Find the equation of the hyperbola shown below. 15 Points, will give Brainliest! Due in 2 HOURS! A. (x - 1)^2/4 - (y + 4)^2/9 = 1 B. (y - 1)^2/4 + (x+4)^2/9=1 C. ( y + 1)^2/4 - (x - 4)^2/9 = 1 D. (y - 1)^2/9 - (x + 4)^2/4 = 1
Answers
Answer:
Solution:
[tex]\frac{\left(y-1\right)^2}{9}-\frac{\left(x+4\right)^2}{4}=1[/tex]
Step-by-step explanation:
We have the general equation for our up - down facing hyperbola as (y - k)² / b²- (x - h)² / a² = 1. Let's start listing the properties of this graph -
• Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1). Therefore (h, k) = (- 4,1).
• Another thing here is our key value a. This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference. Therefore a = 3.
• That leaves us with our asymptotes. Now remember that it will be in the form y = ± b / a. We already know a = 3, so we have to find b. Looking at this graph I can say that another point besides (- 4,1) that lies on the " dotted line " is (- 2, - 2). Calculating the slope of the dotted line would be as follows,
Given: (- 4,1) and (- 2, - 2)
Slope = - 2 + 4 / - 2 - 1 = 2 / 3
We have the equation y = 2 / 3x. Therefore b = 2. Let's substitute to receive our equation...
h = - 4, k = 1, b = 2, a = 3
(y - 1)² / (3)²- (x + 4)² / (2)² = 1
(y - 1)² / 9 - (x + 4)² / 4 = 1 ~ your solution is the last one, option d
Related Questions
Write an expression to model the phrase:
Myles has $635 nd is earning $120 each
week as a lifeguard.
Answers
Answer:
[tex]Y= 120n+635[/tex]
Step-by-step explanation:
Alright!
we are expected to model the total amount of money Myles have\
firstly he has with him $635
and he is earning $120 weekly
Say the number of weeks he worked is given is n
and let the amount of money Myles will have after n weeks be y
hence we can now model the equation to represent how much Myles will have after n weeks
[tex]Y= 120n+635[/tex]
The expression is same as the equation for a straight line
i.e [tex]y= mx+c[/tex]
(50 points!) Whats 7x + 5z(x-z) ÷ 9y, when x = 5, z = 8, and y = 23. Whoever Gives me an answer AND REALLY GOOD EXPLANATION FIRST gets a free brainliest!
Answers
Answer: First we will substitute the numbers given for the variables.
Then we will use order of operations to simplify.
7x + 5z(x - z) ÷ 9y would be equal to
7(5) + 5(8) * (5 - 8) ÷ 9(23)
Simplify:
35 + 40(-3) ÷ 207
Use order of operations to multiply 40 and -3; the equation now looks like:
35 + (-120) ÷ 207
Use order of operations to divide -120 and 207; the equation now looks like:
35 + (-0.6)
Add 35 and -0.6:
34.4
The solution to this equation is 34.4.
Answer:
34.4
Step-by-step explanation:
7x + 5z(x - z) ÷ 9y
7(5) + 5(8) * (5 - 8) ÷ 9(23)
35 + 40(-3) ÷ 207
35 + (-120) ÷ 207
35 + (-0.6)
Add 35 and -0.6:
34.4
Hope this helps!
What is the value of the expression below when w equals
8?
W^2- 4w - 2
Answers
Answer:
When w =8. then...
8^2-4(8)-2.
64-32-2=30.
Answer:
Step-by-step explanation:
Plug in the value of w in the expression and use PEMDAS
w² - 4w - 2 = 8² - 4*8 - 2 {Need to calculate exponents}
= 64 - 4*8 - 2 {Now do multiplication}
= 64 - 32 - 2
= 32 - 2
= 30
Translate the sentence into an inequality.
A number y increased by 6 is less than or equal to - 15.
Answers
Answer:
y ≤ -21
Step-by-step explanation:
y+6≤-15
y≤-21
Hope this helps!
Answer: y + 6 <_ -15
- 6 -6
y <_ -21
There are two 3-digit numbers $n$ having the property that $n$ is divisible by 11 and $\dfrac{n}{11}$ is equal to the sum of the squares of the digits of $n$. Find both values of $n.$ You may submit them in either order.
Answers
Answer:
550 and 803
Step-by-step explanation:
Let the number be N = abc
Then:
abc/11 = (a² + b² + c²) ⇒ abc = 11(a² + b² + c²)There are:
1000 - 100 = 900 3-digit numbersOut of 900 numbers:
1000/11 - 100/11 = 81 are divisible by 11The easiest and simplest way is to try them all.
The trial reveals 550 and 803, so this is the answer.
What is the range of h?
Answers
Answer:
-3 ≤y≤6
Step-by-step explanation:
The range is the output values or the y values
The y values go from -3 to 6 including these values
-3 ≤y≤6
h - 20
Solve for j in the literal equation
=k.
Answers
h - 20/j = k solve for j
isolate each term individually [tex]-\frac{20}{j}[/tex] then [tex]h[/tex] then [tex]-20[/tex]
[tex]h-\frac{20}{j}=k\\-\frac{20}{j}=k-h\\j=-\frac{20}{k-h}[/tex]
A theater company is considering raising the price of its tickets. It currently charges $8.50 for each ticket and sells an average of 200 tickets for
each show. The company estimates that for each $0.25 increase in the price of the ticket, the average ticket sales will go down by 5 people,
Which equation could the company solve to find the number of price increases it could make, x, and still have a revenue of $1,700?
OA. -1.25.12 - 7.50 = 0
OB -- 1.25:2 – 7.50 – 1,700 = 0
Ос. -1.252 + 7.50 = 0
OD. -1.25_2 + 7.53 – 1,700 = 0
Answers
Answer:
The answer is c.
Step-by-step explanation:
Equation which represents the company solve to find the number of price increases it could make, x, and still have a revenue of $1,700 is equals to [tex]-1.25x^{2} +7.5x=0[/tex].
What is equation?" Equation is defined as the relation between the variables with the sign of equality."
According to the question,
'x' represents the price of the ticket
Given,
Total revenue = $1700
Current charges = $8.50
Number of average tickets sells =200
Estimate in increase in the price of each ticket = $0.25
Average sales goes down by 5 people
From the given information we get the equation,
[tex](200-5x)(8.5+0.25x)=\$1700[/tex]
⇒[tex]1700 -42.5x+50x-1.25x^{2} =1700[/tex]
⇒[tex]-1.25x^{2} +7.5x=0[/tex]
Hence, the equation for the given condition is equals to [tex]-1.25x^{2} +7.5x=0[/tex]
Learn more about equation here
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#SPJ2
Please help
Marcus went to the county fair, where he paid to enter and was charged for each ride. This is modeled by the expression 2x + 7. Identify and interpret the constant in the expression. Explain.
Answers
The interpretation of this constant is Marcus paying to enter the county fair.
URGENT!
B is the midpoint of line segment AC. If AB = 4x + 1 and AC = 5x + 20, find the length of BC.
Answers
Answer: 25 units.
Step-by-step explanation:
Given: B is the midpoint of line segment AC.
[tex]\Rightarrow\ AB=\dfrac{AC}{2}[/tex]
If [tex]AB = 4x + 1[/tex] and [tex]AC = 5x + 20[/tex], then we have
[tex]4x+1=\dfrac{5x+20}{2}[/tex]
Multiply 2 on both sides, we get
[tex]2(4x+1)=5x+20\\\\\Rightarrow\ 8x+2=5x+20\\\\\Rightarrow\ 8x-5x=20-2\\\\\Rightarrow\ 3x=18\\\\\Rightarrow\ x= 6[/tex]
Now, AC = 5(6)+20 =30+20=50 units
Then, BC= [tex]\dfrac{50}{2}=25\text{ units}[/tex]
Hence, the length of BC is 25 units.
rationalize the denominator
Answers
Answer:
The answer is
[tex]\frac{84 - 31 \sqrt{6} }{30} [/tex]Step-by-step explanation:
[tex] \frac{5 \sqrt{3} - 4 \sqrt{2} }{4 \sqrt{3} + 3\sqrt{2} } [/tex]To rationalize the denominator multiply both the numerator and the denominator by
4√3 - 3√2
That's
[tex] \frac{5 \sqrt{3} - 4\sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{3} - 3 \sqrt{2} } [/tex]So we have
[tex] \frac{(5 \sqrt{3} - 4 \sqrt{2})(4 \sqrt{3} - 3 \sqrt{2}) }{(4 \sqrt{3} + 3 \sqrt{2} )(4 \sqrt{3} - 3 \sqrt{2} ) } \\ = \frac{60 - 15 \sqrt{6} - 16 \sqrt{6} + 24 }{16(3) - 9(2)} \\ = \frac{84 - 15 \sqrt{6} - 16 \sqrt{6} }{48 - 18} \\ = \frac{84 - 31 \sqrt{6} }{48 - 18} [/tex]We have the final answer as
[tex] \frac{84 - 31 \sqrt{6} }{30} [/tex]Hope this helps you
Mrs.Ruiz bought 4 14 pounds of sliced of ham for $17. At that rate, what is the cost of 1 pound of sliced ham
Answers
Answer:
Cost of 1 pound if sliced ham = $4
Step-by-step explanation:
Mrs. Ruiz bought 4 1/4 pounds of sliced ham for $17. At that rate, what is the cost of 1 pound of sliced ham?
Total pounds of ham bought= 4 1/4 pounds
Total cost = $17
what is the cost of 1 pound of sliced ham
Cost of 1 pound if sliced ham = Total cost of 4 1/4 sliced ham / 4 1/4
= $17 ÷ 17/4
= 17 × 4/17
= 4
Note:4 1/4 = 17/4
Cost of 1 pound if sliced ham = $4
Check:
4 1/4 pounds × $4 per pound
= 17/4 × 4
= $17
Paul and Karina both collect old Nintendo video games. Paul has 72 video games so far and is collecting four each month. Karina has 120 video games so far and is collecting two each month. After how many months will Paul and Karina have the same number of video games? How many video games will each have?
Answers
24 months
168 games
Step-by-step explanation:72 + 4m = 120 + 2m
4m - 2m = 120 - 72
2m = 48
m = 48 : 2
m = 24 months
After how many months will Paul and Karina have the same number of video games ?24 months
How many video games will each have ?72 + 4×24 = 72 + 96 = 168 games
120 + 2×24 = 120 + 48 = 168 games
Given A(1, 5) and B(3, 13), find AB.
Answers
[tex]\dag\bf\:A(x_1,y_1)=(1,5)[/tex]
[tex]\dag\bf\:B(x_2,y_2)=(3,13)[/tex]
We have to find distance between point A and point B[tex].[/tex]
[tex]\bigstar\:\boxed{\bf{AB=\sqrt{(x_2-x_1)^2+(y_2+y_1)^2}}}[/tex]
[tex]:\implies\tt\:AB=\sqrt{(3-1)^2+(13-5)^2}[/tex]
[tex]:\implies\tt\:AB=\sqrt{(2)^2+(8)^2}[/tex]
[tex]:\implies\tt\:AB=\sqrt{4+64}[/tex]
[tex]:\implies\tt\:AB=\sqrt{68}[/tex]
[tex]:\implies\tt\:AB=\sqrt{4(17)}[/tex]
[tex]:\implies\underline{\boxed{\bf{\red{AB=2\sqrt{17}\:unit}}}}[/tex]
solve for x need help asap
Answers
Answer:
X = 12
Step-by-step explanation:
(4x+2) = 50 bc the angles are the same
subtract 2
4x=48
divide by 4
x=12
Which of the following statements about sets of numbers is true?(1 point) All integers are whole numbers. All irrational numbers are integers. All rational numbers are natural numbers. All integers are rational numbers.
Answers
Answer:
lol three of them are true!!hahhahahhah
the statement which is wrong is
~ All rational numbers are natural numbers.
Answer:
All integers are rational numbers
Step-by-step explanation:
Find the value of b. Then find the angle measures of the pentagon.
6
(b +45)
(2b - 90)
90°
Sum of angle
measures: 540°
Answers
Or, 4b + 3b/2 + 45 = 540
Or, (8b+3b)/2 = 495
Or, 11b = 990
Or, b = 90
Now,
b+45 = 135
3/2*b = 135
2b - 90 = 90
The sum of angles in a shape is the addition of all angles in the shape. The value of b is 90.
From the attached pentagon, we have:
[tex]Sum = 540^o[/tex] -- sum of angles.
This means that:
[tex]Sum = b + \frac 32b + 2b - 90 + 90 + b + 45[/tex]
Collect like terms
[tex]Sum = b + \frac 32b + 2b + b- 90 + 90 + 45[/tex]
Evaluate like terms
[tex]Sum = \frac{11}2b +45[/tex]
Substitute 540 for sum
[tex]\frac{11}2b +45 = 540[/tex]
Collect like terms
[tex]\frac{11}2b =-45 + 540[/tex]
[tex]\frac{11}2b =495[/tex]
Isolate b
[tex]b =495 \times \frac 2{11}[/tex]
[tex]b =\frac {990}{11}[/tex]
[tex]b =90^o[/tex]
Hence, the value of b is 90.
Read more about sum of angles at
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The temperature was 70 degrees. At noon, the temperature increased by 8 degrees. By evening, the temperature decreased by 8 degrees. What is the final temperature?
Answers
Answer:
The answer is 70 you would add the 8 degrees but them subtract it again
decrease 216 by 37 1/2%
Answers
Step-by-step explanation:
In this question we need to decrease 216 by [tex]37\dfrac{1}{2}\%[/tex] or 37.5 %.
For this, firstly find 37.5 % of 216.
[tex]37.5\%\ \text{of}\ 216=\dfrac{37.5}{100}\times 216\\\\=81[/tex]
Now subtracting 81 from 216 to find decrease of 216 by 37.5 %.
So,
216-81 = 135
Hence, 135 is the decrease of 216 by 37.5 %.
The percentage decrease of 216 by 37 1/2% be is 135
Given:
Original value = 216
Percentage decrease = 37 ½%
Decrease = 37 ½% of 216
= 75/2 ÷ 100 × 216
= 37.5 / 100 × 216
= 0.375 × 216
= 81
New value = Original value - Decrease
= 216 - 81
= 135
Therefore, the percentage decrease of 216 by 37 1/2% be is 135
Read more:
https://brainly.com/question/11537235
Question 7 (1 point) If square PQRS with vertices P (2, 6), Q (6, 5), R (5, 1) and S (1, 2) is rotated 180 degrees, what are the coordinates of S' ? Blank 1: Blank 2: Blank 3: Blank 4:
Answers
Answer:
S'(-1, -2)
Step-by-step explanation:
Coordinates of the vertices of the square PQRS have been given as P(2, 6), Q(6, 5), R(5, 1) and S(1, 2)
Rule to rotate a point by 180° about the origin,
(x, y) → (-x, -y)
By this rule new coordinates of the image will be,
P(2, 6) → P'(-2, -6)
Q(6, 5) → Q'(-6, -5)
R(5, 1) → R'(-5, -1)
S(1, 2) → S'(-1, -2)
Therefore, coordinates of S' will be (-1, -2).
e:f = 2:3 and f:g = 5:4 work our e:g
Answers
Answer:
5/6
Step-by-step explanation:
e/f = 2/3
Then
e= 2f/3
f/g = 5/4
Then
g= 4f/5
So
e/g= 2f/3 / 4f/5 = 1/3 * 5/2 = 5/6
Answer:
5/6
Step-by-step explanation:
e/f = 2/3 After that e= 2f/3 f/g = 5/4 So then g= 4f/5 at last
e/g= 2f/3 / 4f/5 = 1/3 x 5/2 = 5/6∠A and ∠B are complementary angles. The measure of ∠A=4x° and the measure of ∠B=50°. Find m∠A. * i dont understand can someone help?
Answers
Answer:
m>a is 40
Step-by-step explanation:
4x + 50 = 90
4x = 40
x = 10
10*4 = 40
M>A = 40
A wheel with a radius of 19 meters is moving forward at 164.95 meters per second. How fast is the wheel rotating in radians per second?
Answers
Answer:
8.68 radians per second.
Step-by-step explanation:
The circumference of the wheel is 2 π r
= 38π meters.
So that is 164.95 / 38π of full turns of the wheel.
1 turn of the wheel = 2π radians , so the answer is
(164.95 / 38π) * 2π
= 164.95 / 19
= 8.68 radians per second.
Hailey bought 10 chicken wings for $6. What was the cost of the wings in wings per dollar?
Answers
$6/10wings per dollar = 0.6 cents
Evaluate the following expression, let a = -1, b = 3, and c = 0
10a
lla +4
Answers
Answer:-10,-7
Step-by-step explanation:
10*-1=-10
11*-1+4=-7
(1+√3) (3-√3)
[tex]simplify[/tex]
Answers
Answer:
2√3
Step-by-step explanation:
Multiply these binomials in the usual way:
(1 +√3)(3 -√3) = 1(3 -√3) +√3(3 -√3)
= 3 -√3 +3√3 -3 = (3 -3) +√3(-1 +3)
= 2√3
what is the solution to the equation below?
2(h+8)-h=h+16
(A) No solution
(B) -8
(C) 8
(D) all real numbers
Answers
2h= 0
So your answer is d
1 point
Given –12 = 2(_5n + 11), What would be your first step?
O Distribute the 2 times the 5n and 11
Subtract 11 on both sides
Add the 5 and 11 because they are Like Terms.
O Divide by -5
Answers
What are the coordinates of the point on the directed line segment from (-3, -9) to (4,5)
Answers
Answer:
(2, 1 )
Step-by-step explanation:
Using the Section formula
For endpoints (x₁, y₁ ) and (x₂, y₂ ) partitioned in the ratio m : n
Then coordinates of point are
[ [tex]\frac{mx_{2}+nx_{1} }{m+n}[/tex] , [tex]\frac{my_{2}+ny_{1} }{m+n}[/tex] ]
Here m = 5, n = 2, (x₁, y₁ ) = (- 3, - 9), (x₂, y₂ ) = (4, 5), thus partitioned point
= [ [tex]\frac{5(4)+2(-3)}{5+2}[/tex] , [tex]\frac{5(5)+2(-9)}{5+2}[/tex] ]
= [ [tex]\frac{20-6}{7}[/tex] , [tex]\frac{25-18}{7}[/tex] ]
= ( [tex]\frac{14}{7}[/tex] , [tex]\frac{7}{7}[/tex] )
= (2, 1 )
I need to know what 1/5(6+3+1). And whatever is in the parentheses is to the second power
Answers
Answer:
20
Step-by-step explanation:
1/5(6+3+1)^2
PEMDAS says parentheses first
1/5(10)^2
Then exponents
1/5 *100
Then multiply
20
Answer:
[tex]\Huge \boxed{\mathrm{20}}[/tex]
Step-by-step explanation:
[tex]\Rightarrow \displaystyle \frac{1}{5} \cdot (6+3+1)^2[/tex]
Solve for the brackets or parenthesis first.
Adding the terms in the brackets or parenthesis.
[tex]\Rightarrow \displaystyle \frac{1}{5} \cdot (10)^2[/tex]
Solving for the exponent or power.
[tex]\Rightarrow \displaystyle \frac{1}{5} \cdot (100)[/tex]
Multiplying both terms.
[tex]\displaystyle \Rightarrow \frac{100}{5} \\ \\ \\ \\ \Rightarrow 20[/tex]