Find the inverse of each function
1. f(x) = 4/(x+2) - 2
2. f(x)= -2x^5 - 3
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Answer:
1. f^-1(x) = 4/(x+2) -2
2. f^-1(x) = (-(x+3)/2)^(1/5)
Step-by-step explanation:
1. As with all "inverse function" problems, solve for y:
x = f(y)
x +2 = 4/(y +2) . . . . add 2
y +2 = 4/(x +2) . . . . . multiply by (y+2)/(x+2)
y = 4/(x+2) -2 . . . . . subtract 2
We see that this function is its own inverse. The attached graph shows it is symmetrical about the line y=x.
f^-1(x) = 4/(x+2) -2
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2. x = f(y)
x +3 = -2y^5 . . . . add 3
-(x +3)/2 = y^5 . . . . . divide by 2
(-(x +3)/2)^(1/5) = y . . . . take the 5th root
f^-1(x) = (-(x +3)/2)^(1/5)
In typeset form, that is ...
[tex]\displaystyle f^{-1}(x)=\sqrt[5]{\frac{-(x+3)}{2}}\\\\\text{or}\\\\f^{-1}(x)=-\frac{1}{2}\sqrt[5]{16x +48}[/tex]
This last version is with the denominator "rationalized" and the contents of the radical "simplified." It may be a preferred form.
_____
The graphs show the function and inverse are symmetrical about the line y=x, as they should be.
Urgent please please help It's due soon!
9514 1404 393
Answer:
money market: $1000stock: $238,500mutual fund: $228,500Step-by-step explanation:
We can let x and y represent the amounts invested in the stock and mutual fund, respectively. Then the amount invested in the money market account was (468000 -x -y). Two relations can be written.
x = y + 10000 . . . . . 10,000 more was invested in stock than in mutual funds
0.035(468000-x-y) +0.04(x) -0.03(y) = 2720 . . . . first-year return
Collecting terms in the second equation gives ...
0.005x -0.065y +16380 = 2720
-x + 13y = 2732000 . . . . . . subtract 16380, multiply by -200
12y -10000 = 2732000 . . . . substitute for x using the first equation
y = 2742000/12 = 228,500 . . . . solve for y
x = 228,500 +10,000 = 238,500 . . . . . find x from the first equation
468,000 -x -y = 468,000 -467,000 = 1,000 . . . . find the money market amount
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Pierre invested $1000 in the money market account, $238,500 in the stock, and $228,500 in the mutual fund.
Write the ratio 1.5:9 in simplest form.
Answer:
1 : 6
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer:
2&7
6&3
Definition:
angles located at opposite positions between the two lines that are intersected by a transversal.
Step-by-step explanation:
What are the coordinates of point A?
1.(5,2,0)
2.(5,0,2)
3.(0,2,5)
4.(2,0,5)
The coordinates of point A are (2, 0, 5).
Then the correct option is the fourth one.
How to get the coordinates of point A?The general notation for a point on 3 dimensions is (x, y, z).
First, notice that the vertical axis is the Z-axis, the axis that points towards us is the x-axis, the axis that points to the right is the y-axis.
First, we can see that the x-value of A is x = 2.
The z-value of A is z = 5.
And A lies on the plane x_z, then the y-value is y = 0.
Then the coordinates of point A are (2, 0, 5).
So the correct option is 4.
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I'll. ark brainlyest and give a lot of points for answering this right
Answer:
[tex] \displaystyle T'( 2,4)[/tex]
[tex] \displaystyle U'( 1,1)[/tex]
[tex] \displaystyle S' ( 3,2)[/tex]
Step-by-step explanation:
we current vertices of the given triangle
[tex] \displaystyle T( - 2,4)[/tex][tex] \displaystyle U( - 1,1)[/tex][tex] \displaystyle S ( - 3,2)[/tex]remember that,
[tex] \rm\displaystyle(x,y) \xrightarrow{ \rm reflection \: over \: y - axis}( - x,y)[/tex]
so we obtain:
[tex] \rm\displaystyle \: T( - 2,4) \xrightarrow{ \rm reflection \: over \: y - axis}T'( 2,4)[/tex]
[tex] \rm\displaystyle \: U( - 1,1) \xrightarrow{ \rm reflection \: over \: y - axis}U' ( 1,1)[/tex]
[tex] \rm\displaystyle S( - 3,2) \xrightarrow{ \rm reflection \: over \: y - axis}S'( 3,2)[/tex]
Lipids provide much of the dietary energy in the bodies of infants and young children. There is a growing interest in the quality of the dietary lipid supply during infancy as a major determinant of growth, visual and neural development, and long-term health. An article reported the following data on total polyunsaturated fats (%) for infants who were randomized to four different feeding regimens: breast milk, corn-oil-based formula, soy-oil-based formula, or soy-and-marine-oil-based formula. (Use i= 1, 2, 3, and 4 respectively.)
Sample Regimen Sample Size Sample Mean Sample SD
Breast milk 15 42.9 1.3
CO 17 43.1 1.5
SO 8 43.7 1.2
SMO 14 43.9 1.2
What assumptions must be made about the four total polyunsaturated fat distributions before carrying out a single-factor ANOVA to decide whether there are any differences in true average fat content?
a. The distribution of polyunsaturated fat percentages for each of the four regimens must be uniform with equal variances.
b. The distribution of polyunsaturated fat percentages for each of the four regimens must be normal with unequal variances.
c. The distribution of polyunsaturated fat percentages for each of the four regimens must be normal with equal variances.
d. The distribution of polyunsaturated fat percentages for each of the four regimens must be binomial with unequal variances.
Answer:
c. The distribution of polyunsaturated fat percentages for each of the four regimes must be normal with equal variance's.
Step-by-step explanation:
Single factor ANOVA is used for testing the null hypothesis with same mean of several population. The alternative hypothesis is set against the null hypothesis in order to identify whether the null statement is correct or it will be rejected.
What are the vertices of angle A’B’C’ if angle ABC is dilated by a scale factor of 2?
Answer:
The answer is A
Step-by-step explanation:
a=(0,10)×2, b =(8,6)×2 c=(4,2)×2
Find the measure of each interior angle of the shown figure *
Step-by-step explanation:
Formula to find interior angles of regular polygon=(n-2)180×n
N= number of sides
in figure sides are 5
So,
(5-2)×180
3×180
540 Answer
Answer:
108°
Step-by-step explanation:
Measure of each interior angle
[tex] = \frac{(n - 2) \times 180 \degree}{n} \\ \\ = \frac{(5 - 2) \times 180 \degree}{5} \\ \\ = \frac{3\times 180 \degree}{5} \\ \\ = \frac{540\degree}{5} \\ \\ = 108 \degree[/tex]
Hi please help me with this!
Answer:
it's a and d
Step-by-step explanation:
a.....................
Compared to last month there was a 50% increase in the number of houses sold this month
Answer:
this is either a random fact or unfinished question. its probably caused by population increase
Step-by-step explanation:
A rectangular room is 5 meters longer than it is wide, and its perimeter is 22 meters. Find the dimension of
the room.
Answer:
The dimension of the room is 8m by 3m
The length and width of the rectangle are 8 meters and 2 meters.
Given,
A rectangular room is 5 meters longer than it is wide.
Perimeter = 22 meters.
We need to find the dimension of the room.
What is the perimeter of a rectangle?A rectangle perimeter is given by :
P = 2 ( length + wide )
Find the length and width of the rectangle.
Let width = W
Let length = L
L = W + 5
Find the perimeter of the rectangle.
P = 2 ( L + W )
P = 22
22 = 2 ( W + 5 + W )
Divide both sides by 2.
11 = W + 5 + W
11 = 2W + 5
Subtract 5 on both sides.
11 - 5 = 2W + 5 - 5
6 = 2W
Divide both sides by 2.
3 = W
W = 3
We see that W = 2 and L = W + 5 = 3 + 5 = 8.
Thus the length and width of the rectangle are 8 meters and 2 meters.
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Select the formula for the
xth term of the sequence.
screen shot -
Answer:
Option (3)
Step-by-step explanation:
Given sequence is,
8, -8, 8,...........
Ratio of the 2nd and 1st term = [tex]\frac{-8}{8}[/tex]
= -1
Ratio of 3rd and 2nd term = [tex]\frac{8}{-8}[/tex]
= -1
Therefore, there is a common ratio 'r' = (-1)
And the sequence is a geometric sequence.
Explicit formula for the nth term of a geometric sequence is given by,
[tex]T_n=a(r)^{n-1}[/tex]
Here, 'a' = First term of the sequence
r = Common ratio
n = nth term
For the given sequence xth term of the sequence will be,
[tex]T_x=8(-1)^{x-1}[/tex]
Option (3) will be the answer.
-12 + ( ) = 9 whats the missing number
Answer:
The missing number is 21
Step-by-step explanation:
-12 + x = 9
x = 9 + 12
x = 21
Answer:
21
Step-by-step explanation:
let X = ( )
-12 + X = 9
X = 9 + 12
X = 21
GIVING 43 POINTS AND BRAINLIEST FOR THE FIRST PERSON THAT ANSWERS AND IS CORRECT!!
Translate the following expression
9 more than a number
A. 9r
B. 9 + w
C. 9÷k
D. 9x
Answer:
Step-by-step explanation:
B
To multiply a decimal number by 102, move the decimal point
Answer:
two digits to the right
Step-by-step explanation:
When multiplying a decimal by 102 you would need to move the decimal point two digits to the right. This is because we are multiplying by a hundred number. When multiplying any whole positive number by a decimal, we need to move the decimal point to the right one less than the amount of digits that the positive whole number has. For example, a thousand (1000) has 4 digits so we move the decimal point of the product to the right by 3.
Examples:
102 * 0.02 = 2.04
1000 * 0.02 = 20
10000 * 0.02 = 200
In parallelogram ABCD, the coordinates of A are (3,-1) and the coordinates of C are (-1,5). What are the coordinates of the point of intersection of the diagonals?
Find the perimeter of the figure. AND I'LL MAKE YOU THE BRAINIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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Answer:
97 cm
Step-by-step explanation:
The perimeter is the sum of the side lengths. Starting from the upper left corner and working clockwise, the side lengths are ...
10 +3 +33 +15 +33 +3 = 25+2(36) = 97 . . . cm
The perimeter of the figure is 97 cm.
If you want 100 points plz answer this.
Answer:
It is assumed we need to find the volume and total surface area
Volume is:
V = Al = 1/2ahl = 1/2*2*1*3 = 3 ft³Total surface area is:
S = Pl + 2A= (1 + 2 + 2.2)*3 + 2*(1/2*2*1)= 17.6 ft²Answer:
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Step-by-step explanation:
b) Suppose you throw two fair dice. What is the probability of getting an even number on the first and a 5 or 6
on the second die?
Answer:
Most likely 1/2 of a chance to get it and 1/6 of a chance to roll a 5 or 6
please ????? help mdjshd
A bicycle has a listed price of $516.99 before tax. If the sales tax rate is 8.75%, find the total cost of the bicycle with sales tax included.
Round your answer to the nearest cent, as necessary. HELP QUICK!
Answer:
562.23
Step-by-step explanation:
You are standing 6 feet away from the stage and your friend is standing 7 feet away from the stage.
Answer:
Step-by-step explanation:
Yo diría que Messi
Can y’all help me? I would really appreciate it
Answer:
I think the answer is she
6 + 7 ?
EASY ! Your welcome !
Answer:
the correct answer is 13
Answer:
13.
Step-by-step explanation:
Avery has 6 yards of ribbon. He needs 1/3 yard to make 1 bow.
How many bows can Avery make
The Smithtown water company uses warm water meters that measure water usage in gallons. They charge $.12 per gallon of water. If Jack's previous meter reading was 45,621 gallons and his present water reading is 48,555 gallons what is the amount of his water bill?
Subtract to find the number of gallons used:
48,555 - 45621 = 2,934 gallons.
Multiply gallons used by price per gallon:
2,934 x 0.12 = $352.08
An attic wall is in the shape of a trapezoid. The bases are 12 ft and 25 ft. The area is 185 square feet. What is the height? A = 1/2 h (b + b)
Answer: b = 2A - B
Step-by-step explanation:
2. A = 2 . 1/2 . h (B + b)
2A = h (B+b)
2A/= h/h . (B+b)
2A/h = B+b
2A - B = B - +b
b = 2A - B
Please help me with this ASAP ASAP please please help
Answer:
Step-by-step explanation:
Base perimeter = 2 x 2 x π = 4π in
LA = 4π x 5 = 20π in^2
Base area = 2^2 x π = 4π in^2
SA = 2 x 4π + 20π = 28π in^2
V = 4π x 5 = 20π in^3
What is the equation of the graph below?
Answer:
y = sin(x + 90°)
Step-by-step explanation:
cos 0 = 1
Since the point (0, 1) is on the graph, this graph is y = cos x, but that is not a choice, so this must be the graph of the sine function with a horizontal translation.
sin 0 = 0
sin 90° = 1
The translation is 90°.
Answer: y = sin(x + 90°)