write an equation for each hyperbola.
vertices (0,2),(0,-2)
foci (0, +/- square root of 5)
Answers
Check the picture below, so the hyperbola looks more or less like so, hmmm so is a vertical one, so is opening towards the y-axis, meaning the fraction that is positive is the one with the y-variable, its traverse axis length is 4 units, from +2 to -2, meaning that a = 2, and the distance either focus to the center is √5, so
[tex]\textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ a=2\\ c=\sqrt{5} \end{cases}\qquad \cfrac{(y- 0)^2}{ 2^2}-\cfrac{(x- 0)^2}{ b^2}=1[/tex]
[tex]\sqrt{5}=\sqrt{2^2+b^2}\implies 5=4+b^2\implies 1=b^2\implies \sqrt{1}=b\implies 1=b \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(y- 0)^2}{ 2^2}-\cfrac{(x- 0)^2}{ 1^2}=1\implies \cfrac{y^2}{4}~~ - ~~x^2~~ = ~~1[/tex]
Related Questions
Will V − E + F always equal 2?
Answers
The expression V − E + F is an illustration of the Euler's formula.
The expression V − E + F is always 2
How to determine the true statement?The equation is given as:
V - E + F = 2
Where:
V represents the verticesE represents the edgesF represents the facesAccording to the Euler's formula, the relationship between V, E and F is:
V + F = 2 + E
Subtract E from both sides
V - E + F = 2
Hence, the expression V − E + F is always 2
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If you donate $150 in total a year , How much money did you donate on the first month of the year.
Answers
Answer:
$12.50
Step-by-step explanation:
You donate $150 in total in a year.
To find out how much you donated on the first month, remember the relation between a year and number of months.
⇒ 1 year = 12 months
⇒ 1 month = 1/12 year
Finding the amount donated
Divide the money donated in a year by 12$150/12$12.50Factor the polynomial 3x4 – 2x2 15x2 – 10 by grouping. which product is the factored form of the polynomial? (–x2 – 5)(3x2 2) (x2 – 2)(3x2 5) (x2 5)(3x2 – 2) (3x2 – 5)(x2 2)
Answers
The factor of the given polynomial are (3x^2-2)(x^2+5)
The polynomial
[tex]3x^4-2x^2+15x^2-10[/tex]
What is the factor of the polynomial?Factoring a polynomial is expressing the polynomial as a product.
The rearranged, grouped, and solved as follows
[tex]3x^4+15x^2-2x^2-10[/tex]
[tex]3x^4+15x^2-(2x^2+10)[/tex]
Factor out the common term
[tex]3x^2(x^2+5)-2(x^2+5)[/tex]
[tex](3x^2-2)(x^2+5)[/tex]
That is the third option is the correct option.
Therefore the factor of the given polynomial are (3x^2-2)(x^2+5)
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Beth and Leslie are trying to decide which one of them gets to portray the lead character in a student play. They will use a random number generator to produce an integer. If the integer that comes up is odd, Beth gets to play the lead, and if the integer is even, Leslie gets to play the lead. Having the random integer generated be in which interval will make this a fair decision?
A) from 2 to 10 B) from 3 to 15 C) from 5 to 20 D) from 5 to 25
Answers
The fair interval illustrates a sample space
The interval that will make a fair decision is from 5 to 20
How to determine the fair interval?From the question, we understand that:
Beth plays the lead, and if the integer is even, Leslie plays the lead, if otherwiseSince they choose odd and even integers, then the sample space must be divisible by the number of people (i.e 2 people)
The sample space (S) is calculated as:
S = Highest - Least + 1
A) from 2 to 10S = 10 - 2 + 1 = 9
B) from 3 to 15S = 15 - 3 + 1 = 13
C) from 5 to 20S = 20 - 5 + 1 = 16
D) from 5 to 25S = 25 - 5 + 1 = 21
Only 16 can be divisible by 2
Hence, the interval that will make a fair decision is from 5 to 20
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The wood on the back deck of a house needs waterproofing. The shape of the deck is a rectangle with the length * 35 feet and a width of 5 yards. A gallon can of waterproof stain covers 80 square feet and costs $19.99 per can plus 7% sales tax. You go to the hardware store to purchase the waterproof stain needed to complete the job. You give the cashier $150.
How much change do you receive, or how much additional cash must you find in order to be able to pay for all of the
stain you need? You must show all calculations.
Area of Rectangle = length X width
You cannot split up a can of stain.
You must show all calculations.
Answers
To estimate the product of 44 x 52, what is the best way to round the factors?
45 x 55
40 x 50
50 x 50
40 x 55
WILL MARK BRAINLIEST
Answers
You earn $1,166 gross taxable income every week, and have claimed no exemptions. assuming that you have no other sources of income, what is the amount of income tax withheld each week? for weekly gross income between 1,160 and 1,170 dollars and claiming no exemptions, 340 dollars will be withheld each week. a. $323 b. $337 c. $340 d. $344 please select the best answer from the choices provided a b c d
Answers
They are exempt from income tax and we would get the income tax withheld as $340.
What is tax?
The person does not have another source of income, and there are no exceptions that are claimed by the person.
The withheld tax which is held every week can be calculated as;
Amount of income tax = 30 % of 1,166
Amount of income tax = $339.6
Amount of income tax = $340
Hence, they are exempt from income tax and we would get the income tax withheld as $340.
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plane leaves the airport at 9:15 p.m. and travels at 560 km/h. how far away will it be at midnight?
Answers
t=2 hrs-------so 2 hrs after the second plane leaves it will catch the first plane
CK
720+240*2=600*2
720+480=1200
1200=1200
Parallelogram ABCD has the following vertices: A(3,6), B(6,8), C(9,6), and D(6,4). In two ut more complete sentences, explain how you can use the coordinates of the vertices to prove that parallelogram ABCD is a rhombus.
Answers
Explanation:
A rhombus is a parallelogram in which the diagonals are mutual perpendicular bisectors. The coordinates of the vertices can be used to show ...
the diagonals bisect each otherthe diagonals are perpendicularWhen both these conditions are met, the quadrilateral is a rhombus.
__
Mutual BisectorsThe diagonals will have the same midpoint (bisect each other) if the sum of the coordinates at the ends of one diagonal is the same as the sum of the end point coordinates of the other diagonal:
A +C = B +D
(3, 6) +(9, 6) = (6, 8) +(6, 4)
(3+9, 6 +6) = (6 +6, 8 +4)
(12, 12) = (12, 12) . . . . . . midpoints are the same; ABCD is a parallelogram
__
PerpendicularThe diagonals will be perpendicular if the sum of the products of the coordinate differences of their end points is zero.
AC⋅BD = (C -A)⋅(D -B) = (9 -3, 6 -6)⋅(6 -6, 4 -8)
= (6, 0)⋅(0, -4) . . . . . end point differences; we want their dot-product
= (6)(0) +(0)(-4) = 0 +0 = 0 . . . . diagonals are perpendicular
_____
Additional comment
The midpoints are computed as (A+C)/2 and (B+D)/2. We have multiplied each of them by 2 to simplify the arithmetic. Our resulting sums of (12, 12) must be divided by 2 to get the actual midpoint of the rhombus: (6, 6).
The notion of "dot product" is a vector notion. Two vectors are perpendicular when their dot product is zero. The dot product is the scalar sum of the products of corresponding coordinates.
Write −0.258
as a fraction in simplest form. ITS NOT 129/500
Answers
explanation:
Simplify. 2(x^2 + 5) - 3(x + 1) + 3
Please explain how you got your answer, I'm really confused!! :( I will mark Brainliest!
Answers
Answer:
2x^2+10-3x
Step-by-step explanation:
start by multiplying numberes into the parentheses.
2x^2+10-3x-3+3
now combine like terms
2x^2+10-3x
A point has zero dimension.
Q.A. True
• B. False
SUBMIT
Answers
Can someone help me with this problem?
Answers
Answer:
30(2+1)
Step-by-step explanation:
Again, find common highest number. It is 30.
60/30 =2
30/30 = 1
so,
30(2+1)
which graph represents the solution set of this inequality?
please help!!!
Answers
Answer:
C is the correct answer due to two-step inequality process
Step-by-step explanation:
Your inequality is: 5a + 18 < -27
First, you must remember that the < or > shall not be shaded in.
You could automatically eliminate answer A.
Now you need to do two-step inequalities which is the same thing as two-step equations but with an inequality sign.
5a + 18 < -27
5a < -27-18
5a < -45
**Now, here's something important: If you are multiplying with negatives while dealing with inequalities you must switch the sign to its opposite.
-9 > a
You need to find a number line that has numbers less than -9. It could be -10, -11, -12, -122, etc.
C is the correct answer.
Which expression is equal to
Answers
explanation: below
What is the product? (2 x minus 1)(x 4) 2 x squared minus 4 2 x squared 4 2 x squared 7 x minus 4 2 x squared minus 7 x minus 4
Answers
The product of the given equation (2x - 1)(x +4) is 2x^{2} +7x -4.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given expression is
[tex](2x - 1)(x +4)[/tex]
Multiply term by term,
[tex]2x \times x + 2x \times 4+ (-1)\times x + (-1)\times 4\\2x^{2} +8x -x -4\\2x^{2} +7x -4[/tex]
Thus, The product of the given equation is [tex]2x^{2} +7x -4[/tex].
Learn more about quadratic equations;
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Help me please thanks
Answers
5(w. 9)
hope it really helps...!!!
Lars read that there are about
210,000 grains of salt in one
teaspoon.
How is 210,000 written as a power
of ten?
A. 210 X 104
B. 21 X 104
C. 21 X 108
D. 2.1 X 10^
Answers
Answer
the answer is a
Step-by-step explanation:
Describe the difference between rotation and revolution. Your answer should include a definition of each as well as what each one causes.
Answers
Answer:
Rotation" refers to an object's spinning motion about its own axis.
"Revolution" refers the object's orbital motion around another object.
For example, Earth rotates on its own axis, producing the 24-hour ( a day.)
Earth revolves about the Sun, producing the 365-day (a year).
Write these as ordinary numbers:
A. 4×10³
B. 7×10⁹
C. 4×10⁰
Answers
= 4000
B. 7×10⁹= 7000000000
C. 4×10⁰= 4
( to convert back to ordinary form just move the decimal point according to the power. )
Answer:
A. 4000
B. 7000000000
C. 4
Step-by-step explanation:
A. 4×10³
= 4 × 1000
= 4000
B. 7×10⁹
= 7×1000000000
= 7000000000
C. 4×10⁰
(a⁰=1)
= 4×1
= 4
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What is the quotient of (3x4 – 4x2 8x – 1) ÷ (x – 2)? 3x3 6x2 8x 24 – startfraction 47 over x minus 2 endfraction 3x3 6x2 8x 24 startfraction 47 over 3 x superscript 4 baseline minus 4 x squared 8 x minus 1 endfraction 3x3 6x2 8x 24 startfraction 47 over x minus 2 endfraction 3x3 6x2 8x 24 – startfraction 47 over 3 x superscript 4 baseline minus 4 x squared 8 x minus 1 endfraction
Answers
The quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) is 3x³ + 6x² + 8x + 24
It can be expressed as 3x³ + 6x² + 8x + 24 + 47 / x - 2
What are the Quotients?Quotients is the number obtained by dividing one number by another.
The given expression is;
(3x⁴ - 4x² + 8x - 1) ÷ (x - 2)
Using synthetic division:
(3x⁴ - 4x² + 8x - 1) / (x - 2) = 3x³ + 6x² + 8x + 24 remainder 47
3x⁴ - 4x² + 8x - 1 → Dividend
x - 2 → Divisor
3x³ + 6x² + 8x + 24 → Quotient
47 → Remainder
The quotient is;
[tex]\rm =\dfrac{3x^4-4x^2+8x-1}{x-2}\\\\=\dfrac{(3x^3 + 6x^2 + 8x + 24)(x-2)}{x-2}\\\\=3x^3 + 6x^2 + 8x + 24[/tex]
Therefore, the quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) is 3x³ + 6x² + 8x + 24
learn more on quotients:
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The quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) would be 3x³ + 6x² + 8x + 24.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number.
The given expression
(3x⁴ - 4x² + 8x - 1) ÷ (x - 2)
(3x⁴ - 4x² + 8x - 1) / (x - 2) = 3x³ + 6x² + 8x + 24
remainder is 47
Here,
3x⁴ - 4x² + 8x - 1 = Dividend
x - 2 = Divisor
3x³ + 6x² + 8x + 24 = Quotient
47 = Remainder
The quotient is;
(3x⁴ - 4x² + 8x - 1) / (x - 2)
(3x⁴ - 4x² + 8x +24) (x - 2) / (x - 2)
3x³ + 6x² + 8x + 24
Therefore, the quotient of (3x⁴ - 4x² + 8x - 1) ÷ (x - 2) is 3x³ + 6x² + 8x + 24
learn more about quotients:
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I NEED HELP! I don’t get it at all
Answers
Answer:
5.83 cubic feet
Step-by-step explanation:
Volume of block1 :
l = 4 ft
[tex]\sf w = \dfrac{5}{6} \ ft\\\\ h = 1\dfrac{1}{6}=\dfrac{7}{6} \ ft[/tex]
[tex]\sf Volume \ of \ block1 = l*w*h\\[/tex]
[tex]\sf =4 *\dfrac{5}{6}*\dfrac{7}{6}\\\\ =\dfrac{5}{3}*\dfrac{7}{3}\\\\= \dfrac{35}{9} \ cubicfeet[/tex]
Volume of block2:
l = 4 ft
[tex]w = 1\dfrac{2}{3}-\dfrac{5}{6}\\\\ =\dfrac{5}{3}-\dfrac{5}{6}\\\\ =\dfrac{5*2}{3*2}-\dfrac{5}{6}\\\\=\dfrac{10}{6}-\dfrac{5}{6}\\\\w =\dfrac{5}{6} \ ft\\\\h =\dfrac{7}{12} \ ft[/tex]
[tex]\sf Volume \ of \ block2 = 4 *\dfrac{5}{6}*\dfrac{7}{12}[/tex]
[tex]\sf = \dfrac{5}{6}*\dfrac{7}{3}\\\\= \dfrac{35}{18} \ cubicft[/tex]
Amount of concrete to build stairs = Volume of block1 + volume of block2
[tex]\sf = \dfrac{35}{9}+\dfrac{35}{18}\\\\=\dfrac{35*2}{9*2}+\dfrac{35}{18}\\\\=\dfrac{70}{18}+\dfrac{35}{18}\\\\=\dfrac{105}{18}\\\\= 5.83 \ cubic feet[/tex]
Is 6x^-3x a polynomial
Answers
example: 5xy^2 - 3x + 5y^3 - 3
Choose the square with a perimeter of 24 inches.
A) A
B) B
C) C
Answers
Answer:
A. 6+6+6+6=24
Hope this helps!
Answer:
its a
Step-by-step explanation:
⇒ because if you add 6 four types it equals = 24 inches hope this helped
Jenna concludes that (4, 9) is the solution to the system of these two equations. Which of the following justifies her conclusion?
Only these two lines contain the point (4, 9).
The point (4, 9) appears in both tables.
These two lines have the same rate of change.
These two lines are perpendicular to each other.
Answers
as a point
ok only 3 questions and going to sleep
WILL MARK BRAINLIEST
Answers
Answer:
71.2
Step-by-step explanation:
PEMDAS is Parentheses, Exponent, Multiplication, Addition, Subtraction
This is just the order you do the operations.
First, Parentheses.
Second, Exponents,
Third, Multiplication or Division
Last, Addition or Subtraction
So, in 6 x (2.4 + 10.3) - 5
We first do parentheses which is
(2.4 + 10.3) = 12.7
Now we have,
6 x 12.7 - 5
The next thing is multiplication
6 x 12.7 = 76.2
Now we have,
76.2 - 5
Lastly subtract,
76.2 - 5 = 71.2
Complete the equation below to make an equation that is equal to 1.
Answers
Answer: 5/10 +5/10 =10/10 =1
Step-by-step explanation: I don't think this requires much explanation. Any number with same numerator and denominator equals 1.
When you get 10/10, the first and second box can be figures that sum up to be 10.
It can be 7 and 3, it can be 6 and 4
Select all of the equations that are equivalent to 3x+45=180
1. 3(x+45)=180
2. 3(x+15)=180
3. 3(x+15)=60
4. x+15=60
5. 3x=135
Answers
hello brainly team I need help
Answers
Answer:
5)
x=13.856
y=8
6)
u=4
v=3.464
Step-by-step explanation:
5)
y=hypothesis * sin(opposing angle)/sin(angle opposite of hypothesis)
y = 16*sin(30)/sin(90)
y=8
x=hypothesis * sin(opposing angle)/sin(angle opposite of hypothesis)
x=16*sin(60)/sin(90)
x=13.856
6)
sinA/(opposite of angle A) = sinB/(opposite side of angle B) = sinC/(opposite of side of angle C)
sin(90)/u= sin(30)/2
u *sin(30) = 2* sin(90)
u *sin(30) = 2
u=2/sin(30)
u=2/0.5
u=4
sin(60)/v= sin(30)/2
v *sin(30) = 2* sin(60)
v *sin(30) = 2 * 0.866
v * sin(30) = 1.73
v = 1.73/sin(30)
v = 3.464
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[5] x = 8 and y = 13.856
[6] v = 4 and u = 3.464
≤ Step-by-step explanation ≥-------------------------------------------------------------------------------------------------------------
[5]
sin60° = x/16 = 1/2
x = 16/2 = 8
cos60° = y/16 = √3/2
y = 16√3/2 = 8√3
Can also be : 8√3 = 13.856
-------------------------------------------------------------------------------------------------------------
[6]
sin30° = 2/u = 1/2
u = 2 x 2 = 4
tan30° = 2/v = √3
v = 2√3
can also be: 2√3= 3.464
-------------------------------------------------------------------------------------------------------------
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~lenvy~
Help me with this question, please
Answers
Answer:
Step-by-step explanation:
x+y=10
1.50x+2.50y=22
Then use the the elimination method. The final answer is x=3, y=7.