Answers
The value of (a) and (b) for the hyperbola are [tex]\sqrt 3[/tex] and 2
The equation of the hyperbola is given as:
[tex]\frac{y^2}{b^2} - \frac{x^2}{a^2} = 1[/tex]
The curve of the graph passes through points (0,2) and (-4,3).
So, we have:
[tex]\frac{2^2}{b^2} - \frac{0^2}{a^2} = 1[/tex] and [tex]\frac{(-4)^2}{b^2} - \frac{3^2}{a^2} = 1[/tex]
[tex]\frac{2^2}{b^2} - \frac{0^2}{a^2} = 1[/tex] becomes
[tex]\frac{4}{b^2} = 1[/tex]
Cross multiply
[tex]b^2 = 4[/tex]
Take positive square root of both sides
[tex]b = 2[/tex]
[tex]\frac{(-4)^2}{b^2} - \frac{3^2}{a^2} = 1[/tex] becomes
[tex]\frac{(-4)^2}{2^2} - \frac{3^2}{a^2} = 1[/tex]
[tex]\frac{(-4)^2}{4} - \frac{9}{a^2} = 1[/tex]
[tex]4 - \frac{9}{a^2} = 1[/tex]
Collect like terms
[tex]- \frac{9}{a^2} = -3[/tex]
Cross multiply
[tex]-3a^2 = -9[/tex]
Divide both sides by -3
[tex]a^2 = 3[/tex]
Take square roots of both sides
[tex]a = \sqrt 3[/tex]
Hence, the value of (a) and (b) for the hyperbola are [tex]\sqrt 3[/tex] and 2
Read more about hyperbolas at:
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Related Questions
. Find the missing length for the pair of similar figures. 1.2 cm 1.4 cm 3.5 cm
○ 3 cm
○4.1 cm
O 0.48 cm
○4.5 cm
Answers
Which of the sets of ordered pairs represents a function?
A = {(2,-2), (5, -5),(-2, 2), (-5,5)}
B = {(4,2), (4, -2), (9,3), (9, -3)}
o Only A
O Only B
O Both A and B
O Neither A nor B
Answers
Solve this system of equations 2x+4y=-6 x=y-12
Answers
Answer:
Step-by-step explanation:
2(y-12) +4y = -6
2y -24 +4y = -6
6y -24 = -6
6y= -18
y = -3
x = -3 - 12
x = - 15
x = -15
y = -3
Answer:
x=-9, y=3
Step-by-step explanation:
2(-9)=-18 4(3)=12 -18+12=-6 so, -6=-6, it is determined true
-9=3-12 3-12=-9 so, -9=-9, it is determined true
Hope this helps! Have a nice day! Owa Owa!
Who to Convert 13/4 to a mixed numeral.
Answers
Answer:
3 1/4
Step-by-step explanation:
If correct please give me brainliest. :) :)
A balloon artist wants to make 6 different ut the kinds of balloon animals. She needs 4 balloons to make each animal. If the balloons come in packs of 8, how many packs will she need to buy? Part A Explain what you need to find first to solve the problem.
Answers
Answer:
She will need to buy 3 packs to make 6 different balloon animals.
Step-by-step explanation:
Given that the balloon artist wants to make 6 different animals, and each animal involves using 4 balloons, to make those 6 animals she must use 24 balloons, as the following calculation shows:
6 x 4 = 24
Now, since the balloons come in packs of 8 units, to make those 6 animals she must buy 3 packs of balloons, as this calculation also shows:
24 / 8 = 3.
Which graph represents a proportional relationship? On a coordinate plane, a straight line crosses the y-axis at (0, 0). On a coordinate plane, a straight line crosses the y-axis at (0, negative 2). On a coordinate plane, a straight line crosses the y-axis at (0, negative 3). On a coordinate plane, a straight line crosses the y-axis at (0, 3).
43 points
plz answer fast plz
Answers
Answer:1st one
Step-by-step explanation:
what equation is equal to 3.5 ×7
Answers
multiply and divide by 10
= 7×10/3.5×10
= 70/35
= 14/7
=2
The answer is 2
How do you simplify 4/6 it’s a fraction I NEED IT ASAP PLZ
Answers
Answer:
2/3
Step-by-step explanation:
divide the numerator and denominator by the same number until they are prime numbers
remember: if you divide the numerator by 2 you MUST divide the denominator by 4 as well. The rule is that you divide the numerator and denominator by the same number at the same time
in this case divide both by 2 to get 2/3
Write a 5 digit number so that when you round to the nearest tenth, your answer is 25.9
Answers
PLEASE HELP!
I WILL MARK BRAINLIEST!!!
Answers
Answer:
x=159/8
Step-by-step explanation:
you are supposed to put all those numbers and x's together and combine like terms then subtract from 180 and then divide
jay has an album that holds 900 photos. Each page of the album holds 9 photos. If 67 % of the album is empty, how many pages are filled with photos?
Answers
Heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeh plllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllls
Answers
1.44 /0.6 in long division
Answers
Answer:
The answer is 2.4
Step-by-step explanation:
because I division 1.44/0.6 its gave me 2.4
Una poblacion es atacada por una epidemia de gripe sea N(t)= numero de personas enfermas al tiempo t. En dias la epidemia inicio en N(0)= 50. Un matematico determina que la gripe se extiende a razón de f'(t)= 120t- 3t^2 personas por día. Determina
a) La función original que describe el comportamiento de la epidemia. (Aplica los mismos pasos explicados anteriormente.
b) ¿Cuántos enfermos habrán después de 15 días si no se controla la epidemia?
Answers
Answer:
Habrán 10175 enfermos a los 15 dias.
Step-by-step explanation:
La tasa de cambio de la población enferma por la epidemia de gripe es:
[tex]N'(t)=120t-3t^2[/tex]
Donde t es el tiempo en dias, y se sabe que la epidemia inició en N(0)=50.
a)
Para encontrar la función original que describe el comportamiento de la epidemia, debemos integrar la función:
[tex]N(t)=\int N'(t)dt[/tex]
[tex]N(t)=\int (120t-3t^2)dt[/tex]
Integrando:
[tex]\displaystyle N(t)=120\frac{t^2}{2}-3\frac{t^3}{3}+C[/tex]
Simplificando:
[tex]\displaystyle N(t)=60t^2-t^3+C[/tex]
Para determinar el valor de C, usamos la condición inicial N(0)=50:
[tex]\displaystyle 50=60(0)^2-(0)^3+C[/tex]
Se tiene que C=50, y la función queda determinada como:
[tex]\displaystyle N(t)=60t^2-t^3+50[/tex]
b) El número de enfermos a los t=15 dias se determina substituyendo el valor en la función original:
[tex]\displaystyle N(15)=60(15)^2-(15)^3+50[/tex]
Calculando:
[tex]N(15)=13500-3375+50=10175[/tex]
Habrán 10175 enfermos a los 15 dias.
(3 * 2)2/6 - 5 + (4 - 1)2?
Answers
Answer: The answer is 3.
Answer:
3
Step By step:
A 16 ounce box of cereal costs $4.00. How many cents per ounce does cereal cost?
Answers
Answer:
25cents/ounce
Step-by-step explanation:
Given parameters:
Ounce of cereal box = 16ounces
Cost = $4
Unknown:
cents per ounce = ?
Solution:
To solve this problem;
Convert the dollar bill to cents
$1 = 100cents
$4 will give us 4 x 100 = 400cents
Cost in cents per ounce= [tex]\frac{400}{16}[/tex] = 25cents/ounce
Answer:
what he said
Step-by-step explanation:
Order the set of integers from least to greatest.
0, 100, 50, -150
On a number line, the number furthest to the right has the ________ value.
If you are given any two numbers. Is the GCF or the LCM of those numbers which will be greater?
List a pair of numbers that will have 20 as thier LCM
Answers
Answer:Hi
Step-by-step explanation: like this comment for good luck
2(5r - 5) + 8(5r - 1)
A) 4 - 311 - 49^2
B) 34r – 6 + 28r^2
C) 26r - 6 + 287^2
D) 50r - 18
Answers
Answer:
The answer is 50r-18
Step-by-step explanation:
2(5r-5) +8(5r-1)=2 x 5r/2 x -5 + 8x 5r/8 x -1
=10r-10+40r-8
=10r+40r-10-8
=50r-18
A chef divided 4 1/2 pounds of ground beef into 3 equal packages he then sold the ground beef to other restaurants what was the weight of ground beef in each package
Answers
Answer:
1 1/2
Step-by-step explanation:
what is the answer to 2(x + 6) =
Answers
Answer:
2x+12
Step-by-step explanation:
2*x=2x
2x6=12
2x+12
using half angle identities what is the exact value of sin(9pi/8)
Answers
Step-by-step explanation:
first you put it in degree mode by multiplying 9pi/8 by pi/180.
The table below shows that the number of miles driven by Lily is directly proportional to the number of gallons she used. Gallons Used Miles Driven 37 754.8 47 958.8 50 1020 What is the constant of proportionality between the number of miles driven and the number of gallons used?
Answers
Answer:
20.4
Step-by-step explanation:
Constant of proportionality, k, is given as [tex] \frac{y}{x} [/tex].
Given that number of miles driven by Lily is directly proportional to the number of gallons she used, therefore the constant of proportionality between the number of miles driven and the number of gallons used can be determined by using any given pair from the table of values.
Using, (50, 1020),
constant of proportionality (k) = [tex] \frac{1020}{50} = 20.4 [/tex].
The constant of proportionality is 20.4 miles per gallon.
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
Let y represent the distance driven in miles for x galloons.
From the table, using the points (37, 754.8) and (50, 1020):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-754.8=\frac{1020-754.8}{50-37}(x-37)\\\\y-754.8=20.4(x-37)\\\\y=20.4x[/tex]
Therefore the constant of proportionality is 20.4 miles per gallon.
Find out more at: https://brainly.com/question/13911928
(a movie rental website charges $5.00 per month for membership and $1.25 per movie)
25. Marissa has $18.50 this month to spend on movie rentals
A. how many movies can she view this month
b. Marisa thinks she can afford 11 movies in one month. What mistake could she be making
Pls help me have mean math teacher ;((
Answers
Answer:
a.)she can view 10 movies. b.) One mistake she could be making is that she isn't adding the website fee to her total.
Step-by-step explanation:
Jim took 3 hours to drive 150 miles. At that rate, how far would he drive in 8 hours?
Answers
Answer:
400 miles in 8 hours
Step-by-step explanation:
Divide to find the unit rate.
150 / 3 = 50mph
Multiply.
50 * 8 = 400mi
Best of Luck!
Answer:
400 miles
Step-by-step explanation:
3:150=8:x
X=150x8/3
X=400
what did they do wrong
Answers
help? ik im dumb but i need good grades and i can risk getting anything wrong
Answers
HELP ME HELP
PLZ
PLZ
PLZ
Answers
Answer: 3, 2, 1, 0, -1
Step-by-step explanation:
3, 2, 1, 0, -1
Here you go brainly, thanks
Answers
At a local high school, 30% of the students are on a school sports team, 25% take at least one Advanced Placement (AP) class, and
10% are on a sports team and take at least one AP class. If a student was randomly selected from this school, what is the
probability that the student is on a sports team or takes at least one AP class?
Plz hurryyyy
Answers
0.45 will be the probability that the student is on a sports team or takes at least one AP class
What is probability?Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Given, At a local high school, 30% of the students are on a school sports team, 25% take at least one Advanced Placement (AP) class,
So,
Probability of Getting a student from a sports TeamP(A) = 0.3
Probability of Getting a student from an AP class P(B)= 0.25
Since 10% are on a sports team and take at least one AP class.
P(A ∩ B ) = 0.10
Thus,
P(A∪B) = P(A) + P(B) - P(A ∩ B )
P(A∪B) = 0.30 + 0.25 - 0.10
P(A∪B) = 0.45
therefore, the probability that the student is on a sports team or takes at least one AP class will be 0.45.
Learn more about probability here:
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What do you call that property in division when you divide
12÷ 2 = 6
Answers
Answer: There is no property for that equation but it is called Standard Divison.
Step-by-step explanation:
To find 12/2=6 is by splitting 12 into to groups and you got your answer.
