find the inverse of the function f(x)=-1/25x^2, x<0
The function is :
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex] the inverse function is:
Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Domain: (-[tex]\infty[/tex],9]
Range: [tex](-\infty,0][/tex]
What is an inverse function ?If the inverse function of f is the function g, then x = f(x) gives x = g(y). We just need to reverse the function.
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1. One should not confuse (-1) with exponent or reciprocal here.
If f and g are inverse functions, then f(x) = y if and only if g(y) = x
The function is :
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]
We have to find the inverse of the function.
The inverse, interchange the variables solve for y,
Now,
[tex]f(x) =\frac{-1}{25x^{2} },x < 0[/tex]
[tex]f^-^x(x)=\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
So, [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Hence,
Inverse function: [tex]f^-^x(x)=-\frac{\sqrt{\frac{-1}{x} } }{5}[/tex]
Domain: (-[tex]\infty[/tex],9]
Range: [tex](-\infty,0][/tex]
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find the area of the figure (hint don’t forget units!)
5.2 ft 3 ft 2.4
Answer:
A = 11.4 ft²
Step-by-step explanation:
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the height between the bases
here h = 3 , b₁ = 2.4 , b₂ = 5.2 , then
A = [tex]\frac{1}{2}[/tex] × 3 × (2.4 + 5.2) = 1.5 × 7.6 = 11.4 ft²
a. The following is the input/output table for two industries X and Y. The values are in million of rupees.
Producers
X
Y
X
14
7
Users
Y
6
Final Demand
8
Total Output
28
18
11
36
Determine the outputs if the final demand changes to 20 for X and 30 for Y.
[3]
The outputs for industries X and Y will be 31 million and 43.2 million, respectively supposedly the final demand changes to 20 for X and 30 for Y.
How do we calculate?We will start with industry X.
The final demand for X hade an increment from 14 million to 20 million with an increase of 6 million, hence the final output of X must also increase by 6 million to make up for demand.
Users Final Producers
Demand X Y
X 14 7
Y 6 18
Total 20 25
The table tells us that for every additional million of final demand for X, the producers in industry X need to produce 0.5 million of output.
So the new total output for industry X is 28 + 3 = 31 million.
For industry Y
The same scenario occurred for Industry Y which had final output of 12 in order to meet the demand increment.
So the new total output for industry Y is 36 + 7.2 = 43.2 million.
In conclusion, the outputs for industries X and Y will be 31 million and 43.2 million, respectively, if the final demand changes to 20 for X and 30 for Y.
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Prove that sinθ cosθ = cotθ is not a trigonometric identity by producing a counterexample.
Answer:
cmon man
Step-by-step explanation:
We want to show that sinθ cosθ = cotθ is not true for all values of θ. To do this, we just need to find one counterexample, i.e., one value of θ for which the equation is not true.
Recall that cotθ = cosθ/sinθ. So, the equation sinθ cosθ = cotθ can be rewritten as sinθ cosθ = cosθ/sinθ.
Multiplying both sides by sinθ, we get:
sin^2θ cosθ = cosθ
Dividing both sides by cosθ, we get:
sin^2θ = 1
Taking the square root of both sides, we get:
sinθ = ±1
So, we need to find a value of θ such that sinθ is equal to ±1. This occurs when θ = π/2 + kπ, where k is an integer.
Now, let's check whether sinθ cosθ = cotθ is true for this value of θ. We have:
sin(π/2 + kπ) = ±1
cos(π/2 + kπ) = 0
cot(π/2 + kπ) = undefined (since cos(π/2 + kπ) = 0)
Therefore, sinθ cosθ = cotθ is not true for θ = π/2 + kπ, and we have found a counterexample. This shows that sinθ cosθ = cotθ is not a trigonometric identity.
The Sky Train from the terminal to the rental car and long term parking center is supposed to arrive every 8 minutes. The waiting times for the train are known to follow a uniform distribution.
What is the probability of waiting less than 2 minutes or more than 6 minutes?
The probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train is 0.5 or 50%.
To calculate the probability of waiting less than 2 minutes or more than 6 minutes for the Sky Train from the terminal to the rental car and long term parking center, we need to find the probability of each event separately and then add them together.
The probability of waiting less than 2 minutes can be calculated as the ratio of the time interval from 0 to 2 minutes (2 minutes) to the total time interval of 8 minutes;
P(waiting less than 2 minutes) = (2 minutes) / (8 minutes) = 0.25
The probability of waiting more than 6 minutes can be calculated as the ratio of the time interval from 6 to 8 minutes (2 minutes) to the total time interval of 8 minutes;
P(waiting more than 6 minutes) = (2 minutes) / (8 minutes) = 0.25
Now, to find the probability of waiting less than 2 minutes or more than 6 minutes, we can add the two probabilities together;
P(waiting less than 2 minutes or more than 6 minutes) = P(waiting less than 2 minutes) + P(waiting more than 6 minutes)
= 0.25 + 0.25
= 0.5
Therefore, the probability of waiting less than 2 minutes or more than 6 minutes will be 0.5 or 50%.
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gingerbread house is shaped like the image below. How many square centimeters of frosting will take to cover the outside?
(NEED HELP!!!)
There are 32 cm² of frosting will take to cover the outside.
Given that;
Base of house = 2 cm
And, Height of house = 3 cm
Since, The shape of house is like a prism.
We know that;
Area of Prism is,
SA = 2B + ph,
where B, stands for the area of the base, p represents the perimeter of the base, and h stands for the height of the prism.
Hence, We get;
SA = 2 × (2 × 2) + 2 (2 + 2) × 3
SA = 8 + 24
SA = 32 cm²
Hence, There are 32 cm² of frosting will take to cover the outside.
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Sebastian va a elegir el color, el patrón, el tipo de letra y la imagen para el diseño de un suéter para su equipo de danza. Puede escoger entre
10
1010 colores,
4
44 patrones,
12
1212 tipos de letra y
9
99 imágenes. (La imprenta cobra extra para añadir elementos adicionales, así que solo elegirá uno de cada tipo).
Sebastian can choose between 4,320 different sweaters.
How many different sweaters can Sebastian choose?to find the total number of different sweaters, we need to take the product between the numbers of options for each of the given selections, we have the numbers:
Color = 10 options.
Pattern = 4 options.
Letter type = 12 options.
Image = 9 options.
Then the total number of different options is:
D = 10*4*12*9 = 4,320
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What is the domain of the function y=tan (x/8)
The domain can be written as follows:
R - {x = n*12pi or m*4pi | n, m ∈ Z}
where pi = 3.14 and R is the set of real numbers.
What is the domain of the function?Here we want to find the domain of the function:
y = tan(x/8)
The tangent is the quotient between the cosine and the sine, then we will get:
sin(x/8)/cos(x/8)
The problems of the tangent are all the values that make the denominator equal to zero, then we need to remove these.
The zeros are:
cos(x/8) = 0
We know that cos(pi/2) = cos(3pi/2) = 0
Then:
x/8 = pi/2
x = 4pi
x/8 = 3pi/2
x = 12pi
So the domain is the set of all real numbers except the ones in the next set:
{x = n*12pi or m*4pi | n, m ∈ Z}
Where Z is the set of integers.
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if u are given the midpoint of a segment and one endpoint find the other endpoint (6,2) (1,3)
The other endpoint is (11, 1).
We have,
Midpoint = (6, 2) and endpoint = (1, 3).
and, ratio of m: n = 1 :1
Using section formula
6 = ( 1 + a) / (1+1)
6 = (1+a)/2
1 + a = 12
a = 11
and, 2 = (3 + b) / (1+1)
2 = (b + 3) /2
b +3 = 4
b = 1
Thus. the other endpoint is (11, 1).
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johnathannes brahms destoryed or left many because of his work unplublished because
A. He didnt want to be sucessful
B. He thought they were too good to publish
C. He was a perfectionist and was never satisfied with them.
Answer asap for brainlist
Mary has the qualities of being a team leader.
Here, we have,
Team leaders upload any other stage of control. They’re employed to persuade and construct relationships, to make matters happen. Team chief’s to-do lists may be vast, however through categorizing them, it’ll come up with readability approximately the reason of your job.
A group chief has an outline of a set of humans, motivates, offers guidance and video display units performance. It is probably an professional identify alternate or a delegation exercising out of your management, however both way, being a group chief separates you out of your friends as a depended on individual to manipulate a assignment or institution of humans.
Team leaders and executives have exceptional responsibilities. Unlike managers, group leaders won’t have the authority to direct, alternate plans, put in force or construct their groups via hiring and firing. Their position is mostly a motivational and inspirational one inside an organization. They’re professional dating developers and mediators, liaising among the humans and management.
Thus this are the qualities of team leader.
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complete question;
Mary is a perfectionist . She loves participating on teams and often takes on too many tasks because she wants to ensure that they are done on time and on budget.
The Jackson Hole Aerial Tram takes passengers from an elevation of 6311 ft to an elevation of 10,450 ft up the slope of Rendezvous Mountain in Wyoming. If the tram runs on a cable measuring 12,463 ft in length, what is the angle of incline of the tram to he nearest tenth of a degree?
The angle of incline of the tram is 19.4 degree.
According to the question:
h=(10450-6311)ft
= 4139 ft
We know that, sinθ=Opposite/Hypotenuse
So, sinθ=h/12463
sinθ= 4139/12463
sinθ= 0.3321
Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.
θ=19.39
θ≈19.4°
Therefore, the angle of incline of the tram is 19.4 degree.
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Elijah can spend up to $23 on groceries. He wants to buy 3 pounds of tomatoes, 4 pounds of oranges, and x pounds
of lean ground beef. The tomatoes cost $1.35 per pound, the oranges $1.65 per pound, and the ground beef $4.94
per pound. Write an inequality that represents the possible number of pounds of ground beef, x, he can buy. Find
the value of x.
A. 1.35 x 3 +
B. 1.35 x 3 +
1.65 x 4 +
1.65 x 4 +
c.
1.35 x 3 + 1.65 x 4 +
D. 1.35 x 3 + 1.65 x 4 +
4.94x < 23; x<25
4.94x ≤ 23; x ≤ 25
4.94x >
23; x > 25
4.94x ≥
23;x ≥ 25
Answer1.35+ 4:
Step-by-step explanation:
Citywide Delivery Inc. budgets $190 per month for telephone costs, which include the 3% federal excise tax. Citywide uses approximately 4,000 minutes per month, so the company signed up for the $96.00 plan. What is the maximum number of lines Citywide can sign up for and stay within their budget? Use the figure below:
Since we can't have a fractional number of lines, Citywide can sign up for a maximum of 1 line and still stay within their budget.
Let's start by calculating the total amount Citywide pays for their telephone costs without the federal excise tax. We can do this by subtracting the 3% tax from the total budget:
$190 / 1.03 = $184.47
The $96 budget plan includes 4,000 minutes, which means that each minute costs:
$96 / 4,000 = $0.024
If Citywide wants to stay within their budget, they need to make sure that the total cost of the lines they sign up for plus the federal excise tax is less than or equal to $190.
Let's represent the number of lines Citywide signs up for as "n". The total cost of the lines plus tax can then be represented as:
n * $96 * 1.03
Setting this expression less than or equal to $190, we get:
n * $96 * 1.03 <= $190
Simplifying, we get:
n <= $190 / ($96 * 1.03)
n <= 1.945
Thus, Citywide can sign up for a maximum of 1 line and still stay within their budget.
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clara is running a bakery she has made a street sign to direct people to her bakery . She painted one of the post and sign. What is the painted area?8in,8in,5in, 60in, 4in
The painted area of the sign is approximately 324 square inches. This was calculated by finding the area of the pole, square signboard, and triangle portion of the signboard and adding them together.
To find the painted area, we need to find the area of the pole, the area of the square signboard, and the area of the triangular portion of the signboard.
Area of pole
The pole is a rectangular prism with height 60in and width 4in. Therefore, the area of the pole is:
60in x 4in = 240 sq. in.
Area of square signboard
The square signboard has a side length of 8in. Therefore, the area of the square signboard is:
8in x 8in = 64 sq. in.
Area of triangular portion of the signboard
The triangular portion of the signboard has a base of 8in and a height of 5in. Therefore, the area of the triangular portion of the signboard is:
(1/2) x 8in x 5in = 20 sq. in.
Total painted area
The total painted area is the sum of the area of the pole, the area of the square signboard, and the area of the triangular portion of the signboard. Therefore, the painted area is:
240 sq. in. + 64 sq. in. + 20 sq. in. = 324 sq. in.
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--The given question is incomplete, the complete question is given
" clara is running a bakery she has made a street sign to direct people to her bakery . She painted one of the post and sign. What is the painted area?8in,8in,5in, 60in, 4in "--
Select the correct answer. Which statement correctly describes this expression? |X^3| +5 A. the absolute value of three times a number added to 5 B. the cube of the sum of a number and 5 C. 5 more than the absolute value of the cube of a number D. the sum of the absolute value of three times a number and 5
The statement that correctly describes the expression |x^3|+5 is 5 more than the absolute value of the cube of a number.
Given this expression: |x^3|+5
| | = This sign means Absolute value,
x^3 = x³ = x × x × x
Hence, the statement that correctly describes the expression |x^3|+5 is : 5 more than the absolute value of the cube of a number.
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Help me with this................
The distribution of the numbers of siblings is best described as skewed to the right so, the median will be a more appropriate measure of the center than the mean
What is positively skewed data?If data is positively skewed - which means that the tail of the distribution leans towards higher values - the median will often be a superior indicator for ascertaining the center than the mean.
This advantage can be attributed to the fact that the median outright ignores extreme values, unlike the median which may become influenced by them and thus pulled towards the extremes of the overall set. Since it is simply the middle value obtained upon sorting the data, its sensitivity to conspicuous outliers is more limited.
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Find the interquartile range using the following.
Minimum: 1
Q1: 3
Median: 5
Q3: 7
Maximum: 9
A. 8
B. 4
C. 5
D. 10
Answer: B. 4
Step-by-step explanation: The interquartile range is just the distance in between the upper and lower quartiles. Therefore, to find the interquartile range, the equation in this case is 7 - 3, which equals 4.
There may be many polynomial equations with integer coefficient which have the square root of 8 - 1 and the square root of 8 + 1 as its roots. Construct an equation of smallest degree with integer coefficients that has the square root of 8 - 1 and the square root 8 + 1 as its roots
The equation of smallest degree with integer coefficients will be f(x) = x^2 - (3 + √7)x + 3√7
How to explain the equationIt should be noted that to begin, let us establish the following:
x = √(8 - 1) which is equal to √7.
y = √(8 + 1) which is equivalent to √9. Therefore, y equals 3.
For the value of x, its conjugate coincides with √7; hence:
(x - x') × (x - y') = (x - √7)(x - 3)
Equation expansion yields:
f(x) = x^2 - (3 + √7)x + 3√7
By substituting for both values x and y in the equation above, we can show that f(x) satisfies the given specifications:
When x takes on a value of √7:
f(√7) = (√7)^2 - (3 + √7)√7 + 3√7 = 7 - 7 = 0
With an input value of 3:
f(3) = 3^2 - (3 + √7)(3) + 3√7 = 9 - 9 - 3√7 + 3√7 = 0
The lowest degree polynomial with rational coefficients having √(8 - 1) and √(8 + 1) as its roots is: f(x) = x^2 - (3 + √7)x + 3√7
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PLEASE HELP (WILL GIVE BRAINLIEST)
Answer:
$5.50(2/3)π(6.5^3) = $3,163.45
$5.50(2/3)(3.14)(6.5^3) = $3,161.85
$3,161.85 is the correct answer.
n + 8 => 14
what makes it false
6, 8, 22, or 10
Answer:6
Step-by-step explanation: It’s 6 because it’s only greater than, not greater than or equal to
20x-12 factor out gcf in order to rewrite expression
Which ordered pair is a solution to the system? X>4 Y≥12
Some solutions for the given system of inequalities are:
(5, 12)
(6, 12)
(7, 13)
And so on.
Which ordered pair is a solution for the system?Here we have the following system of inequalities:
x > 4
y ≥ 12
We want to see which ordered pair, of the form (x, y), is a solution for the system.
A solution is a pair that makes both inequalities true.
So, x must be larger than 4.
y can be equal to 12, or larger than 12.
Then some solutions are:
(5, 12)
(6, 12)
(7, 13)
And so on.
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Solve the equation 4m = 28 for m.
A. 3
B. 4
C. 5
D. 7
Answer:
Dividing both sides by 4, we get:
4m/4 = 28/4
Simplifying, we get:
m = 7
Therefore, the answer is D. 7.
When graphing the inequality y s 2x - 4, the boundary line needs to be graphed first. Which graph correctly shows the boundary line?
The graph that correctly shows the boundary line for y ≤ 2x − 4, is B. Graph B.
How to find the graph ?The inequality y ≤ 2x − 4, shows that the y - intercept is - 4. What this means is that the boundary line must pass through ( 0, - 4 ). As Graphs C and D do not cross ( 0, - 4 ), neither of them can be the boundary line.
Also, when representing an inequality on a graph, the signs of ≤ and ≥ are presented with a solid line. > and < are the ones presented with a broken line. This means that Graph A cannot the boundary line for the inequality.
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A sack of rice wieghs 50 kilos. What is the weight of 85 sacks of rice?
Answer:
4250 kilos
Step-by-step explanation:
What are the values of the trigonometric ratios for this triangle?
Drag the answers into the boxes.
The values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.
From the given right triangle hypotenuse= 17 units and legs of triangle are 15 units and 8 units.
We know that, sinθ = Opposite/Hypotenuse
sinθ = 8/17
We know that, cosθ = Adjacent/Hypotenuse
cosθ = 15/17
We know that, tanθ = Opposite/Adjacent
tanθ = 8/15
Therefore, the values of the trigonometric ratios for the given triangle are sinθ = 8/17, cosθ = 15/17 and tanθ = 8/15.
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if u were to flip a coin 15 times how many times will the coin land on tails
Find the angle between the pair of vectors to the nearest tenth of the degree
The value of angle between the two vectors is 86⁰.
What is the angle between the two vectors?The value of angle between the two vectors is calculated as follows;
tan θ = vy/vx
where;
vy is the sum of the vertical directionvx is the sum of vectors in horizontal direction( -8, 9), (-9, -6)
vy = (-6 - 9) = -15
vx = (-9 + 8) = -1
tan θ = ( -15 ) / ( -1 )
tan θ = 15
The value of θ is calculated by taking arc tan of the fraction,;
θ = tan ⁻¹ ( 15 )
θ = 86⁰
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Triangle LMN is an obtuse triangle with l = 6, n = 8.3, and m∠M = 132°. What is the area of ΔLMN?
The area of triangle LMN is 49.61 square units.
We have,
To find the area of triangle LMN.
Area = (1/2) x base x height
where the base and height are the sides of the triangle perpendicular to each other.
First, we need to find the length of side L.
We can use the Law of Cosines.
L² = M² + N² - 2MNcos(132°)
L² = 6² + 8.3² - 268.3cos(132°)
L² = 36 + 68.89 + 99.36
L² = 204.25
L = √204.25
L = 14.28
Now that we know the length of the base of the triangle, we can find the height by dropping a perpendicular from vertex M to side LN.
Since triangle LMN is obtuse, the perpendicular will fall outside of the triangle.
Let's call the foot of the perpendicular point P.
Since M∠M is 132°, we can find the measure of the acute angle ∠LMP:
M∠LMP = 180° - M∠M
M∠LMP = 180° - 132°
M∠LMP = 48°
We can use trigonometry to find the length of MP:
tan(48°) = h/6
h = 6 x tan(48°)
h = 6.93
The area of triangle LMN is:
Area = (1/2) x base x height
Area = (1/2) x 14.28 x 6.93
Area ≈ 49.61
Thus,
The area of triangle LMN is 49.61 square units.
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The box plots display the scores that two different groups of students got on their last math quiz.
The correct option is A.
The interquartile range for Data Set A is 15 and the interquartile range for Data Set B is 10.
Given that, the box plots display the scores that two different groups of students got on their last math quiz.
We need to find the interquartile range of each data set.
So, the interquartile range of data set A = 80-65 = 15
the interquartile range of data set B = 90-80 = 10
Hence, the interquartile range for Data Set A is 15 and the interquartile range for Data Set B is 10.
The correct option A.
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