Answer:
The solution is D, -11.
Step-by-step explanation:
Which statements about the hyperbola are true? Check all that apply. There is a vertex at (–5, 2). The center of the hyperbola is at (–2, 2). There is a vertex at (–2, 7). The transverse axis is vertical. The directrices are vertical lines.
First , second and last option are relevant to hyperbola . So , they are correct.
Review each statement to determine if it is true for a hyperbola
It is confirm that the first statement is true because a vertex of a hyperbola is a point on the hyperbola that lies on the transverse axis
It is It is confirm that the second statement is true because the center of a hyperbola is the midpoint of the vertices
It is confirm that the third statement is false because a vertex of a hyperbola is a point on the hyperbola that lies on the transverse axis
It is confirm that the fourth statement is false because the transverse axis of a hyperbola is the line segment that contains the vertices and the foci
It is confirm that the fifth statement is true because the directrices of a hyperbola are two lines parallel to the conjugate axis and located a distance from the center equal to the distance from the center to the foci.
Therefore, the first, second, and last options are correct.
Question :
Equation of the axes: The equation of the axes of a hyperbola is x = h, where h is the x-coordinate of the center of the hyperbola.
Equation of the asymptotes: The equation of the asymptotes of a hyperbola is y = ±(b/a)x, where a and b are the distances from the center to the vertices along the transverse and conjugate axes.
Equation of the conjugate hyperbola: The equation of the conjugate hyperbola can be found by interchanging a and b in the equation of the original hyperbola.
Review each statement to determine if it is true for a hyperbola
1. "A point on a hyperbola that sits on the transverse axis is called a vertex." - True. That's because the vertices of a hyperbola are indeed points on the hyperbola that line up with the transverse axis.
2. "The center of a hyperbola is right in the middle of its vertices." - True. Think of it like finding the midpoint between two ends. That's where the center of the hyperbola sits.
3. "A hyperbola's vertex is exactly where it meets the transverse axis." - false.
4. "The transverse axis of a hyperbola is the line connecting its vertices and foci." - False. The transverse axis actually links the vertices directly, not the vertices and the foci.
5. "The directrices of a hyperbola are two lines that run parallel to its conjugate axis, and they're positioned at a distance from the center to match the distance from the center to the foci." - True. It's like setting up boundaries at a certain distance from the center to guide the shape of the hyperbola.
So, yes, you're right about the first, second, and last statements being true.
incomplete question
9-6a-24a^2 factor completely
-3 (2a - 1) (4a + 3)
I NEED HELP PLS
A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi, and make certain to show your work. Hint: you may need to find the volume of the component shapes.
I WILL GIVE BRAINLIEST AND 95 POINTS I NEED HELP FAST. I NEED HELP PLS
A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi, and make certain to show your work. Hint: you may need to find the volume of the component shapes.
I WILL GIVE BRAINLIEST AND 95 POINTS I NEED HELP FAST.
Answer:
114.5 in³
Step-by-step explanation:
Volume of cone:
⅓ × 3.14 × 8² × 12
= 803.84 cm³
Volume of hemisphere:
⅔ × 3.14 × 8³
= 1071.786667 cm³
Total = 803.84 + 1071.786667
= 1875.626667 cm³
1 cm = 0.393701 inches
1 cm³ = 0.393701³ inches
Volume in in³:
1875.786667/0.393701³
= 114.4579471 in³
Mags and Vector are playing a board game. They use a spinner to determine if they should move forward or backward. They roll a number cube with the numbers 1-6 on it to determine how many spaces to move. What is the probability of moving backward an even number of spaces?
Answer:
1/4
Step-by-step explanation:
17. A bottlenose dolphin jumps out of the water. The path the dolphin Travels can be
modeled by h = -0.2d2 + 2d, where h represents the height of the dolphin and d
represents horizontal distance.
a. What is the maximum height the dolphin reaches?
b. How far did the dolphin jump?
The maximum height that the dolphin reaches is 5 units, which occurs at a horizontal distance of 5 units. The dolphin's total horizontal jump distance is 10 units.
Explanation:The maximum height the dolphin reaches (the vertex of the parabola) is found by the formula -b/(2a) for the maximum or minimum of a parabola ax^2 + bx + c. In your equation, a = -0.2 and b = 2. Therefore, the horizontal distance, d, at the maximum height is d = -b/(2a) = -2/(-0.4) = 5 units. Substituting d = 5 into the original equation gives h = -0.2*5^2 + 2*5 = 5 units. Thus, the maximum height the dolphin reaches is 5 units.
The dolphin's horizontal distance (the 'd' value when h = 0) specifies the full length of the jump. Solving the equation -0.2*d^2 + 2*d = 0 gives d = 0 (the start of the jump) and d = 10 (the end of the jump). Thus, the dolphin jumped 10 units horizontally.
Learn more about Parabolic Motion here:https://brainly.com/question/34164083
#SPJ3
The maximum height reached by the dolphin is 5 meters, and it jumps a horizontal distance of 10 meters. This is determined by analyzing the quadratic equation for maximum height and the point where the dolphin returns to the water surface.
To determine the maximum height (h) the dolphin reaches, we need to analyze the given quadratic equation h = -0.2d² + 2d. Because the coefficient of d² is negative, the parabola opens downward, indicating that the vertex of the parabola will give us the maximum height. The vertex of a parabola in the form of h = ad² + bd + c is given by the formula d = -b/(2a). In this case, a = -0.2 and b = 2, so the horizontal distance (d) at the vertex is d = -2/(2 × (-0.2)) = 5 meters. Plugging this back into the equation, we get h = -0.2(5)² + 2(5) = -0.2(25) + 10 = -5 + 10 = 5 meters.
So, the maximum height reached by the dolphin is 5 meters.
The dolphin jumps until it returns to the water surface, which means the height h becomes 0. We solve the quadratic equation 0 = -0.2d² + 2d by factoring out d: 0 = d(-0.2d + 2). This gives us two solutions: d = 0 (the starting point) and -0.2d + 2 = 0 which leads to d = 10.
Therefore, the dolphin jumped a horizontal distance of 10 meters
Help me answer me some one please I will do 34 points 2 parts A and B
Given:
Funnel is in the shape of a cone.
Radius = 4 inches
Height = 10 inches
To find:
a) The volume of the funnel
b) How many quarts of oil are in the funnel.
Solution:
Volume of cone:
[tex]$V=\frac{1}{3}\pi r^2 h[/tex]
[tex]$V=\frac{1}{3}\times 3.14 \times 4^2 \times 10[/tex]
[tex]$V=167.47[/tex] in³
The volume of the funnel is 167.47 in³.
1 qt ≈ 58 in³
To convert cubic inch to quarts divide by 58.
[tex]$167.47in^3=\frac{167.47}{58}[/tex]
= 2.9 quarts
Therefore 2.9 quarts of oil are in the funnel.
Put the following numbers in order from least to greatest:
4/7 12/26 1/2 18/35
Answer:
12/26, 1/2, 18/25, 4/7
Step-by-step explanation:
Help me serious answers please
Ryan is putting a clothesline in his rectangular backyard. He wants to put it between two trees on the edge of his
property. He has measured his property, and made the sketch shown below, where all the lengths listed are in
meters.
10
Tree
What is the smallest length of rope that Ryan could buy which would stretch from one tree to the other?
Answer: 25 meters.
Step-by-step explanation:
The missing figure is attached.
Draw a Right triangle as the one shown in the second picture, where "a" is the smallest length of rope (in meters) that Ryan could buy, which would stretch from one tree to the other tree.
You need to use the Pythagoream Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" are "c" are the legs of the Right triangle.
In this case you can identify that:
[tex]b=25-10=15\\\\c=20[/tex]
Knowing those values, you can susbtitute into [tex]a^2=b^2+c^2[/tex] and then solve for "a" in order to find its value.
You get:
[tex]a^2=15^2+20^2\\\\a=\sqrt{15^2+20^2}\\\\a=25[/tex]
Alice and Briana each participate in a 5 kilometer race. Alice's distance covered, in kilometers, after t minutes can be modeled by the equation a(t) =
Answer:
a. Alice
b. Briana
c. 0.51 minutes
Step-by-step explanation:
a. Alice formula is valid for any t > 0 minutes, but Briana formula is only valid for
2t - 1 > 0
2t > 1
t > 1/2 minutes
b. They finish when their covered distance is equal to 5 kilometers. For Alice:
t/4 = 5
t = 5*4 = 20 minutes
For Briana:
√(2t - 1) = 5
2t - 1 = 5²
2t = 25 + 1
t = 26/2
t = 13 minutes
c. They are side by side when they have covered the same distance, that is:
t/4 = √(2t - 1)
(t/4)² = 2t - 1
t²/16 = 2t - 1
t² = 16*(2t - 1)
t² = 32t - 16
t² - 32t + 16 = 0
Using quadratic formula:
[tex]t = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)} [/tex]
[tex]t = \frac{32 \pm \sqrt{-32^2 - 4(1)(16)}}{2(1)} [/tex]
[tex]t = \frac{32 \pm 30.98}{2} [/tex]
[tex]t_1 = \frac{32 + 30.98}{2} [/tex]
[tex]t_1 = 31.49 [/tex]
[tex]t_2 = \frac{32 - 30.98}{2} [/tex]
[tex]t_2 = 0.51 [/tex]
Only the second answer has sense for this problem because the race already finished before they spent 31.49 minutes in it.
Answer:
a) Alice starts first, b) Briana gets the finish line first, c) [tex]t \approx 0.509\,min[/tex]
Step-by-step explanation:
a) Alice starts first, since binomial inside the squared root is equal to zero when [tex]t = \frac{1}{2}\,min[/tex], whereas Alice begins at [tex]t = 0\,min[/tex].
b) The instant when each competitor reach finish line is:
Alice
[tex]5\,km = \frac{t}{4}[/tex]
[tex]t = 20\,min[/tex]
Briana
[tex]5\,km = \sqrt{2\cdot t - 1}[/tex]
[tex]25\,km^{2} = 2\cdot t - 1[/tex]
[tex]t = 13\,min[/tex]
Briana gets the finish line first.
c) Alice and Briana are side by side when [tex]a(t) = b(t)[/tex]. Then:
[tex]\frac{t}{4} = \sqrt{2\cdot t - 1}[/tex]
[tex]\frac{t^{2}}{16} = 2\cdot t - 1[/tex]
[tex]t^{2} - 32\cdot t + 16 = 0[/tex]
The roots of the second order polynomial are:
[tex]t_{1} \approx 31.492\,min[/tex] and [tex]t_{2} \approx 0.509\,min[/tex]
Just the second roots makes sense, as they must be side by side at one instant before getting the finish line.
I’m the equation (h+9+g) what are the constants?
Answer:
if you subscride to my yotube i will tell you it is ytmonkey do now if you want help
Step-by-step explanation:
Find the infinite geometric sum, if possible: 50 + 150 + 450 + …
Answer:
Find the infinite geometric sum, if possible: 50 150 + 450 +... -75 25 1000000 Does not exist and
Step-by-step explanation:
What is this data an example of?
*serious answers only*
Each time x goes up by 2, y decreases by 4
This indicates we have a linear function. The slope in this case would be
m = rise/run = (change in y)/(change in x) = -4/2 = -2
The y intercept can be found by following these steps
y = mx+b
0 = -2(5)+b
0 = -10+b
10 = b
b = 10
Therefore, the equation of this line is y = -2x+10. Plug in something like x = 1 and it should lead to y = 8. The same applies for any other column of x,y values.
What is the next term of the arithmetic sequence 10,13,16
Answer:
The next term should be 19
Step-by-step explanation:
Each time you add 3, from 10 to 13, and 13 to 16
The next number would be 19 because 16 + 3 = 19
Find all real square roots of 64
Answer:
8 and -8
Step-by-step explanation:
The definition of a square root is 'a number which produces a specified quantity when multiplied by itself.' Though a negative number cannot have a square root or be a perfect square, it can be a square root.
8 is the only positive square root, but every number that has a square root, also has a second one, the negative version.
-8 is also the square root because it can be multiplied by itself to get 64 :D
The real square roots of the integer 64 will have 8 and -8.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
Let's say the square root of 64 is x.
x = √64
Square both sides
x² = (√64)² = 64
x² = 64
Now, find two equal number that gives 64 by multiplying.
Consider, 8 and 8 → 8² = 64
Thus, x = 8
Another could be -8 and -8 → (-8)² = 64
Hence "The real square roots of the integer 64 will have 8 and -8".
For more about the number system,
https://brainly.com/question/22046046
#SPJ3
96^2+b^2=100^2
what is b?
Answer:
b = ± 28
Step-by-step explanation:
Given
96² + b² = 100² ( subtract 96² from both sides )
b² = 100² - 96² = 10000 - 9216 = 784 ( take the square root of both sides )
b = ± [tex]\sqrt{784}[/tex] = ± 28
Alice buys a book for £19.80
A year later she sells the book for £12.87
Calculate the percentage decrease in the value of the book.
Answer:35%
Step-by-step explanation:
The percentage decrease in the value of the book is 35%.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Cost of the book = £19.80
Selling price of the book = £12.87
The percentage decrease in the value of the book.
= (19.80 - 12.87)/19.80 x 100
= 6.93/19.80 x 100
= 35%
Thus,
The percentage decrease is 35%.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ2
What is the property of equation for -1/3+1/3=0
Answer:
Additive inverse property
Step-by-step explanation:
-1/3 + 1/3 =0
We are adding opposites to get to zero
a+ -a =0
Oxidation state of O in H3O+
Answer:
Step-by-step explanation:
The oxidation state of O in H₃O⁺ is -2
From the question, the given ion is H3O+.
This can be written properly as H₃O⁺
To determine the oxidation state of O (that is Oxygen) in H₃O⁺,
The oxidation state of H (Hydrogen) here is +1
∴ We can form the equation
(+1 × 3) + O = +1
(NOTE: The expression is equated to +1 because the overall charge on the given ion is +1)
Then, we have
+3 + O = +1
Now, subtract 3 from both sides
+3 -3 + O = +1 -3
∴ O = -2
Hence, the oxidation state of O in H₃O⁺ is -2
Learn more here: https://brainly.com/question/9691633
Two cards are drawn from a standard deck of 52 cards. A king is drawn first and not replaced. Find the probability of drawing a second card that is not a king.
P(not a king|king) =
Answer:
48/51
Step-by-step explanation:
The probability of not choosing a king after you've chosen the first king is 48/51 since there are 48 cards in the deck that are not kings and there are 51 cards left in the deck, including king cards.
Answer: Their are 4 kings in a deck of cards, so the answer would be P( Cards that aren't Kings/Total cards) so the probability is .92 or 92%.
What is d + 11 =26
..............???
Answer:
15
Step-by-step explanation:
subtract 11 from 26 which the opposite operation to get your answer.
I need help with this asap please !!
Answer:
Answer is x=7
Step-by-step explanation:
[tex]given \: that \: triangle \: stu \: is \: \\ similarto \: triangle \: plm \\ by \: similarity \: theorem \\ \frac{st}{pl} = \frac{tu}{lm} = \frac{su}{pm} \\ \frac{x + 1}{72} = \frac{2x - 3}{99} \\ cancelling \: by \: 9 \: which \: is \: common \\ \frac{x + 1}{8} = \frac{2x - 3}{11} \\ 11(x + 1) = 8(2x - 3) \\ 11x + 11 = 16x - 24 \\ 11 + 24 = 16x - 11x \\ 35 = 5x \\ therefore \: x = 7[/tex]
HAVE A NICE DAY!
THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION.
Make a table of 4 additional speeds equivalent to 50 miles per hour.
Answer:
80.4672kmh
22.352m/s
43.4488 knots
73.3333 fps
Step-by-step explanation:
Suppose the exact weight of a gallon of water is 8.3 pounds. Four students weighed the gallon of water. Which measurement is most accurate? A) 131.84 ounces B) 133 ounces C) 133.44 ounces D) 140 ounces
please help!, thank you so much!
Answer: 8? What are the answer choices??
Explanation: C= 2(3.14)r
50= 2(3.14)r
First do 50 divided by 2 which equals 25. Then divide 25 by 3.14 to equal 7.96.... Or 8
Mr. Smith wants to rent a car but is not sure how long he is going to need it.The rental car company he finds charges a $50.00 fee and then they also add on a $0.15 per mile charge for driving it. Write an expression to represent the cost of renting a car for any number of weeks.
Answer:
total cost = 50 + 0.15 * x
Step-by-step explanation:
We have a fixed charge and a variable charge, which would be the number of miles you travel with the car. Therefore, the expression that represents this, would be the following:
x = is the number of miles traveled in a given period
total charge = 50 + 0.15 * x
This total charge corresponds to the cost of renting a car in any amount of time (weeks)
Jack tossed a coin 3 times. Which tree diagram shows all the possible outcomes of the coin landing heads up or tails up?
Since tree diagram is not given in the question, I am attaching a tree diagram for the coin tossed 3 times.
Step-by-step explanation:
The coin is tossed 3 times. We need to find the tree diagram that shows all the possible outcomes of the coin landing heads up or tails up
Since tree diagram is not given in the question, I am attaching a tree diagram for the coin tossed 3 times.
Answer:
the first one is 8 then the seconed one is 3
Step-by-step explanation:
i just took the quiz
If George bought 2 cookies for the price of $1, and he had $5, how much does he have now?
Answer:
4 dollars
Step-by-step explanation:
5 minus 1 equals 4
Evaluate the expression when b=-5.
b^2-8b-6
Step-by-step explanation:
[tex] {b}^{2} + 8b - 6 \\ {5}^{2} - 8 \times 5 - 6 \\ 25 - 40 - 6 \\ = - 21[/tex]
Answer:
59
Step-by-step explanation:
This is a substitution question
So we will have to solve by substituting the given value into the equation
So let's solve
b^2-8b-6
And b is given to be-5
So let's substitute
(-5)^2-8(-5)-6
25+40-6
65-6
59
Therefore the final answer is 59
Plz help me outt ASAP
Answer:
53
Step-by-step explanation:
tanx=opp/adj
x=tan^-1(72/54)
x=53.130