The function f(x) is shown below.
X
-6
اس
-3
5
8
f(x)
1
2
5
3
0
If g(x) is the inverse of f(x), what is the value of f(g(2))?
O-6
O-3
02
O 5
Answers
The function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.
If g(x) is the inverse of f(x), 2 is the value of f(g(2)).
What is meant by inverse function?An inverse in mathematics is a function that "undoes" another function. In other words, if f(x) yields y, then y entered into the inverse of f yields the output x.
The function y as a function of x, i.e., y = f(x), and then solve for x as a function of y, to determine the inverse of a function.
Given
[tex]&x \rightarrow f(x) \\[/tex]
[tex]&-6 \rightarrow 1 \\[/tex]
[tex]&-3 \rightarrow 2[/tex]
[tex]$$g(x)=f^{-1}(x)[/tex] inverse
To find the value of f(g(2)).
For two functions f(x) and g(x) where f(x) and g(x) are inverse; f(g(x))=x
So, by comparison: f(g(2)) = 2.
Therefore, the inverse of the function f(g(2)) = 2.
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Related Questions
A bag contains 6 red marbles and 4 yellow marbles. A marble is drawn at random and not replaced. Two further draws are made, again without replacement.
What is the probability of drawing at least one red marble?
Answers
Answer:
6/10
Step-by-step explanation:
I think, however I may be very wrong, sorry.
Answer:
[tex]\sf \dfrac{29}{30}[/tex]
Step-by-step explanation:
A bag contains:
6 red marbles.4 yellow marbles.Therefore, the total number of marbles in the bag is 10 marbles.
The possible outcomes for drawing 3 marbles (without replacement) are:
R R RR R YR Y RR Y YY R RY R YY Y RY Y YTherefore, the only outcome where at least one red marble is not drawn is {Y Y Y}.
To find the probability of drawing at least one red marble, subtract the probability of drawing 3 yellow marbles from one.
The probability of drawing 3 yellow marbles without replacement is:
[tex]\implies\sf P(3\; yellow \;marbles)=\dfrac{4}{10} \times \dfrac{3}{9} \times \dfrac{2}{8}=\dfrac{24}{720}=\dfrac{1}{30}[/tex]
Therefore, the probability of drawing at least one red marble is:
[tex]\implies \sf P(At\;least\;one\;red\;marble)=1-\dfrac{1}{30}=\dfrac{29}{30}[/tex]
This can be confirmed by drawing a tree diagram (see attached).
To find the probability of drawing at least one red marble, add the probabilities at the end of each relevant final branch:
[tex]\begin{aligned}\implies \sf P(At\;least\;one\;red\;marble)&=\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{6}+\dfrac{1}{10}+\dfrac{1}{10}\\\\&=\dfrac{4}{6}+\dfrac{3}{10}\\\\&=\dfrac{20}{30}+\dfrac{9}{30}\\\\&=\dfrac{29}{30}\end{aligned}[/tex]
Solve using augmented matrices.
x+y=1
3x-y=7
Answers
The solution to the system of equation {x + y = 1, 3x - y = 7 } using augmented matrices is ( 2,-1 ).
What is the solution to the system of equation using augmented matrices?Given the system of equation in the question;
x + y = 1
3x - y = 7
First, we write the system of equation in matrix form.
[tex]\left[\begin{array}{ccc}1&1&1\\3&-1&7\\\end{array}\right][/tex]
Next, we find the reduced row echelon form
Row operation R₂ = R₂ - 3R₁ to make the entry at 2, 1 a 0.
[tex]\left[\begin{array}{ccc}1&1&1\\3-3*1&-1-3*1&7-3*1\\\end{array}\right] \\\\\left[\begin{array}{ccc}1&1&1\\0&-1\4&4\\\end{array}\right][/tex]
Next, multiply each element of R₂ by -1/4 to make the entry at 2, 2 a 1.
[tex]\left[\begin{array}{ccc}1&1&1\\-\frac{1}{4}*0 &-\frac{1}{4}*-4 &-\frac{1}{4}*4 \\\end{array}\right] \\\\\left[\begin{array}{ccc}1&1&1\\0&1&-1\\\end{array}\right][/tex]
Now, perform the operation, R₁ = R₁ - R₂, to make the entry at 1,2 a 0.
[tex]\left[\begin{array}{ccc}1-0&1-1&1+1\\0&1&-1\\\end{array}\right] \\\\\left[\begin{array}{ccc}1&0&2\\0&1&-1\\\end{array}\right][/tex]
Using the result from the matrix, x = 2 and y = -1.
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Perimeter Given Coordinates
Oct 15, 11:32:13 AM
The points E(7,-5), F(7, 2), G(4, 8), and H(4, 1) form parallelogram EFGH. Plot
he points then click the "Graph Quadrilateral" button. Then find the perimeter of the
parallelogram. Round your answer to the nearest tenth if necessary.
4
Answers
Perimeter of the parallelogram which points are E(7,-5), F(7, 2), G(4, 8), and H(4, 1) = 24 units.
There are 4 types of parallelograms, including 3 special types. The four types are parallelograms, squares, rectangles, and rhombuses.
A parallelogram is a shape with only two dimensions. It has four sides, two parallel pairs of which make up each side. The lengths of the parallel sides are also the same. The form is not a parallelogram if the lengths of the parallel sides are not equal.
Properties of parallelograms
Opposite sides are congruent (AB = DC).Opposite angels are congruent (D = B).Consecutive angles are supplementary (A + D = 180°).If one angle is right, then all angles are right.The diagonals of a parallelogram bisect each other.Given points are
E(7,-5),
F(7, 2),
G(4, 8), and
H(4, 1)
Perimeter of the parallelogram EFGH=2(EF+FG)
Distance between two points(x₁ , y₁) and (x₂ , y₂ ) can be calculated using the formula
√(x₂ - x₁ )² + (y₂ - y₁)²
Hence ,length of EF =
√(7 - 7 )² + (2 - (-5))²
=√49
=7units
And length of FG =
√(4 - 7 )² + (8 - 4)²
= √16 + 9
= √25
=5units
Hence, Perimeter of the parallelogram EFGH=2(EF+FG)=2(5+7)=24units
We have form parallelogram EFGH. For the result see the attachment-
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Answer:
27.4 units
Step-by-step explanation:
Given parallelogram EFGH with vertices E(7,-5), F(7, 2), G(4, 8), and H(4, 1), you want to know its perimeter.
Distance between two pointsThe distance between two points can be found from their coordinates using the distance formula ...
d = √((x2 -x1)² +(y2 -y1)²)
ApplicationThe distance between points F and G is ...
d = √((4 -7)² +(8 -2)²) = √(9 +36) = √45 ≈ 6.708
The distance between points E and F will be the difference of their y-coordinates:
d = √((7 -7)² +(2 -(-5))²) = √(0 +7²) = 7
PerimeterSince opposite sides of a parallelogram are the same length, the perimeter is twice the sum of two adjacent sides:
P = 2(EF +FG)
P = 2(7 +6.708) = 2(13.708) = 27.416
The perimeter of EFGH is about 27.4 units.
Consider the chart of millionaires and population
Answers
The number of millionaires Los Angeles should have will be equal to 5,065 millionaires.
Proportion may be defined as part or share of a complete unit compared with respect to the whole unit. A proportion is basically the equality of ratios. Two different ratios can be treated as equals if they are in proportion to each other. Now, the number of millionaires in Los Angeles will be equal to the Proportion of Millionaires in Dubai multiplied by the Population of Los Angeles that is
= 0.00124 × 4,085,014
= 5,065 millionaires
The Data and Calculations will be given as:
City Millionaires Population Proportion
Los Angeles 11,560 4,085,014 0.00283 (11,560/4,085,014)
Casablanca 6,900 3,752,357 0.00184 (6,900/3,752,357)
Berlin 6,750 3,562,038 0.00189 (6,750/3,52,038)
Dubai 3,570 2,878,344 0.00124 (3,570/2,878,344)
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Complete Question:
City Millionaires Population
Los Angeles 11,560 4,085,014
Casablanca 6,900 3,752,357
Berlin
6,750
3,562,038
Dubai
3,570
2,878,344
Consider the chart of Millionaires and Population. If Los Angeles were
proportional to Dubai with respect to population, how many millionaires
should we expect Los Angeles to have? Round your answer to a whole number.
191% as a mixed or whole number
Answers
Answer:
1 91/100
Step-by-step explanation:
everything you need is in the picture
goodluck :)
In ΔSTU, \text{m}\angle S = (6x-15)^{\circ}m∠S=(6x−15)
∘
, \text{m}\angle T = (2x-2)^{\circ}m∠T=(2x−2)
∘
, and \text{m}\angle U = (4x-7)^{\circ}m∠U=(4x−7)
∘
. What is the value of x?x?
Answers
The value that makes the triangle a valid triangle is x = 17
What are angles?Angles are formed when two or more lines intersect.
This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the measure of x?The given parameters are
Shape = Triangle STU
Angle S = 6x - 15
Angle T = 2x - 2
Angle U = 4x - 7
The sum of angles in a triangle is 180 degrees
This means that
Angle S + Angle T + Angle U = 180
Substitute the known values in the above equation
So, we have the following:
6x - 15 + 2x - 2 + 4x - 7 = 180
Evaluate the like terms in the equation
So, we have the following:
12x = 180 + 15 + 2 + 7
Evaluate the like terms in the equation
So, we have the following:
12x = 204
Divide by 2
x = 17
Hence, the value of x is 17
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-4(w + 5) + 5w simplify use distributive property
Answers
Answer:
w - 20
Step-by-step explanation:
Simplifying the expression:Remove the parenthesis by multiplying each term of (w + 5) by (-4)
-4(w + 5) + 5w = -4*w + 5*(-4) + 5w
= -4w - 20 + 5w
= -4w + 5w - 20
Combine like terms. Like terms have same variable with same power.
= w - 20
X-intercept
Find f(-2)
Find x for f(x)=2
Answers
By using the graph we can see:
x-intercept: x = 0.f(-2) = 4f(x) = 2 for x = -1.3How to find the requested values?First, we want to find the value of x such that the graph touches (intercepts) the x-axis.
On the graph, we can see that it intercepts the x-axis at x = 0, so that is the x-intercept.
Now we want to find f(-2), this is the value of the function when x = -2, to find that we first need to find x = -2 in the horizontal axis.
f(-2) = 4
Now we want to find the value of x such that:
f(x) = 2
so now we need to find 2 in the vertical axis. we can see that the function is equal to 2 for x = -1.3 (approximation).
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The diameter of a basketball rim is 18 inches. What is the circumference of the rim? Write your answer using pi. Show your work.
Answers
Explanation:
The equation of the circumference of a circle is 2 x Pi x radius
The radius is one half of the diameter. So to find the radius we can divide the diameter by 2.
18 divided by 2 is 9
So to find the circumference we can just do Pi x 9 x 2
9 x 2 = 18
So the answer is 18Pi, or 56.52
Answer:
18 pi
Step-by-step explanation:
2xpixr d divided by 2 equals 9 pi x 2 x 9 =18
Determine the minimum sample size required when you want to be % confident that the sample mean is within one unit of the population mean and. Assume the population is normally distributed.
Answers
The minimum sample size of the given condition is 89.
In given condition,
For 95% confidence level, critical value of z is z* = 1.96
The margin of error given is E = 1
Standard deviation ( α ) = 4.8
Final required sample size is;
n = [tex](\frac{z*\alpha }{E} )^{2}[/tex]
= [tex](\frac{1.96 * 4.8}{1} )^2[/tex]
= 88.51
n ≅ 89
The minimum sample size of the given condition is 89.
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-4 -3 -2 -1
3+
2+
-2
Y
-3
-4
What is the slope of the line?
2 3
4
Answers
Answer:
-1/2
Step-by-step explanation:
whats is 2 thirds minus a half
Answers
Step-by-step explanation:
I hope it will be helpful for you.
Two consecutive integers have a sum of 77. What are the two integers?
Answers
Answer: 38 and 39
if you add them together you get 77
Answer:
38 & 39
Step-by-step explanation:
Forming the equation,
→ x + (x + 1) = 77
→ 2x + 1 = 77
Now the value of x will be,
→ 2x + 1 = 77
→ 2x = 77 - 1
→ x = 76/2
→ [ x = 38 ]
Then the required integers are,
→ x = 38
→ x + 1 = 38 + 1 = 39
Hence, the integers are 38, 39.
PLEASE HELP QUICK. NOW NEEDED
Answers
pls tell me u understand the drawing
Using the graph, determine the coordinates of the x-intercepts of the parabola.
Answers
Answer:
2 points
Step-by-step explanation:
According to the graph, the parabola has two x-intercept, where is (0,-2) and (0,-8).
Simpilfy the variable expression below as much as you can :
7x+(5*6)z
NEED ANSWER ASAP THANK YOU!!!!
Answers
Answer:
7x + 30z
Step-by-step explanation:
7x +(5*6)z
= 7x + 30z
In a word processing document or on a separate piece of paper, use the guide to construct a two column proof proving SM = RN, given RM = SN and ∠MRS = ∠NSR. Submit the entire proof to your instructor.Given:RM = SN∠MRS = ∠NSRProve:SM = RNSTATEMENTREASON1.1.2.2. Reflexive Property3.3.4.4.
Answers
EXPLANATION:
Given;
We are given two triangles labeled MRS and NSR.
Required;
We are required touse the information provided rto rove tside SM is equal to side RN.
Solution;
[tex]RM=SN---Given[/tex][tex]RS=SR---Reflexive\text{ }property[/tex][tex]\angle MRS=\angle NSR---Congruent\text{ }angles[/tex][tex]\begin{gathered} \Delta MRS\cong\Delta NSR---SAS \\ \end{gathered}[/tex]If two sides and the included angle of one triangle are congruent to the corresponding parts of a second triangle, then we can conclude that both triangles are congruent.
Therefore;
[tex]SM=RN[/tex]Victor made a scale drawing of bedroom using a scale in which 3 inches represents 2 feet. The height of his bedroom is 10 feet.What is the height of the scale drawing in inches?
please help due in 10 mintuees!!!
Answers
The height of the scale drawing in inches is 15.
As per the scale factor, the ratio of measurement in real is equal to the measurement to measurement of scale drawing. So, representing the two ratio -
3 inches : 2 feet = Height : 10 feet
Rearranging the formed ratio to find the height of bedroom in scale drawing is -
Height = (3 inches × 10 feet ) ÷ 2 feet
Performing division to find the height of bedroom in scale drawing
Height = 3×5
Performing multiplication to find the height of bedroom in scale drawing
Height = 15 inches
Therefore, scale drawing of 10 feet high bedroom will be 15 inches.
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What is this number in standard form?
sixty-eight and fifty-four thousandths
Answers
Answer:
68.054
Step-by-step explanation:
I don't really have an explanation for this, it just is.
Sixty-eight (68) and fifty-four thousandths (.054, because the thousandths place is the third digit after the decimal point).
Brandon has seven pieces of chocolate.
He gives Colton one piece and Jill three pieces.
What fraction of chocolate does Brandon have now?
Answers
Answer:
4/7
Step-by-step explanation:
Answer:
Brandon has [tex]\frac{3}{7}[/tex] of the chocolate left with him.
Step-by-step explanation:
Step 1: Identify the fractions
Colton is given one of the seven pieces, so he has [tex]\frac{1}{7}[/tex] of the chocolate.
Jill is given three of the seven pieces, so she has [tex]\frac{3}{7}[/tex] of the chocolate.
Brandon himself had seven pieces at the beginning, so he had [tex]\frac{7}{7}[/tex] (the whole) of the chocolate.
Step 2: Do calculations with the fractions
Collectively, Colton and Jill have taken:
[tex]\frac{1}{7}+\frac{3}{7}\\\\\text{Add the fractions:}\\\frac{1+3}{7}\\\\\text{Calculate:}\\\frac{4}{7}~\text{of the chocolate}[/tex]
So, the fraction that Brandon has currently is:
[tex]\frac{7}{7}-\frac{4}{7}\\\\\text{Subtract the fractions:}\\\frac{7-4}{7}\\\\\text{Calculate:}\\\frac{3}{7}[/tex]
Brandon has [tex]\frac{3}{7}[/tex] of the chocolate left with him.
Please help me. It’s due today I do not understand it
Answers
The slope of the line above is -2.
How to find the slope of a line?The slope of a line can be defined as the change in y with respect to the change in x .
The slope can be regarded as rise over run.
The slope can be express in mathematical form as follows;
slope = m = y₂ - y₁ / x₂ - x₁
using the coordinates on the graph,
(0, 3)(3, - 3)
x₁ = 0
x₂ = 3
y₁ = 3
y₂ = - 3
Therefore,
slope = -3 - 3 / 3 - 0
slope = - 6 / 3
Hence,
slope = - 2
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1. The area in square feet of a rectangular field is 2x2+x-15. If the length of
the field, in feet, is x + 3 what is the width in terms of x?
A. 2x+3
B. 2x-5
C. 2r-3
D. 2x+5
Answers
Answer: B. 2x-5
Step-by-step explanation:
Decompose the polynomial into factors:
[tex]2x^2+x-15=\\\\2x^2+6x-5x-15=\\\\2x(x+3)-5(x+3)=\\\\(x+3)(2x-5)[/tex]
[tex]S=length*width\\\\The \ lenght=x+3\\\\Hence,\ \\\\The \ width=2x-5[/tex]
Factor out the GCF of 9x^−24x
Answers
9x^2/3x = 3x
24x/8 = 3x
Original equation: 9x^2 - 24x
Factored out: 3x - 8
A financial planner has a client with 16000$ to invest. If he invests $10,000 in a certificate of deposit paying 12% annual simple interest, at what rate does the remainder of the money need to be invested so that the two investments together yield at least $1620 in yearly interest?
Answers
As per the Simple interest concept, at 7% of rate the remainder of the money need to be invested so that the two investments together yield at least $1620 in yearly interest.
Simple interest.
Simple interest is calculated by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Given,
A financial planner has a client with 16000$ to invest.
Here we need to calculate the rate does the remainder of the money need to be invested so that the two investments together yield at least $1620 in yearly interest when he invests $10,000 with the annual simple interest 12%.
Let us consider R represents the rate that remainder of money needs to be invested
Here we know that, $10,000 is invested at 12%
So, according to the formula the interest at 12% is evaluated as,
=> $10,000 * 0.12 * 1 = $1200
And the remaining $6000 is invested at R%
Then the interest at R%=$6000 * R * 1 = $6000R
Now we need to find that the two investments together need to yield at least $1620, so our equation to solve is:
$1620 = $1200 + $6000R
Now, we have to subtract $1200 from both sides, then we get,
$1620 - $1200=$6000R
Then collect similar terms
$420=$6000R
Now, divide both sides by $6000
R=0.07 or 7%
Therefore, the answer is 7%.
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please answer the question below the top question. on both.
Answers
The value of x is 6 degrees.
It is given in the question that:-
HI is parallel to JK and FG is the transversal intersecting HI at L and JK at M.
∠LMK = 115 degrees
∠MLI = (8x + 17) degrees
We have to find the value of x.
We know that,
Angles on the same side of the transversal sum up to 180 degrees.
Hence, we can write,
∠LMK + ∠MLI = 180 degrees.
115 + (8x + 17) = 180 degrees
8x + 132 = 180 degrees
8x = 180 - 132
8x = 48 degrees
x = 48/8 degrees
x = 6 degrees
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9,999 divided by 9
Two answers
Answers
Answer:
1111...................... ................
A model car has a list price of $46.20. The model is on
sale at 15% off. Find the total cost to the nearest cent
after a 4.5% sales tax is added to the sale price.
Answers
Answer:The total cost is $41.04
Step-by-step explanation:
Hurry Pls) Enter the rational number as
a/b where a and b are integers.
7 1/3
(Note: this isn't my work, it's my siblings and I have no idea how to answer it.)
Answers
The rational number of 7¹/₃ as; a/b where a and b are integers.
How to convert a rational number?A rational number is defined as any number that can be written as a fraction, where both the numerator (the top number) and the denominator (the bottom number) are integers, and the denominator is not equal to zero
Now, we are given the fraction as; 7¹/₃
This given number is expressed as a mixed fraction and so we convert it to improper fraction to get; 22/7
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A cup of fruit contains 12 graps and 3 strawberries Compare strawberries to the total number of fruit
Answers
Answer:
There are 3 strawberries and the total number of fruit is 15, so 3:15 is the ratio, or 3/15.
Step-by-step explanation:
The total number is all of the fruits added together, so 12 + 3.
The 3 means the number of strawberries, so you just put them together into a ratio.
Hope this helps.
Mark as brainliest please
Estimate the square root of 39 to the nearest integer