Find the equation of the hyperbola with the following properties. Express your answer in standard form.Foci at (7, 0) and (7, 10)Asymptotes ofy -5 = t;( -7
Answer:
\(\frac{(y-5)^2}{16}-\frac{(x-7)^2}{9}=1\)
Explanation:
The standard form of an hyperbola is:
\(\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1\)Where (h, k) are the coordinates of the center.
We are given the asyptotes and the foci.
The foci are (7, 0) and (7, 10)
The y value of the center of the parabola is midway from the two foci. Then, the y-coordinate of the center is 5
The coordinated of the center are (7, 5)
Now, we can use that the form of the asymptotes are:
\(y=k\pm\frac{a}{b}(x-h)\)We have:
\(y-5=\frac{4}{3}(x-7)\)Then:
\(\frac{a}{b}=\frac{4}{3}\)a = 4
b = 3
Now we can write:
\(undefined\)if no accidents have occurred within the last six months, what is the probability that an accident will occur within the next year?
Step-by-step explanation: The number of traffic accidents at a certain intersection is thought to be well modeled by a Poisson process with a mean of 3
accidents per year.
Find the probability that more than one year elapses between accidents.
I am not really sure if I am doing this problem correctly but here was my attempt.
I know that the expected value is 3
accidents per year, and I have to find the probability that more than one year elapses between accidents.
can somebody help me i dont know how to do this
Answer:
The line y = -2 - 4x has slope -4.
Slopes of perpendicular lines have product -1, so the slope of a line perpendicular to a line with slope -4 will be 1/4.
Slopes of parallel lines are the same, so the slope of a line parallel to a line with slope -4 will be -4.
Answer:
\(\frac{1}{4}\) and - 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
y = - 2 - 4x , or
y = - 4x - 2 ← in slope- intercept form
with slope m = - 4
given a line with slope m then the slope of a line perpendicular to it is
\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-4}\) = \(\frac{1}{4}\)
slope of perpendicular line is \(\frac{1}{4}\)
• Parallel lines have equal slopes , then
slope of parallel line is - 4
what is the value of 2^3+5^2
Answer: The value of 2^3+5^2 is 18.
Step-by-step explanation:
2^3 = 2 × 2 × 2 = 8
5^3 = 5 × 2 = 10
10 + 8 = 18
I hope this helped! :D
what is 574 ÷ 82 my math say use compatible numbers to round first then awnser the actual queston
Answer: 7 explanation:574\(%\)%82=7 7x82=574
Answer:
compatible answer= 7.5
Real answer: 7
Step-by-step explanation:
3+4|3x+7> or = -89
Solve the inequality and graph, if possible
For the given inequality 3 + (4/3)x + 7 ≥ -89 the value of x ≥ (-297 / 4).
Graph of the given inequality is attached.
As given in the question,
For the given inequality we have:
3 + (4/3)x + 7 ≥ -89
Simplify the given inequality by taking all like terms together we have,
(4/3)x + 10 ≥ -89
Subtract 10 from both the side we get,
(4/3)x + 10 -10 ≥ -89 -10
⇒ (4/3)x ≥ -99
Multiply both the side by (3/4) we get,
x ≥ -99 × (3/4)
⇒ x ≥ (-297 /4)
Graph of the given 3 + (4/3)x + 7 ≥ -89 is attached .
Therefore, for the given inequality 3 + (4/3)x + 7 ≥ -89 the value of
x ≥ (-297 / 4).
Graph of the given inequality is attached.
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Solve this equation, 2.5y = 13.75 Explain pleaseeeee
I'll give 25 points i'm desperate...
Answer:
5.5
Step-by-step explanation:
13.75 divided by 2.5 = 5.5
solve for p: 5.31=p/9.2
Answer:
48.852
Step-by-step explanation:
\(5.31=\dfrac{p}{9.2}\)
Multiply both sides by 9.2:
\((5.31)\times9.2=(\dfrac{p}{9.2} )\times9.2\)
\(48.852=p\)
\(\boxed{p=48.852}\)
Johnny's Towing Company charges a one-time towing fee of $50, plus $20 per day
that they keep each car.
If Johnny changes his one-time towing fee to $75, describe how the graph of his
function would change.
Please help with this.... picture is attached on the bottom
explaination:
12x8= 96
12messages/5message posts
meaning that if you posted 40messages you'd get 96back.
Suppose you deposit $2,000 in a savings account that pays interest at an annual rate of 5%. If no money is added or withdrawn from the account, answer the following questions.
a. How much will be in the account after 4 years?
b. How much will be in the account after 16 years?
c. How many years will it take for the account to contain $2,500?
d. How many years will it take for the account to contain $3,000?
years.
d. For the account to contain $3,000, it will take years
(Type a whole number.)
Answer:
a. After 4 years, the amount in the account can be found by using the formula for simple interest:
A = P * (1 + r * t), where P is the initial deposit, r is the annual interest rate as a decimal, and t is the number of years.
Plugging in the values, we get:
A = $2,000 * (1 + 0.05 * 4) = $2,000 * 1.2 = $2,400
So after 4 years, there will be $2,400 in the account.
b. After 16 years, the amount in the account can be found using the same formula:
A = $2,000 * (1 + 0.05 * 16) = $2,000 * 1.8 = $3,600
So after 16 years, there will be $3,600 in the account.
c. To find the number of years it will take for the account to contain $2,500, we can use the formula:
t = (A - P) / (P * r), where A is the desired amount.
Plugging in the values, we get:
t = ($2,500 - $2,000) / ($2,000 * 0.05) = ($500) / ($100) = 5 years
So it will take 5 years for the account to contain $2,500.
d. To find the number of years it will take for the account to contain $3,000, we can use the same formula:
t = ($3,000 - $2,000) / ($2,000 * 0.05) = ($1,000) / ($100) = 10 years
So it will take 10 years for the account to contain $3,000.
Step-by-step explanation:
pls mark brainlist
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
\(16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)
find equations of the line that is parallel to the z-axis and passes through the midpoint between the two points (0, −2, 7) and (−2, 3, 5). (enter your answers as a comma-separated list of equations.)
The equations of the line parallel to the z-axis and passing through the midpoint between the two given points are x = -1, y = 0.5, and z = t, where t represents the distance along the z-axis.
Since the line is parallel to the z-axis, its direction vector will be (0, 0, 1). Now, let's find the midpoint between the two given points:
Midpoint = ((0 + (-2))/2, (-2 + 3)/2, (7 + 5)/2)
= (-1, 0.5, 6)
Therefore, the line parallel to the z-axis and passing through the midpoint (-1, 0.5, 6) can be represented by the following set of parametric equations:
x = -1 (remains constant)
y = 0.5 (remains constant)
z = t (where t is a parameter representing the distance along the z-axis)
In Cartesian form, the equation of the line can be written as:
x = -1
y = 0.5
z = t
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HELP ASAP !!! The table shows several points for function j(t).
A 2-column table with 4 rows. Column 1 is labeled t with entries 1, 8, 10, 17. Column 2 is labeled j (t) with entries 1, 2, 10, 250.
Which table shows points for the inverse function j–1(t)?
Answer:
d on edge
Step-by-step explanation:
its just the table flipped
Answer:
it's d
Step-by-step explanation:
If polygons are similar then what do you know about the corresponding sides and the corresponding angles ?
Answer:
Step-by-step explanation:
In Similar polygons, the corresponding angles are congruent, but the corresponding sides are proportional. So, similar polygons have the same shape, whereas their sizes are different. There would be certain uniform ratios in similar polygons.
A tabletop in the shape of a trapezoid has an area of 5,700 square centimeters. its longer base measures 135 centimeters, and the shorter base is 105 centimeters. what is the height? the height of the tabletop is centimeters.
Answer:
47.5 cm
Step-by-step explanation:
You want the height of a trapezoid with bases of lengths 135 cm and 105 cm, and an area of 5700 cm².
AreaThe formula for the area of a trapezoid is ...
A = 1/2(b1 +b2)h
Filling in the given values, we have ...
5700 = 1/2(135 +105)h
5700 = 120h
h = 5700/120 = 47.5
The height of the tabletop is 47.5 cm.
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factorise \(x^{2} + 11x\)
Answer:
x(x+11)
Step-by-step explanation:
x^2+11x
Factor out x
x*x+11x
x(x+11)
18. Given that g(x) = -(x^2)/4, what is the value of g(+8) ?
F. -16
G. 4
H. -1
J. 4
K. 16
Answer:
F. -16
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
\(\displaystyle g(x) = -\frac{x^2}{4}\)
Step 2: Evaluate
Substitute in x [Function g(x)]: \(\displaystyle g(-8) = -\frac{(-8)^2}{4}\)Exponents: \(\displaystyle g(-8) = -\frac{64}{4}\)Divide: \(\displaystyle g(-8) = -16\)Find the x-intercept of the graph of the equation y = -2.65x + 25.
What does the x-intercept mean in terms of the situation?
Answer:
x=9.4
Step-by-step explanation:
x intercept is the point where the graph crosses the x axis and y always =0
-2.65x+25=0
-2.65x=-25
x=-25/-2.65
x=500/53
x=9.4
a factorial design involves a) manipulating two or more independent variables. b) an inability to specify the overall effect of an independent variable. c) having multiple dependent measures. d) all of these
The correct answer is
(a) manipulating two or more independent variables.
A factorial plan could be a sort of test plan utilized in investigating to examine the impacts of two or more free factors on a subordinate variable.
In a factorial plan, analysts control each free variable over different levels to watch the one-of-a-kind impacts of each free variable and how they connected with each other to impact the subordinate variable.
For case, in a ponder examining the impacts of two autonomous factors (e.g., temperature and mugginess) on a subordinate variable (e.g., plant development), analysts may control the temperature at three distinctive levels (moo, medium, and tall) and mugginess at two diverse levels (moo and tall) to watch how these components influence plant development individually and in combination.
Therefore, the correct answer is (a) manipulating two or more independent variables.
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Light sample A has a frequency of 4.30×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. What is the wavelength of light sample A in meters? Light sample A has a frequency of 4.30×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. What is the wavelength of light sample B in meters? Light sample A has a frequency of 4.30 ×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. Based on frequency, which set gives the most correct description of the types of light for samples A and B respectively? Light sample A has a frequency of 4.30 ×1015 Hz and light sample B has a frequency of 8.70×1018 Hz. Based on frequency, which set gives the most correct description of the types of light for samples A and B respectively?
1) The wavelength of A is equal to 6.98 × \(10^{-8}\)meters
2) The wavelength of B is equal to 3.45 × \(10^{-11}\) meters
Since we know that the wavelength = speed of light / frequency
The speed of light is 3.00 × \(10^8\) meters per second.
For light sample A with a frequency of 4.30 × 10^15 Hz can be calculated as;
wavelength of A = (3.00 × \(10^8\) m/s) / (4.30 × 10^15 Hz)
wavelength of A = 6.98 × \(10^{-8}\) meters
For light sample B with a frequency of 8.70 × \(10^18\) Hz can be calculated as;
wavelength of B = (3.00 × \(10^8\) m/s) / (8.70 ×\(10^18\) Hz)
wavelength of B = 3.45 × \(10^{-11}\) meters
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To determine the number of ways to arrange items when order does matter but the items are not replaced is done with a permutation. True or false
ANSWER
True
EXPLANATION
When the order matters, the number of ways to arrange items is determined with a permutation. This way, sets of items with the same items but in different order are counted as different sets. For example, (blue, red, green) is not the same as (green, red, blue).
On the other hand, when order does not matter, the number of ways to arrange items is determined with a combination. This way, sets with the same items are counted as the same set. In the previous example, both sets have the same combination of colors, so they are counted as the same set.
Hence, it is true that when the order does matter, the number of ways to arrange items is determined with a permutation.
The graph of the cubic parent equation, y=x3
, is plotted on the coordinate plane.
Select two equations that represent a shift of the graph of the parent equation to the right on the coordinate plane.
The two equations that represent a shift of the graph are y=(x-12)³ and y=(x+8)³.
What is an equation?
Variable terms are frequently used in complex algorithms to reconcile two opposing claims. Academic statements known as equations are used to express the equivalence of different academic quantities. Rather than using a specific algorithm to divide 12 into two parts and assess the data obtained from y + 7, normalization in this case leads to b + 7.
The two equations describe a shift of the graph of the parent equation on the coordinate plane towards the right.
=> y=(x-12)³
=> y=(x+8)³
Therefore , the solution of the given problem of equation comes out to be y=(x-12)³ and y=(x+8)³.
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how many centimeters are in a meter?
Answer:
1 metre =100centimeter
Lana has a bowl of marbles the bowl contains 5 green marbles,3 red marbles and 2 blue marbles from the bowl one at a time. What is the probability that lana will select a green marble first, replace the marble, then select a red marble
Answer:
3/20
Step-by-step explanation:
5 green marbles,3 red marbles and 2 blue marbles from the bowl = 10 marbles
P( green) = green/total = 5/10 = 1/2
Replace
5 green marbles,3 red marbles and 2 blue marbles from the bowl = 10 marbles
P( red) = red/total = 3/10
P(green,replace, red) = 1/2 * 3/10 = 3/20
suppose denzel's score is 25, give one score that could possibly be bianca's score in the test
Answer:
3
Step-by-step explanation:
SMART PPL PLEASE LOOK AT THIS I BEG YOU AND I WILL DO ANYTHING U WANT!!
Answer:
the real answer is
2X/19
Angles p and q are complementary. p is four times the size of q. what is the size of q.
Angles p and q are complementary, which means that their sum is equal to 90 degrees. Let's assume the size of angle q is x degrees. Since p is four times the size of q, we can write the equation p = 4q.
To find the size of q, we need to substitute the value of p in terms of q into the equation for the sum of the angles: p + q = 90.
Substituting 4q for p, we get:
4q + q = 90
Combining like terms:
5q = 90
To solve for q, we divide both sides of the equation by 5:
q = 90/5
Simplifying:
q = 18
Therefore, the size of angle q is 18 degrees.
when angles p and q are complementary and p is four times the size of q, the size of angle q is 18 degrees.
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Line segment is a_____
of a line with two end points
Answer:
A line segment is a segment of a line with two endpoints
Step-by-step explanation:
A line segment is the distance between two endpoints. Lines by definition are infinite so a portion of a line is a line segment.
The figure below is a net for a right rectangular prism. Its surface area is 416 m² and the area of some of the faces are filled in below. Find the area of the missing faces, and the missing dimension.
The area of each of the missing faces is 40 m².
The length of each of the missing faces is 10 m.
The missing dimension is 10 m by 4 m.
What is area?Area is the region bounded by a plane shape.
To calculate the area of each missing face, we use the formula below.
Formula:
a = [A-2(48+120)]/2.............. Equation 1Where:
a = Area of each missing facesA = Total surface area of the rectangular prismFrom the question,
Given:
A = 416 m²Substitute these values into equation 1
a = [416-2(48+120)]/2a = (416-336)/2a = 40 m²And the length of each of the missing edge can be calculated using the formula below
Formula:
l = a/w.................Equation 2Where:
l = Length of each of the missing edgew = width of each of the missing edgeFrom the diagram in the question,
Given:
w = 4 ma = 40 m²Substitute into equation 2
l = 40/4l = 10 mHence, the length is 10 m.
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