Answers
Answer:
The center is (8 , -9)
The vertices are (11 , -9) and (5 , -9)
The foci are (8 , -9 + √58) and (8 , -9 - √58)
The equations of the asymptotes are y = 3/7(x − 8) - 9 , y = -3/7 (x − 8) - 9
Step-by-step explanation:
- The standard form of the equation of a hyperbola with
center (h , k) and transverse axis parallel to the y-axis is
(y - k)²/a² - (x - h)²/b² = 1
- The length of the transverse axis is 2 a
- The coordinates of the vertices are ( h ± a , k )
- The length of the conjugate axis is 2 b
- The coordinates of the co-vertices are ( h , k ± b )
- The coordinates of the foci are (h , k ± c), where c² = a² + b²
- The equations of the asymptotes are y = ± a/b (x − h) + k
* Now lets solve the problem
∵ (y + 9)²/9 - (x - 8)²/49 = 1
∴ h = 8 and k = -9
∴ a² = 9 ⇒ a = ± 3
∴ b² = 49 ⇒ b = ± 7
∵ c² = a² + b²
∴ c² = 9 + 49 = 58
∴ c = ± √58
∵ The center is (h , k)
∴ The center is (8 , -9)
∵ The coordinates of the vertices are ( h ± a , k )
∴ The vertices are (8 + 3 , -9) and (8 - 3 , -9)
∴ The vertices are (11 , -9) and (5 , -9)
∵ The coordinates of the foci are (h , k ± c)
∴ The foci are (8 , -9 + √58) and (8 , -9 - √58)
∵ The equations of the asymptotes are y = ± a/b (x − h) + k
∴ The equations of the asymptotes are y = 3/7 (x - 8) - 9 and
y = -3/7 (x − 8) - 9
Answer:
Center = (-9,8)
Foci = (0,±7.6)
Vertices = (0,±3)
Asymptotes y = 8±(3/7)(x+9)
Step-by-step explanation:
We need to find the center, vertices, foci and asymptotes of hyperbola:
[tex]\frac{(y+9)^2}{9} - \frac{(x-8)^2}{49}=1[/tex]
The hyperbola has vertical transverse axis having standard equation:
[tex]\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2}=1[/tex]
The center is (h,k), foci (0,±c) , vertices = (0,±a) and
asymptotes = y= k±(a/b)(x-h)
Solving for the given equation by comparing with standard equation:
a^2 = 9 => a = 3
b^2 = 49 => b =7
h= -9
k= 8
c^2 - a^2 = b^2
c^2 = b^2 + a^2
c^2 = 49+9
c^2 = 58
c = 7.6
Now Center(h,k) = (-9,8)
Vertices (0, ±a) = (0,±3) or (0,+3), (0,-3)
Foci (0,±c) = (0, ±7.6) or (0+7.6), (0,-7.6)
Asymptotes = y= k±(a/b)(x-h)
Putting values:
y= 8±(3/7)(x-(-9)
y = 8±(3/7)(x+9)
or y = 8+(3/7)(x+9) and y= 8-(3/7)(x+9)
Related Questions
Can you help me with this word problem?
Answers
Answer:
The ratio of flour to sugar is 2:1
Step-by-step explanation:
Let f = weight of a bag of flour
Let s = weight of a bag of sugar
3f+2s = 32
4f = 32
We have 2 equations and 2 unknowns, we can solve
4f=32
Divide by 4
4f/4 = 32/4
f = 8
Each bag of flour weights 8 pounds
Substitute this back into the first equation
3(8) +2s = 32
24+2s = 32
Subtract 24 from each side
24-24 +2s =32-24
2s = 8
Divide by 2
2s/2 = 8/2
s = 4 pounds
Flours weighs 8 pounds and sugar weights 4 pounds
We want the ratio of flour to sugar
Flour: sugar
8:4
We can divide each side by 4
8/4: 4/4
2:1
Select all of the expressions that are equal to 6,
(6)
(-6)
-(6)
-(-6)
(0-6)
(-2) •(3)
Answers
Answer:
(6), -(-6)Step-by-step explanation:
[tex](6)=6\\\\(-6)=-6\neq6\\\\-(6)=-6\neq6\\\\-(-6)=6\\\\(0-6)=(-6)=-6\neq6\\\\(-2)\cdot(3)=-6\neq6[/tex]
The expressions that are equal to 6 are:
(6) , -(-6)
Step-by-step explanation:We are asked to find the expressions which are equal to 6.
a)
(6)
We know that on opening the parentheses term if the sign before the parentheses is positive then the number remains the same.
but if the sign before the parentheses is negative then the number gets reversed.
Hence, the number is equal to 6.
b)
(-6)
The number is equal to -6.
c)
-(6)
The number is equal to -6.
d)
-(-6)
The number is equal to 6.
e)
(0-6)
The number is equal to -6.
f)
(-2) · (3)
The number is equal to -6.
( We know that the multiplication of a negative and a positive number is always a negative number ).
Please help with this math question will give BRAINLIEST and 10 points
Answers
I got B for the answers
Answer:
( 3 × 2 ) × 7
Step-by-step explanation:
To find the volume of a rectangular prism you have to do
Length × Width × Height
3 × 2 × 7 = 42 yd³
PLEASE HELP!!!! 25 POINTS!!!!! I NEED THIS ASAP!!!!!!
Answers
Answer:
[tex]\large\boxed{\left\{\begin{array}{ccc}y-17z=-15&(a)\\-2y+17z=13&(b)\end{array}\right}[/tex]
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2x-3y+5z=5&(1)\\4x-5y-7z=-5&(2)\\-6x+7y+2z=-2&(3)\end{array}\right\\\\\\\text{From (1) and (2)}\\\left\{\begin{array}{ccc}2x-3y+5z=5&(1)&\text{multiply both sides by (-2)}\\4x-5y-7z=-5&(2)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-4x+6y-10z=-10\\4x-5y-7z=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad y-17z=-15\qquad(a)[/tex]
[tex]\text{From (1) and (3)}\\\left\{\begin{array}{ccc}2x-3y+5z=5&(1)&\text{multiply both sides by 3}\\-6x+7y+2z=-2&(3)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}6x-9y+15z=15\\-6x+7y+2z=-2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-2y+17z=13\qquad(b)[/tex]
If f(×)= x^1/2-× and g(×) = 2x^3-×^1/2-×, find f(×)-g(×). Pleade ASAP
Answers
Answer:
-2x^3 + 2x^(1/2)
Step-by-step explanation:
step one- plug in the values of each in f(x) - g(x)
x^(1/2)-x - (2x^3-×^(1/2)-x) ; g(x) is in parentheses bc we need to distribute the negative
x^(1/2)-x-2x^3 + x^(1/2) + x ; combine like terms (letters with the same exponents) ; the x's cancel, and the x^(1/2) + x^(1/2) combine to form 2x^(1/2); the -2x^3 remains
you should get
-2x^3 + 2x^(1/2)
Answer:
[tex]f(x) - g(x) = 2(\sqrt{x}-x^3)[/tex]
Step-by-step explanation:
We have the functions
[tex]f(x)= x^{\frac{1}{2}}-x[/tex] and [tex]g(x) = 2x^3-x^\frac{1}{2}-x[/tex]
The operation [tex]f (x) -g (x)[/tex] is the subtraction of the function f(x) minus the function g(x). Thus
[tex]f(x) - g(x) = x^{\frac{1}{2}}-x -(2x^3-x^\frac{1}{2}-x)[/tex]
Simplifying the expression we have left that:
[tex]f(x) - g(x) = x^{\frac{1}{2}}-x -2x^3+x^\frac{1}{2}+x[/tex]
[tex]f(x) - g(x) = 2x^{\frac{1}{2}}-2x^3[/tex]
[tex]f(x) - g(x) = 2(\sqrt{x}-x^3)[/tex] Because [tex]x^{\frac{a}{n}} = \sqrt[n]{x^a}[/tex]
Lucie is 5 years younger than her brother. Three years ago, Lucie was twice younger than her brother. How old is each now?
Answers
Answer: Lucie is 8 and her brother is 13
Step-by-step explanation: the only possible way for Lucie to be half her brother's age while being 5 years younger at the same time, is if she's 5 and he's 10. that's how old they were 3 years ago. now you just add 3 to 5 and 10 to find their current ages; 5+3=8 so Lucie is 8, and 10+3=13 so her brother is 13.
:)
Answer:
Lucie is 8 and her brother is 13
Step-by-step explanation:
Lucie is 5 years younger than her brother. Three years ago, Lucie was twice younger than her brother.
Let L be the Lucie age
and B be the brothers age
Lucie is 5 years younger than her brother
L= B-5
Three years ago, Lucie age is L-3
brother is B-3
Lucie was twice younger than her brother.
2(L-3)= B-3
Plug in B-5 for L
2(B-5-3)= B-3
2B - 16= B-3
Subtract B from both sides
B - 16 = -3
Add 16 on both sides
B= 13
Age of brother = 13
Age of Lucie = brother -5 = 13-5 = 8
what is the zero of the function below? f(x)=3 square root x+3 -6
x=1
x=-1
x=9
x=-3
Answers
Answer:
x = 1Step-by-step explanation:
[tex]f(x)=3\sqrt{x+3}-6\\\\\text{Domain:}\ x+3\geq0\to x\geq-3\\\\\text{The zero}\to f(x)=0\\\\3\sqrt{x+3}-6=0\qquad\text{add 6 to both sides}\\\\3\sqrt{x+3}=6\qquad\text{divide both sides by 3}\\\\\sqrt{x+3}=2\iff x+3=2^2\\\\x+3=4\qquad\text{subtract 3 from both sides}\\\\x=1[/tex]
Answer:
x=1
Step-by-step explanation:
Given function,
[tex]f(x)=3\sqrt{x+3}-6[/tex]
Since, the zeroes of a function are those input values for which the function gives the output zero,
So, for the zeroes of f(x),
f(x) = 0
[tex]\implies 3\sqrt{x+3}-6=0[/tex]
[tex]3\sqrt{x+3}=6[/tex] ( Adding 6 on both sides )
[tex]\sqrt{x+3}=2[/tex] ( Dividing both sides by 3 )
[tex]x+3=4[/tex] ( Taking square of both sides )
[tex]x = 1[/tex] ( Subtracting 3 from both sides )
Hence, the zero of the given function is, x = 1.
First option is correct.
SHOW YOUR WORK
A quadratic equation is shown below:
3x2 − 11x + 10= 0
Part A: Find the vertex. Show your work.
Part B: Solve for x using an appropriate method. SHOW THE STEPS OF YOUR WORK.
Answers
Answer: x=-16/11
6+11x+10=0
We add all the numbers together, and all the variables
11x+16=0
We move all terms containing x to the left, all other terms to the right
11x=-16
x=-16/11
Answer:
Vertex:
Roots: [tex]x=\frac{5}{3}[/tex] or [tex]x=2[/tex]
Step-by-step explanation:
The given quadratic equation is:
Let [tex]f(x)=3x^2-11x+10[/tex]
We obtain the vertex form by completing the square;
[tex]f(x)=3(x^2-\frac{11}{3}x)+10[/tex]
Add and subtract the square of half the coefficient of x.
[tex]f(x)=3(x^2-\frac{11}{3}x+(-\frac{11}{6})^2+10-3(-\frac{11}{6})^2)[/tex]
This simplifies to
[tex]f(x)=3(x-\frac{11}{6})^2-\frac{1}{12}[/tex]
Hence the vertex is [tex](\frac{11}{6},-\frac{1}{12})[/tex]
We now solve to obtain:
[tex]3(x-\frac{11}{6})^2-\frac{1}{12}=0[/tex]
[tex]3(x-\frac{11}{6})^2=\frac{1}{12})[/tex]
[tex](x-\frac{11}{6})^2=\frac{1}{36})[/tex]
[tex](x-\frac{11}{6})=\pm \sqrt{\frac{1}{36}}[/tex]
[tex]x=\frac{11}{6}\pm \frac{1}{6}[/tex]
[tex]x=\frac{5}{3}[/tex] or [tex]x=2[/tex]
identify the amplitude of the graph
Answers
ANSWER
The amplitude is 1.6
EXPLANATION
The amplitude is half of the highest value minus the least values.
The highest value on the graph also occurs at 0, which is 5.20
The least value is 2
The amplitude is
[tex] = \frac{5.20-2}{2} = 1.6[/tex]
Therefore the amplitude is 1.6
Which of the following has the same value as C(10, 3)? P(10, 3) C(10, 7) C(9, 6)
Answers
Answer: second one P(10,3)?
Step-by-step explanation:
Answer:
The Answer is C(10,7) Just did it on my homework
Step-by-step explanation:
what is the positive difference between-8 and -14
Answers
Answer:
22
Step-by-step explanation:
8 - (-14)
keep, change, change
8 + 14 = 22
Answer:
6
Step-by-step explanation:
-14 is smaller than -8. We subtract -14 from -8, obtaining +14 - 8, or +6.
The positive difference between -8 and -14 is 6.
hurry nowwwwwww which inequality and soulition represent the following situation? when 4 is subtracted from 10 times a number the result is greater than 1.5
A)10b-4>1.5;>-0.25
B)4-10b<0.25
C)10b-4>1.5;b>0.55
D)4-10b>1.5b;>0.25
Answers
Liza finished studying at half past 3. What time did Liza finish studying?
Answers
3:30
Half past means 30 min after
Hope this helped!
Liza finished studying at 3:30
What is slope intercept form
Answers
Answer:
y = mx+b
Step-by-step explanation:
Answer:
y = mx +b
Step-by-step explanation:
m=slope
b=y-intercept
Please help with this question
Answers
Answer:
90-73=17
the correct answer is 17
For this case we must find the angle "x" of the figure shown.
If we look at the figure, we have to:
AC equals 90 degrees.
So we have to:
[tex]73 + x = 90[/tex]
We clear the value of "x":
[tex]x = 90-73\\x = 17[/tex]
Thus, the value of "x" is 17 degrees.
Answer:
17 degrees
Option A
1) Select the equations that are equivalent to the equation y-4=5(x+2). Select all that apply.
A) y=2x+5
B) y=5x+14
C) 5x-y=-14
D) 2x+y=14
2) Which of the following represents an equation of a line with a slope of 5 and a y-intercept of 1?
A) y=5x+1
B) y=5x-5
C) x-5y=-5
D) y= -1/5x+1
Answers
Answer:
see explanation
Step-by-step explanation:
1
Given
y - 4 = 5(x + 2) ← distribute parenthesis
y - 4 = 5x + 10 ( add 4 to both sides )
y = 5x + 14 → B
Subtract y from both sides
0 = 5x - y + 14 ( subtract 14 from both sides )
- 14 = 5x - y → C
--------------------------------------------------
2
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = 5 and c = 1, thus
y = 5x + 1 → A
Find the length of side ab.
Answers
Answer:
41
Step-by-step explanation:
First, set up the equation (2x+5) + (3x-2)+(3x)+(x)= 57. Add all of the sides together and solve for x. Next, plug in x to 2x+5, and you have your answer. I hope this helps
What is the answer to
4x-x
Answers
4x - x
If there is a single variable with no number in front you can assume that there is a 1. How I think of it is that all singular variables have an invisible one in front
so...
4x - 1x
Since these are like terms you may subtract them like normal numbers. The only difference is that you'll have to add an x at the end of your answer
4 - 1
3
(REMEMBER to add the x back to the three)
so...
4x - x = 3x
Hope this helped!
~Just a girl in love with Shawn Mendes
I need to know the correct trigonometric ratios that could be sued to determine the length of LN
Answers
Answer:
A, E
Step-by-step explanation:
Remember SOH-CAH-TOA:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
Therefore, we can say:
sin 20° = LN / 8
cos 70° = LN / 8
tan 70° = MN / LN
Only the first and last options are correct.
2/3(1/4x—2)=1/5(4/3x—1)
Answers
Answer:
I got 15 and 1/3.
Given that (Triangle)MNO is similar to (Triangle)RST, determine the perimeter of (Triangle)RST.
Answers
Answer:
C
Step-by-step explanation:
Given that the 2 triangles are similar then the ratios of corresponding sides are equal.
This enables RT to be found, that is
[tex]\frac{4}6}[/tex] = [tex]\frac{10}{RT}[/tex] ( cross- multiply )
4RT = 60 ( divide both sides by 4 )
RT = 15
Hence
perimeter of ΔRST = 6 + 12 + 15 = 33 units
The perimeter of triangle RST which is similar to triangle MNO is: C. 33 units.
What is the Perimeter of a Triangle?The perimeter of a triangle = sum of all its 3 sides.
Since triangles MNO and RST are similar triangles, then their corresponding side lengths are proportional to each other.
This means that:
MN/RS = MO/RT = NO/ST
Find RT using MN/RS = MO/RT:
4/6 = 10/RT
RT = (10×6)/4
RT = 15 units.
Perimeter of triangle RST = RS + ST + RT = 6 + 12 + 15 = 33 units.
Learn more about the perimeter of a triangle on:
https://brainly.com/question/24382052
#SPJ5
(X-1)^2 + (y-3)^2=10 convert equation from rectangular form to polar form
Answers
Answer:
[tex]r= 2(cos(\theta) + 3sin(\theta))[/tex]
Step-by-step explanation:
To convert an equation of rectangular shape to polar form use the following equivalences
[tex]x=rcos(\theta)[/tex]
[tex]y=rsin(\theta)[/tex]
[tex]x^2 + y^2=r^2[/tex]
In this case we have the following equation.
[tex](x-1)^2 + (y-3)^2=10[/tex]
First we expanded the expression
[tex](x-1)^2 + (y-3)^2=10\\\\(x^2 -2x +1) +(y^2 -6y + 9) = 10\\\\\\x^2 +y^2 -2x -6y = 10-9-1\\\\x^2 +y^2 -2x -6y = 0[/tex]
Now we know that [tex]x^2 + y^2=r^2[/tex], [tex]x=rcos(\theta)[/tex] and [tex]y=rsin(\theta)[/tex]
So
[tex]r^2 -2rcos(\theta) -6rsin(\theta) = 0\\\\r^2 - 2r(cos(\theta) + 3sin(\theta))=0\\\\r^2 = 2r(cos(\theta) + 3sin(\theta))\\\\r= 2(cos(\theta) + 3sin(\theta))[/tex]
Which figures can have two sides of the same length, but are not parallelograms?
quadrilateral
rectangle
square
isosceles trapezoid
Multiple Choice Question
Answers
Answer:
Isosceles trapezoid.
Step-by-step explanation:
That would be an isosceles trapezoid. The 2 non-parallel sides are equal.
Answer:
isosceles trapezoid
rectangle
Two poles are located 3.2m apart. A wire links the tops of the two poles. Find the length of the wire if the poles are 3.8m and 6m in height. (one decimal place)
Answers
considering the diagram,the top part is a triangle with the base of 3.2m and height of 2.2m. since the triangle 8s is a right angle triangle. we use Pythagoras theorem to solve for the hypotenus
Final answer:
The length of the wire connecting the tops of two poles of heights 3.8m and 6m, and spaced 3.2m apart is approximately 3.9 meters when calculated using the Pythagorean theorem.
Explanation:
To calculate the length of the wire connecting the tops of two poles of different heights, we can use the Pythagorean theorem.
This theorem states that in a right angle triangle, the square of the length of the hypotenuse (the wire) is equal to the sum of the squares of the lengths of the other two sides (the distances between the tops of the poles and the ground).
Let's denote:
Pole A as the shorter pole with a height of 3.8m
Pole B as the taller pole with a height of 6m
The distance between the two poles as 3.2m
The difference in height between the two poles is 6m - 3.8m, which is 2.2m. Thus, we have a right triangle where one leg is 3.2m (distance between poles) and the other leg is 2.2m (height difference between poles).
Applying Pythagorean theorem:
c² = a² + b²
c² = 3.2² + 2.2²
c² = 10.24 + 4.84
c² = 15.08
c = √15.08
c ≈ 3.9m
Therefore, the length of the wire is approximately 3.9 meters.
greatest common factor of 117 and 19,110?
Answers
Answer:
1
Step-by-step explanation:
These numbers have no common factors. The only comon factor they have is one. Therefore, the GCF of 117, 19, and 110 is one.
A 3-gallon bucket of paint costs $98.52 what is the price per quart?
Answers
Answer:
3 gallons = 12 quarts
$98.52/12 quarts = $8.21/quart
To find the price per quart of a 3-gallon bucket of paint costing $98.52, divide the total cost by the number of quarts in 3 gallons, which is 12. The price per quart comes out to be approximately $8.21.
Explanation:To find the price per quart for a bucket of paint that costs $98.52 per 3 gallons, we first need to know the number of quarts in 3 gallons. Since 1 gallon equals 4 quarts, 3 gallons will be equal to 3 × 4 quarts, which is 12 quarts.
Therefore, if a 3-gallon bucket costs $98.52, to find the cost per quart, we need to divide the total cost by the total number of quarts.
So, the equation to find the price per quart would be:
Price per quart = Total cost / Number of quarts
Substituting the given values:
Price per quart = $98.52 / 12
Calculating the above, we find:
Price per quart = $8.21 (rounded to two decimal places)
Thus, the price per quart of the paint is approximately $8.21.
Sara and Triston want to collect data to find out what games should be played at the elementary school’s field day. Describe a group that they could survey to collect quality data.
Answers
i would think teachers
If m is a prime number, list all factors of m×m.
Answers
For a prime number m, the only factors of m x m would be 1, m, and [tex]m^2[/tex]
If m is a prime number, the factors of m would be 1 and m itself since prime numbers have no divisors other than 1 and themselves. When you calculate m x m which is [tex]m^2[/tex], the factors list expands slightly but remains quite simple due to the nature of prime numbers.
1 (1 can divide any number)m (since m is a prime and can divide its square)[tex]m^2[/tex] (the square of the prime number is a factor of itself)Those would be all the factors of [tex]m^2[/tex] when m is a prime number.
The form he builds is 35 1/2 inches long, 20 inches deep, and 6 inches high. How much cement is neede to fill the form
Answers
Answer:
4260 square inches
Step-by-step explanation:
35.5 times 20 times 6 is 4260
which of the following isnot a valid FICO credit store
Answers
Answer:
Where are the followings
Step-by-step explanation:
A valid FICO credit score ranges from 300 to 850. A score outside this range is not valid. Key components of a FICO score include credit mix and the impact of new credit, both accounting for 10% of the score respectively.
When it comes to determining what is not a valid FICO credit score, it's important to understand that FICO scores range from 300 to 850. Any score that is not within this range would be considered invalid. Components that make up a FICO score include payment history, amounts owed, length of credit history, new credit, and credit mix. Credit mix refers to the variety of credit types you have, such as credit cards, retail accounts, installment loans, finance company accounts, and mortgage loans, and makes up 10% of your FICO score. Regarding new credit, opening a new account can temporarily lower your score because it reduces the average age of your accounts, which also accounts for 10% of your FICO score.
Two common myths are that opening a new retail credit card is always good for your credit score and that it hurts your score to comparison shop for loans. In reality, opening a retail credit card can lower your score initially, though responsibly managing your new credit can eventually have a positive effect. When it comes to loan comparison shopping, FICO provides a grace period for hard inquiries that are related, bundling them into a single inquiry if they occur within a 14 to 45-day span, depending on the type of credit. This is designed to not penalize consumers who are responsibly shopping for the best rates.