what’s the inverse function of
h(x)=2/x+1 ?
Answers
Answer:
h(x)=log2(x)
Step-by-step explanation:
The find the inverse of an invertible function y=f(x),
swap y and x and solve for y.
We have h(x)=y=2x.
Swapping x and y gives x=2y.
We now wish to solve for y.Take the log with base 2 of both sides of the equation to free the y variable.
x=2ylog2(x)=log2(2y)=yThus, y=h(x)=log2(x).
See that we used the fact that logn(nx)=x
Answer:
If I understand correctly, your trying to find the inverse function of:
h(x)= \(\frac{2}{x} \) + 1, If so...
Answer:
Related Questions
Solve for the value of a.
Answers
Answer:
7 will be the answer.
Step-by-step explanation:
The angles are complementary angles i.e their sum is 90°.
(5a+3)°+52°=90°
5a+55°=90°
5a=90°-55°
5a=35°
a=35°/5
a=7
Maxine wants to buy a fax machine that has a full price of $220.00, plus a 7% sales tax. At store A, the fax machine is on sale for 15% off, while at store B, the fax machine is being sold for full price, but Maxine has a $35 coupon she can use at only store B. Help Maxine decide if she should buy the fax machine at store A or at store B. Part I: What is the sale price of the fax machine at store A, not including tax? Part II: What is the total amount that Maxine would pay for the fax machine at store A, including tax?Part III: What is the price of the fax machine, not including tax, at store B after the coupon has been applied? Part IV: What is the total amount that Maxine would pay for the fax machine at store B, including tax?Part V: Assuming that Maxine wants to spend the least amount of money as possible, should she buy the fax machine at store A or at store B?
Answers
EXPLANATION
Let's see the facts:
Machine price = $220.00
Sales tax=7%
At Store A-----> Discount=15%
At Store B----->Coupon for $35
Part I:
Sale price at Store A (including discount)= Machine Price*[100%-Discount] (In decimal form)
Sale price at Store A (including discount)= 220.00 * 0.85 = $187
Part II:
Sale price at Store A (including tax) = Sale price at Store A (including discount) + Sale price at Store A (including discount)* Tax in decimal form
Sale price at Store A (including tax) = 187 + 187*0.07 = $200.09
Part III:
Sale price at Store B (including coupon)=Machine Price-coupon discount
Sale price at Store B (including coupon)=220-35 = $185
Part IV
Sale price at Store B (including tax) = Sale price at Store B (including coupon) + Sale price at Store A (including coupon)* Tax in decimal form
Sale price at Store B (including tax) = 185 + 185*0.07 = $197.95
Part V:
Assuming that Maxine wants to spend the least amount of money as possible, he should buy the fax machine at Store B.
Answers:
Part I: $187
Part II: $200.09
Part III: $185
Part IV: $197.95
Part V: Store B
A national consumer agency selected independent random samples of 45 owners of newer cars (less than five years old) and 40 owners of older cars (more than five years old) to estimate the difference in mean dollar cost of yearly routine maintenance, such as oil changes, tire rotations, filters, and wiper blades. The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46. For older cars, the mean was $286 with a standard deviation of $58.
Required:
What represents the 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars?
Answers
Answer:
The 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars is (-$113.44, -$68.56)
Step-by-step explanation:
Subtraction of normal variables:
When we subtract the normal distributions, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
45 owners of newer cars (less than five years old). The agency found the mean dollar cost per year for newer cars was $195 with a standard deviation of $46
This means that:
\(\mu_N = 195\)
\(s_N = \frac{46}{\sqrt{45}} = 6.8573\)
40 owners of older cars (more than five years old). For older cars, the mean was $286 with a standard deviation of $58.
This means that:
\(\mu_O = 286\)
\(s_O = \frac{58}{\sqrt{40}} = 9.17\)
Subtaction:
Sample mean:
\(\mu = \mu_N - \mu_O = 195 - 286 = -91\)
Standard error:
\(s = \sqrt{s_N^2 + s_O^2} = \sqrt{6.8573^2+9.17^2} = 11.45\)
Confidence interval:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.95}{2} = 0.025\)
Now, we have to find z in the Ztable as such z has a pvalue of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.
Now, find the margin of error M as such
\(M = zs\)
In which s is the standard error.
So
\(M = zs = 1.96*11.45 = 22.44\)
The lower end of the interval is the sample mean subtracted by M. So it is -91 - 22.44 = -$113.44
The upper end of the interval is the sample mean added to M. So it is -91 + 22.44 = -$68.56
The 95 percent confidence interval to estimate the difference (newer minus older) in the mean dollar cost of routine maintenance between newer and older cars is (-$113.44, -$68.56)
Mia hired a moving company. The company charged $500 or its services, and Mia gives the movers a 16% tip.
Answers
Answer:
The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580
Step-by-step explanation:
Write 2,000,000 + 70,000 + 5,000 + 40 + 6 in word form?
Answers
Answer:
You can add the numbers or count according to the number of zeroes present in the expanded form and write the digits down.
2075046
Answer:
Step-by-step explanation:
two million seventy five thousand forty-six
The degree measures of the four angles of a quadrilateral are w,x, y, and z respectively. If w is the average (arithmetic mean) of x, y, and z, then x + y + z =A. 45 degreesB. 90 degreesC.120°D.270⁰
Answers
It is stated that the sum of the interior angles of a quadrilateral is 360°. It means that:
\(w+x+y+z=360\)If w is the average of x, y and z, then:
\(w=\frac{x+y+z}{3}\)Use this information to replace w in the first equation:
\(\begin{gathered} \frac{x+y+z}{3}+x+y+z=360 \\ \frac{4}{3}(x+y+z)=360 \\ x+y+z=360\cdot\frac{3}{4} \\ x+y+z=270 \end{gathered}\)x+y+z=270°.
The sum of two integers is 9 their difference is 5 what are the 2 integers
Answers
For the pyramid below draw the net and then calculate its total surface area using your net. ( picture is uploaded)
Answers
The total surface area of the pyramid from the net is 286 square cm
Calculating the total surface area from the netTo calculate the total surface area of a pyramid from its net, you need to add up the areas of all its faces.
The net of a pyramid is a two-dimensional representation of the pyramid, where the edges of the net represent the edges of the pyramid.
In this case, the nets are
Rectangle of: 10 by 7Pair of triangles of: 10 by 12.5, 7 by 13Using the above as a guide, we have the following:
Area = 10 * 7 + 2 * (1/2 * 10 * 12.5 + 1/2 * 7 * 13)
Evaluate
Area = 286
Hence, the surface area is 286 square cm
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What is the area of this figure?
15 mm
4 mm
Submit
3 mm
3 mm
5 mm
5 mm
7 mm
8 mm
Write your answer using decimals, if necessary.
square millimeters
Answers
solve for r.
4(r+15)+4r=300
Answers
Answer:
r=30
Step-by-step explanation:
first expand:
4r+60+4r=300
8r+60=300
8r=300-60
8r=240
r=30
hope this works:)
2. Consider the following equation with radicals and rational exponents. 11^19/4 • ^a√11^b = 11^9/4 • √11^3 What is the quotient of b and a?
Answers
The given expression :
\(11^{\frac{19}{4}}\cdot\sqrt[a]{11^b}=11^{\frac{9}{4}}\cdot\sqrt[]{11^3}\)The exponents in the form of root can be express as :
\(x^{\frac{n}{m}}=\sqrt[m]{x^n}\)So, the given expression simplify as :
\(\begin{gathered} 11^{\frac{19}{4}}\cdot\sqrt[a]{11^b}=11^{\frac{9}{4}}\cdot\sqrt[]{11^3} \\ 11^{\frac{19}{4}}\cdot11^{\frac{b}{a}}=11^{\frac{9}{4}}\cdot11^{\frac{3}{2}} \end{gathered}\)Since the base of the exponents are same and the bases are multiply so, the exponents will sum up
\(\begin{gathered} 11^{\frac{19}{4}}\cdot11^{\frac{b}{a}}=11^{\frac{9}{4}}\cdot11^{\frac{3}{2}} \\ 11^{\frac{19}{4}+\frac{b}{a}}=11^{\frac{9}{4}+\frac{3}{2}} \end{gathered}\)Now, the bases of exponents on both side are equal so, the exponents will equate together
\(\begin{gathered} 11^{\frac{19}{4}+\frac{b}{a}}=11^{\frac{9}{4}+\frac{3}{2}} \\ \frac{19}{4}+\frac{b}{a}=\frac{9}{4}+\frac{3}{2} \\ \frac{b}{a}=\frac{9}{4}+\frac{3}{2}-\frac{19}{4} \\ \frac{b}{a}=\frac{9+6-19}{4} \\ \frac{b}{a}=\frac{-4}{4} \\ \frac{b}{a}=(-1) \\ b=(-1)a \\ \text{ From the divsion alogrithm } \\ \text{Dividend = Divisor}\times Quotient+\text{ Remainder} \\ b=(-1)a \\ \text{Quotient of b =(-1)} \\ \text{Now, for a} \\ \frac{b}{a}=-1 \\ \frac{b}{a}=\frac{-1}{1} \\ \text{Apply cross multiplication} \\ b(1)=(-1)a \\ \text{Multiply by (-1)} \\ (-1)b=a \\ a=(-1)b \\ \text{From Division alogrithm} \\ \text{Quotient of a is (-1)} \end{gathered}\)Answer : Quotient of b and a is ( -1 ).
Brandon has 10 but each bag has 6 chocolates how many chocolates does he have in total
Answers
Answer:
10 what
Step-by-step explanation:
81 students at a college were asked whether they had completed their required English 101 course, and 53 students said "yes". Construct the 99% confidence interval for the proportion of students at the college who have completed their required English 101 course. Enter your answers as decimals (not percents) accurate to three decimal places. The Confidence Interval is ( , )
Answers
Answer:
\((0.518,0.790)\)
Step-by-step explanation:
Use the formula \(CI=\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }\) where \(\hat{p}\) is the sample proportion, \(n\) is the sample size, and \(z^*\) is the corresponding z-value for a given confidence level.
We know that \(\hat{p}=\frac{53}{81}\), \(n=81\), and \(z^*=2.5758\) for a 99% confidence level.
Therefore, the 99% confidence interval is \((0.518,0.790)\)
The speed of a passenger train is 8 mph faster than the speed of a freight train. The passenger train travels 280 miles in the same time it takes the freight train to travel 240 miles. Find the speed of each train.
Answers
The speed of the freight train is 30 mph, and the speed of the passenger train is 30 + 8 = 38 mph.
We have,
Let's denote the speed of the freight train as x mph.
Since the speed of the passenger train is 8 mph faster, we can denote the speed of the passenger train as (x + 8) mph.
To find the speeds of each train, we can use the formula:
Speed = Distance / Time
For the passenger train: (x + 8) = 280 / t, where t is the time taken to travel 280 miles.
For the freight train: x = 240 / t, where t is the time taken to travel 240 miles.
Since the times taken for both trains are the same, we can set the two equations equal to each other:
(x + 8) = 280 / t = x = 240 / t
Cross-multiplying the equation, we have:
(x + 8) t = x (280 / t)
xt + 8t = 280
xt - x = 240
Simplifying the equation, we get:
xt - x = 240
x(t - 1) = 240
Dividing both sides by (t - 1):
x = 240 / (t - 1)
Substituting the value of x in the first equation:
(x + 8) = 280 / t
240 / (t - 1) + 8 = 280 / t
Simplifying the equation, we get:
240t + 8(t - 1) = 280(t - 1)
240t + 8t - 8 = 280t - 280
248t - 8 = 280t - 280
280 - 8 = 280t - 248t
272 = 32t
t = 272 / 32 = 8.5
Substituting the value of t in the equation for x:
x = 240 / (t - 1) = 240 / (8.5 - 1) = 30
Therefore,
The speed of the freight train is 30 mph, and the speed of the passenger train is 30 + 8 = 38 mph.
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Boris started on the treadmill after setting timer for 99 minutes. The display says he have finished 43% of his run. How many minutes have gone by. Round to the nearest tenth
Answers
99 minutes * 0.43 = 42.57 minutes
Rounding to the nearest tenth, we can say that approximately 42.6 minutes have gone by.
{ (-2, 4), (0, 2), (-1,3), (4, -2)}
The set of ordered pairs above:
A: Function
B: not a function
Answers
Answer:
its a function
Step-by-step explanation:
hope that helps>3
OLGA went on an 82 mile bike trip last week by Thursday night she travel 64 miles of the total distance which president is reasonable estimate of how much of the trip OLGA completed by Thursday
Answers
Answer:Note: This symbol ≈ means approximately.
629 ≈ 600
215 ≈ 200
111 ≈ 100
588 ≈ 600
Now, we add the simplified numbers up: 600 + 200 + 100 + 600 = 1500. So, your answer is D or 1,500.
Step-by-step explanation:PLZZZ GIVE BRAINLYEST HOPE IT HELPS
Find the missing length indicated.
A)100
B)36
C)25
D)9
Answers
Answer:
100
100
100
Step-by-step explanation:
15+9+15+9+65
If u(x) = −2x² +3 and v(x)=1/x, what is the range of (uv)(x)?
Answers
Given:
\(\begin{gathered} u(x)=-2x^2+3 \\ v(x)=\frac{1}{x} \end{gathered}\)Required:
To find the range of the function (uv)(x).
Explanation:
We know that
\(\begin{gathered} (uv)(x)=u(v(x)) \\ \\ =u(\frac{1}{x}) \\ \\ =-2(\frac{1}{x^2})+3 \\ \\ =-\frac{2}{x^2}+3 \end{gathered}\)The horizontal asymptote of this function is at y=3.
So, the range of this function is from
\((-\infty,3)\)Final Answer:
The range of (uv)(x) is
\((-\infty,3)\)To prove that there is a unique element x such that P(x) is true is the same as showing which of these statements is true?a) 3xAy(P (y) ↔ x = y)b) 3x(P(x) & Ay( y =/ x --> notP(y)))c) 3x(P(x) & Ay(P(y) --> x = y))
Answers
The statement that proves that there is a unique element x such that P(x) is true is: c) 3x(P(x) & Ay(P(y) --> x = y)).
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms.
Here,
In this statement, the quantifier "3x" says that for every element x, and the condition "P(x)" says that x satisfies a certain property. The statement "Ay(P(y) --> x = y)" says that for every other element y, if y also satisfies the property, then it must be equal to x. Hence, if there is a unique element x such that P(x) is true, then this statement is true.
Option (a) says that for every element y, P(y) is equivalent to y = x, but this statement alone does not imply that there is only one element that satisfies P(x).
Option (b) says that for every element x, if P(x) is true, then there is no other element y that also satisfies P(y) and is not equal to x. However, this statement alone does not imply that there exists an element x that satisfies P(x).
The following assertion establishes that there is a unique element x such that P(x) is true: c) 3x(P(x) & Ay(P(y) --> x = y)).
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Use your understanding of transformations and key features to write the slope-intercept equation of this linear function.
Enter the correct answer in the box by replacing the values of m and b.
Answers
Answer:
f(x)=-2x+5
Step-by-step explanation:
The line shown in the graph is always decreasing at a constant rate, has a slope of -2, and has a y-intercept of 5.
So the parent function has been reflected across the x-axis (multiplied by -1), vertically stretched by a factor of 2 (multiplied by 2), and vertically translated up 5 units (5 added to it).
Therefore, the slope-intercept equation that represents this linear function is f(x)=-2x+5.
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of the given line is y=-2x+5.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The given line passes through two points with coordinates (0,5) and (1,3). Therefore, the slope and the y-intercept of the given equation of a line can be written as,
Slope, m = (5 - 3)/(0 - 1) = 2/-1 = -2
y-intercept, c = 5
Now, the equation of the line can be written as,
y = mx + c
y = -2x + 5
Hence, the equation of the given line is y=-2x+5.
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Are the triangle similar
Answers
Answer:AAS
Step-by-step explanation:
how do i know which one?
Answers
The inequality value that would be able to show/x/ ≤ 5 is option A
What is inequality?
In mathematics, inequality refers to a mathematical statement that expresses a relationship between two quantities, indicating that one quantity is greater than, less than, or not equal to the other.
The symbol that we have is telling us that the value of the x would be less than or it would be seen to be equal to five.
We can see that /x/ ≤ 5 would exclude the negative values and this can be seen in the option that is marked option A
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In the diagram, AITP - ANGO. Find the values of
x and y.
y =
X=
Answers
Answer:
x = 25, y = 9
Step-by-step explanation:
Since the triangles are congruent then corresponding angles and sides are congruent, thus
∠ O = ∠ P , substitute values
6y - 14 = 40 ( add 14 to both sides )
6y = 54 ( divide both sides by 6 )
y = 9
and
NG = IT , that is
x - 2y = 7 ( substitute y = 9 into the equation )
x - 2(9) = 7
x - 18 = 7 ( add 18 to both sides )
x = 25
Desperate Need Of Help
Answers
The domain and range of the graph above in interval notation include the following:
Domain = [-6, 3]
Range = [-3, 3]
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-6, 3] or -6 ≤ x < 3.
Range = [-3, 3] or -3 < y < 3
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The sum of nine times a number, and 4, is equal to eight times the number.
Answers
Answer:
-4
Step-by-step explanation:
Let's put this in math notation. We can call the number x:
9x+4=8x
Subtract 8x from both sides:
x+4=0
Subtract 4 from both sides:
x=-4
Answer:
Step-by-step explanation:
For this, we will use the variable x.
9x + 4 = 8x
4 = -1x
x = -4
If they are looking for just the formula, it is 9x + 4 = 8x
If they are looking for the solved answer, it is x = -4
HELP ASAAAPPPO! Dawn is making an abstract painting with two triangles. The dimensions of the painting are shown below:
Two triangles share the same height of 8 inches. One triangle has a base of 6 inches and the other is 10 inches.
The total area of the two triangles is
???
square inches.
Answers
the total area of the two triangles as shwon in the image is 70 in²
What is area?Area can be defined as the total portion occuppied by a plane fiqure.
To calculate the total area of the two triangles, we use the formula below.
Formula:
Total area of the triangle = Area of the pink triangle+Area of the purple triangleArea of the purple triangle = bh/2.................. Equation 1Where:
b = Base of the purple triangle = 8 inh = Height of the purple triangle = 10 inSubstitute these values into equation 1
Area of the purple triangle = 8×10/2Area of the purple triangle = 40 in²Similarly,
Area of the pink triangle = BH/2........ Equation 1Where:
B = 6 inH = 10 inSubstitute these values into equation 2
Area of the pink triangle = 6×10/2Area of the pink triangle = 30 in²Therefore, the total area of the two triangles is 40+30 = 70 in².
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Consider a triangle ABC . Suppose that B=126°, a=38, and c=22. Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
Answers
Answer:
b = 54; A = 34.7°; C = 19.3°
Step-by-step explanation:
To solve the triangle means that we have to calculate the values of the missing angles and the missing sides.
We are given;
B = 126°, a = 38, and c = 22
Using law of cosines, we can find side b.
So;
b² = a² + c² - 2ac*cosB
Thus;
b² = 38² + 22² - 2(38 × 22)cos 126
b² = 1444 + 484 - 1672(-0.5878)
b² = 2910.8016
b = √2910.8016
b = 53.9518 ≈ 54
Using Law of sines, we can find the other 2 angles a and c.
Thus;
a/sin A = b/sinB = c/sinC
Thus, for A;
a/sin A = b/sin B
38/sin A = 53.9518/sin 126
sinA = (38 × sin 126)/53.9518
sinA = 0.5698
A = sin^(-1) 0.5698
A = 34.7363° ≈ 34.7°
Likewise;
b/sinB = c/sinC
53.9518/sin 126 = 22/sinC
sinC = (22 × sin 126)/53.9518
sinC = 0.3299
C = sin^(-1) 0.3299
C = 19.2627 ≈ 19.3°
1/3 x (21.69 – 24.99)
Answers
Answer:
I think it might be 0.30
Step-by-step explanation:
Question content area top Part 1 Consider a political discussion group consisting of 7 Democrats, 5 Republicans, and 3 Independents. Suppose that two group members are randomly selected, in succession, to attend a political convention. Find the probability of selecting a Republican and then an Independent.
Answers
The probability of selecting a Republican and then an Independent is 1/15
Finding the probability of selecting a Republican and then an Independent.From the question, we have the following parameters that can be used in our computation:
Political discussion group consisting of
7 Democrats5 Republicans3 Independents.If the people are replaced, then we have
P(Republicans) = 5/15
P(Independents) = 3/15
So, we have
The probability of selecting a Republican and then an Independent
P = 5/15 * 3/15
Evaluate
P = 1/15
Hence, the probability of selecting a Republican and then an Independent is 1/15
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