The equation of the asymptote is y = 3x - 5. The correct answer is option C
What is Asymptote of an Hyperbola ?The distance from a point and the distance to a line in hyperbola is known as asymptote. The general equation is [tex]x^{2}/ a^{2} - y^{2}/b^{2} = 1[/tex]
From the given equation of hyperbola, which is
[tex]\frac{(x - 2)^{2}}{4}[/tex] - [tex]\frac{(y - 1)^{2} }{36}[/tex] = 1
The center (h , k) of the hyperbola = C(2, 1)
a = 2
b = 6
Where C = [tex]\sqrt{a^{2} + b^{2} }[/tex]
C = [tex]\sqrt{4 + 36}[/tex]
C = [tex]\sqrt{40}[/tex]
C = [tex]2\sqrt{10}[/tex]
The equation of the asymptote will be y - K = +/-(b/a)(x - h)
That is,
y - 1 = +/-(6/2)(x - 2)
y - 1 = +/-3(x - 2)
y - 1 = +/-3x - 6
y = +/-3x - 6 + 1
y = +/- 3x - 5
Therefore, the equation of the asymptote is y = 3x - 5.
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Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answer to at least three decimal places. Level 95%, sample size 10.
Using the t-distribution, the critical value needed is: t = 2.2622.
How to find the critical value for the t-distribution?The critical value is found using a calculator, with two parameters:
The confidence level.The number of degrees of freedom, which is one less than the sample size.For this problem, we have a confidence level of 95% and 10 - 1 = 9 df, hence the critical value is t = 2.2622.
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Is this Network a HAMILTONIAN Circuit? If so write the path.
The path of the given Hamiltonian diagram is A, E, B, C, D, F. See explanation below.
What is a Hamiltonian Path?A Hamiltonian path, also known as a traceable path, is one that visits each vertex of the graph precisely once.
A traceable graph is one that contains a Hamiltonian path.
Hence, the path is given as;
A, E, B, C, D, F
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tiff basic insurance cost is $613.50 per year. His insurance company offers a typical "safe-driver discount." What would be his rate if he went three years without an accident? Annual premium?
The rate if he went three years without an accident based on the information about the insurance is $552.15.
How to calculate the insurance?From the information given, his basic insurance cost is $613.50 per year and his insurance company offers a typical "safe-driver discount.
The amount will be:
= 613.50 - (20.45 × 3)
= 552.15
In conclusion, the rate is $552.15.
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As seen in the diagram below, Shandra is building a walkway with a width of feet
to go around a swimming pool that measures 8 feet by 6 feet. If the total area of the
pool and the walkway will be 168 square feet, how wide should the walkway be?
The walkway should be about 2.57feet.
What is the total surface area?
The total surface area of the building is the sum of the total faces of an object contains.
The formula is expressed as:
TSA = 2(lw + wh + lh)
where,
l is the length ,w is the width , h is the height
Calculation
Given the following parameters
TSA = 168 square feet
length = 8 feet and Height = 6 feet
Required
Width of the walkway, Substitute the given values in the formula
168 = 2(lw + wh + lh)
84 = (8(6) + 6w + 8w)
84 = 48 + 14w
4w = 84 - 48
14w = 36
w = 2.57feet
The walkway should be about 2.57feet.
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I need help with my work
(In c) * 1/c = 0.0604 is the change in the function.
According to the statement
y = (In x)^2 on interval [1,4]
By mean value theorem
we use this formula to find a change f '(c)= [f(b) - f(a)] / (b - a)
Let it f(y) = (In x)^2
Now, f(4) = (In 4)^2
f(4) = (0.602)^2
f(4) = 0.3624
and
f(1) = (In 1)^2
f(1) = (0)^2
f(1) = 0
Now, f'(c) = 2 (In c) * 1/c
Substitute all these values in a formula
2 (In c) * 1/c = 0.3624 - 0 / 4 - 1
2 (In c) * 1/c = 0.3624/3
2 (In c) * 1/c = 0.1208
(In c) * 1/c = 0.0604
So, (In c) * 1/c = 0.0604 is the change in the function.
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Nicky opened a savings account with a single deposit of R1 000 on 1 April 2011. She
then makes 18 inonthly deposits of R700 at the end of every month. Her first payment
is made on 30 April 2011 and her last payment on 30 September 2012. The account
earns interest at 15% per annum compounded monthly.
Determine the amount that should be in her savings account inmediately after her last
deposit is made (that is on 30 September 2012).
The amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.
What is the future value?The future value refers to the compounded value (at an interest rate) of the present value, including the periodic cash investments, over a period.
The future value can be determined using either the future value formula, future value table, or an online finance calculator, as below.
Data and Caluclations:N (# of periods) = 18 months
I/Y (Interest per year) = 15%
PV (Present Value) = R1,000
PMT (Periodic Payment) = R 700
Results
FV = R15,282.91 (R12,600 + R1,000 + R1,682.91)
Sum of all periodic payments = R12,600 (R700 x 18)
Total Interest = R1,682.91
Thus, the amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.
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A company's year-end data shows the following amounts. Current assets $65,000 Current liabilities $25,000 Net income $7,500 Net sales $125,000 Total assets $150,000 Based on this information, what is the company's current ratio?
The company's current ratio is 2.6.
What is the current ratio?
Current ratio is an example of a liquidity ratio. Liquidity ratios are financial ratios measure a firm's ability to honour its short terms obligations.
Current ratio = current asset /current liability
$65,000 / 25,000 = 2.6
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Michael starts a new paper company. The function fff models the company's net worth (in thousands of dollars) as a function of time (in months) after Michael starts it.
Considering the function for the net worth of the function, it is found that it will not be in debt for the first time after 6 months in month 14, at point (14,0), which is plotted on the graph.
When a company is in debt?A company is said to be in debt if it's net worth is negative. On a graph, it is represented by the curve being below the x-axis.
From month 2 until the end of month 13, the company is in debt, hence it will not be in debt for the first time after 6 months in month 14, at point (14,0), which is plotted on the graph.
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need help asap. i keep getting these wrong
4x - 10 = 7 - 2x (given)
6x - 10 = 7 (addition property of equality)
6x = 17 (addition property of equality)
x = 17/6 (division property of equality)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the equation:
4x - 10 = 7 - 2x (given)
6x - 10 = 7 (addition property of equality)
6x = 17 (addition property of equality)
x = 17/6 (division property of equality)
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Rebecca is playing a video game that involves planting and cutting down trees. She moves up an energy level for each tree she plants, and she moves down a level for each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.
Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: 1 tree cut
Answer the questions to find out whether Rebecca earned bonus points in the next 3 turns. Use the number line to help you add.
Answer:
She does not get bonus points and she ends up at level 5.
Equation: 4 - 6 + 8 -1 = 5
Equation using only addition: 4 + -6 + 8 + -1 = 5
I hope this helps!
Select the correct locations on the graph.
Select the lines that represent functions.
Answer:
(I've marked the lines considered functions with a check mark)
Step-by-step explanation:
The area of a rectangle is 44 ft², and the
Length of the rectangle is 3 ft less than twice
The width. Find the dimensions of the rectangle.
Answer:
Width = 5.5ft, Length = 8ft.
Step-by-step explanation:
Area of Rectangle = Length x Width
Let w be the Width of the rectangle.
From the information given from the question,
Length = 2w - 3 (3ft less than twice the width)
Area of Rectangle = [tex](2w-3)w\\=2w^{2} -3w[/tex] = 44
Now we can solve for w to find the dimensions.
[tex]2w^{2} -3w-44=0[/tex] (Quadratic Equations)
We can use the Quadratic formula to find w.
[tex]w=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]
Since a = 2, b = -3 and c = -44,
[tex]w=\frac{-(-3)+/-\sqrt{(-3)^{2}-4(2)(-44) } }{2(2)} \\= 5.5 or -4 (reject)[/tex]
We reject negative values here.
Therefore, the width of the Rectangle = 5.5ft
While the length of the rectangle = 2(5.5) - 3 = 11 - 3 = 8ft
The length of a rectangle is 1 yd more than double the width, and the area of the rectangle is 66 yd^2 . Find the dimensions of the rectangle.
The dimensions of the rectangle as described in the task is; 12.4 by 5.7 yd.
What is the dimension of the rectangle?Since the area, length and breadth of the rectangle are as described, it follows that;
66 = x(2x+1)
66 = 2x² + 1
x² = 32.5
x = 5.7
Therefore, the dimensions are 5.7 and 12.4.
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Which is the graph of the function f(x)= - squared x
Answer:
top left graph
Step-by-step explanation:
The function is not defined for negative x.
Eliminate top middle and top rightAlso, the range should not include positive numbers.
Eliminate bottom left.So, the answer is the top left graph.
A roller coaster’s height is given by the equation h = –.025t2 + 4t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? Hint: Set h = 0.
11.65 seconds
50.00 seconds
171.65 seconds
210.00 seconds
The time it will take the roller coaster to reach the ground is 171.65 seconds
Function and valuesGiven the roller coaster’s height given by the following parameters
h = –0.025t² + 4t + 50
On the ground level, the height will be zero. Substitute h = 0 and determine the value of t
–0.025t² + 4t + 50 = 0
0.025t² - 4t - 50 = 0
Factorize
On factorizing the time it will take the roller coaster to reach the ground is 171.65 seconds
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Pamela is 9 years younger than Jiri and the sum of their ages is 41 what is jiri's age
Answer:
Jiri is 25 years old.
Step-by-step explanation:
1)Pamela =Jiri-9 ( Pamela is 9 years younger than Jiri)
2)Pamela +Jiri=41
Substitute equation 1 into equation 2
(J-9)+J= 41
2J-9=41
Add 9 to both sides:
2J=41+9
Divide by 2:
2J=50
J=25
the required Jiri's age is 25 years.
Pamela is 9 years younger than Jiri and the sum of their ages is 41. What is Jiri's age is to be determined.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements.
Let the age of Pamela and Jiri is x and y respectively
Pamela is 9 years younger than Jiri. so,
y = x + 9 - - - - (1)
the sum of their ages is 41
x + y = 41 - - - - (2)
From equation 1 put y in equation 2
x + x + 9 = 41
2x + 9 = 41
2x = 41 - 9
2x = 32
x = 32/2
x = 16
Now put this x =16 in equation 1
y = 16 + 9
y = 25
Thus, the required Jiri age is 25 years
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A number is negative if and only if it is less than 0.
p. A number is negative.
q. A number is less than 0.
Which represents the inverse of this statement? Is the inverse true or false?
~p4~9
The inverse of the statement is sometimes true and sometimes false.
Oq+p
The inverse of the statement is true.
q→P
~q→ ~p
The inverse of the statement is false.
The inverse statement is:
¬q ⇒ ¬p
Which is true.
How to get the inverse statement?
Here we have the biconditional statement:
A number is negative if and only if it is less than zero.
Where:
p = a number is negative.q = a number is less than 0.So we can write the statement as:
p ⇔ q
The inverse statement is:
if not q, then not p.
or
¬q ⇒ ¬p
Replacing p and q, we have:
"if a number is not less than zero, then the number is not negative".
This is true, if the number is not less than zero, then the number is 0 or larger, so that number is not negative.
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Answer:
D.
∼p↔∼q
and
G.
The inverse of the statement is true.
Step-by-step explanation:
25 mice were involved in a biology experiment involving exposure to chemicals found in ciggarette smoke. 15 developed at least 1 tumor, 9 suffered re[iratory failure, and 4 suffered from tumors and had respiratory failure
The number of mice that didn't get a tumor is 9 mice out of the 25 mice.
How to know how many mice didn't have a tumor?Identify the total mice who did not have any effects or the effects did not include a tumor.
Repiratory failure: 9 mice
Based on this, it can be concluded 9 mice did not have a tumor, while 21 mice hat at least a tumor and some of them had a tumor and respiratory failure.
Note: This question is incomplete; here is the missing section:
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1. The mean urine sodium concentrationof18caseswas120mmol/L with standard deviation of 15 mmo/L. assume the urine sodium is normally distributed, what is the 95%confidence interval within which the mean of the total population of such cases is expected lie
Using the t-distribution, the 95% confidence interval within which the mean of the total population of such cases is expected lie is:
(112.5, 127.5).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 18 - 1 = 17 df, is t = 2.1098.
The parameters for this problem are:
[tex]\overline{x} = 120, s = 15, n = 18[/tex].
Hence the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 120 - 2.1098\frac{15}{\sqrt{18}} = 112.5[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 120 + 2.1098\frac{15}{\sqrt{18}} = 127.5[/tex]
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find RY if RV=8 and VW=12
pls help giving all my points!! Find the probability of “landing” in the shaded region of the figures below. Round your answer to the nearest hundredth.
Big circle r = 25 cm
Small circle r = 8 cm
The probability of landing on the shaded region of the figure is 0.10
How to find the probability of landing on the shaded region?The probability of landing on the shaded region can be calculated as follows;
area of the bigger circle = πr² = 3.14 × 25² = 1962.5 cm²
area of the smaller region = πr² = 3.14 × 8² = 200.96 cm²
Therefore,
the probability of landing on the shaded region of the figure = 200.96 / 1962.5
the probability of landing on the shaded region of the figure = 0.10
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The cost of b tickets at $20 a ticket algebraic expression
The algebraic expression is 20b
How to determine the algebraic expression?The statement is given as:
$20 a ticket
This means that the cost of 1 ticket is $20.
So, the cost of b tickets is
Cost = 20 * b
Evaluate
Cost = 20b
Hence, the algebraic expression is 20b
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suppose that fanf g are continuous functions,
12_(^28 f(x)dx=19, and 12 (^28 g(x)dx =35.
Find
12_ f^28 [kg(x)-2f(x)] dx, where the coefficient
k=7
those are intergral symbols with numbers on
top and bottom. please show work. thanks
The required result based on given continuous functions is: 207. See the explanation for same below.
A continuous function in mathematics is one in which a continuous variation (that is, a change without a jump) of the argument causes a continuous variation of the function's value.
Since G and F are continuous functions,
[tex]\int_{12}^{28}) \, f(x) dx[/tex] = 19
[tex]\int_{12}^{28}) \, f(x) dx[/tex] = 35
Therefore,
[tex]\int_{12}^{28}) \, [K g(x) - 2 f(x)] dx[/tex]
= K [tex]\int_{12}^{28}) \, g(x) dx -2 \int_{12}^{28}) \, f(x) dx[/tex]
So, given that K = 7, we have
7 x 35 - 2 x 19
= 245 - 38
= 207
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guillermo has sold 95,47,114, and 72 appliances in the last fourth months,respectively.how many appliances will he need to sell this month to maintain an average of 80 sales per month?
The number of appliances that Guillermo needs to sell this month to main an average of 80 sales per month is 72 units.
What is an average?An average refers to a central value obtained after adding together several amounts and then dividing this total by the number of variables added.
An average is a central value in a dataset.
Data and Calculations:Average sales per month = 80 units
Number of months involved = 5 months
Total for five months based on the average = 400 units
Total units sold in four months = 328 (95 + 47 + 114 + 72)
Sales units required to meet the average target = 72 (400 - 328)
Thus, the number of appliances that Guillermo needs to sell this month to main an average of 80 sales per month is 72 units.
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I need help with the slope
Answer:
1/5 :D
Step-by-step explanation:
Lets pick 2 point on the graph :)
We need this to find the slope!
Lets use (-5,1) and (0,2) :)
First we subtract the y coordinates! :)
2 - 1 = 1
Then we subtract the x coordinates!
0 - (-5) = 5
Now we divide!
1/5
Our answer is 1/5!
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
first choice : 1/5
Step-by-step explanation:
need 2 points
one point is (0,2)
another is (5,3)
slope formula is
y2 - y1 / x2 - x1
3 - 2 / 5 - 0
1/5
Which inequality in standard form represents the
shaded region?
The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)
What inequality represents the figure
In accordance with the figure, we have an inequation of the form y ≥ f(x). Now we proceed to find the quadratic equation of the parabola:
f(x) = a · (x + 1) · (x - 9)
- 125 = a · (4 + 1) · (4 - 9)
- 125 = a · 5 · (- 5)
- 125 = - 25 · a
a = - 5
f(x) = 5 · (x + 1) · (x - 9)
f(x) = 5 · (x² - 8 · x - 9)
f(x) = 5 · x² - 40 · x - 45
The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)
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14-yard fishing line is cut into two pieces. Three times the length of the longer piece is four times the length of the shorter piece. Find the length of each piece.
(Hint: Let x = smaller piece...)
Answer:
The small piece is 6 yards and the large piece is 8 yards.
Step-by-step explanation:
Let x = small
Let y = large
x + y = 14 3y = 4x
3y = 4x Divide both sides of the equation by 3 to solve for y
y = [tex]\frac{4}{3}[/tex] x Plug [tex]\frac{4}{3}[/tex] x in for y in the first equation above.
x + y = 14
x + [tex]\frac{4}{3}[/tex] x = 14 x and 1 x mean the same thing. Another name for 1 is [tex]\frac{3}{3}[/tex]
[tex]\frac{3}{3}[/tex]x + [tex]\frac{4}{3}[/tex]x = 14
[tex]\frac{7}{3}[/tex]x = 14 Multiple both sides by [tex]\frac{3}{7}[/tex] to solve for x
([tex]\frac{3}{7}[/tex])([tex]\frac{7}{3}[/tex]x) = 14([tex]\frac{3}{7}[/tex]) you can write 14 as [tex]\frac{14}{1}[/tex]([tex]\frac{3}{7}[/tex]) = [tex]\frac{42}{7}[/tex]= 6
x = 6
If x = 6, then y must be 8 because 6 + 8 = 14
Assume that the average healthy body temperature is 98.249 degrees and the standard deviation is 0.733 degrees. How many standard deviations below the mean would I be if my body temp is 97.2 degrees,
The standard deviation is 1.43 below the mean
How to determine the number of standard deviation?The given parameters are:
Mean = 98.249
Standard deviation = 0.733
x = 97.2
To calculate the number of standard deviation below the mean, we use
[tex]x = \bar x - n\sigma[/tex]
So, we have:
[tex]97.2 = 98.249 - n * 0.7333[/tex]
Evaluate the like terms
[tex]-1.049 =- n * 0.7333[/tex]
Divide both sides by -0.733
n =1.43
Hence, the standard deviation is 1.43 below the mean
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Maritza desea ir de viaje con su familia, que está conformada por ella, su esposo y sus 3 hijos. Ella comprará pasajes cuyo costo es de S/75 por persona (sólo ida), también desea comprar un paquete turístico para cuatro personas cuyo valor es de S/800, además contrató 3 habitaciones por el precio de S/60 cada una. También se proyectó gastar en alimentación 150 diarios y una bolsa de viaje de S/130 por persona. Si su viaje es de 5 días y 4 noches y actualmente ella cuenta con S/1000 y su esposo con S/1800, ¿Cuánto dinero les falta para cubrir todos los gastos de su viaje?
El dinero que le falta a Maritza y su esposo para viajar es 330.
¿Cuánto dinero les falta?Para calcular el dinero que les falta debemos identificar la cifra total que les va a costar el viaje:
75 x 10 = 75080060 x 3 = 180 150 x 5 = 750130 x 5 = 650750 + 800 + 180 + 750 + 650 = 3,130El valor total del viaje es s/3,130, entonces les faltarían s/330.
3,130 - 2,800 = 330
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Find the time required for an investment of 5000 dollars to grow to 6000 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Answer:
2.4536 years
Step-by-step explanation:
compound formula:
A=P*(1+r/n)^nt
A = 6000
P = 5000
r = rate
n = 4 times per year compounded
t = time in years
6000 = 5000(1 + .075/4)^4t
divide both sides by 5000
1.2 = (1.01875)^4t
log both sides
log(1.2) = 4t * log(1.01875)
solve for t
t = 2.4537 years