9514 1404 393
Answer:
g^-1(x) = 1/(x+2)
Step-by-step explanation:
To find the inverse of the function ...
y = g(x)
swap the variables and solve for y.
x = g(y)
x = 1/y -2 . . . . . . . use the given g(x)
x +2 = 1/y . . . . . . . add 2
y(x +2) = 1 . . . . . . multiply by y
y = 1/(x +2) . . . . . divide by the coefficient of x
The inverse function is ...
\(\boxed{g^{-1}(x)=\dfrac{1}{x+2}}\)
_____
Additional comment
Please observe that when the fraction is typeset, as in the boxed answer, the fraction bar serves as a grouping symbol. It shows you that the denominator is the sum x+2.
When the same expression is written in plain text, only the first item after the division symbol (/ or ÷) is considered to be in the denominator. That is, 1/x+2 = (1/x)+2. The presence or absence of a (space) has no bearing on the correct interpretation of the expression. Only parentheses will serve as a grouping symbol in plain text expressions.
g^-1(x) = 1/(x+2)
which polynomial correctly combines the like germs and expresses the five polynomial in standard form
Answer:
i say the 3rd row
Step-by-step explanation:
A dairy farmer wants to mix a 85% protein supplement and a standard 60% protein ration to make 1200 pounds of a high-grade 70% protein ration. How many pounds of each should he use?
Answer:
• 85% protein supplement: 480 pounds
,• 60% protein ration: 720 pounds
Explanation:
Let the number of pounds of 85% protein supplement required = x
The farmer wants to make 1200 pounds (of a high-grade 70% protein ration).
Therefore, the number of pounds of 60% protein ration required = (1200-x) lbs
First, we add the constituents we are mixing together.
\(0.85x+0.6(1200-x)\)The final protein ration we want to obtain:
\(1200\times0.7\)Equate both:
\(0.85x+0.6(1200-x)=1200\times0.7\)Then solve the equation for x.
\(\begin{gathered} 0.85x+720-0.6x=840 \\ 0.85x-0.6x=840-720 \\ 0.25x=120 \\ \implies x=\frac{120}{0.25} \\ x=480\text{ pounds} \end{gathered}\)The number of pounds of the 85% protein supplement he should use is 480 pounds.
\(1200-x=1200-480=720\text{ pounds}\)The number of pounds of the 60% protein ration he should use is 720 pounds.
6th grade math help me pleasee
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1. Kris
2. Katie
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Plssss helpppp!!! I’ll give brainliest
Shane is standing near a cell tower. The angle of elevation from him to the top of the tower is 73°. Cara is standing 10 feet behind Shane (further away from the cell tower). From her, the angle of elevation to the top of the tower is 65°. What is the height of the tower, rounded to the nearest tenth of a foot?
A.9.1 ft
B. 59.0 ft
C. 62.3 ft
D.65.7 ft
Answer:
Either c or d
Step-by-step explanation:
what is the lowest base in which the number 1000 could be a valid number?
The highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.
In mathematics, a base is the number of digits or distinct symbols used to represent numbers in a positional numeral system. For example, in the decimal system (which we commonly use), the base is 10 because we use 10 distinct digits from 0 to 9.
Now, let's consider the number 1000. In order to find the lowest base in which this could be a valid number, we need to break down 1000 into its constituent digits. Since 1000 has 4 digits, we can represent it as:
1000 = 1 x base^3 + 0 x base^2 + 0 x base^1 + 0 x base^0
where base is the number system we are using. Now, we need to find the lowest value of base that makes this equation valid.
We can see that if we set base = 2, then the equation becomes:
1000 = 1 x 2^9 + 0 x 2^8 + 0 x 2^7 + 0 x 2^6 + 0 x 2^5 + 0 x 2^4 + 0 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0
Here, we have used the binary system, which has a base of 2. As we can see, the highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.
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What is the 50th term of the arithmetic sequence 32, 27, 22, 17, 12
Answer:
5n - 27
n
5 because you minus 5 each time
27 because 32-5=27
(5×50) -27=
223
How do you graph a rational function example?
To graph a rational function example, start by writing the equation in the form y = (ax + b)/(cx + d).
Then, plot the points where the denominator equals zero (when x = -d/c). These points are called vertical asymptotes.Next, plot the points where the numerator equals zero (when x = -b/a). These are called horizontal asymptotes.Finally, plot points between the vertical and horizontal asymptotes to graph the rational function.Plotting the points between the vertical and horizontal asymptotes will allow you to see the shape of the graph. Start by plotting points on either side of the vertical and horizontal asymptotes. Then, plot points at evenly spaced x-values between the vertical and horizontal asymptotes. For example, if the vertical asymptote is at x=-d/c, and the horizontal asymptote is at x=-b/a, you can plot points at x=-1.5d/c, x=-0.5d/c, x=-1.5b/a, and x=-0.5b/a. By plotting these points and connecting them with a smooth curve, you can graph the rational function.
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20 ÷ ........... = (-2)
Answer:
20÷(-10)=-2 is the answer
45,60
8, 16, 32
PJ
n) 60, 90, 120 o)
Find the least (smallest) number which is exactly divisible by 12 and 16.
Find the smallest number which is exactly divisible by 24 and 36.
Find the smallest numharthotic divided by 26 and 49 without leaving
Answer:
Step-by-step explanation:
I don't understand what the numbers before the language mean. I will answer the questions that have a definite language.
12 = 2 * 2 * 3
16 = 2 * 2 * 2 * 2
The answer is going to require you have 4 fours and one 3
2 * 2 * 2 * 2 * 3 = 48
24 = 2 * 2 * 2 * 3
36 = 2 * 2 * 3 * 3
The answer is going to require two threes and three 2s
2 * 2 * 2 * 3 * 3 = 72
What is this word numharthotic
26 = 2 * 13
49 = 7 * 7
The smallest number that can be divided by both with no remainder is
2 * 7 *7 * 13 = 1276
1. If f(x) = (3x-2)/(2x+3), then f'(x) =
Answer:
\(f'(x)= \frac{13}{(2x+3)^2}\\\)
Step-by-step explanation:
\(f(x)= \frac{3x-2}{2x+3} \\\)
\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)
\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)
What goes on the green box ?
Answer:
5^9 / 5^3 = 5^6
the answer is 6
Step-by-step explanation:
what is the first quartile of the set of data 14,28,33,42,53,81,97
The first quartile of the data set is 28.
Determining the first quartileFrom the question, we are to determine the first quartile of the given data set
The first quartile or lower quartile, (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.
The given data set is
14,28,33,42,53,81,97
In the given data set, the first quartile is 28.
Hence, the first quartile of the data set is 28
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question is attached
Answer:
56
Step-by-step explanation:
Top line:
100% - 80% = 20%
20% of 60 = 0.2 × 60 = 12
Small piece on top is 12.
Second line:
Small piece is 12.
100% - 60% = 40%
Small piece is also 40%.
40% of x = 12
0.4x = 12
x = 12/0.4
x = 30
The entire second line is 30.
60% of 30 = 0.6 × 30 = 18
60% of second line is 18.
Third line:
30% of third line = 18
100% - 30% = 70%
30/18 = 70/x
30x = 18 × 70
x = 42
Larger part of third line is 42.
Fourth line:
75% of 4th line is 42.
100/x = 75/42
75x = 100 × 42
x = 56
Answer: 56
4x2 - 5x + 9 = 0
How many solutions does this problem have please help
Answer: x=17/5
Step-by-step explanation:
convertir 60° a minutos
To convert 60° to minutes, we need to understand the relationship between degrees and minutes in a circle. In a circle, there are 360 degrees, and each degree can be further divided into 60 minutes.
So, to convert 60° to minutes, we can use the following formula:
Minutes = Degrees × 60
Substituting the given value, we have:
Minutes = 60° × 60
Minutes = 3600
Therefore, 60° is equal to 3600 minutes.
This conversion is based on the fact that a degree can be subdivided into minutes. In this case, each degree represents 60 minutes. By multiplying 60° by 60, we obtain the equivalent in minutes. Thus, 60° is equivalent to 3600 minutes.
It's important to note that this conversion is specific to angles and circles. Degrees are commonly used to measure angles, while minutes are used to provide a finer level of detail when measuring small angles. By converting from degrees to minutes, we can express an angle in a more precise manner.
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Mario simplified the expression (4 z Superscript 8 Baseline) Superscript negative 3 as shown. (4 z Superscript 8 Baseline) Superscript negative 3 = 4 z Superscript 8 times (negative 3) Baseline = 4 z Superscript negative 24 Baseline = StartFraction 4 Over z Superscript 24 Baseline EndFraction Which statement explains Mario's error?
Answer:
Step-by-step explanation:
Given the expression \((4z^8)^{-3}\), to evaluate this, we will use one of the law of indices as shown;
\((a^m)^n = a^{mn}\)
\(4^{-3} * z^{8*-3}\)
\(= \frac{1}{4^3} * z^{-24}\\ \\= \frac{1}{64} * \frac{1}{z^{24}}\\ \\= \frac{1}{64z^{24}}\)
Mario's error was that she did not raise the value of 4 to the power of -3. She only raised z^8 to the power of -3 when it is supposed to affect both 4 and z^8
Answer:
The last one
Step-by-step explanation:
I really need a tutor, but I don’t have the option, help:(
Answer:
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Step by Step Explanation:
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I need help with this question
8x4=(x times 7) - (x times 3)
Answer:
Step-by-step explanation:
Nothing further can be done with this topic. Please check the expression entered or try another topic.
8 x 4 = (xtimes⋅7) − (xtimes⋅3)
F(x)=x2-5+6 what are the values of coefficient and consistent in the function
The coefficients and constant in the quadratic function f(x) = x² - 5x + 6 are coefficients: 1, -5 and constant: 6.
What in math is a quadratic function?A quadratic function is an algebraic function with one or more variables where the largest exponent of the variable is two. The equation for a quadratic function is of the form f(x) = ax² + bx + c, where 'a' is a non-zero integer and a, b, and c are real numbers. A quadratic function is a polynomial of degree 2, and its definition is as follows.
The "a", "b", and "c" from "ax2 + bx + c" are used in the quadratic formula; they are known as the "numerical coefficients" of the quadratic equation. Therefore,
f(x) = x²– 5x + 6
a = 1
b = -5
c = 6
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Question:
Identifying the Coefficients and Constanta
Consider the quadratic function f(x) = x2 – 5x + 6.
What are the values of the coefficients and constant in the function?
A recent study by a researcher found that 82% of teenagers have used cellphones while driving a vehicle. Suppose a random sample of 100 teen drivers is taken. (a) Calculate the probability that the sample proportion is less than 0.80. (b) Calculate the probability that the sample proportion is more than or equal to 0.82. (c) Calculate the probability that the sample proportion is at most 0.85.
(a) The probability that the sample proportion is less than 0.80 is approximately 0.1867.
(b) The probability that the sample proportion is more than or equal to 0.82 is approximately 0.8133.
(c) The probability that the sample proportion is at most 0.85 is approximately 0.8577.
To calculate the probabilities related to the sample proportion in this scenario, we can use the properties of the sampling distribution of proportions and assume that the sample follows a binomial distribution.
(a) To calculate the probability that the sample proportion is less than 0.80, we can use the normal approximation to the binomial distribution. The mean of the sampling distribution is equal to the population proportion, which is 0.82 in this case, and the standard deviation is calculated as the square root of (p(1-p)/n), where p is the population proportion and n is the sample size.
Let's calculate the z-score for a sample proportion of 0.80:
z = (0.80 - 0.82) / sqrt(0.82 * (1 - 0.82) / 100) ≈ -0.8944
Using the z-table or a calculator, we can find the probability associated with this z-score. The probability that the sample proportion is less than 0.80 is approximately 0.1867.
(b) To calculate the probability that the sample proportion is more than or equal to 0.82, we can use the same approach. Let's calculate the z-score for a sample proportion of 0.82:
z = (0.82 - 0.82) / sqrt(0.82 * (1 - 0.82) / 100) ≈ 0
The probability that the sample proportion is more than or equal to 0.82 is equal to 1 minus the probability that it is less than 0.82. From part (a), we know that the probability of being less than 0.82 is approximately 0.1867. Therefore, the probability that the sample proportion is more than or equal to 0.82 is approximately 1 - 0.1867 = 0.8133.
(c) To calculate the probability that the sample proportion is at most 0.85, we can once again use the normal approximation. Let's calculate the z-score for a sample proportion of 0.85:
z = (0.85 - 0.82) / sqrt(0.82 * (1 - 0.82) / 100) ≈ 1.0645
Using the z-table or a calculator, we can find the probability associated with this z-score. The probability that the sample proportion is at most 0.85 is approximately 0.8577.
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the question is in the picture
Answer:
(x) = 1/2x-3/2
Step-by-step explanation:
The inverse is the opposite of the equation given in this case is 2x+3 and the inverse is when you switch the x and the y and you solve for y.
Yacouba purchased a three bedroom house in Kingwood, TX for $185,000. Housing prices are expected to increase 2.1% annually.Which of the following functions best represents the price of the house after x years?
The equation for the price of house after x years is,
\(f(x)=185000(1+\frac{2.1}{100})^x\)Simplify the equation to obtain the equation for value of house after x years.
\(\begin{gathered} f(x)=185000(1+0.021)^x \\ =185000(1.021)^x \end{gathered}\)So option B is correct.
approximate the nonlinear system by a linear system at (0,0) and find the eigenvalues.
We can approximate the nonlinear system by a linear system at (0,0) using the Jacobian matrix and can find the eigenvalues using the formula det(J(0,0) - λI) = 0.
We have to approximate the nonlinear system by a linear system at (0,0) and find the eigenvalues.
Identify the nonlinear system.
First, you need to provide the nonlinear system of equations you're working with. The system should be in the form of:
dx/dt = f(x, y)
dy/dt = g(x, y)
Calculate the Jacobian matrix.
To linearize the system, compute the Jacobian matrix, J, which contains the partial derivatives of f and g with respect to x and y. The Jacobian matrix is given by:
J(x, y) = [ ∂f/∂x ∂f/∂y ]
[ ∂g/∂x ∂g/∂y ]
Evaluate the Jacobian at (0,0).
Substitute the point (0,0) into the Jacobian matrix to obtain J(0,0).
Find the eigenvalues.
To find the eigenvalues, solve the characteristic equation, which is given by:
det(J(0,0) - λI) = 0
Here, λ represents the eigenvalues, and I is the identity matrix. Solve the resulting polynomial equation for λ to obtain the eigenvalues of the linearized system.
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Please help with spanish! I just need three examples for each one. Thank you!!
Answer:
Hola and Como estas
Step-by-step explanation:
Hola means hello and you can use it formally and informally when speaking to friends or respected family members.
Como estas is a informal way of saying how are you to friends.
The points (-2, a) and (-4, -10) fall on a line with a slope of 8. What is the value of a ?
а=
Answer:
(-2, -3)
Step-by-step explanation:
4 - 2 =2 + 1= 3 welcome :)
Nonstop trains leave Toronto and Montreal at the same time each day going to the other city along the main line. One train travels at 120 km/h and the other at 90 km/h. Assuming the track is straight, how far apart are they one hour before they meet?
pls help ( ˘︹˘ )
Assuming the track is straight, the distance at which they are apart one hour before they meet is; 30 km
How to find the distance from speed and time?We are told that a Nonstop trains leave Toronto and Montreal at the same time each day going to the other city along the main line.
Speed of Train 1 = 120 km/h
Speed of Train 2 = 90 km/h
Time spent by train 1 = 1 hour
Time spent train 2 = 1 hour
Formula for distance is;
Distance = Speed * time
If they leave the same time each day, it means that;
Distance of train 1 = 120 * 1 = 120 km
Distance of train 2 = 90 * 1 = 90 km
Thus, distance at which they will be apart before meeting each other is;
Distance apart = 120 - 90
Distance apart = 30 km
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In a circle, an angle measuring 2.4 radians intercepts an arc of length 24.4. Find the radius of the circle to the nearest
The radius of the circle is approximately 10.17 units (rounded to two decimal places).
To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:
arc length = radius x central angle
In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:
24.4 = r x 2.4
Solving for r, we get:
r = 24.4 / 2.4
r ≈ 10.17
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when the logarithmic transformation is applied to the nonlinear model y=β0eβ1xε, the resulting model is intrinsically linear with an intercept of:
When the logarithmic transformation is applied to the nonlinear model y=β0eβ1xε, the resulting model is intrinsically linear with an intercept of ln(β0).
This transformation involves taking the natural logarithm of both sides of the equation, which yields ln(y) = ln(β0) + β1x + ε. The resulting equation is now linear, as it has a constant slope (β1) and an intercept (ln(β0)). This transformation is often used to simplify the analysis of nonlinear relationships, as it allows for the use of linear regression techniques. Additionally, taking the logarithm of the dependent variable can help to stabilize the variance of the errors, which can improve the accuracy of the model. However, it is important to note that this transformation can also make the interpretation of the coefficients more difficult, as they now represent the percentage change in y associated with a one-unit increase in x, rather than the absolute change in y. Overall, the logarithmic transformation can be a useful tool in analyzing nonlinear relationships, but it is important to carefully consider the implications of this transformation on the interpretation of the model and its coefficients.
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Rihanna next year julian is planning to walk for several hours if she walks at the same speed next year how many miles will she walk you will need to extend the label to show 7 hours
Rihanna will walk next year if she walks for 7 hours at the same speed, we need to know her walking speed. Let's assume her walking speed is 3 miles per hour.
To find the total distance, we can multiply the speed (3 miles per hour) by the time (7 hours):
3 miles/hour × 7 hours = 21 miles
Therefore, if Rihanna walks for 7 hours at the same speed next year, she will walk 21 miles.
It's important to note that this calculation assumes Rihanna maintains a consistent walking speed throughout the entire duration of 7 hours. If her speed changes, the total distance she covers would be different.
Remember, this answer is based on the assumption that Rihanna walks at a speed of 3 miles per hour. If her walking speed is different, the result would change accordingly.
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