Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].
Given, that a hyperbola centred at the origin has vertices at (0, ±9) and foci at (0, ±10).
What is hyperbola?In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
The formula for a hyperbola centred at the origin is [tex]\frac{(x-h)^{2} }{a^{2} } -\frac{(y-k)^{2} }{b^{2} } =1[/tex]
Where (h, k) is the center = (0, 0)
Distance from centre to vertices a = 9 ⇒ a² = 81
Distance from centre to vertices which is given from the foci c = 10
⇒ c² = 100
Using the Pythagorean formula, c²= a²+ b²
Substituting the values 100 = 81 + b²
So we get, b²= 100 - 81 = 19
Substituting the values in the standard form [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].
Therefore, the equation of the hyperbola with a given origin has vertices at (0, ±9) and foci at (0, ±10) is [tex]\frac{x^{2} }{81}-\frac{y^{2} }{19} =1[/tex].
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Caitlyn and Steve are planning their wedding reception and must decide between two catering halls. The first site, A Wedding Space, rents for $900 for one day and charges $50 per person for dinner. The second venue, A Wedding Place, costs $450 to rent for one day and charges $75 per person for the same dinner. Solve the equation 900+50x=450+75x to determine how many guests they can invite so that the cost they pay will be the same at both wedding catering halls.
The guest they can invite so that the cost they pay will be the same at both wedding catering halls is 18.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
The given equation is
900+50x=450+75x
To solve;
900 - 450 = -50x +75x
450 = 25x
x = 450 /25
x = 18
The guest they can invite so that the cost they pay will be the same at both wedding catering halls is 18.
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El perímetro de un rectángulo es de 72 cm. Halla el área del rectángulo si su largo es el 25% más grande que su ancho
Answer:
Las dimensiones del rectángulo son:
ancho = 16 cm
largo = 20 cm
Step-by-step explanation:
Consideración:
La formula del perímetro de un rectángulo es:
perímetro = 2(largo + ancho)
25% más grande = 125% = 125/100 = 1.25
Planteamiento:
2(a+b) = 72
b = 1.25a
a = longitud del ancho
b = longitud del largo
Desarrollo:
de la primer ecuación del planteamiento:
a+b = 72/2
a+b = 36
b = 36 - a Ec. 3
Igualando la segunda ecuación del planteamiento con la Ec. 3:
1.25a = 36 - a
1.25a + a = 36
2.25 a = 36
a = 36/2.25
a = 16
de la Ec. 3:
b = 36 - a
b = 36 - 16
b = 20
Comprobación:
de la primera ecuación del planteamiento:
2(a+b) = 72
2(16+20) = 72
2*36 = 72
If BC is 1
CD is 2
DA is 3
AB is 4,
what is EF?
The approximate length of the side EF will be 1 unit.
The complete figure is attached below.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The figure is given below.
The length of EF will be
EF = CF – CE
Then the value of CF will be
CF = BC × cos 30
CF = 2 × 0.866
CF = 1.732
Then the value of CE will be
CE = BC × cos 42
CE = 1 × 0.743
CE = 0.743
Then we have
EF = 1.732 – 0.743
EF = 0.989 ≈ 1
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The sides, s, of the base of this right square pyramid are 5 inches, and the slant height, l, is 12 inches. What is the surface area of this pyramid?
no pressure! thanks to those who try to help
Answer:
145 square inches
Step-by-step explanation:
The surface area of a square pyramid can be found using the formula ...
A = s(s +2h) . . . . . where s is the base side length, and h is the slant height
__
applicationUsing this formula with s=5 inches and h=12 inches, we find the area to be ...
A = (5 in)(5 in +2(12 in)) = (5 in)(29 in) = 145 in²
The area of the pyramid is 145 square inches.
_____
Additional comment
This formula comes from the sum of the areas of the square base (s²) and the four triangular faces (4 × 1/2sh). That sum is ...
A = s² +2sh = s(s +2h)
Consider the given density curve.
A curve starts at (2, 0), curves up to (10, question mark), and then curves down to (18, 0).
Suppose that the mean value is 10. What is the best approximation for the median?
9
9.5
10
11
Picture posted below…
Answer:
11 is best answer for it ....,..........
Answer:
10
Step-by-step explanation:
Simplify 1-4 can you show how you got the answer on a sheet of paper. Really need help
Answer:
first 1*3+1-3*4+1
then it is in fraction
the answer is -5
On Friday, a local hamburger shop sold a combined total of 396 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number
of hamburgers sold. How many hamburgers were sold on Friday?
Answer:792
Step-by-step explanation:
Suppose that in the country of Workanda, the population is 330 million, and 170 million people are working (have a job). If 70 million people are ineligible to work and the Labor Force Participation Rate is 70%, what is the unemployment rate in Workanda? [Use two significant digits for your answer]. A BIU - PE III Suppose that in the country of Workanda , the population is 330 million , and 170 million people are working ( have a job ) . If 70 million people are ineligible to work and the Labor Force Participation Rate is 70 % , what is the unemployment rate in Workanda ? [ Use two significant digits for your answer ] .
Answer:
30%
Step-by-step explanation:
The unemployment rate is 30%
Two owners of a cattle ranch, Robert and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows:
1. Robert weighs 25 cows and gets an average weight of 1,550 pounds (stdev = 50)
2. Val weighs 100 cows and gets an average weight of 1,380 pounds (stdev = 50)
The margin of error will be 20 and 10 respectively.
How to calculate the margin of error?The margin of error for Robert will be:
= 1.96 × 50/✓25
= 1.96 × (50/5)
= 1.96 × 10
= 20 approximately
The margin of error for Val will be:
= 1.96 × 50/✓100
= 1.96 × 50/10
= 1.96 × 5
= 10 approximately
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Given the line y=10x+3, determine the slope of a line parallel to the given line. Typ the number answer only!
Answer: 10
Step-by-step explanation:
The slope of the given line is 10, and since parallel lines have equivalent slopes, the slope of a line parallel to the given line is also 10
Find the surface area of the composite figure
4 cm
13 cm
3 cm
4 cm
12 cm
SA = [?] cm²
5 cm
3 cm. Pls help
What is the slope-intercept equation for the line below?
10
(0, 2)
(5, 4)
Answer:slope is 0.4
Step-by-step explanation:
y2-y1 divided by x2-x1
2-4/0-5=0.4
A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.77 hours. Assume that a random sample of 40 mechanics is selected and the mean rebuild time of the sample is computed. Assuming the rebuilding times are normally distributed, what percentage of sample means are greater than 8.8 hours? Express your answer as a percent rounded to hundredths of a percent.
Answer:
40.9 %
Step-by-step explanation:
8.8 is .4 hours above the mean this is .4/1.77 = .226 standard deviations above the mean
Using z-score table this corresponds to ~ .5910 (59.10%)
this percentage is LESS than 8.8 hours
the percentage ABOVE this is 40.9%
(Not asked, but this is 40.9 (40 ) = ~ 16 of the 40 mechanics sampled)
Question 1 of 10
Solve the rational equation:
2x/ x - 3 = 3x/ x - 2
Ratio 6 to 5 of 20000
Answer:
24000
Step-by-step explanation:
6/5×20000
=24000
Which expression is modeled by this arrangement of tiles?
40 positive tiles are broken up into 10 groups of 4 positive tiles.
The answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is:
Which expression is modeled by this arrangement of tiles? 40 positive tiles are broken up into 10 groups of 4 positive tiles.
40/(-10) 40/10 40/40 40/(-40)Please refer to the attached picture.
We have a rectangular shape as shown in the picture.
Total number of square units = 40
Each row has 10 units cube.
Each cube = 40/10
Thus, the answer is 40/10 because the total number of square units is 40 option second 40/10 is correct.
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[Question 10]
Two banks calculate the yearly interest they pay customers.
Westminster Bank
4% of the total that you invest
For example: Invest £700
Interest = 4% of £700.
Ashna has £500 to invest for one year.
Work out which bank will pay her more interest.
State how much extra interest she will earn.
District Bank
(4 marks]
1% of the first £300 that you invest and
6% of the amounts over £300 that you invest.
For example: Invest £700
Interest 1% of £300 + 6% of £400,
Answer:
yes
Step-by-step explanation:
because bank
Solve the following compound inequality: x greater-than-or-equal-to negative 1 or x less-than 2.
a.
Negative 1 less-than-or-equal-to x less-than 2
c.
x greater-than-or-equal-to negative 1
b.
no solution
d.
all real numbers
Answer:
x greater than equal to (-1)
x less than 2
all no. greater than -1 = -1,1, 0 , 1 ,2 ......
no. less than2 = 1, 0, -1,.......
-1,0, 1
Option CHELPPPPPPP
What are the solutions to the system of equations graphed below?
A. (2,0) and (0,-4)
B. (-2,0) and (2,0)
C. (0,-2) and (0,2)
D. (0,2) and (-4,0)
Answer:
It's A. (2, 0) and (0, -4)
Question 4: 11 pts
Elena wants to earn at least $180 a week to help her parents with bills. She determines that
she can charge $15 an hour to babysit and can earn $10 an hour bagging groceries. She can
only work 13 hours per week. Write and graph a system of linear inequalities that shows the
number of hours she can work so she can help her parents. Use x for the number of hours
babysitting and y for the number of hours bagging groceries.
our system of inequalities is:
x + y ≤ 13.
x*$15 + y*$10 ≥ $180.
The graph can be seen at the end.
How to get the system of inequalities?Here we have the variables:
x = number of hours babysitting.y = number of hours bagging groceries.We know that she can only work 13 hours per week, then we have:
x + y ≤ 13.
And she wants to earn at least $180 per week, then:
x*$15 + y*$10 ≥ $180.
So our system of inequalities is:
x + y ≤ 13.
x*$15 + y*$10 ≥ $180.
The graph of the system can be seen below. The solution set is defined by the zone where the two shaded regions intersect (where we also should add the restrictions x >0, y > 0).
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Help please and thank you!! :)
Answer:
33 elements
Step-by-step explanation:
Set A has 59 elements. Set A and Set B share 26 elements.
This means that 26 out of the 59 elements in Set A are also in set B.
Therefore, to find the number of elements not in Set B, you need to subtract the common elements from the total amount of elements in Set A.
59 (total in Set A) - 26 (common in Set A) = 33 (unshared elements).
Explain the steps you would take to find the quotient of
1
3
÷ 4
3
NEED HELP ASAP WILL MARK BRAINLIEST!
Answer:
1.5
Explanation:
Given that:
[tex]\sf log_{b} (3) = 1.099[/tex][tex]\sf log_{b} (5) = 1.609[/tex]While solving this problem, the above following is not required to use.
[tex]\rightarrow \sf log_b ([b^3])^{1/2}[/tex]
apply log rule
[tex]\rightarrow \sf \dfrac{1}{2}\log _b\left(b^3\right)[/tex]
[tex]\boxed{\sf \log _b\left(b^3\right)=3}[/tex]
[tex]\rightarrow \sf \dfrac{1}{2}(3)[/tex]
distribute
[tex]\rightarrow \sf \dfrac{3}{2} \quad or \quad 1.5[/tex]
Here is the histogram of a data distribution. All class widths are
What is the median of the distribution?
The median of the distribution is 4.
What is the median?
A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval.
The median is the number at the center of the data set.
Arranging the numbers in the histogram in ascending order is: 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 8, 9, 10
Total numbers = 21 Median = 1/2 x (n + 1)1/2 x 22 = 11th number 4
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What is the point of intersection of the lines represented by these equations
Jy = -2x + 2
y = x - 4
A. (-2, 2)
B. (1, -3)
c. (2,-2)
D. (3,-4)
To find the point of intersection of two lines, we can use substitution to find the x and y coordinates.
Solving the QuestionWe're given:
[tex]y = -2x + 2[/tex][tex]y = x - 4[/tex]Use substitution to find x:
[tex]-2x + 2=x-4\\-2x=x-6\\-3x=-6\\x=2[/tex]
Use substitution to find y:
[tex]y=x-4\\y=2-4\\y=-2[/tex]
AnswerThe point of intersection is (2,-2).
A water wheel is designed in the shape of a regular octagon. What is the perimeter of the water wheel?
The graph shows an eight-sided polygon. Some major points are (0, 4), (3, 3), (4, 0), (3, minus 3), (0, minus 4), (minus 3, minus 3), (minus 4, 0), and (minus 3, 3).
A.
B.
C.
D.
Perimeter is the sum of the length of the sides used to make the given figure. The perimeter of the regular octagon is 8√58 units.
What is the perimeter?Perimeter is the sum of the length of the sides used to make the given figure.
For a regular octagon, the length of each side of the octagon is the same. Therefore, the length of a single side of the octagon is,
Length of the side of the octagon = √[(-4-3)² + (0 + 3)²] = √58
Now, the perimeter of the octagon is 8 times of√58.
Perimeter = 8 ×√58 = 8√58
Hence, the perimeter of the regular octagon is 8√58 units.
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Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the y-axis, the origin, or neither.
f(x)=x³ - 2x
Answer: The function is odd and symmetric with respect to the origin.
Step-by-step explanation:
A function is even if f(x)=f(-x), and odd if f(x)=-f(-x). If a function satisfies neither of these, it is neither even nor odd.
[tex]f(x)=x^{3}-2x\\\\f(-x)=(-x)^{3}-2(-x)=-x^{3}+2x=-f(x)[/tex]
Therefore, the function is odd, and thus the function is symmetric about the origin
Find the slope and distance.
(6,-6) and (-6,+8)
Answer:
[tex]\rm slope: -\dfrac{7}{6}[/tex]
[tex]\rm Distance: 2\sqrt{85} \ units[/tex]
Part A[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} = \dfrac{\triangle y }{\triangle x} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Here given points are: (6, -6), (-6, 8)
Insert the values:
[tex]\sf \rightarrow slope: \dfrac{8-(-6)}{-6-6}[/tex]
[tex]\sf \rightarrow slope: \dfrac{8+ 6}{-12}[/tex]
[tex]\sf \rightarrow slope: \dfrac{14}{-12}[/tex]
[tex]\sf \rightarrow slope: -\dfrac{7}{6}[/tex]
Part B[tex]\sf Distance \ between \ points : \sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Using the formula,
[tex]\sf d = \sqrt{(-6 - 6)^2 + (8-(-6))^2}[/tex]
[tex]\sf d = \sqrt{(-12)^2 + (14)^2}[/tex]
[tex]\sf d = \sqrt{144 +196}[/tex]
[tex]\sf d = \sqrt{340}[/tex]
[tex]\sf d = \sqrt{85 \times 4}[/tex]
[tex]\sf d = 2\sqrt{85}[/tex]
Hence, the distance is 2√85 units.
Hii!
___________________________________________________________
[tex]\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}\circ\leftharpoonup}}[/tex]
Slope =
Distance =
[tex]\stackrel\bigstar{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}\circ\leftharpoonup}}[/tex]
[tex]\bullet[/tex] Let's work out the slope
[tex]\twoheadrightarrow\sf \cfrac{y2-y1}{x2-x1}[/tex]
[tex]\bullet[/tex] Stickin the values
[tex]\twoheadrightarrow\sf \cfrac{8-(-6)}{-6-6}[/tex]
[tex]\bullet[/tex] Simplify
[tex]\twoheadrightarrow\sf \cfrac{8+6}{-12}[/tex]
[tex]\bullet[/tex] Finish simplifying
[tex]\twoheadrightarrow\sf \cfrac{14}{-12}[/tex]
[tex]\bullet[/tex] Reduce the fraction
[tex]\twoheadrightarrow\sf \cfrac{7}{-6}[/tex]
____________________________________[tex]\bullet[/tex] Work out the distance
[tex]\twoheadrightarrow\sf \sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
[tex]\bullet[/tex] Stick in the values
[tex]\twoheadrightarrow\sf \sqrt{(-6-6)^2+(8-(-6)^2}[/tex]
[tex]\bullet[/tex] Simplify the radical expression
[tex]\twoheadrightarrow\sf \sqrt{(-12)^2+14^2}\\\\\twoheadrightarrow\sf \sqrt{144+169} \\\\\twoheadrightarrow\sf \sqrt{340}\\\\\twoheadrightarrow\sf \sqrt{85\cdot4} \quad (simplifying\,the\,surd)[/tex]
[tex]\ddagger[/tex] [tex]\boldsymbol{DISTANCE=2\sqrt{85} \,Units}[/tex] [tex]\ddagger[/tex]
--
Hope that this helped! Best wishes.
--
look at the picture
Jessica and Josh are selling Entertainment Books to raise money for the art room at their school. One book sells for $15. Jessica received the prize for selling the most books in the school. Jessica sold 15 times more books than Josh. Together they sold 256 books. How many did each one of them sell?
Jessica sells = 240 books,
Josh sells = 16 books.
Given:-The price of one book is = $15
Jessica sold 15 times more books than Josh.
In total, they have sold 256 books.
Solution:-We can easily find the answer using variables.
Let,
Josh sold a total of x books whereas Jessica sold a total number of 15x books.
together they sold 16x books.
So we can form the equation
16x= 256
by solving this equation we will get x=16
So, Josh sold 16 books and Jessica sold 16×15=240 books in total.
Answer:
Jessica=240
Josh=15
Step-by-step explanation:
