x))
f(g(x))f(3x)f(3x) = (3x)² + 5(3x) + 2f(3x) = 9x² + 15x + 2f(g(x)) = 9x² + 15x + 2Answer:
[tex]f(g(x)) = 9x^2 + 15x + 2[/tex]
Step-by-step explanation:
Step 1: State the equations
[tex]f(x) = x^2 + 5x + 2[/tex]
[tex]g(x) = 3x[/tex]
Step 2: Insert the equation and solve
[tex]f(g(x)) = (g(x))^2 + 5(g(x)) + 2[/tex]
[tex]f(3x) = (3x)^2 + 5(3x) + 2[/tex]
[tex]f(3x) = 9x^2 + 15x + 2[/tex]
[tex]f(g(x)) = 9x^2 + 15x + 2[/tex]
Answer: [tex]f(g(x)) = 9x^2 + 15x + 2[/tex]
How can I rename 1/4 and 5/8 in the least common denominator
Answer:
2/8 and 5/8
Step-by-step explanation:
4=2×2
8=2×2×2
LCM=2×2×2=8
1/4 × 2/2 = 2/8
What would be the best method of achieving a valid simple random sample of students at UTSA?
Going to the website UTSA
Item 7
Which of the following has a slope of –2 and a y-intercept of 4?
y = –2x – 4
y = 2x + 4
y = 2x – 4
y = –2x + 4
Please help me with this , I will give 30 POINTS !.
======================================================
Explanation:
Through trial and error, we can set up these equations
4^5 = 10242^10 = 102432^2 = 1024This shows that choices A, C and D are eliminated. This is because 5, 10 and 32 all can work as either x or y in x^y = 1024, and that the other value is some other integer.
On the other hand, x = 16 doesn't work and neither does y = 16 if we wanted the other value to be an integer.
Solving x^16 = 1024 leads to approximately x = 1.5422 when we focus on the positive real number solution. This isn't an integer, so x^16 = 1024 doens't have any integer solutions.
Solving 16^y = 1024 leads to a similar situation as described in the previous paragraph. It doesn't have any integer solutions either (instead the value is y = 2.5)
So we have a few ways of arriving at why choice B is the final answer.
Shelly and Terrence earned points in a game by completing various tasks. Shelly completed x tasks and scored 90 points on each one. The expression below shows Terrence's total points in the game:
90x − 20
What does the constant term of the expression represent?
A :The total points Terrence earned
B :The total number of tasks Terrence completed
C : The sum of Shelly's and Terrence's total points
D :The difference between Shelly's and Terrence's total points
Answer:
D: difference between Shelly and Terrence total points
Solve the system of equations.
V = 4x+1
y = x^2+ 2x-2
Answer:
x = 1, y = 5 or (1, 5)Step-by-step explanation:
Given
y = 4x + 1y = x² + 2x + 2Equating them
4x + 1 = x² + 2x + 2x² - 2x + 1(x - 1)²x = 1Substituting x in the 1st Equation
y = 4(1) + 1y = 5Solution :
x = 1, y = 5 or (1, 5)So far this season, the Utah Jazz have won 16
out of 48 games. What percent of games have
the Jazz won?
Answer:
33%
Step-by-step explanation:
16 is one third of 48
Suppose we want to choose 5 objects, without replacement, from 18 distinct objects.
(a) How many ways can this be done, if the order of the choices is taken into consideration?
(b) How many ways can this be done, if the order of the choices is not taken into consideration?
Answer:
(a) 1,028,160
(b) 8,568
Step-by-step explanation:
(a)
[tex]18 \times 17 \times 16 \times 15 \times 14 = 1028160[/tex]
(b) 18! / (5! 13!) =
[tex] \frac{18 \times 17 \times 16 \times 15 \times 14}{5 \times 4 \times 3 \times 2 \times 1} = 8568[/tex]
Solve for x
x=
4x+2 3x+24
Answer:
x = - 8/3
Step-by-step explanation:
Hope this helps
I LITTERALY BEG OF YOU TO HELP ME!!
LMN≅PQR
What is the value of x in degrees?
Answer: 56
Step-by-step explanation:
Help Please.
I'm not the sharpest knife in the drawer
Step-by-step explanation:
Area = 1/2 × base × height
= 1/2 × 23/6 × 2.4
= 23×2.4/12
= 4.6 ft²
For all numbers x, if 3(x + 2) = 72 – 3, then x = ?
Answer:
A.
Step-by-step explanation:
A ring-shaped region is shown below.
Its Inner diameter is 26 it, and its outer diameter is 34 ft.
16
Find the area of the shaded region.
Use 3.14 Do not round your answer
Answer:
4.16
Step-by-step explanation:
Which equation has a slope of 3? *
Y = 5x + 3
y = 1/5 x - 3
y = 1/3 x + 5
y = 3x + 5
What number is bigger 18.84 or 28.8
Answer:
In terms of decimal places, 18.84 is bigger because of the hundredths place(4). In terms of whole numbers, 28.8 is bigger.
Answer: 28.8
Step-by-step explanation:
If you look at the first digit on the left in the number 28.8, which is 2, then you look at the first digit of 18.84, which is 1, you can see that 2 is larger than 1, so therefore 28.8 is larger.
A truck travels 350 miles on 25 gallons of gas. how far can it travel with 60 gallons of gas?
Answer:
840
Step-by-step explanation:
because he can drive 14 with one gallon of gas so 14x 60
Is the following function even, odd, or neither? f(x) = -2x + 6
NEED ANSWER ASAP !!!!!!!!!!!! :(
Answer:
its an odd
Step-by-step explanation:
The leading coefficient is negative
hope this helps
Mrs. Leger has a rectangular garden with side lengths measuring (3x + 10) inches
and (2x + 7) inches. She needs to purchase fertilizer to cover the area of her
garden. Given the side lengths, what is the area of Mrs. Leger's garden?
The area of Mrs. Leger's garden with length of (3x + 10) in and width of (2x + 7) in is 6x² + 41x + 70 in²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The area of a rectangle = length * width, hence:
Area of rectangular garden = (2x + 7) * (3x + 10) = 6x² + 41x + 70
The area of Mrs. Leger's garden with length of (3x + 10) in and width of (2x + 7) in is 6x² + 41x + 70 in²
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I think of a number, multiply it by 2 and add 1. My
answer is 15. What number was I thinking of?
Answer :: 7
Explanation ::
Okay, I'm going to stretch this explanation long so people can understand! Hopefully this helps :) I will also provide a shorter explanation so if people want to find out how to do it quicker without details to help you understand better, they can read the shorter explanation!
- long explanation -
Equation provided from the info :: (x * 2) + 1 = 15
We need to find out what number is the x. First of all, one way to do it is do the equation backwards. And the operators will be the opposite too, for example addition is the opposite of subtraction and multiplication is the opposite of division. Now once we flip the equation it should look like this:
(15 - 1) / 2 = x
Let's break the equation apart so it's easier to work with. Remember, the rule PEMDAS. Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. Why I put "and" between some words, is because they are the same level and you should go left to right from the equation. So the equation in parentheses is (15 - 1). So we just have to solve it! The answer is 14, which is an even number, so we don't have to fiddle with decimals. But if you want to know how to divide an odd natural number, feel free to comment on this answer! The equation should look like this:
14 / 2 = x
Now, all we have to do now is divide 14 in half! As someone who memorised their whole multiplication and division table, it's easy for me to figure it out. But if you haven't, try using addition! All you have to do is count up your numbers.
1 + 1 = 2
2 + 2 = 4
3 + 3 = 6
4 + 4 = 8
5 + 5 = 10
6 + 6 = 12
7 + 7 = 14!
So now we know 14 / 2 is 7. Sorry if this is too easy, I'm just giving attention to some who learn slowly, which is absolutely alright! So now we have our 2 answers. The equation now looks like this:
14 / 2 = 7.
Well we now know what the x is, and if you want to make sure it's the correct answer just flip the equation!
(7 * 2) - 1
7 * 2 = 14
14 - 1 = 15
Your answer is the same one provided, so the number is 7!
- short explanation -
The equation with the numbers provided is (x * 2) + 1 = 15
Let's flip the equation so it's easier! It should look like this:
(15 - 1) / 2 = x
Now all we have to do is solve it!
15 - 1 = 14
14 / 2 = 7
So our answer is 7! To check if the answer is correct, just re-do the unflipped equation!
(7 x 2) + 1 = ??
7 x 2 = 14
14 + 1 = 15
15 is the answer given in the text, so 7 is the correct answer.
M ∠ 4 = ______ °
m ∠ 5 = ______ °
m ∠ 6 = ______ °
Answer:
Step-by-step explanation:
Ethan and Logan read a total of 23 books over the summer. Ethan read 5 more books than Logan. How many books did Logan read this summer? How many books did Ethan read this summer?
Answer:
Logan: 9
Ethan: 14
Step-by-step explanation:
Let Ethan = e
Let Logan = l
1) We can set up two equations and solve them simultaneously.
e + l = 23
5 + l = e
1.1) To solve these equations, we can either use substitution or elimination.
5 + l + l= 23
2l = 23 - 5
2l = 18
l = 18/2
l = 9
2) Plug the result of l into one of the two equations above.
5 + 9 = e
14 = e
Mr. Pearson drives a bus for the city of Greenwood. Last month, he kept track of the number of bus riders each day.
Bus riders
50
60
70
80
90
100
What was the least number of bus riders?
What is an equation of the line that passes through the points (-7,3) and (5,3)?
Answer:
y=3
Step-by-step explanation:
Answer:
y = 3
Step-by-step explanation:
first the slope:
[tex]m = \frac{3-3}{-7-5} =0[/tex]
The equation
[tex]y-3=0(x-(-7))\\y-3=0[/tex]
[tex]y=3[/tex]
The line is parallel to the "x" axis, has no slope.
Hope this helps
can someone please help me with my homework :) please it would really help because its due tmr thanks if you could.
Answer:
Answer are in the steps.
Step-by-step explanation:
Most of the problems is parallelogram some angles are the same. 2 angles add up to 180° are known as supplementary angles also known as linear pair.
#1:
<1 = 148° , <2= 32° , <3 = 148° , <1 = 32° , <5 = 148° , <6 = 32° , <7 = 32°
#2: All of them are 90° because of linear lines that add up to 180° / parallelogram.
#3: If <1 = 130°, then <8 = 148°.
Because Parallelogram <1 and <8 transversal.
#4 If <5 = 53° , then <3 = 127°
Because <5 = <4 so <5 + <3 = 180°
#5 If <7 = 71° , then <3 = 109°
Because <7 + <3 = 180°
#6 If <4 = 65° , then <6 = 115°
Because <5 = <4 so <4 + <6 = 180°
Sullivan had to show 5 of his
coworkers how it's done. His boss
wanted him to roar! Of the 5
coworkers, 40 percent were clapping.
How many coworkers were clapping
Answer:
2 workers
Step-by-step explanation:
If you want to find 40 percent of 5, just mutiply 40% which = to .4 and 5
Louis bought a giant sub sandwich for the party. He wants to cut into 6-inch sections. If the sandwich is 18.25 feet, how many sections can he cut?
Which explanation justifies how the area of a sector of a circle is derived?.
Step-by-step explanation:
We know the area of a circle is
[tex]\pi {r}^{2} [/tex]
That is when the cricle is 360 degrees full, so another formula is
[tex] \frac{360}{360} \pi {r}^{2} [/tex]
If we the find the area of the sector with angle x, then that formula will be
[tex] \frac{x}{360} {\pi}r^{2} [/tex]
Answer:
The area of a sector is part of an area of the entire circle. Determine the fraction of the circle that the sector represents and multiply it by the area of the circle.
Step-by-step explanation:
answer what the question is asking
Answer:
12 and 6
Step-by-step explanation:
12×6=72
12÷6=2
I hope this may help you