Main answer:[tex]x^{2}[/tex]/4 - [tex]y^{2}[/tex]/5=1
Definition of Hyperbola=a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.
Formula=[tex](x-x1)^{2}[/tex]/[tex]a^{2}[/tex] - [tex](y-y1)^{2}[/tex]/[tex]b^{2}[/tex]=1
Given,
origin o(0,0) , focus s(-3,0) , vertex v(-2,0)
and , x1=0, y1=0
then, equation of hyperbola becomes= [tex]x^{2}[/tex]/[tex]a^{2}[/tex]-[tex]y^{2}[/tex]/[tex]b^{2}[/tex]=1
a is the distance between center and the vertex,
distance between o and v = 2
c is the distance between center and the focus,
distance between o and s =3
[tex]a^{2}[/tex]+[tex]b^{2}[/tex]=[tex]c^{2}[/tex]
4+[tex]b^{2}[/tex]=9
[tex]b^{2}[/tex]=5
Then the equation of hyperbola becomes=[tex]x^{2}[/tex]/4 -[tex]y{2}[/tex]/5=1
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Write equations for the horizontal and vertical lines passing through the point (1,6) .
Answer:
the horizontal and vertical lines passing through the point (1,6)
y-6=
x-1=
Step-by-step explanation:
Answer:
x=1 and =
Step-by-step explanation:
When Ricardo was 9 years old, he was 56
inches tall. Ricardo is now 12 years old and
he is 62 inches tall. Find the percent of
increase in Ricardo's height to the nearest
centh.
Answer:
10.7%
Step-by-step explanation:
The formula for calculating the percent change in a value between two points in time is:
p
=
N
−
O
O
⋅
100
Where:
p
is the percent change - what we are solving for in this problem.
N
is the New Value - 62 inches in this problem.
O
is the Old Value - 56 inches in this problem.
Substituting and solving for
p
gives:
p
=
62
−
56
56
⋅
100
p
=
6
56
⋅
100
p
=
600
56
p
=
10.7
rounded to the nearest tenth.
Ricardo gres 10.7%
Somone help me on this free 20 poins
Answer:
T = 3.67 years
Step-by-step explanation:
What is the image of ( − 4 , 12 ) after a dilation by a scale factor of 1/2 centered at the origin?
The image of ( − 4 , 12 ) after a dilation by a scale factor of 1/2 centered at the origin is ( 2, -6 ).
What is Coordinate plane?
Coordinate plane, is represented as the values on the x-axis and y-axis of the graph.
Given that,
To determine the image of (-4,12) after dilation by a scale factor of 1/2 centered at the origin.
Now, For the point, we have a dilation factor of 1/2,
So, a dilated coordinate,
= (1/2 * - 4 , 1/2 * 12)
= (-2 , 6)
To form the image across the origin,
= - (-2, 6)
= (2, -6)
Therefore, The image of ( − 4 , 12 ) after a dilation by a scale factor of 1/2 centered at the origin is ( 2, -6 ).
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Macmillan Learning
The summer monsoon rains bring 80% of India's rainfall and are essential for the country's agriculture. Records going back
more than a century show that the amount of monsoon rainfall varies from year to year according to a distribution that is
approximately Normal with mean 852 millimeters (mm) and standard deviation 82 mm. Use the 68-95-99.7 rule to answer the
questions.
Between what values do the monsoon rains fall in the middle 95% of all years? Enter your answer as an interval "(lower bound.
upper bound)" and as a whole number.
The middle 95% of the distribution of moonsoon rainfall amount:
How small are the monsoon rains in the driest 2.5% of all years? Give your answer as a whole number.
The driest 2.5% of monsoon rainfall amount are less than:
MD
688
Sep 8
mm
mm
10:30
Using the Empirical Rule, it is found that:
The middle 95% of the distribution of moonsoon rainfall amount: (688 mm, 1016 mm).The driest 2.5% of monsoon rainfall amount are less than: 688 mm.What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.Hence, the middle 95% of values is within 2 standard deviations of the mean, with bounds given as follows:
852 - 2 x 82 = 688 mm.852 + 2 x 82 = 1016 mm.The middle 95% of the distribution of moonsoon rainfall amount: (688 mm, 1016 mm).
For the driest 2.5% of years, considering the symmetry of the normal distribution, we have to look at 2 standard deviations below the mean, as 5/2 = 2.5%, hence:
The driest 2.5% of monsoon rainfall amount are less than: 688 mm.
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5 more than three times a number is -7
What is 8 x 1 plus 5 x 1/1000 plus 9 x 1/1000
The value of the expression 8 × 1 plus 5 × 1/1000 plus 9 × 1/1000 is 8.014.
Consider the expression,
8 × 1 plus 5 × 1/1000 plus 9 × 1/1000
Now,
8 × 1 = 8 and;
5 × 1/1000 = 5/1000
and;
9 × 1/1000 = 9/1000
Now,
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 + 5/1000 + 9/1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 + [ ( 9 + 5 ) / 1000 ]
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 + 14 / 1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = ( 8 / 1 ) + ( 14 / 1000 )
Now, LCM of 1 and 1000 is 1000.
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8 × ( 1000/1000) + 14/1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8000/1000 + 14/1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = ( 8000 + 14 ) / 1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8014/1000
8 × 1 + 5 × 1/1000 + 9 × 1/1000 = 8.014
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Write the quadratic equation whose roots are 1 and -3, and whose leading coefficient is 1.
(Use the letter X to represent the variable)
Answer:
y = x²+2x-3
Step-by-step explanation:
y = a(x-p)(x-q)
p = 1
q = -3
a = 1
y = 1(x-1)(x-(-3))
y = (x-1)(x+3)
y = x²+2x-3
What is the greatest common factor of 38 and 30?
The greatest common factor of 38 and 30 is 2
The HCF (Highest Common Factor) of two or more numbers is the largest number among all the common divisors of the given numbers.Simply put, the HCF (Highest Common Factor) of two natural numbers x and y is the largest number that divides both x and y. Let's try to understand this definition using two numbers, 18 and 27. The common divisors of 18 and 27 are 1, 3, and 9. Of these numbers, 9 is the largest (greatest) number. So the HCF of 18 and 27 is 9.
We have given two numbers 38 and 30 .
Prime factorization of 38 is given by
[tex]38=2\times19[/tex]
Prime factorization of 30 is given by
[tex]30=2\times3\times5[/tex]
Prime factorization of 30 and 38 contains 2 as common primes factors so , GCF will be [tex]2[/tex] .
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You are building an arc entrance over a roadway. The road under
the arc is 20 feet wide with a 6-foot sidewalk on both sides of
the road. Write an equation to accomplish this task.
The equation of the parabolic arc that accomplishes this task is:
y = (-k/256)(x - 16)² + k.
In which k is the maximum height of the arc.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the arc has these following characteristics:
Parabolic.Concave down.The peak is at half the road.The road under the arc is 20 feet wide with a 6-foot sidewalk on both sides of the road, hence it's total length is of 20 + 2 x 6 = 32 feet, and the peak of the arc will be at h = 16.
Hence:
y = a(x - 16)² + k.
The height is of 0 at x = 0 and x = 32, hence:
0 = 256a + k.
a = -k/256
y = (-k/256)(x - 16)² + k.
In which k is the maximum height of the arc.
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if only one fourth the amount of brown sugar in the recipe were used how much brown sugar would be used
if only one-fourth the amount of brown sugar in the recipe were used
When adding 1/4 cup of brown sugar to a recipe, you would use
twelve teaspoons
0.015625 gallons
0.0625 quarts
0.125 pints
59.147 ml
3.086472 pounds
Volume, or how much liquid a container can hold, is measured in quarts in both British Imperial and US customary measurements. A quart is equal to two pints or one-fourth of a gallon.
One standard imperial quart, which is equal to two imperial pints or one-fourth of an imperial gallon, is used in the British imperial system for both dry and liquid measurements. The US Customary system has two units called quarts, one for measuring liquids and the other, a little bigger, for measuring dry goods.
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f(x)=√x
Find the derivative using the definition of derivatives
The derivative of the given expression is as follows = [tex]\frac{1}{2 \sqrt{x_0}}[/tex]
definition of derivatives:The derivative is the rate of change in a function without respect to a variable in mathematics. Derivatives are essential for solving calculus as well as differential equations problems.
What is a derivative and what are the many types?Options, forwards, futures, and swaps are the four primary types of derivative contracts. Options represent derivative contracts that provide the buyer the right to buy or sell the underlying asset at a predetermined price during a specific time period. The purchaser is not required to execute the option.
According to the given data:Let f:(0,∞)→R;
f(x)=√x, and x₀∈(0,∞) be an accumulation point of (0,∞).
We must find f′ such that for all x₀, f′(x₀) defined as:
limx→x₀(f(x)−f(x₀))/(x−x₀) exists.
Now,
x−x₀=(√x−√(x₀))(√x +√(x₀)).
Then:
[tex]\lim _{x \rightarrow x_0} \frac{f(x)-f\left(x_0\right)}{x-x_0}[/tex] = [tex]\lim _{x \rightarrow x_0} \frac{\sqrt{x}-\sqrt{x_0}}{\left(\sqrt{x}-\sqrt{x_0}\right)\left(\sqrt{x}+\sqrt{x_0}\right)}[/tex]
= [tex]\lim _{x \rightarrow x_0} \frac{1}{\sqrt{x}+\sqrt{x_0}}[/tex]
= [tex]\frac{1}{2 \sqrt{x_0}}[/tex]
The derivative of the given expression is as follows = [tex]\frac{1}{2 \sqrt{x_0}}[/tex]
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The question you are looking for is:
Use the definition to find the derivative of f(x)=(√x), for x>0. Is f differentiable at zero? Explain.
Please graph the following questions!!
Answer:
F(x)=82(2)+il/3
Step-by-step explanation:
h(x)=x squared +1 k(x)=x-2 (h+k)(2)
The value of the function (h+k)(2) is 1
What is a function?
A function can be defined as an expression or rule that shows relationship between an independent and dependent variable.
Given the functions;
h(x)= x ² +1 k(x)=x-2To determine ( h + k), we have
( h + k) = x² + 1 + x - 2
Then,
(h+k)(2), substitute the value of x as 2
(h+k)(2) = (2)² + 1 - (2) - 2
(h+k)(2) = 4 + 1 - 4
(h+k)(2) = 1
Thus, the value of the function (h+k)(2) is 1
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what is c cubed = -64
The value of the expression is -4
What is cube root?
The cube root of a number can be defined as the factor multiplied by three times by itself to get that number.
Cube root is represented using the formula, '∛'
From the information given,
c³ = -64
Take the cube root of both sides
∛c³ = ∛ - 64
c = - 4
Thus, the value of the expression is -4
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What is the value of k?
Answer:
k = 2
Step-by-step explanation:
in such a case we look immediately at the cases y = 0 and/or x = 0
only if that does not lead us to an answer, do we need to look further.
y = 0, that means according to the graph that x = -2.
so, we have
0 = |x + k| = |-2 + k|
that can only be the case, if k = 2
and we are done.
According to Sea World, baleen whales weigh 6,000 to 8,000 pounds at birth. identify the absolute value inequality that describes the expected weight of a newborn baleen whale. let w represent the actual weight at birth.
On the weekdays a grocery store has 14239 customers and on the weekends the grocery store has
11634 customers. How many more customers does the grocery store have on weekdays than on
weekends?
Answer: 2605 more on weekdays
Step-by-step explanation:
14239 - 11634 = 2605
Kaylee owns a food truck that sells tacos and burritos. She only has enough supplies to make 120 tacos or burritos. She sells each taco for $3 and each burrito for $6. Kaylee must sell at least $480 worth of tacos and burritos each day. If xx represents the number of tacos sold and yy represents the number of burritos sold, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities is:
x + y ≤ 120
x*3 + y*6 ≥ 480
And one possible solution to it is x = 20 and y = 80.
How to find the system of inequalities?
First, we need to define two variables, we will be using:
x = number of tacos.y = number of burritos.We know that she can make at most 120 units, then:
x + y ≤ 120
And she wants to win at leastt $480, then:
x*3 + y*6 ≥ 480
So our system of inequalities is:
x + y ≤ 120
x*3 + y*6 ≥ 480
And the graph can be seen in the image below, the solution set of the system is given by the region where both shaded areas intersect.
There we can see that one possible solution is x = 20 and y = 80, in that case the total number of items made is:
20 + 80 = 100, which is less than 120
And the income is:
20*3 + 80*6 = 540.
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At a particular restaurant, each mini hotdog has 90 calories and each pizza roll has 50 calories. A combination meal with pizza rolls and mini hotdogs is shown to have 860 total calories and 6 more pizza rolls than mini hotdogs. Write a system of equations that could be used to determine the number of mini hotdogs in the combination meal and the number of pizza rolls in the combination meal. Define the variables that you use to write the system.
The system of equations we need to solve is:
x*90 + y*50 = 860
y = x + 6
Solving that we will see that there are 4 mini hot dogs and 10 pizza rolls.
How to write the system of equations?First, we need to define the variables we will be using, these are:
x = number of mini hotdogs.
y = number of pizza rolls.
We know that the combination has 860 calories in total, so:
x*90 + y*50 = 860
We also know that there are 6 more pizza rolls than mini hotdogs, so:
y = x + 6
Then the system of equations is:
x*90 + y*50 = 860
y = x + 6
Replacing the second equation into the first one, we will get:
x*90 + (x + 6)*50 = 860
Now we can solve this for x.
x*90 + x*50 + 300 = 860
x*140 + 300 = 860
x*140 = 860 - 300
x*140 = 560
x = 560/140 = 4
So there are 4 mini hotdogs, and:
y = x + 6
y = 4 + 6 = 10
There are 10 pizza rolls.
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A student claims that 2-4=0 because you cant have less than nothing
Answer: -2
Step-by-step explanation:
Stefan drove to work in rush hour traffic, going just 25 miles in 1 hour and 8 minutes. Later that day, he left work early to avoid the rush and was able to take the same route home in 32 minutes. What was Stefan's average speed overall?
The average speed of stefan is 0.57 miles per hour.
Given, In heavy traffic, Stefan covered just 25 miles in 1 hour and 8 minutes on his way to work.
He left work early to beat the rush hour and made it home in 32 minutes using the same route.
speed of steven in heavy traffic = distance/ time
distance = 25 miles
time = 1 hour and 8 minutes = 68 minutes
therefore, speed = 25/68 = 0.36 miles per hour.
speed of steven while returning back to home.
distance = 25 miles
time = 32 minutes.
speed = 25/32 = 0.78 miles per hour.
average speed = 0.36 ₊ 0.78/2
= 1.14/2
= 0.57 miles per hour.
hence we get the average speed as 0.57 miles.
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A student states that a triangle can be formed with side lengths 4 in, 5 in, and 8 in. Is the student correct? Why, or why not?
Its formed an obtuse triangle with side lengths 4 in, 5 in, and 8 in.
What is obtuse triangle?
A triangle is said to have an obtuse angle if one of the inner angles is greater than 90 degrees. If one of the angles of an obtuse triangle is greater than 90°, then the total of the other two angles is also less than 90°.Any two of a triangle's angles that are equal in size are said to be in an isosceles triangle. Furthermore, the length of the two sides that are opposite those equal angles is also equal. A triangle is said to be obtuse if one of the angles is between 90 and 180 degrees, while the other two are acute (less than 90 degrees).When given 3 sides of a triangle, the longest side must be less than the sum of the other 2 sides.
8 < 4 + 5 so a triangle can be formed.
In fact it will be an obtuse triangle.
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Can somebody help me if you know what this is
Answer:
[tex]f^{-1}x=\frac{2x}{x-1}[/tex]
well give u brainliest What is the value of the function when x=−2?
Enter the answer in the box.
The value of the given function when x = -2 is; y = 1
How to interpret Linear Graphs?
We are given a linear graph as seen in the given image. Now, in graphs like these, there are input values which are x-values while there are also output values which are values on the y-axis.
Now, looking at the graph, we can see that;
At x = 5, y = -6
At x = 4, y = -5
At x = 3, y = -4
At x = 2, y = -3
At x = 1, y = -2
At x = 0, y = -1
At x = -1, y = 0
At x = -2, y = 1
Thus, we can conclude that the value of the given function when x = -2 is, y = 1
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Given f(x) = -x - 9 and g(x) = 3x + 8, find (f + g)(−8).
Answer: -17
Step-by-step explanation:
f(x) = -x - 9 and g(x) = 3x + 8
(f + g)(−8)=
f(-8)+g(-8)=
-(-8)-9+3(-8)+8=
8-9-24+8=
-1-16=-17
A research group surveyed 250 students. The students were asked how often they go to the movies and whether they prefer comedies or dramas
A percentage can be defined as any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
The percentage of the students who go to the movies three times a month or more is given by:
Total students = 30 + 55 = 85 students.
Percentage = 85/250 × 100
Percentage = 0.34 × 100
Percentage = 34%.
The percentage of the students who prefer dramas is given by:
Total students = 85 + 55 = 140 students.
Percentage = 140/250 × 100
Percentage = 0.56 × 100
Percentage = 56%.
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Complete Question:
A movie club surveyed 250 high school students. The students were asked how often they go to the movies and whether they prefer comedies or dramas. Their responses are summarized in the following table.
(a) What percentage of the students go to the movies three times a month or more?
(b) What percentage of the students prefer dramas?
I need some help with this!
first steps in factoring a polynominal with four terms
Answer:
Subtract two sides
Step-by-step explanation:
what is the answer for 1/ 2−6=10
Answer:
-1/10
Step-by-step explanation:
1/2-6/10
5/10-6/10
= -1/10