Answers
Solution:
The equation of the ellipse in the question is given as
[tex]\frac{(y-3)^2}{9}-\frac{(x-3)^2}{9}=1[/tex]Concept:
The general formula of a hyperbola is
[tex]\begin{gathered} \frac{(y-h)^2}{b^2}-\frac{(x-k)^2}{a^2}=1 \\ \text{Where } \\ h,k\text{ are the centres} \end{gathered}[/tex]From the above equation by comparing coeficient, we will have
[tex]\begin{gathered} a^2=9 \\ a=3 \\ b^2=9 \\ b=3 \\ (a,b)\Rightarrow(3,3) \\ h=3,k=3 \end{gathered}[/tex]The linear eccentricity c, will be
[tex]\begin{gathered} c=\sqrt[]{a^2+b^2} \\ c=\sqrt[]{3^2+3^2} \\ c=\sqrt[]{9+9} \\ c=\sqrt[]{18} \\ c=3\sqrt[]{2} \end{gathered}[/tex]The vertices of the hyperbola will be calculate using the formula below
[tex]\begin{gathered} (h,k-b)\Rightarrow(3,3-3)\Rightarrow(3,0) \\ (h,h+b)\Rightarrow(3,3+3)\Rightarrow(3,6) \end{gathered}[/tex]The co-vertex are calculated using the formula below
[tex]\begin{gathered} (h-a,k)\Rightarrow(3-3,3)\Rightarrow(0,3) \\ (h+a,k)\Rightarrow(3+3,3)\Rightarrow(6,3) \end{gathered}[/tex]The foci of the hyperbola will be calculated using the formula below
[tex]\begin{gathered} \mleft(h,k-c\mright)\Rightarrow(3,3-3\sqrt[]{2)} \\ \mleft(h,k+c\mright)\Rightarrow\Rightarrow\Rightarrow\mleft(3,3+3\sqrt[]{2}\mright) \end{gathered}[/tex]The eccentricity, e is
[tex]e=\frac{c}{b}=\frac{3\sqrt[]{2}}{3}=\sqrt[]{2}[/tex]Hence,
The sketch of the graph is given below as
The foci is represented with the two red dots on the graph
The vertices are represented above by the two coordinates
Related Questions
Write the quadratic equation whose roots are -3 and -1, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
Answers
The quadratic equation will be; 3x² + 6x + 9
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.
Given that roots are x = -3 and x = - 1, and whose leading coefficient is 3.
The factors are; (x + 3) and (x + 1)
f(x) = a(x + 3)(x + 1)
As, a = 3.
Then we get;
f(x) = 3(x + 3)(x + 1)
= 3(x² + 2x + 3)
= 3x² + 6x + 9
The quadratic equation will be; 3x² + 6x + 9
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Determine the total number of roots of each polynomial function.
g(x) = 5x - 12x²+3
Answers
The highest degree is 2 (in -12x^2), so there must be two factors and therefore two roots.
(To check if the roots are real, the discriminant can be used.)
Find the nth term of this quadratic sequence
-1, 2, 7, 14, 23, . . .
Answers
Answer:
The pattern the sequence follows is a perfect square, minus 2
Step-by-step explanation:
esentially use ( n^2 - 2 ) to find the nth number in the sequence.
the 5th number ( n = 5 ), would look like ( 5^2 - 2 ), simplfiying to ( 25 - 2 ), then being 23.
The same applies to all numbers listed in the sequence.
Need help on probability. Please explain how you did it so I can know how to do it.
Answers
Answer:
I believe it should be 5/6
Step-by-step explanation:
Here's why, the probability of getting a B, or an even number is 3/6 since there are 3 even numbers on a dice. The probability of getting a multiple of 3 is 2/6 since the only multiples of 3 are 1 and 3. Add the 2 together to get 5/6. Hope this helps.
Answer:
[tex]\text{P}(B \text{ or }C)=\dfrac{5}{6}[/tex]
Step-by-step explanation:
Mutually Exclusive Events
For two events, A and B, where A and B are mutually exclusive:
[tex]\boxed{\text{P}(A \text{ or }B)=\text{P}(A)+\text{P}(B)}[/tex]
Probability distribution table:
[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\cline{1-7} x & 1 & 2 & 3 & 4 & 5 & 6 \\\cline{1-7} \text{P}(X=x)\phantom{\dfrac11}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}&\frac{1}{6}\\\cline{1-7}\end{array}[/tex]
where X is the score on a fair, six-sided dice.
P(B or C) means "the probability of rolling an even number or a multiple of 3".
As an even number of a fair, six-sided dice can never be a multiple of 3, the two events B and C are mutually exclusive.
Calculate the probabilities for events B and C.
Event B
Rolling an even number.
[tex]\begin{aligned}\implies \text{P}(X \text{ is even})&=\text{P}(2 \text{ or }4\text{ or }6)\\\\&=\text{P}(X=2)+\text{P}(X=4)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{3}{6}\end{aligned}[/tex]
Event C
Rolling a multiple of 3.
[tex]\begin{aligned}\implies \text{P}(X \text{ is multiple of 3})&=\text{P}(3 \text{ or }6)\\\\&=\text{P}(X=3)+\text{P}(X=6)\\\\& = \dfrac{1}{6}+ \dfrac{1}{6}\\\\&=\dfrac{2}{6}\end{aligned}[/tex]
Solution
[tex]\begin{aligned}\implies \text{P}(B \text{ or }C)&=\text{P}(B)+\text{P}(C)\\\\& = \dfrac{3}{6}+\dfrac{2}{6}\\\\& = \dfrac{5}{6}\end{aligned}[/tex]
Solve the proportion.
Answers
t = 6
I WILL USE CROSS MULTIPLICATION
[tex]t(1.3) = 6.5(1.2) \\ 1.3t = 7.8 \\ \frac{1.3t}{1.3} = \frac{7.8}{1.3} \\ t = 6 [/tex]
ATTACHED IS THE SOLUTION
How many tiles measuring 20cm by 50cm are needed to completely cover a wall 4m by 8m?
Answers
The number of tiles measuring 20cm by 50cm that are needed to completely cover a wall 4m by 8m is :320.
Number of tiles neededFirst step is to convert the Meters to Centimeters
4m = 400cm
8m = 800 cm
Hence,
4m by 8m = 400 cm × 800 cm
4m by 8m = 320,000 cm²
Second step is to determine the how many tiles are needed
Number of needed tiles = 320,000 cm² / ( 20 cm × 50 cm)
Number of needed tiles = 320,000 cm² /1,000 cm²
Number of needed tiles = 320
Therefore 320 tiles are needed.
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Felicity put down $800 on a used car. She took out a loan to pay off the balance of the cost of the car. Her monthly payment will be $175. After 9 months how much will she have paid for the car?
Enter your answer in dollars.
Answers
Its honestly quiet easy to do in your head tbh
3. Solve the compound inequality −2(x + 1) < 4 and
4x +1 -3. Graph the solution.
Answers
So x>-2-1
x>-3
Find the approximate side length of a square game board with an area of 160
in2.
Answers
The approximate side length of a square game board with an area of 160in² is equal to 12.6 inches.
As given in the question,
Area of the square game board is equal to 160in².
Let 'x' inches be the side length of the square game board.
Area of the square game board = (side length)²
⇒ 160 = ( x )²
Take square root both the sides we get,
x = √160
⇒ x = 12.649 inches
⇒ x = 12.6 inches( approximately)
Therefore, the approximate side length of a square game board with an area of 160in² is equal to 12.6 inches.
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Find a and b*
9√√3
2
a
60°
b
Answers
The value of a is 9 and b is 4.5
What is trigonometric function ?The measurement of angles and issues relating to angles are covered in the fundamentals of trigonometry. Trigonometry has three fundamental operations: sine, cosine, and tangent. The cotangent, secant, and cosecant are three crucial trigonometric functions that can be derived from these three fundamental ratios or functions. These functions serve as the foundation for all the key ideas in trigonometry.
[tex]sin(60)=\frac{opposite}{hypotenuse} \\\frac{\sqrt{3} }{2}=\frac{\frac{9\sqrt{3} }{2} }{a}\\ a =9\\ tan(60)=\frac{opposite}{adjacent}\\ \sqrt{3}=\frac{\frac{9\sqrt{3} }{2} }{b} \\b=4.5[/tex]
The value of a is 9 and b is 4.5
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Evaluate,f(-4) for f(x)=-x^2-4x+42
Please explain by step by step please!
Answers
The output value of f( -4 ) in the function f(x) = -x² - 4x + 42 is 42
What is the output value of f( -4 ) in the given function?A function is simply a relationship that maps one input to one output. Every x-value can only have one y-value to qualify as a function.
Given the data in the question;
f( x ) = -x² - 4x + 42f( -4 ) = ?To find the output value of f( -4 ), replace all the occurrence of x with -4 in the function and simplify.
f( x ) = -x² - 4x + 42
f( -4 ) = -(-4)² - 4(-4) + 42
f( -4 ) = -( 16 ) + 16 + 42
f( -4 ) = -16 + 16 + 42
f( -4 ) = 42
Therefore, the output value of f( -4 ) is 42, this forms an ordered pair of (-4, 42).
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Ang has x dollars in his savings account, and Julia has y dollars in her savings account. Ang gives Julia 1/3 of the money in his savings account, which Julia deposits into her savings account. Julia then spends 1/4 of the total in her savings account. Express the amount of money Julia spent non terms of x and y.
Answer choices
1. y/4 + x/12
2. y/4 + x/3
3. y/4 + x/7
4. 3y/4 + x/4
Answers
In terms of x and y, Julia's withdrawal from her savings account was equal to y/4 + x/12.
What does algebraic expression mean?An expression obtained by performing a finite number of algebraic fundamental operations on symbols representing numbers.
What is an illustration of an algebraic expression?Algebraic expressions have at least one variable and one operation (addition, subtraction, multiplication, division). 2(x + 8y) is an example of an algebraic expression.Both Ang and Julia have savings balances of x and y dollars, respectively.
Ang = x dollars
Julia = y dollars
Ang offers Julia a third of his savings, which she then transfers to her own savings account.
Amount in Julia's account = (1/3)x + y
Julia then spends a quarter of the total into her savings account.
Amount of money Julia spent = 1/4 × [(1/3)x + y]
= (1/12)x + (1/4)y
= y/4 + x/12
Therefore, in terms of x and y, the amount Julia spent from her savings account is y/4 + x/12.
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You have $28 to go bowling. It costs $3.00 to rent a pair of bowling shoes and $3.25 per
game. At most, how many games will you be able to bowl?
Answers
Answer: 7 games
Explanation:
1. take the information and put it into a equation (being y=3.25x+3 or f(x)=3.25+3)
2. replace the x with a whole number because you can't bowl half a game.
Ex: f(3)=12.75 or f(6)=22.50
3. The highest you can go without going over your money is 7 games ($25.75) leaving you with a total of 2.25.
Hope this helps :)
 I REALLY NEED HELP WITH THIS!!
Determine the angles of a rotation
A) 90º clockwise
B) 90º counterclockwise
C) 180º
D) 270º clockwise
E) 270º counterclockwise
is 2 correct answers ❗️
Answers
Answer: B) 90º counterclockwise
Step-by-step explanation:
First, let us look at clockwise vs counterclockwise. Clockwise is in the direction of a clock, spinning around to the right. Counterclockwise is the opposite, spinning to the left.
A) 90º clockwise
➜ This is 90 degrees to the right.
B) 90º counterclockwise
➜ This is 90 degrees to the left
C) 180º
➜ This is directly flipped.
D) 270º clockwise
➜ This is 270 degrees to the right.
E) 270º counterclockwise
➜ This is 270 degrees to the left.
We will look at the answer options and decide which makes the most sense. This looks to be option B, 90º counterclockwise as shown in the image attached.
Need help simple stuff that I forgot in algebra. How do u get 5x/2-x???
Answers
Answer: 7/12 =x
Step-by-step explanation:
Jordan needs to order some new supplies for the restaurant where he works. The restaurant needs at least 730 knives. There are currently 204 knives. If each set on sale contains 10 knives, write and solve an inequality which can be used to determine xx, the number of sets of knives Jordan could buy for the restaurant to have enough knives
Answers
Answer:
53 sets
Step-by-step explanation:
730 - 204 = 526
526 / 10 = 52 r 6
therefore he'd have to buy 53 sets to have enough knives.
There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The restaurant needs at least 730 knives.
There are currently 204 knives.
And, each set on sale contains 10 knives.
Now,
By the given condition, we formulate;
⇒ 730 ≤ 204 + 10x
Solve for x as;
⇒ 730 ≤ 204 + 10x
⇒ 730 - 204 ≤ 204 + 10x - 204
⇒ 529 ≤ 10x
Divide by 10 as;
⇒ 52.9 ≤ x
After rounding, we get;
⇒ 53 ≤ x
Thus, There are 53 number of sets of knives Jordan could buy for the restaurant to have enough knives.
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Suppose a jar contains 11 red marbles and 38 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answers
22.44% probability that the marbles are red, 77.55% probability that they are blue
What would 6 + -4 3/4 + -2 1/8 be?
Answers
Answer: -0.875
Step-by-step explanation:
Answer: -1 1/8
Step-by-step explanation:
6 - 4 3/4 = 1 1/4
1 1/4 - 2 1/8 = -1 1/8
A car uses 3 1/8 gallons of gasoline per hour when driving on the highway, how many gallons will it use after three hours?
Answers
Answer:
The car will use 9 3/8 or 9.375(simple form) gallons of gasoline on the highway
Step-by-step explanation:
if a car uses 3 1/8 gollon per one hour
Multiply the gallon usage of the car by the hours the car will travel on the road
3 1/8(gallons) x 3(hours on the road)
9 3/8 or if you change it to simple form it will be equal to 9.375
A printer prints 75 pages in 5 minutes.
At the same rate, how many pages does the printer print in 7 minutes?\
Answers
Answer:
105
Step-by-step explanation:
5 minutes=75 pages
1 minute=15 pages
7 minutes=15*7
7 minutes=105pages
Answer: 105
Step-by-step explanation:
75pg —-> 5mins
X ——> 7 mins
•
•
x= (75 x 7)/5 = 105pages
answer the 2 questions in the photo for a brainliest
Answers
Answer:
180 Degrees for both
they are symmetrical therefore 180 degrees
Here are two expressions whose sum is a new expression, A.
(2x²+5)+(6x0-7)=A
Select all the values that we can put in the box so that A is a polynomial.
Answers
All the values that we can put in the given box so that A is a polynomial,
[tex]A=(2x^{2} +5-7)\\A =2(x^{2} -1)\\A=2(x+1) (x-1)[/tex]
[tex]x[/tex] can take any value except ±1.
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Each handmade pin needs inch 1/4 of wood. How much wood would you need to make 120 pins?
Answers
We can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.
What do we mean by mathematical operations?A mathematical "operation" is the process of calculating a value using operands and a math operator.There are predefined rules associated with the math operator's symbol that must be applied to the supplied operands or numbers.The arithmetic operators perform the operations of addition, subtraction, multiplication, division, exponentiation, and modulus.So, the wood we need to make 120 pins:
The wood used to make 1 pin is ¼.Then, 120 pins:120 × ¼ = 30Therefore, we can conclude that 30 inches of wood is needed to make 120 pins by solving some mathematical operations.
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Suppose 84% of students chose to study German their sophomore year, and that meant that there were 525 such students. How many students chose not to take German their sophomore year?
Answers
Answer: 100
Step-by-step explanation:
525/84 x 100= 625 total students
625 - 525 = 100
Denver,Colorado often experiences snowstorms resulting in multiple inches of accumulated snow. During the last snow storm, the snow accumulated at 4/5 inch/hour. If the snow continues at this rate for 10 hours, how much snow will accumulate?
Answers
Answer:8
Step-by-step explanation:if it is 4/5 per hour then you mulitply 4/5 x 10
and 4/5=.8
.8 x 10=8
How to make x the subject if m=n+x/p
Answers
Variable x as the subject of the equation given is expressed as: x = p(m - n).
How to Make a Variable the Subject of the Formula?To make a variable the subject of a formula implies that we express the equation in terms of the variable. Thus, to make a variable the subject of the formula, we have to make the variable stand alone on one side of the equation.
Given the equation, m = n + x/p, make x the subject as explained below:
m = n + x/p [given]
Subtract n from both sides
m - n= n + x/p - n (subtraction property of equality)
m - n = x/p
Multiply both sides by p
p(m - n) = x/p(p) (multiplication property)
p(m - n) = x
x = p(m - n)
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The number of bald eagles in the state in the winter of 2000 is
(Round to the nearest whole number.)
Save
The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function
f(x) = -3.334x4 +35.607x3-97.645x² +41.268x + 177.537
where x is the number of years since 1996. Find the number of bald eagles in the state in the winter of 2000.
Answers
Answer:
206
Step-by-step explanation:
Let x=4.
[tex]f(4)=-3.334(4)^4+35.607(3)^3-97.645(4)^2+41.268(4)+177.537 \approx 206[/tex]
Calculate the force created from an object with a mass of 1250 grams and an acceleration of 3 m/s^2
Please help!! I will mark as brainliest
Answers
The force created by the object is 3.75 Newton.
Given
Mass of the object (m) = 1250 grams
Convert 1250 grams to kilograms by dividing it by 1000.
Mass (m) = 1.25 kg
Acceleration of the body (a) = 3 [tex]m/s^{2}[/tex]
From Newton's second law we know [tex]F= m *a[/tex]
By Substituting in the above equation we get
Force = 1.25 x 3
Force = 3.75 [tex]kg/m /s^{2}[/tex]
It can also be written as force = 3.75 N
Hence Force created by the body is 3.75 Newton.
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If h(x)=x^2/f(x) and f(3) = 2 and f'(3) = 4, then h' (3) = -12.
true
false
Answers
Answer:
FALSE.
Step-by-step explanation:
Given:
h(x)=x^2/f(x) f(3) = 2 f'(3) = 4To Find:
Whether h'(3) = -12 or not.Formula used:
For a function y = f(x)/g(x), the differentiation of y is defined as y' = [f'(x)*g(x) - g'(x)*f(x)]/(g(x))^2. This is know as quotient rule of differentiation.Using the above formula, we have
h'(x) = [2x*f(x) - f'(x)*x^2]/(f(x))^2
So, h'(3) = [2*3*2 - 4*(3)^2]/(2)^2
h'(3) = (12-36)/4
h'(3) = -24/4 = -6
So, h'(3) = -6 and not -12.
So, the given value is FALSE.
4x-6(3x+4)
please help, i cannot find an answer :( (Ill give crown or wtv)
Answers
Answer:
Is this correct??
if yes then reply
Answer/Step-by-step explanation:
I don't know whether to distribute -6 or multiply 4x - 6 by 3x + 4. So I'll do both.
1. Multiply
(4x - 6)(3x + 4)
4x (3x + 4) - 6 (3x + 4)
12x² + 16x - 18x - 24
12x² - 2x - 24
2. Distribution
4x - 6(3x + 4)
4x - 18x - 24
-14x - 24
I hope either of my answers helps!