Answers
A one-to-one function has an inverse. The inverse is another function that undoes the action of the first one, so if we evaluate a function [tex]f[/tex] at some point [tex]x[/tex] to get the number [tex]f(x)[/tex], evaluating the inverse at [tex]f(x)[/tex] will recover the original input [tex]x[/tex]. In other words,
[tex]f^{-1}(f(x)) = x[/tex]
The process works in the opposite direction, too:
[tex]f\left(f^{-1}(x)\right) = x[/tex]
From the given definition of [tex]g[/tex], we have [tex]g(-4) = 3[/tex], so taking inverses on both sides, we find
[tex]g(-4) = 3 \implies g^{-1}(g(-4)) = g^{-1}(3) \implies \boxed{g^{-1}(3) = -4}[/tex]
Given [tex]h(x)=2x-13[/tex], evaluating [tex]h[/tex] at its inverse will recover [tex]x[/tex], so that
[tex]h\left(h^{-1}(x)\right) = x \implies 2h^{-1}(x) - 13 = x \implies \boxed{h^{-1}(x) = \dfrac{x+13}2}[/tex]
[tex](h\circ h^{-1})(x)[/tex] is another way of writing the compound function [tex]h\left(h^{-1}(x)\right)[/tex]. As already discussed, this reduces to [tex]x[/tex], so
[tex]\boxed{\left(h\circ h^{-1}\right)(-9) = -9}[/tex]
Related Questions
(3x + 5y = 7
{ 4x - y = 5
Answers
Answer:
Step-by-step explanation:
Solution by substitution method
3x+5y=7
and 4x-y=5
Suppose,
3x+5y=7→(1)
and 4x-y=5→(2)
Taking equation (2), we have
4x-y=5
⇒y=4x-5→(3)
Putting y=4x-5 in equation (1), we get
3x+5y=7
⇒3x+5(4x-5)=7
⇒3x+20x-25=7
⇒23x-25=7
⇒23x=7+25
⇒23x=32
⇒x=32/23
→(4)
Now, Putting x=32/23
in equation (3), we get
y=4x-5
⇒y=4(32/23)-5
⇒y=(128-115)/23
⇒y=13/23
∴y=13/23 and x=32/23
Consider the algebraic expression √ 7 x 18 + 12.1 x 15 + π 4 x 6 + 1 9 . What is the degree of this polynomial? Identify the leading coefficient. Identify the leading term.
Answers
The degree of the provided polynomial is 18, and the leading term is √7.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have given an expression:
[tex]= \rm \sqrt{7}x ^{18} + 12.1x^{ 15} + \pi 4 x^ 6 + 1 9[/tex]
As we can see in the expression the greatest degree is 18.
So the degree of the polynomial is 18
And the coefficient of the variable which has a height degree is the leading term.
The leading term = √7
Thus, the degree of the provided polynomial is 18, and the leading term is √7.
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Two angles are complentary if the sum of their measures is 90 °. Find two complentary angles such that one of the angles is 165° less than 4 times the other angle
Answers
Answer:
51° and 39°
Step-by-step explanation:
x + 4x - 165 = 90
5x = 90 + 165
5x = 255
x = 255 / 5
x = 51
4 x 51 = 204
204 - 165 = 39
2 angles are 51 and 39
x^2 - 20x= -2x - 80 what is the intermediate step
Answers
Find the slope of every line that is parallel to
the line on the graph
Answers
Answer:
[tex] - \frac{1}{6} [/tex]
Step-by-step explanation:
Using the slope formula:
[tex] \frac{ - 1 - 0}{0 - ( - 6)} = - \frac{1}{6} [/tex]
6 Solve each equation. Round to the nearest ten-thousandth. Check your answers.
2.
4x = 19
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\text{4x = 19}\\\\\large\textbf{DIVIDE 4 to BOTH SIDES}\\\\\rm{\dfrac{4x}{4} = \dfrac{19}{4}}\\\\\large\textbf{SIMPLIFY IT!}\\\\\rm{x = \dfrac{19}{4}}\\\\\rm{x = 19 \div 4}\\\\\text{x = 4.75}\\\\\rm{x \approx 4.7500}\\\\\\\huge\text{Therefore, the answer should be: \boxed{\mathsf{4.7500}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
1. Which of the following numbers is
rational?
A. 0.78
B. 0.303003000
C. √6
D. 0.3841697
Answers
Answer:
A. 0.78
Step-by-step explanation:
A rational number is a number that you can express as [tex]\frac{x}{y}[/tex] where [tex]y\neq 0[/tex].
What is the value of this expression when c = -4 and d = 10?
A.
2
B.
9
C.
21
D.
41
Answers
The complete question is
"What is the value of this expression when c= -4 and d= 10?
1/4 (c^3+d²)
A.2
B.9
C.21
D.41"
The value of this expression when c = -4 and d = 10 will be option B 9.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The given expression is
[tex]1/4 (c^3+d^2)\\\\1/4 ((-4)^3+(10)^2)\\\\1/4 ( -64 + 100)\\\\1/4 (36)\\\\9[/tex]
Hence, the value of this expression when c = -4 and d = 10 will be option B 9.
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A formula for the normal systolic blood pressure for a man age A, measured in mmHg, is given as
P = 0.006A2 − 0.02A + 120. Find the age to the nearest year of a man whose normal blood pressure measures 125 mmHg.
Answers
Solving a quadratic equation, the age of the man with a blood pressure of 125 mmHg is of 27 years old.
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex][tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]In which:
[tex]\Delta = b^2 - 4ac[/tex]
The pressure is given by:
P = 0.006A² - 0.02A + 120.
When the pressure is of 125 mmHg, we have that:
0.006A² - 0.02A + 120 = 125.
0.006A² - 0.02A - 5 = 0.
Hence the coefficients are a = 0.006, b = -0.02, c = -5, and the solutions, applying the formula are:
A = -30 and A = 27.
Age has to be positive, hence the man is 27 years old.
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What is the scale factor from AABC to ADEF?
B
48
AA
6
A4 CE
48
6
O A.
C
B. 8
32
D
Answers
Answer: 8
Step-by-step explanation:
We are going from a smaller triangle to a larger triangle, so the scale factor is greater than 1.
Eliminate A and D.We know scale factor = (image)/(preimage), so the scale factor is 32/4 = 8
The scale factor of dilation of the triangle is k = 8
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔDEF
where the measures of sides of ΔABC are
AB = 6 , BC = 6 and AC = 4
The measure of sides of triangle ΔDEF are
DE = 48 , EF = 48 and DF = 32
The scale factor of dilation k = measure of side DE / measure of side AB
k = 48 / 6
k = 8
Hence , the dilation factor is k =8
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A man has to be at a certain place at a certain time. He finds that he shall be 20 minutes late if he walks at 3 km/h speed and 10 minutes earlier if he walks at a speed of 4 km/h_The distance he has to walk is
Answers
Answer:
0.5km or 500m
Step-by-step explanation:
Given Distance = Speed x Time
In this case, we should use the difference in speed and time of the 2 scenarios.
Difference in Time = 20 mins(late) + 10 mins(early)
= 30 mins or 0.5 hour
Difference in Speed = 4km/h - 3km/h = 1km/h
Distance = 1km/h x 0.5 hr = 0.5km or 500m.
The school play sold $550 in tickets one night. The number of $8 adult tickets was 10 less than twice the number of $5 child tickets. How many tickets were sold for the adults vs the child tickets?
Answers
Answer:
This is my answer↓:
Step-by-step explanation:
He school play sold $550 in tickets one night.
The number of $8 adult tickets was 10 less than twice the number of
$5 child tickets.
How many of each ticket were sold
Let say child ticket sold = x
Adult tickets was 10 less than twice the number of child tickets.
=> Adult ticket sold = 2x - 10
Child ticket sold = x
$5 child tickets price
=> Revenue = 5x $
Adult ticket sold = 2x - 10
$8 Adult tickets price
=> Revenue = 8(2x - 10) =16x - 80 $
5x + 16x - 80 = 550
=> 21x = 630
=> x = 30
Child ticket sold = 30
Adult ticket sold = 50
Total ticket sold = 80
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Graph A: A horizontal line goes from (1, 0.5) to (2, 0.5). Another horizontal line goes form (2, 0.2) to (7, (0, 2). Graph B: A curve starts at (0, 0), curves up to (1, 1), and then curves down to (2, 0).
Which graph represents a density curve, and why?
graph A only, because the curve is above the horizontal axis, and the area under the curve from 2 to 7 is 1
graph B only, because the curve is above the horizontal axis, and the area under the curve is equal to 1.57
both graph A and graph B, because both curves are above the horizontal axis, and both areas are positive
neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1
Pictures posted below
Answers
Answer: neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1
Step-by-step explanation:
Areas under the graphs:
Graph A
[tex](1)(0.5)+(7-2)(0.2)=1.5\\\\[/tex]
Graph B
[tex]\frac{\pi}{2}(1^{2})=\frac{\pi}{2}[/tex]
As neither of these graphs have an area of 1, neither of them are density curves.
The statement - "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.
A few fundamental principles apply to density curves:
A density curve's area beneath it represents probability.A density curve's area under it equals one.Base x height in a uniform density curve equals one.The likelihood that x = a will never occur.The likelihood that x < a is the same as that of x ≤ a.Neither curve of Graph A nor of Graph B has the area under the curve summed up as 1, though the curve is above the horizontal axis.
Hence, because neither graph has an area of 1, even if both curves are above the horizontal axis, the statement "neither graph A nor graph B, because, even though both curves are above the horizontal axis, neither graph has an area of 1" is true.
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Each year the Royal London company gives
its employees a gift box containing 6 bags of
coffee, 4 boxes of tea, and 2 boxes of biscuits.
If in the first three years, the number of
employees grew from 2 to 12 to 18, what was
the total quantity of coffee, tea, & biscuits
distributed by the company in those years?
Answers
The total number of tea received in three years is 192.
The total number of coffee received in three years is 128.
The total number of biscuits received in three years is 64.
What is the total quantity of tea, coffee and biscuits distributed in the three years?The total quantity of tea, coffee and biscuits received in the first year = (6 x 2) , (4 x 2) , (2 x 2) = 12, 8, 4 respectively
The total quantity of tea, coffee and biscuits distributed in the second year = (6 x 12) , (4 x 12) , (2 x 12) = 72, 48, 24 respectively
The total quantity of tea, coffee and biscuits distributed in the third year = (6 x 18) , (4 x 18) , (2 x 18) = 108, 72, 36 respectively
Total number of tea received in three years = 108 + 72 + 12 = 192
Total number of coffee received in three years = 8 + 48 + 72 = 128
Total number of biscuits received in three years = 4 + 24 + 36 = 64
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I cannot crack this one, somebody please assist me
Answers
These [tex]N[/tex] outcomes make up the entire sample space, so
[tex]\displaystyle \sum_{k=1}^N P(e_k) = P(e_1) + P(e_2) + P(e_3) + \cdots + P(e_N) = 1[/tex]
We're given that [tex]P(e_{j+1}) = 2 P(e_j)[/tex] for all [tex]j\in\{1,2,\ldots,N-1\}[/tex], so
[tex]P(e_1) + 2 P(e_1) + 2^2 P(e_1) + \cdots + 2^{N-1} P(e_1) = 1 \\\\ \implies P(e_1) = \dfrac1{1 + 2 + 2^2 + \cdots + 2^{N-1}} = \dfrac1{2^N - 1}[/tex]
Then we can solve the recurrence relation to get the probability of the [tex]j[/tex]-th outcome,
[tex]P(e_{j+1}) = 2 P(e_j) = 2^2 P(e_{j-1}) = 2^3 P(e_{j-2}) = \cdots \\\\ \implies P(e_{j+1}) = 2^j P(e_1) \\\\ \implies P(e_j) = 2^{j-1} P(e_1) = \dfrac{2^{j-1}}{2^N - 1}[/tex]
The probability of getting this sequence of [tex]k[/tex] outcomes is then
[tex]\displaystyle P(E_k) = P(e_1) + P(e_2) + \cdots + P(e_k) = \sum_{j=1}^k \frac{2^{j-1}}{2^N-1} = \frac{2^k-1}{2^N-1}[/tex]
as required.
Some preliminary results: If [tex]S[/tex] is the sum of the first [tex]n[/tex] terms of a geometric series with first term [tex]a[/tex] and common ratio [tex]r[/tex], then
[tex]S = a + ar + ar^2 + \cdots + ar^{n-1}[/tex]
[tex]\implies rS = ar + ar^2 + ar^3 + \cdots + ar^n[/tex]
[tex]\implies S - rS = a(1 - r^n)[/tex]
[tex]\implies S = \dfrac{a(1 - r^n)}{1 - r}[/tex]
which gives us, for instance,
[tex]1 + 2 + 2^2 + \cdots + 2^{N-1} = \dfrac{1 - 2^N}{1 - 2} = 2^N-1[/tex]
Determine the number of zeros of the polynomial function. f(x) = x^4 − 6x
Answers
The factor of the function will be x and (x³ – 6). Then the zeroes of the function will be 0 and √6.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The polynomial function is given below.
f(x) = x⁴ − 6x
Then the factor of the function will be
f(x) = x(x³ – 6)
Then the zeroes of the function will be
x = 0, √6
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has a bag containing twenty balls. There are twice as many yellow balls than blue balls, but the yellow balls are only a third of the red balls. The green balls are the same number as the blue balls. How many are each of the colour ball?
Answers
Answer:
Yellow: 4
blue: 2
red: 12
green: 2
Giving out brainliest to whoever answers!
Answers
Explanation: Since volume consists of *L x W x H, you need to multiply all three components together, 25, 3, and 16. When you multiply all these together, you get your volume, which is 1200 cubic meters. *Length x Width x Height
John is 5 years younger than David. Four years later David will be twice as old as John. Find their present age.
Answers
David will be 10 and John will be 9
my dad began paying me an allowance when i was in eighth grade. what is the indirect object?
Answers
Answer:
Step-by-step explanation:
The answer would be "me" as the indirect object
Here is the histogram of a data distribution. All class widths are 1.
SO
4
3
2-
2 3
Which of the following numbers is closest to the mean of this distribution?
A. 2
OB. 3
O C. 10
OD. 5
5 6 7 8 9 10
E. 4
Answers
The correct answer is option B which is 3
What is mean?
Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.
Given data:-
4,3,2
The mean will be calculated as:-
Mean = (4 + 3 + 2) / 3
Mean = 9 / 3
Mean = 3
Therefore the correct answer is option B which is 3
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If the present value of a growing perpetuity is 214, the required rate of return is 10%, and growth rate is 3%, what is the cash flow in year 1? (Round to the nearest whole number).
Answers
The cash flow in year 1 is $15.
What is the cash flow in year 1?A growing perpetuity increases continuously and indefinitely.
Cash flow = present value x (rate of return - growth rate)
214 x (10% - 3%)
214 x 0.07 = $15
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Which pairs of angles are congruent?
Answers
Answer:
b) angles 1 and 4 are congruent.
Hope it helps!
What is the solution to this system of equations?
Negative 3 x + 5 y = negative 2. 3 x + 7 y = 26.
(4, 2)
(2, 3 and one-third)
no solution
infinitely many solution
Answers
The solution to the system of equation is (-4 , 2) , Option A is the right answer.
What are System Of equation ?A set of equation whose factors are common are called system of equations.
It is given in the question
3x +5y = -2
3x +7y = 2
On solving this we get
-2y = -4
y = 2
On substitution in any equation
x = -4
Therefore solution to the system of equation is (-4 , 2) , Option A is the right answer.
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Answer:
A.
Step-by-step explanation:
took tha quiz
The points (0, -8) and (10, 2) represent the endpoints of a diameter of a circle. Which of the following represents the equation of this circle?
Answers
Answer:
(x-5)²+(y+2)²=200.
Step-by-step explanation:
1) using the given coordinates it is possible to calculate
- the centre of the given circle:
[tex]x_0=\frac{10+0}{2}=5; \ y_0=\frac{2-8}{2}=-2;[/tex]
- the radius of the given circle:
[tex]r=\sqrt{(10-0)^2+(2+8)^2} =\sqrt{200} ;[/tex]
2) finally, the required equation (common form is (x-x₀)²+(y-y₀)²=r²):
(x-5)²+(y+2)²=200.
If x is a positive integer, what is the value of x for the equation (x!-(x-3)!)\23=1?
I think the first step is knowing (x!-(x-3)!) equals to 23, but after that i'm stuck, can someone help me?
Answers
[tex]\dfrac{x!-(x-3)!}{23}=1\\x!-(x-3)!=23\\(x-3)!((x-2)(x-1)x-1)=23\\(x-3)!((x^3-x^2-2x^2+2x)-1)=23\\(x-3)!((x^3-3x^2+2x)-1)=23[/tex]
23 is a prime number, therefore there are two possibilities:
[tex]\text{I.}\, (x-3)!=1 \wedge x^3-3x^2+2x-1=23[/tex]
or
[tex]\text{II.}\, (x-3)!=23 \wedge x^3-3x^2+2x-1=1[/tex]
[tex]\text{I.}\\(x-3)!=1\\x-3=0 \vee x-3=1\\x=3 \vee x=4[/tex]
Now, we check if any of these solutions is also a solution to the second equation:
[tex]3^3-3\cdot3^2+2\cdot3-1=23\\27-27+6-1-23=0\\ -18=0[/tex]
Therefore, 3 is not a solution.
[tex]4^3-3\cdot4^2+2\cdot4-1=23\\64-48+8-1-23=0\\0=0[/tex]
Therefore, 4 is a solution.
[tex]\text{II.}[/tex]
[tex](x-3)!=23[/tex]
We know that [tex]3!=6[/tex] and [tex]4!=24[/tex], therefore there isn't any [tex]n\in\mathbb{N}[/tex], for which [tex]n!=23[/tex], so there's no solution.
So, the only solution is [tex]x=4[/tex].
Each conditional statement below is true. Write its converse. If the converse is also true, combine the statements as a biconditional.If x = —10, then x2 = 100.
Answers
The converse of the statement will be : if x^2 = 100 then x = -10, which is not true.
How to find the true statement?In order to write a converse of a conditional statement "p then q", will be "q then p" the hypothesis and conclusion interchanges.
Then the converse of the statement will be :
if x^2 = 100 then x = -10,
which is not true.
Since , x = +10, then x^2 = 100
Therefore, if x^2 = 100 then x = -10, which is not true.
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Suppose a bag contains a set of 10 tiled letters: M, T, O, A, T, P, J, A, K, A You draw a tile from the bag, and record the letter and leave it on the table. You shake up the bag, and draw another tile out of the bag. Calculate the probability you will select the letter M on the first draw and the Letter T on the second draw?
Answers
Answer:
1/90
Step-by-step explanation:
Comment
To begin with, there are 10 tiles.. You draw one and don't replace it. Then you draw another tile from the 9 that remain. The job is to figure out the probability of that happening.
You have a 1/10 chance of drawing the M.
But now there are only 9 tiles left and you have a 1 in 9 chance of drawing a T
Solution
P(M,T) = 1/10 * 1/9 = 1 / 90
You have a 1 in 90 chance of getting the two tiles in the order you have specified.
Help me with this please!!!!
Answers
Answer:
3
Step-by-step explanation:
Cardinalities are the number of elements in a set.
(A∩B∩C) is the very middle part of the circle, and there are 3 elements there.
urgent help algebra 2
Answers
y=3/4x-7
Point slope form is:
y − y1 = m(x − x1)
so
y +7 = 3/4(x -0)
or
y + 7 = 3/4x
