Answers
Given the function
[tex]f(x)=2^{3-x}-2[/tex]Substitute y = f(x) into the function above
[tex]y=2^{3-x}-2[/tex]Make 'x' the subject of the formula
[tex]y+2=2^{3-x}[/tex]Take the log₂ of both sides
[tex]\begin{gathered} \log _2(y+2)=\log _22^{(3-x)} \\ \log _2(y+2)=3-x\log _22 \\ \end{gathered}[/tex]Note:
[tex]\log _22=1[/tex]Therefore,
[tex]\begin{gathered} \log _2(y+2)=(3-x)\times1 \\ \log _2(y+2)=3-x \end{gathered}[/tex]Isolating 'x'
[tex]x=3-\log _2(y+2)[/tex]Replace 'x' with 'y'
[tex]y=3-\log _2(x+2)[/tex]Hence,
[tex]f^{-1}(x)=3-\log _2(x+2)[/tex]The correct option is Option 2.
Related Questions
At a local restaurant, the amount of time that customers have to wait for their food isnormally distributed with a mean of 12 minutes and a standard deviation of 2minutes. Using the empirical rule, determine the interval of minutes that the middle99.7% of customers have to wait.
Answers
By the empirical rule 99.7% of the customers fall within the interval bounded by
[tex]\bar{x}-3\sigma\text{ and }\bar{x}+3\sigma[/tex]In this case,
[tex]\begin{gathered} \bar{x}=12\min \text{ and} \\ \sigma=2\min \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \bar{x}-3\sigma=12-3(2)=12-6=6\min s \\ \bar{x}+3\sigma=12+3(2)=12+6=18\min s \end{gathered}[/tex]Hence, the interval of minutes that the middle 99.7% of customers have to wait is given by
(6mins, 18mins)
O EXPONENTIAL AND LOGARITHMIC FUNCTIONSExpanding a logarithmic expression: Problem type 1
Answers
Given:
a logarithm is given as
[tex]log(z^5x)[/tex]Find:
we have to expand the given logarithm expressionusing properties of logarithm.
Explanation:
we know from the properties of logarithm that
[tex]\begin{gathered} log(m^n)=nlog(m) \\ and \\ log(mn)=log(m)+log(n) \end{gathered}[/tex]we will use above properties to expand the given logarithm expression as follows
[tex]log(z^5x)=logz^5+logx=5logz+logx[/tex]Therefore, the expansion of the given logarithm is 5 log(z)+ log(x)
Using the graph below, write two ordered pairs to show that the equation y = 15x represents the data.
Answers
By using the points (2, 30) and (4, 60) that we can see on the graph, we can see that the linear equation that models the data is:
y = 15*x
How to find the equation that models the data?A general linear equation is of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂), the slope is given by:
a = (y₂ - y₁)/(x₂ - x₁)
In this case we can use two points that appear on the graph, I will use the first two ones:
(2, 30) and (4, 60)
Then the slope is:
a = (60 - 30)/(4 - 2) = 30/2 = 15
Thus, the line is of the form:
y = 15*x + b
To find the value of b we use the point (2, 30), replacing these values we get:
30 = 15*2 + b
30 = 30 + b
30 - 30 = b
0 = b
We conclude that the linear equation that models the data is y = 15*x
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Question 2 George is 5 feet 8 inches tall. How many inches tall is he? (1foot = 12 inches) 58 inches O 60 inches O 68 inches O 12 inches
Answers
Answer:
68
Step-by-step explanation:
1 foot = 12 inches
Multiply 5 by 12 inches
5 feet = 60 inches
Add the extra 8 inches
60 + 8 = 68 inches
George is 68 inches tall.
Answer:
Step-by-step explanation:
George is 5 feet and 1 foot equals 12 inches, so do 12x5 + the actual 8 inches
12x5=60
60+8=68 inches total
Consider the steps James uses to solve the equation 2(x – 10) = 24. Equation: 2(x - 10) = 24 Step 1: 2x - 10 = 24 Step 2: 2x = 34 Step 3: x = 17 In which step, if any, did James make an error? A. Step 1 B. Step 2 C. Step 3 D. James did not make an error.
Answers
In the steps that James uses to solve the given equation he made a mistake:
We have:
[tex]2\cdot(x-10)=24\Rightarrow2x-20=24[/tex]James needed to apply the distributive property in the first step. However, he did not.
Therefore, James made an error in Step 1, that is, option A.
What is the product?
1/2•(12 64)
(78 30)
Answers
10. Sydney wants to buy soda and juice for her birthday party. A bottle of soda costs $1.99 each and a jug of juice costs $2.49 each. If Sydney has $30, what equation could be used to find how many soda bottles and how many jugs of juice she can purchase? let x = let y = Equation
Answers
ANSWER
1.99x + 2.49y = 30
EXPLANATION
A bottle of soda costs $1.99 each and a jug of juice costs $2.49.
Sydney has $30.
Let x be the number of bottles of soda she can get.
Let y be the number of jugs of juice that she can buy.
This means that the cost of x bottles of soda is:
1.99 * x = $1.99x
This also means that the cost of y jugs of juice is:
2.49 * y = $2.49y
The total cost must be equal to $30, so this means that the total cost of bottles of soda and jugs of juice she can purchase is:
1.99x + 2.49y = 30
That is the equation that represents it.
How do I calculate the shaded area of this shape ?
Answers
SOLUTION:
We are to calculate the shaded area of the given shape.
CONCEPT:
This is a triangle that a rectangle was cut out from.
To calculate the shaded area of the given shape, we are to find the area of the triangle and then subtract the area of the recangle that was cut out.
[tex]\begin{gathered} \text{Area of Triangle:} \\ A\text{ = }\frac{1}{2}\text{ base }\times\text{ height} \\ \\ A\text{ = }\frac{1}{2}\text{ }\times\text{ 6m }\times7m\text{ } \\ \\ A=21m^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of Rectangle:} \\ A=L\text{ }\times\text{ W } \\ A\text{ = 4m }\times\text{ 2m} \\ A=8m^2 \end{gathered}[/tex]The shaded area = Area of the triangle - Area of the rectangle
[tex]\begin{gathered} \text{Shaded area = 21 m}^2-8m^2 \\ \text{Shaded area = 13 m}^2 \end{gathered}[/tex]CAN SOMEONE PLS HELP ME WITH MY PRACTICE MATH QUESTIONS!!!
Answers
some fhdf
djfsirsisdsjfsd
fdfjjjf9d094--djjf9939=3030395944./445335
Help me please!! I don’t understand
Answers
Answer:
-3
Step-by-step explanation:
To find the answer, you need to use the formula y2-y1/x2-x1.
2-17/2-(-3)
2-17=-15
2-(-3)=5
-15/5=
-3
Hope this helps :D
line segment QR is parallel to line segment ST. x = ___ m
Answers
In order to find the value of x, consider that triangles PQR and PST are similar. Then, you have the following equivalence:
PQ/PS = PR/PT
Where:
PQ = x
PS = 45m
PR = 16m
PT = 36m
replace the previous values of the length of the segments and solve for x, just as follow:
x/45 = 16/36 multiply by 45 both sides
x = (16/36)45
x = 20
Hence, the value of x is x = 20
If 2(x-8)= - 4x+2 , then x=
A) -7
B) -5
C) 3
D) 9
Answers
Answer:
C) 3
Step-by-step explanation:
2(x - 8) = -4x + 2
2x - 16 = -4x + 2
6x - 16 = 2
6x = 18
x = 3
Match the two lines that are parallel and the two lines that are perpendicular. Then, match the equations.
Answers
Step-by-step explanation:
A and C are parallel. equations G and E.
B and D are perpendicular (standing at a right angle = 90° to each other). equations F and H.
parallel means that both lines have the same slope.
the slope is the factor a of x when the equations look like
y = ax + b (slope-intercept form)
or
y - y1 = a(x - x1) (point-slope form)
"a" being the slope, b being the y-intercept (the y- value when x = 0), (x1. y1) being a point on the line.
the slope is specified as ratio (y coordinate difference / x coordinate difference) when going from one point to another.
the perpendicular slope to y/x is the upside down ratio and the sign is flipped.
e.g. the perpendicular slope to 5/4 is -4/5.
equation E is already in point-slope form.
the slope is 2/3, and the point (-9, -2) must be on the line.
only one line goes through the point (-9, -2) : C.
equation H is already in slope-intercept form.
the slope is 3/2, and the y-intercept is 5, meaning the line goes through the point (0, 5).
only one line goes through that point : D
equation F
2x + 3y = -21
3y = -2x -21
y = (-2/3)×x - 7
the slope is -2/3, which is perpendicular to 3/2 (equation H).
the y-intercept is -7, meaning the line goes through the point (0, -7).
only one line goes through that point : B
equation G
-2x + 3y = -6
3y = 2x - 6
y = (2/3)×x - 2
the slope is 2/3 (parallel to equation E).
the y-intercept is -2, meaning the line goes through the point (0, -2).
only one line goes through that point : A
Determine the perimeter of this rectangle. » 526 m 78 m P = I on m m
Answers
1) Since the Perimeter (2P) is the sum of all sides of a rectangle. And this rectangle has 526m w and 78 m. And also, a rectangle is a parallelogram that has the property of having a pair of congruent sides. Then
2) Then we can state:
2p = 526 +526+78+78
2p =1052+156
2p= 1208 meters
PLS HELP WILL MARK BRAINLIEST
Answers
Answer:
l = [tex]\frac{P-2w}{2}[/tex]
Step-by-step explanation:
P = 2l + 2w ( subtract 2w from both sides )
P - 2w = 2l ( isolate l by dividing both sides by 2 )
[tex]\frac{P-2w}{2}[/tex] = l
find the rate of change of its elevation when x=22
Answers
To find the rate of change of its elevation we can derive the position function:
[tex]y=-\frac{1}{110}x^2+127[/tex][tex]y^{\prime}=\frac{d(y)}{dx}=d(-\frac{1}{110}x^2+127)/d(x)[/tex][tex]y^{\prime}=\frac{-1}{55}x[/tex]The rate of change of its elvation when x=22 is
[tex]\frac{-1}{55}\cdot22=\frac{-22}{55}=\frac{-2}{5}=-0.4[/tex]That represents the slope of the tangent line to the function at x=22.
The Sugar Sweet Company is going to transport its sugar to market. It will cost $5500 to rent trucks plus $125 for each ton of sugar transported. The total cost,
C (in dollars), for transporting n tons is given by the following.
C=125n+5500
Answer the following questions.
(a) What is the total cost of transporting 11 tons?
(b) If the total cost is $8125, how many tons is the company transporting?
Answers
C=125*11+5500
C=1375+5500
C=$6875
(B) For this part you follow the same concept as part a just change what and where you are substituting since the question gives you total cost C you plus 8125 in for C and solve for n
C=125n+5500
8125=125n+5500 (subtract 5500 from BOTH sides)
2625=125n (divide BOTH sides by 125 to get n alone)
n= 21 tons
Add.
Your answer should be an expanded polynomial in
standard form.
(-4b³ + b − 1) + (6b - 6) =
Answers
Answer:
-4b^3 + 7b - 7
Step-by-step explanation:
We have to look at terms which look like each other, for example 1b and 6b.
We can add and subtract terms which have the same degree of b.
In this question, we can safely add -1 and -6, and also b and 6b,
which gives us (-4b^3 + b - 1 ) + 6b - 6) = -4b^3 + (1+6)b +( -1 - 6) = -4b^3 + 7b - 7
The three remaining terms all have different degrees of b's (respectively 3, 1, 0), so we can't add those up any further, which tells us that this is the right answer.
Answer:
Step-by-step explanation:
classify the triangle with the given side lengths as acute, right, obtuse, or not a triangle 11, 13, 25
Answers
Notice that if a = 11 and b = 13 are two sides of the triangle, then:
[tex]a+b=11+13=24[/tex]since the larger side measures 25 units, then we cannot write a triangle with the given measures, since a + b cannot be less than the larger side. Therefore, it is not a triangle
Writing an equation of a hyperbola give me the Foci and vertices
Answers
Given the Foci of the hyperbola:
[tex]\begin{gathered} (-1,-9) \\ (-1,9) \end{gathered}[/tex]And the Vertices:
[tex]\begin{gathered} (-1,-3) \\ (-1,3) \end{gathered}[/tex]You can plot the Foci on a Coordinate Plane:
Notice that the blue line represents the Vertical Transverse Axis. Then, the equation has this form:
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]You need to find the Center using the Midpoint Formula, in order to find the Midpoint between the Foci and the Midpoint between the vertices:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]- For the Foci:
[tex]M=(\frac{-1-1}{2},\frac{-9+9}{2})=(-1,0)[/tex]- For the Vertices:
[tex]M=(\frac{-1-1}{2},\frac{-3+3}{2})=(-1,0)[/tex]Therefore:
[tex]\begin{gathered} h=-1 \\ k=0 \end{gathered}[/tex]Now you need to find "a". This is the distance from the center to the vertices:
[tex]a=3-0=3[/tex]Find "b" with this formula:
[tex]b^2=c^2-a^2[/tex]Knowing that "c" is the distance from the Foci to the center:
[tex]c=9[/tex]You get:
[tex]b^2=9^2-3^2=72[/tex]Therefore, you can write this equation:
[tex]\frac{y^2}{9}-\frac{(x+1)^2}{72}=1[/tex]Hence, the answer is:
[tex]\frac{y^2}{9}-\frac{(x+1)^2}{72}=1[/tex]30 60 90° triangles find the measure of the missing two sides for each figure below leave answer and rationalize and simple light form
Answers
Given : 30 60 90 triangle as shown in the following figure :
As shown : the hypotenuse of the triangle = 28√5
The side length opposite to the angle 30 =
[tex]\frac{1}{2}\cdot28\sqrt[]{5}=14\sqrt[]{5}[/tex]The side length opposite to the angle 60 =
[tex]\frac{\sqrt[]{3}}{2}\cdot28\sqrt[]{5}=\frac{28}{2}\sqrt[]{3\cdot5}=14\sqrt[]{15}[/tex]Please help again please help me
Answers
Answer:
-0.5,-1/5,0.7,3/4 its correct
Answer:
-0.5, -1/5, 0.7, 3/4
Step-by-step explanation:
We can convert the fractions into decimals.
-1/5 = -0.2
3/4 = 0.75
-0.5 is the least, then -1/5, then 0.7, and lastly 3/4.
Hope this helps!
P.S, Can I get a brainliest if this is right? Thanks!
What is a valid conclusion that can be reached by reading the graph?A.Joel and Nancy own 62 cards when you add their cards together.B.Joel and Nancy own more cards than Jim when you add their cards together.C.Nancy and Ricardo own more cards than Jim when you add their cards together.D.Tina owns 350 cards.
Answers
Answer:
C. Nancy and Ricardo own more cards than Jim when you add their cards together.
Explanation:
Taking into account the graph, we can conclude the following:
Nancy and Ricardo own more cards than Jim when you add their cards together
This is because, Nancy and Ricardo have bars with heights that are greater than 40, when we add their cards, we will get a bar with a height greater than 80, and 80 is greater than the height of Jim's bar.
Therefore, the answer is
C. Nancy and Ricardo own more cards than Jim when you add their cards together.
What is the domain and range? What does it mean in terms of the graph?
Answers
The domain of the graph is [0,14] and the range of the graph is [0, 7]
In this question, we have been given a graph of height of a falling object.
In this graph, x-axis represents the time in seconds and y-axis represents the height in meters.
We know that, the domain of a graph consists of all the input values which are on the x-axis and the range is the set of possible output values, which are shown on the y-axis.
In this graph we can see that the input (time) takes the values between [0, 14] and the output (height) has values in the interval [0, 7]
Therefore, the domain of the graph is [0,14] and the range of the graph is [0, 7]
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E Match the corresponding congruent parts.(G.6)(6 point) DE DF / A Lc ZB EF
Answers
By definition:
Congruent figures in geometry are identical in shape and size.
This means that two figures are congruent with each other even if they are rotated, flipped or trasnlated as long as they have the identical shape and size.
For example, look at the following picture
We notice that the triangle has the same size and shaped, hence they are congruent. Furthermore we can say that the side BC is congruent to the side ZY and so on.
You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $3500 per month. You have access to an account that pays an APR of 4.8% compounded monthly. This requires a nest egg of $610,823.48.
What monthly deposits are required to achieve the desired monthly yield at retirement? (Round your answer to the nearest cent.)
Answers
The monthly deposit that is required to achieve the desired monthly yield at retirement is $1,056.71.
What is the monthly deposit?An annuity is a series of payment that is made over a period of time. The annuity in this question would last for 25 years. When an investment is compounded monthly, it means that the investment would grow at an exponential rate once in a month.
The formula that would be used to determine the monthly payment is:
Monthly payment = future value / annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = monthly interest rate = 4.8% / 12 = 0.4%n = number of periods = number of compounding x number of years: 12 x 25 = 300$610,823.48 ÷ [{(1.004^300) - 1} / 0.004] = $1,056.71
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The average of three test scores of the first two scores are 77 and 89
Answers
Answer:
A = (166+s)/3
Step-by-step explanation:
Average test-score:
Sum of all scores divided by the number of tests.
In this question:
First two tests: 77 and 89.
Third test: s
Number of tests: 3
Average:
Finding the sum: 77 + 89 + s = 166 + s
The average is:
A = (166+s)/3
The perimeter of a rectangle is equal to 138. The width of the rectangle is 5 less than the length . What is the area the rectangle?
Answers
Step 1: Concept
Perimeter of a rectangle = 2( L + W)
L = length
W = width
Area of a rectangle = Lenght x Width
Step 2:
Given data
The perimeter of a rectangle = 138
Length L = m
Width W = m - 5
Step 3:
[tex]\begin{gathered} \text{Use the perimeter of the rectangle to find the length(L) and width(W).} \\ \text{Perimeter = 2(L + W)} \\ 138\text{ = 2(m + m - 5)} \\ 138\text{ = 2m + 2m - 10} \\ 138\text{ = 4m - 10} \\ \text{Collect similar terms} \\ 138\text{ + 10 = 4m} \\ 148\text{ = 4m} \\ m\text{ = }\frac{148}{4}\text{ = 37} \end{gathered}[/tex]Step 4:
Length = 37
Width = 37 - 5 = 32
Step 5:
Find the area
Area = length x width
Area = 37 x 32
Area = 1184
Final answer
Area of the rectangle = 1184
2+4-2÷3 please help
Answers
A easy way to operate fractions is convert the integer in a fraction, to operate fractions with the same denominator:
[tex]6\cdot\frac{3}{3}-\frac{2}{3}=\frac{18}{3}-\frac{2}{3}=\frac{16}{3}[/tex]You purchase six municipal bonds on the first of the year. The current market value price is 103. The commission charge is $5 per bond. What is the cost of the purchasing these bonds?
a.
$6210
b.
$633
c.
$648
d.
$3090
Answers
Answer:
C
Step-by-step explanation:
(103 + 5) * 6 = 648
Letter C
Explanation:
Why letter C?
You purchased 6 bonds for the price of 103 dollars the commission is 5 dollars for each, therefore we will add 103 + 5 and multiply by 6
(103 + 5) 6
(108)6
648
Or
6(103)+6(5)
618+30
648