The function f(x) = 3x/(x-9) has a vertical asymptote at x=9, a horizontal asymptote at y=3 as x->±∞, and a horizontal asymptote at y=-3 as x->±∞.
To identify the asymptotes and state the end behavior of the function f(x) = 3x/(x-9), we need to analyze the behavior of the function as x approaches positive and negative infinity.
First, let's look at the denominator of the fraction, which is x-9. This means that the function has a vertical asymptote at x=9, as the denominator approaches zero at that point. This vertical asymptote divides the x-axis into two regions, x<9 and x>9.
Now let's consider the behavior of the function as x approaches positive infinity. In this case, the numerator grows faster than the denominator, and the function approaches a horizontal asymptote at y=3. To see this, we can use the limit definition:
lim (x->∞) f(x) = lim (x->∞) 3x/(x-9) = lim (x->∞) 3(1/(1-9/x)) = 3
Similarly, as x approaches negative infinity, the function also approaches a horizontal asymptote at y=-3. Again, we can use the limit definition to confirm this:
lim (x->-∞) f(x) = lim (x->-∞) 3x/(x-9) = lim (x->-∞) 3(1/(1-9/x)) = -3
Therefore, the function f(x) = 3x/(x-9) has a vertical asymptote at x=9, a horizontal asymptote at y=3 as x->±∞, and a horizontal asymptote at y=-3 as x->±∞.
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Ted's company has received an order to print 106 pages. Ted's company has 100 machines, each of which can print 104 pages a day.
Ted’s company can print the 106 pages in
10 days
.
In exponent form, this number of days can be represented as
10^1
.
The number of days required to complete the job in exponent form is 10¹ = 10.
What is the exponent form of the number of days?
The exponent form of the number of days is calculated as follows;
number of pages that can be printed by all machines = n x P
where;
n is the number of machinesP is the pages per machineN = 100 x 104
N = 10400 pages/day
However, the Ted's company needs 10 days to print 106 pages, our equation is formed as follows;
x = log(y)
where;
y is the number of days = 1010ˣ = y
10ˣ = 10
x = 1
so the exponential form = 10¹ = 10
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Just look at the picture
Answer:
perimeter = 84 feet
Step-by-step explanation:
using Pythagoras' identity in the right triangle to find a
a² + 35² = 37²
a² + 1225 = 1369 ( subtract 1225 from both sides )
a² = 144 ( take square root of both sides )
a = [tex]\sqrt{144}[/tex] = 12
then
perimeter = 35 + 37 + 12 = 84 feet
Find the median of the data. $93,81,94,71,89,92,94,99$
Answer:
92.5
Step-by-step explanation:
First, we need to put the data in order from smallest to largest:
$71, 81, 89, 92, 93, 94, 94, 99$
There are 8 numbers in the data set, which is an even number. To find the median, we need to average the two middle numbers.
The middle two numbers are 92 and 93, so the median is:
$(92+93)/2 = 92.5$
Therefore, the median of the data is 92.5.
(a + 2)/(1 + a + a ^ 2) - (a - 2)/(1 - a + a ^ 2) - (2a ^ 2)/(1 + a ^ 2 + a ^ 4)
If sin 0 = 3/4 and angle 0 is in quadrant I, what is the exact value of tan20 in simplest radical form?
The exact value of tan2θ in simplest radical form is -21/√7.
What is the value of tan2θ?The value of tan2θ is calculated as follows;
From Pythagorean identity, we know that;
sin² θ + cos² θ = 1
cos² θ is calculated as follows;
(3/4)² + cos² θ = 1
9/16 + cos² θ = 1
cos² θ = 1 - 9/16
cos² θ = 7/16
cos θ = √(7/16)
tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7
Now, we will find tan 2θ;
tan 2θ = 2tan θ / (1 - tan² θ)
tan 2θ = 2(3/√7) / (1 - (3/√7)²)
tan 2θ = (6/√7) / (-2/7)
tan 2θ = -21/√7
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Find the missing angle
A
B
C
D
Answer:
53
Step-by-step explanation:
20+8=28
90-28=62
62-9=53
90 angle!
Does anyone know the answer to this question
Cindy has a new job offer but will need a new car for the job. After planning a budget, they determine that they can afford to pay at most $215 per month for a 6-year car loan. If an annual percentage rate of 2.1% is available to finance the car loan, calculate the value of the most expensive car loan that Cindy can afford. Round to the nearest whole
number
The most expensive car loan that Cindy can afford is $14,534.
What is the most expensive car loan?The most expensive car loan is calculated by applying the following formula.
M.P = (Pr) / (1 - (1 + r)^(-n))
Where;
P is the principalr is the monthly interest rate = 21%/12 = 0.175%n is the number of months = 6yrs x 12 = 72 monts215 = (P x 0.00175) / (1 - (1 + 0.00175)^(-72))
215 = (P x 0.00175)/0.1183
(P x 0.00175) = 215 x 0.1183
P x 0.00175 = 25.44
P = $14,534
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If diameter EF bisects BC, what is the angle of intersection?
Answer:
The angle of the intersection is 90 degrees
Step-by-step explanation:
How I know this is because EF is the diameter, which means that arc EF is equal to 180 degrees. Because we know this that means when it is spilt into two parts, the arc and angle measure has to be 90 degrees.
Another way to do this is to remember that a circle is 360 degrees and the circle is split into 4 parts. So all you have to do is divide 360/4 to get 90. Your answer.
Analyze a CSR capital investment proposal for Ganon Inc.
Ganon Inc. is evaluating a proposal to replace its HID (high intensity discharge) lighting with LED (light emitting diode) lighting throughout its warehouse. LED lighting consumes less power and lasts longer than HID lighting for similar performance. The following information was developed:
Line Item Description Value
HID watt hour consumption per fixture 500 watts per hr.
LED watt hour consumption per fixture 300 watts per hr.
Number of fixtures 800
Lifetime investment cost (in present value terms)
to replace each HID fixture with LED $300
Operating hours per day 10
Operating days per year 300
Metered utility rate per kilowatt-hour (kwh)* $0.12
*Note: A kilowatt-hour is equal to 1,000 watts per hour.
a. Determine the investment cost for replacing the 800 fixtures.
$240,000
b. Determine the annual utility cost savings from employing the new energy solution.
c. Should the proposal be accepted?
Yes
Evaluate the proposal using net present value, assuming a 15-year life and 8% minimum rate of return. (Click here to view Present Value of Ordinary Annuity.)
a)
The investment cost for replacing the 800 fixtures is $240,000.
b)
Annual utility cost savings is $57,600/year.
c)
Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.
We have,
a.
The investment cost for replacing the 800 fixtures is given as $300 per fixture, so the total investment cost would be:
Total Investment Cost = Number of fixtures x Investment cost per fixture
Total Investment Cost = 800 x $300
Total Investment Cost = $240,000
b.
To calculate the annual utility cost savings, we need to find the difference in the watt-hour consumption per fixture between HID and LED lighting, and multiply it by the number of fixtures, operating hours per day, operating days per year, and the metered utility rate per kilowatt-hour:
Energy consumption savings per fixture per hour = HID watt hour consumption - LED watt hour consumption
Energy consumption savings per fixture per hour = 500 watts/hr - 300 watts/hr
Energy consumption savings per fixture per hour = 200 watts/hr
Total energy consumption savings per hour for 800 fixtures:
= Energy consumption savings per fixture per hour x Number of fixtures
Total energy consumption savings per hour for 800 fixtures.
= 200 watts/hr x 800
Total energy consumption savings per hour for 800 fixtures.
= 160,000 watts/hr
Total energy consumption savings per year = Total energy consumption savings per hour x Operating hours per day x Operating days per year
Total energy consumption savings per year = 160,000 watts/hr x 10 hrs/day x 300 days/year
Total energy consumption savings per year = 480,000,000 watt-hours/year
Total energy consumption savings per year in kilowatt-hours (kWh):
= Total energy consumption savings per year / 1,000
Total energy consumption savings per year in kWh = 480,000,000 / 1,000
Total energy consumption savings per year in kWh = 480,000 kWh/year
Annual utility cost savings:
= Total energy consumption savings per year in kWh x Metered utility rate per kWh
Annual utility cost savings = 480,000 kWh/year x $0.12/kWh
Annual utility cost savings = $57,600/year
c.
To evaluate the proposal using net present value (NPV), we need to calculate the present value of the investment cost and the present value of the annual utility cost savings over a 15-year period.
Using the Present Value of the Ordinary Annuity formula with a 15-year life and 8% minimum rate of return, we get:
PV of Investment Cost = -$240,000 (negative because it's a cash outflow)
PV of Annual Utility Cost Savings = $514,883.81
NPV = PV of Annual Utility Cost Savings - PV of Investment Cost
NPV = $514,883.81 - (-$240,000)
NPV = $754,883.81
Therefore,
The investment cost for replacing the 800 fixtures is $240,000.
Annual utility cost savings is $57,600/year.
Since the NPV is positive, the proposal should be accepted as it generates a positive return and is expected to be profitable.
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Solve the following for θ, in radians, where 0≤θ<2π.
6sin2(θ)−3sin(θ)−8=0
Select all that apply:
0.6
0.16
2.68
5.08
4.34
0.27
Answer:5.08
4.34 are correct
Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):
6u^2 - 3u - 8 = 0
We can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 6, b = -3, and c = -8. Substituting these values, we get:
u = (3 ± sqrt(9 + 192)) / 12
u = (3 ± sqrt(201)) / 12
Therefore, either:
Sophia wishes to retire at age 65
with $1,600,000
in her retirement account. When she turns 28
, she decides to begin depositing money into an account with an APR of 9%
compounded monthly. What is the monthly deposit that Sophia must make in order to reach her goal? Round your answer to the nearest cent, if necessary
Answer:
To determine the monthly deposit that Sophia must make in order to reach her retirement goal, we can use the formula for the future value of an annuity:
FV = P * ((1 + r/n)^(nt) - 1) / (r/n)
where:
FV = future value of the annuity (which is Sophia's retirement goal of $1,600,000)
P = monthly deposit
r = annual interest rate (which is 9%)
n = number of times interest is compounded per year (which is 12 for monthly compounding)
t = number of years until retirement (which is 65 - 28 = 37)
Substituting the given values, we get:
1600000 = P * ((1 + 0.09/12)^(12*37) - 1) / (0.09/12)
Simplifying and solving for P, we get:
P = 1600000 * (0.09/12) / ((1 + 0.09/12)^(12*37) - 1)
P ≈ $524.79
Therefore, Sophia must make a monthly deposit of approximately $524.79 in order to reach her retirement goal of $1,600,000.
Step-by-step explanation:
Marco, Garret, and Dino are hiding during a game of hide-and-seek. Their relative locations are shown in the diagram.
What is the distance between Garret and Dino?
Enter your answer in the box. Round your final answer to the nearest yard.
The distance between Garret and Dino to the nearest yard is: 21 yds
How to find the missing length of the triangle?The Law of Cosines is defined as a numerical formula that expresses the relationship between the side lengths and points of any triangle. It usually expresses that the square of any particular side of a triangle is equal to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.
Numerically, the Law of Cosines can be expressed as:
c² = a² + b² - 2abcos(C),
where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.
Thus, the distance here is expressed as:
d² = 15² + 17² - 2(15 * 17)cos(81)
d = √434.218
d = 20.838 yds
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The mass of a bowling ball is 9ibs and the volume is 135 in³. How many lbs per cubic inch is its density? Round to the nearest hundreth
Answer:
9 pounds/135 cubic inches
= 1 pound/15 cubic inches
= .07 pounds/cubic inch
I can prove that 2=1, where is the error?
X = 1
X+X = 1+X
2x = 1+X
2x = X+1
2X-2 = X+1-2
2x-2 = X-1
2 (x-1)/(x-1) = X-1/X-1
2 times 1 = 1 1-1 / 1-1
2 = 1
I subtracted -2
because thats the # I chose to subtract with.
The mistake is when you try to divide by X - 1, because you can't divide by zero.
Where is the problem in this procedure?Here we start by defining:
X = 1
The second step makes sense, we are adding the same value in both sides:
X + X = X + 1
2X = X + 1
Now subtract 2 in both sides:
2X - 2 = X + 1 - 2
2X - 2 = X - 1
Here is the mistake, you divide both sides by X - 1
But we already defined that X = 1
Then you are trying to divide by zero, and that opeartion is not defined, that is why you reach a false equation.
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Suppose f(x) =8^3x and g(x) =8^4x which of these function operations are correct select all that apply
Suppose [tex]f(x) =8^{3x[/tex] and [tex]g(x) =8^{4x[/tex], function operations that are correct include the following:
A. (f + g)(x) = [tex]8^{3x} + 8^{4x}[/tex]
B. (f × g)(x) = [tex]8^{7x}[/tex]
C. (f - g)(x) = [tex]8^{3x} - 8^{4x}[/tex]
What is an exponent?In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
This ultimately implies that, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the division and multiplication law of exponents for powers of the same base to the functions, we have the following:
(f × g)(x) = [tex]8^{3x+ 4x}=8^{7x}[/tex]
(f ÷ g)(x) = [tex]8^{3x- 4x}=8^{-x}[/tex]
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Let GH be the directed line segment beginning at point G(4,4) and ending at point H(-7,-1). Find the point P on the line segment that partitions the line segment into the segments GP and PH at a ratio of 5:6.
The coordinates of point P are (-1, 1 8/11).
We have,
G(4, 4) and H(-7, 1)
m :n = 5:6
Using Section formula
x = (mx₂ + nx₁)/ (m+n) and y = (my₂ + ny₁)/ (m+n)
Here, x₁ = 4, y₁ = -7, x₂ = 4 and y₂ = -1
So, x = (5(-7) + 6(4))/ 11 and y = (5(-1) + 6(4))/ 11
x = -35+24/11 and y = -5 + 24/11
x = -11/11 and y = -19/11
x = -1 and y = 1 8/11
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The perimeter of a rectangle is 120 meters and the length is 40 meters longer than the width. Find the dimensions of the rectangle. Let x= the length and y= the width. The corresponding modeling system is {2x+2y=120x−y=40 . Solve the system graphically.
The dimension of the rectangle is 50 meters by 10 meters
What is the perimeter of a figure?The perimeter of a figure is the sum of all the external sides of the figure
The formula for calculating the perimeter of rectangle [tex]= 2(\text{l}+\text{w})[/tex]
If the length is 40 meters longer than the width, then:
[tex]\text{l} = 40 + \text{w}[/tex]
Substitute
[tex]120 = 2(40+2\text{w})[/tex]
[tex]60 = 40 + 2\text{w}[/tex]
[tex]30 = 20+ \text{w}[/tex]
[tex]\bold{w = 10 \ meters}[/tex]
Since [tex]\text{l} =40 + \text{w}[/tex]
[tex]\text{l} =40 +10[/tex]
[tex]\bold{l=50 \ meters}[/tex]
Hence the dimension of the rectangle is 50 meters by 10 meters
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the sum of three numbers is 56. the difference of the larges and smallest is 44 and the sum of the two smaller numbers is 16. what are the numbers?
The three numbers are -2, 42 and 16 these we obtained by solving the equations
Let the three numbers x, y, and z. We know that:
x + y + z = 56 (Equation 1)
z - x = 44 (Equation 2)
x + y = 16 (Equation 3)
From Equation 3, we can solve for one of the variables in terms of the other:
y = 16 - x
Substituting this into Equation 1, we get:
x + (16 - x) + z = 56
Simplifying this equation, we get:
z = 40 - x (Equation 4)
Substituting Equation 4 into Equation 2, we get:
(40 - x) - x = 44
Simplifying this equation, we get:
40 - 2x = 44
Subtracting 40 from both sides, we get:
-2x = 4
Dividing both sides by -2, we get:
x = -2
z = 40 - (-2) = 42
Finally, using Equation 1, we can solve for y:
-2 + y + 42 = 56
y=16
Hence, the three numbers are -2, 42 and 16
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18. What is the slope of the line that passes through
the points
Check the picture below.
bearing in mind that a vertical line always has that slope.
Hurry pls Time limit
Tell me the domain and the range
Tell me whether the graph is a function or not
The answer choices are below
Answer:
its not a function
Step-by-step explanation:
A researcher started tracking the number of mice in the lab.
Which of the following equations models how many mice there will be in the lab after 10 months?
Select one:
m(10) = 3 + 2(10)
m(10) = 2(3)^10
m(10) - 3(10)^2
m(10) = 3(2)^10
The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.
We have,
From the given data, we can see that the number of mice is being multiplied by 2 every month.
That means the growth is exponential.
We can use the formula for exponential growth:
[tex]m(t) = a \timesr^t[/tex]
where m(t) is the total number of mice after t months, a is the initial number of mice (when t = 0), and r is the common ratio
From the given data, we can see that when t = 0, there are 3 mice.
So, a = 3.
Also, we can see that the common ratio is 2 (i.e., the number of mice is being multiplied by 2 every month).
Now,
The equation that models how many mice there will be in the lab after 10 months is:
m(10) = 3 × 2^10
Simplifying this equation gives:
m(10) = 3 × 1024
m(10) = 3072
Therefore,
The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.
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48 inches by 36 inches what is the square feet
Answer:
1728 square ft²
Step-by-step explanation:
48x36=1728
Answer:
[tex]\large \boxed{\mathrm{Area}}[/tex] = [tex]\large \boxed{\mathrm{12 \ ft^2}}[/tex]
Steps:
12 inches = 1 foot
48 / 12 = 4 [tex]\meduim \boxed{\mathrm{feet}}[/tex]
36 / 12 = 3 [tex]\large \boxed{\mathrm{feet}}[/tex]
Answer:
3 x 4 = 12 ft²
PLEASE HELP (WILL GIVE BRAINLIEST
Answer: C. V ≈ 635.2 cm^3.
Explanation: The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height (or slant height in this case).
Using the given values, we have:
V = (1/3)π(4.25 cm)^2(12 cm)
V ≈ 635.2 cm^3 (rounded to the nearest tenth)
Therefore, the answer is C. V ≈ 635.2 cm^3.
What are the angles of △ABC with side lengths a=12, b=21, and c=14?
Round each angle to the nearest tenth of a degree and use that rounded value to find the remaining angles.
Answer: the answer is A=33∘, B=107.5∘, and C=39.5∘ is correct or c
Step-by-step explanation:
To find the angles of triangle ABC with side lengths a=12, b=21, and c=14, we can use the Law of Cosines and then apply the Law of Sines to find the remaining angles. Let's denote the angles as A, B, and C respectively.
According to the Law of Cosines:
c^2 = a^2 + b^2 - 2ab * cos(C)
Plugging in the given side lengths:
14^2 = 12^2 + 21^2 - 2 * 12 * 21 * cos(C)
196 = 144 + 441 - 504 * cos(C)
504 * cos(C) = 389
cos(C) = 389 / 504
C = arccos(389 / 504)
Using a calculator to find the approximate value of C, we get C ≈ 43.5°.
14. Describe a pattern in the numbers.
9, 12, 15, 18, 21, 24
Find the surface area of the square pyramid (above) using its net (below)
Answer:
Step-by-step explanation:
the square base = 5 * 5 = 25
each of the triangular sides = 4*2.5=10
so… 25+(10*4)=25+40=65
The parent function for the graph to the right is of the form y = ab*. Write the parent function. Then write a function for the
translation indicated.
translation: left 6 units, down 7 units
The parent function is [tex]y = ab^x[/tex]
A function for the translation indicated is [tex]y = ab^{x+6} - 7[/tex].
What is a translation?In Mathematics and Geometry, the vertical translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the negative y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.
Where:
N represents an integer.g(x) and f(x) represent functions.In this scenario, we can logically deduce that the graph of the parent function was translated or shifted to the left (horizontally) by 6 units and downward (vertically) by 7 units;
[tex]y = ab^x[/tex]
[tex]y = ab^{x+6} - 7[/tex]
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Verify Euler’s theorem: (, ) =
3
+
3
.
math hw for tonight
help solve this problem! Thank you!
ap cal bc
The magnitude of the speed of the particle is determined as √ (17), m/s.
option A.
What is the particle's speed?The speed of a particle is defined as the rate of change of the particle's displacement with time.
Mathematically, the formula for the speed of the a particle is given as;
v = dx/dt
where;
dx is the change in the particle's displacementdt is the change in the time of motion of the particleThe speed of the particle is calculated as;
v = u + at
where;
u is the initial speeda is the accelerationat time, t = 0, the equation for the speed of the particle becomes;
v = u
v = i + 4j
The magnitude of the speed is calculated as follows;
v = √ (1² + 4²)
v = √ (17), m/s
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