Answers
Answer:
9(x-8)/3-1Step-by-step explanation:
The inverse function for a set of ordered pairs can be found by swapping the x- and y-coordinates in each pair.
[tex]g^{-1}(-1)=9\qquad\text{from the $g(x)$ ordered pair $(9, -1)$}[/tex]
__
The inverse of a function expressed algebraically can be found by swapping the x- and y-variables and solving for y.
[tex]h^{-1}(x)\qquad\text{is found from }x=h(y)\\\\x=3y+8\\x-8=3y\\\\y=\dfrac{x-8}{3}\\\\\boxed{h^{-1}(x)=\dfrac{x-8}{3}}[/tex]
A function of its own inverse returns the original value:
[tex]\boxed{\left(h\circ h^{-1}\right)(-1)=-1}[/tex]
Related Questions
ANSWER PLEASE! Hopefully someone can figure out.
Answers
Answer:
B
Step-by-step explanation:
The domain is the input values, that is the x- values
The range is the output, that is the y- values.
Thus using values from table
domain : {- 2, 0, 2 }, range : { - 1, 0, 1 }
Evaluate : 9⁴xa⁷b⁴/ 3⁵xa⁴b⁴
Answers
Answer:
27a³
Step-by-step explanation:
9⁴xa⁷b⁴ / 3⁵xa⁴b⁴
(3²)⁴xa⁷b⁴ / 3⁵xa⁴b⁴
3⁸xa⁷b⁴ / 3⁵xa⁴b⁴
3³a³
27a³
given that (y+2) (y+3) and (2y^2+1) are consecutive terms of an arithmetic progression, find the possible value of y
Answers
Answer:
-3/2 and 1
Step-by-step explanation:
Given the arithmetic sequence (y+2) (y+3) and (2y²+1), the common difference is gotten by taking the difference in their terms. For example if we have 3 terms T1, T2, T3... the common difference d = T2-T1 = T3-T2
From the sequence given;
T1 = y+2, T2 = y+3 and T3 = 2y²+1
d = y+3-(y+2) = 2y²+1- (y+3)
open the parenthesis
y+3-y-2 = 2y²+1- y-3
1 = 2y²+1- y-3
1 = 2y²- y-2
2y²- y-2-1 = 0
2y²- y-3 =0
Factorize the resulting expression
2y²- y-3 =0
2y²- 2y+3y-3 =0
2y(y-1)+3(y-1) = 0
(2y+3)(y-1) = 0
2y+3 = 0 and y-1 = 0
2y = -3 and y =1
y = -3/2 and 1
Hence the possible values of y are -3/2 and 1
What two factors of 24 have a sum of 11
Answers
Answer:
8 and 3
Step-by-step explanation:
8+3=11
8*3=24
The length of a rectangle is shown below: (look at the picture) If the area of the rectangle to be drawn is 12 square units, where should points C and D be located if they lie vertically below the line that connects B and A, to make this rectangle? C(−2, −1), D(1, −1) C(−2, −4), D(1, −4) C(−2, −2), D(1, −2) C(−2, −5), D(1, −5)
Answers
================================================
Explanation:
The distance from B to A, or vice versa, is 3 units. You can count out the spaces between the points, or you could subtract the x coordinate values then use absolute value
|B - A| = |-2-1| = |-3| = 3
or
|A - B| = |1-(-2)| = |1+2| = |3| = 3
Whichever method you prefer, the distance between the two points is 3 units.
----------
The area of the rectangle is 12 square units, and we know one dimension of the rectangle is 3 units. The other dimension must be 12/3 = 4 units.
Point C is directly below point B. Specifically C is 4 units below B.
Start at B(-2,2) and move down 4 units to get to C(-2,-2). Then move to the right 3 units to get to D(1,-2)
Or you could start at A(1,2) and move 4 units down to get to D(1,-2) and then move 3 units to the left to get to C(-2,-2)
Answer:
Answer choice = B - C(−2, −4), D(1, −4)
. Suppose the coordinate of A is 0 and AR = 5 and AT = 7.
a. What are the possible coordinates of R? Of T
Answers
==================================================
Explanation:
If we're on a number line, then R could be at either R = 5 or R = -5. This is so the distance from A to R is 5 units. Distance is never negative. You count out the spaces to get the distance, or use subtraction and absolute value.
Saying "distance from A to R is 5" can be written as AR = 5. Meaning segment AR is 5 units long.
Now if AT = 7, then T could be at 7 or -7 on the number line. The reasoning as similar as to why R could be at -5 or 5.
Jan is painting a square canvas. The length of one side of the canvas is 4 feet. Write an equation to show how to show how to find the area of the canvas
Answers
Step-by-step explanation:
It is given that, Jan is painting a square canvas. The length of one side of the canvas is 4 feet.
We need to write an equation to show how to find the area of the canvas.
For a square, all its sides are equal. Let the side is x. The area of a square is given by :
[tex]\text{Area}=\text{side}^2\\\\A=x^2\\\\A=4^2\\\\A=16[/tex]
So, the equation that shows the area of the canvas is [tex]A=x^2[/tex].
How many solutions are there for the system of equations shown on the graph?
Answers
Answer:
Hey there!
These lines only intersect at one point, so there is only one solution.
Let me know if this helps :)
Answer:
one solution
Step-by-step explanation:
The solutions are where the graphs intersect
There lines cross at one point (0,3), so there is one solution
In a study appearing a Science journal, a research team reports that plants in southern England are flowering earlier in the spring. Records of the first flowering dates for 385 species over a period of 47 years show that flowering has advanced an average of 15 days per decade, an indication of climate warming, according the the authors. What is the population of interest? *
Answers
Answer:
Its about plants
Step-by-step explanation:
In one day, a book store earned $199 in sales for 4 copies of a new cookbook and 5 copies of a new science fiction novel. On the next day, it earned $152 in sales for 3 copies of the cookbook and 4 copies of the science fiction novel. What was the price of each book?
Answers
Answer:
The cookbook costs $36 per copy while the science fiction costs $11 per copy
Step-by-step explanation:
Here in this question, we are interested in calculating the price of the cookbook and the price of the science fiction novel.
Since we do not know the price of each, we start by assigning variables to stand in for these unknown prices.
Let the price of the cookbook be $x , while the price of the science fiction be $y
Now, on the first day, 4 copies of the cookbook and 5 copies of the fiction;
mathematically that would be 4 * x and 5 * y
We add both and sum to be $199
Thus we have;
4x + 5y = 199 ••••••••••(i)
On the second day;
3 copies of cookbook 3 * x = 3x with 4 copies of science fiction 4 * y
Adding both yielded 152;
Thus, we have ;
3x + 4y = 152••••••••••(ii)
So we need to solve both equations simultaneously to get the values of x and y
4x + 5y = 199
3x + 4y = 152
Multiply equation i by 3 and equation ii by 4
3 * 4x + 5y = 199
4 * 3x + 4y = 152
12x + 15y = 597
12x + 16y = 608
Now, subtract multiplied equation ii from multiplied equation i
(12x-12x) + (15y-16y) = (597-608)
-y = -11
y = 11
To get x, simply substitute in any of the equations;
let’s use equation 1
4x + 5y = 199
4x + 5(11) = 199
4x + 55 = 199
4x = 199-55
4x = 144
x = 144/4
x = 36
27.2163 rounded to the nearest hundredth
Answers
Answer:
27.0000
Step-by-step explanation:
27.2163 rounded to the nearest hundredth is 27.0000 or 27 because the hundredth place held a 1 and 5 or above rounds up and 4 or below rounds down. The .2163 turned into zeros because the second number (the hundredths place) was a 1 so it rounded down, and hen it rounds down, all the numbers round to 0.
Use the frequency distribution shown below to construct an expanded frequency distribution.
High Temperatures (°F)
Class
16-26
27-37
38-48
49-59
60-70
71-81
82-92
Frequency, f
17
45
66
67
82
66
22
Answers
Answer and Step-by-step explanation:
The calculation of midpoints, relative frequencies and cumulative frequencies are shown below:-
For Midpoint = [tex]\frac{Lower\ limit\ +\ Upper\ limit}{2}[/tex]
For Relative frequency = [tex]\frac{Frequency}{Total\ number\ of\ frequency}[/tex]
Class Frequency Midpoints Relative Cumulative
frequency frequency
16-26 17 21 0.047 0.047
27-37 45 32 0.123 0.17
38-48 66 43 0.181 0.351
49-59 67 54 0.184 0.535
60-70 82 65 0.225 0.76
71-81 66 76 0.181 0.941
82-92 22 87 0.060 1.001
Total 365
Therefore for computing the cumulative frequency we simply added relative frequency with previous cumulative frequency for class 27-37 and in the same manner of every class.
The rate at which something occurs over a particular period of time or in a given sample:
"An increase in the frequency of accidents due to increased overtime"
GivenUse the frequency distribution shown below to construct an expanded frequency distribution.
The formula to calculate the midpoint and relative frequency are given below.
[tex]\rm Midpoint = \dfrac{Lower \ limit + Upper \ limit }{2}[/tex]
[tex]\rm Relative \ frequency = \dfrac{Frequency}{total \ frequency}[/tex]
The frequency distribution to construct an expanded frequency distribution is given below.
Class Frequency Midpoints Relative frequency Cumulative frequency
16-26 17 21 0.047 0.047
27-37 45 32 0.123 0.17
38-48 66 43 0.181 0.351
49-59 67 54 0.184 0.535
60-70 82 65 0.225 0.76
71-81 66 76 0.181 0.941
82-92 22 87 0.060 1.001
Total 365
To know more about Frequency click the link given below.
https://brainly.com/question/17740069
What is the value of 20 + 3 (7 + 4) + 5 + 2 (7 + 9)? PLEASE HELP ASAP
Answers
Answer:
90
Step-by-step explanation:
in the following graph, AABC is congruent to AA'B'C'. A teacher asks a student Janine to state the
translation rule for this transformation janine focuses on point and states that the translation rule is
(x,y) (x-2, y-6). In other words, to shift from the blue to the red triangle, you must shift each point two
units left and six units down
State whether Janine's answer was correct or incorrect. In at least three sentences, support your
response with a brief explanation. Be sure to use the term transformation in your explanation
Answers
Answer:
Janine's answer is incorrect.
Step-by-step explanation:
Rigid transformations are methods by which the image of a given figure or object can be produced either by rotation, translation, dilation or reflection.
Since Janine used translation method for the transformation, the dimension of the shape is preserved but not its initial position. To translate AABC to AA'B'C', each point should shift three units left and five units down.
Therefore, the appropriate translation rule is:
(x, y) ⇒ (x + 3, y + 5)
when bisecting an angle, one of the steps is to draw an arc centered on a point on a ray of the angle. in particular this angle is to be drawn on the interior of the angle, why must The Arc be drawn in the interior of the angle?
Answers
Step-by-step explanation:
The arc drawn must be in the interior side of the angle to be bisected because while constructing the angular bisector, we make an arc cutting both the rays of the angle, so in order to cut the angle in to two equal part, we should make arcs in the interior part of the angle subtended so that it bisects the angle in two equal parts.
3b^2+6b-28
which of the following describes 3 in the expression above
A. quotient
B. coefficient
C. sum
D. product
Answers
Answer:
3 is a coefficient. (Option B)
Step-by-step explanation:
A coefficient in a term is the number placed before the variable. The coefficient multiplies the variable.
In the given expression, 3 would be the coefficient in [tex]3b^2[/tex].
A, C, and D are answers to an expression depending on the expression's operation.
In this case, option B would be the correct answer.
Hope this helps.
Answer:
[tex]\huge \boxed{\mathrm{B. \ coefficient}}[/tex]
Step-by-step explanation:
[tex]3b^2[/tex]
[tex]b^2[/tex] is being multiplied by 3.
A coefficient is a number used to multiply a variable.
Find x, if 3x − 5(y + x ) ^2 = 16 and 4x + 2(y + x )^ 2 = 30
Answers
Answer:
x = 7
Step-by-step explanation:
Start by solving for [tex](y+x)^2[/tex] which is a common expression for both equations. Then in the first equation:
[tex]3\,x5\,(y+x)^2=16\\3x-16=5\,(y+x)^2\\(y+x)^2=\frac{3\,x-16}{5}[/tex]
and in the second equation:
[tex]4\,x+2\,(y+x)^2=30\\2\,(y+x)^2=30-4\,x\\(y+x)^2=15-2\,x[/tex]
Now we make the two [tex](y+x)^2[/tex] expressions equal so we get:
[tex]\frac{3\,x-16}{5} =15-2\,x\\3\,x-16=75-10\,x\\13\,x=75+16\\13\,x=91\\x=7[/tex]
Which number line represents the solution |2x|-12 =
Answers
Answer:
Third option, last one
Step-by-step explanation:
Let's solve for x first.
|2x| - 12 = -2
|2x| = 10
2x = 10 or -2x = 10
x = 5 or x = -5
The number line that represents this is the last one.
() and () are inverses of one another and drawn on the same graph with the same scale on both the horizontal and vertical axis. Which of the following would be true?
A.
By reflecting the entire coordinate grid over the line =, () would land on ().
B.
() is the same as (), translated up 3 units.
C.
By rotating () 90° clockwise around the origin you would get ().
D.
By rotating () 180° clockwise around the origin you would get ().
Answers
Answer: Option A.
Step-by-step explanation:
We have the functions f(x) and g(x), that are inverses between them.
This means that if:
f(x) = y
then:
g(y) = x.
now, remember that:
When we have a point (x, y), and we reflect it over the line y = x, our new point will be (y, x).
So before we whe had:
f(x) = y.
and now in that same place, we have:
g(y) = x.
So the old graph of f(x) now coincides with the graph of g(x). (And the old graph of g(x) now coincides with the graph of f(x) )
So A is true.
B) This depends on the function:
if we have f(x) = x + 1.5
then f(0) = 1.5
now we want that:
g(1.5) = 0, then we can write:
g(x) = x - 1.5
Now f(x) and g(x) are inverses, and we would have that:
f(x) = g(x) + 3.
So f(x) is g(x) translated up by 3 units, but this is a particular case, not a general one, so B is not always true.
C and D) When we do rotations of 90° or 180°, we are effectively changing the quadrant of our point. so rotations will cause not only changes as the reflection over the x = y line, those will also cause changes in the sign of our variables, so, while for some functions f(x) and g(x) we can have that the rotations will map one into the other, this is not the general case.
POINTS......!!!!
Please answer!!!
Please state the width (part a)
And length (part b)
Answers
Answer:
(a) = 71 cm
(b) = 89 cm
Step-by-step explanation:
(a.)
perimeter of a rectangular field = 324 m
length (l) = 91 m
width (w) = ?
Now,
Perimeter Of Rectangle
= P = 2(l + w)
= 2(91 + w) = 324m
= 182 + 2w = 324m
= 2w = 324 - 182m
= 2w = 142m
= w = 142/2
= w = 71
(b.)
area of rectangular painting = 5696 cm²
width (w) = 64 cm
length (l) = ?
Now,
Area Of Rectangle
A = l × w
= l × 64 = 5696
= l = 5696/64
= l = 89 cm
VERIFICATION:-FOR (a)
= P = 2(l + w)
= P = 2(91 + 71) = 324 cm
FOR (b)
= l × w
A = 89 × 64 = 5696
Find the mass of the lamina described by the inequalities, given that its density is rho(x, y) = xy. 0 ≤ x ≤ 2, 0 ≤ y ≤ 2
Answers
Answer: Mass of lamina = 4
Step-by-step explanation: A lamina is a plate in 2 dimensions, described by the plane it covers and its density function, [tex]\rho(x,y)[/tex].
To determine mass of the lamina:
mass (M) = [tex]\int {\int\limits_D \rho(x,y) \, dA[/tex]
where D is region bounded by the axis.
For the question:
M = [tex]\int\limits^2_0 {\int\limits^2_0 xy \, dy \,dx[/tex]
Calculating the double integral:
M = [tex]\int\limits^2_0 { x\frac{y^{2}}{2} \,dx[/tex]
M = [tex]\int\limits^2_0 { x(\frac{2^{2}}{2}-0)} \,dx[/tex]
M = [tex]\int\limits^2_0 { 2x} \,dx[/tex]
M = [tex]\frac{2.2^{2}}{2} - 0[/tex]
M = 4
The mass of lamina is 4 units.
3(3x-2)=39
Solve equation
Answers
A .......... divides a two dimensional shape in two congruent shapes
Answers
Answer:
A diagonal. (A rectangle is divided into two triangles by a diagonal, for example.)
Hope this helps!
PLEASE HELP !
How many ounces are there is 2.59 gallons of lemonade? (There are quarts in a gallon. ) ounces in a quart and 4 quarts in a gallon .)
Answers
Answer:
331.52 oz
Step-by-step explanation:
Google :D
Answer:
a
Step-by-step explanation:
when factoring 6x^2 -7x-20 by grouping , how should the middle term be rewritten
Answers
Answer: -7x should be written as -15x+8x or 8x-15x
===============================================
Explanation:
Multiply the first coefficient 6 and the last term -20 to get -120
We need to find factors of -120 that add to the middle coefficient -7
Through trial and error you should find that
-15 + 8 = -7
-15 * 8 = -120
Therefore, we break the -7x into -15x+8x
----------------------------
Extra info: if you want to fully factor by grouping, then follow these steps
6x^2 - 7x - 20
6x^2 - 15x + 8x - 20 ... break up -7x
(6x^2 - 15x) + (8x - 20) .... group into pairs
3x(2x - 5) + 4(2x - 5) .... factor each group
(3x + 4)(2x - 5) ..... pull out the overall GCF 2x-5
So 6x^2-7x-20 fully factors to (3x+4)(2x-5)
We can check the answer by FOILing out the last expression above to get the original expression back again. The box method works as well. So does the distributive property.
A population of bacteria is growing rapidly. The population at any hour, h, can be represented
by the function f(h) = 2 • 4h. What is the population of bacteria after 4 1/2 hours?
Answers
Answer:
36
Step-by-step explanation:
Function is:
f(h) = 2*4hAfter 4 1/2 hours, h = 4 1/2 = 4.5
f(4.5) = 2*4*4.5 = 36Answer:
36
Step-by-step explanation:
4×4.5=18
18×2=36
f(x)=x2–5x+7, find f(3)
Answers
Answer:
[tex]f(3) = 1[/tex]Step-by-step explanation:
f(x) = x² - 5x + 7
To find f(3) substitute the value of x that's 3 into f(x) that's replace every x in f (x) by 3
We have
[tex]f(3) = {3}^{2} - 5(3) + 7 \\ = 9 - 15 + 7 \\ = - 6 + 7[/tex]We have the final answer as
[tex]f(3) = 1[/tex]Hope this helps you
Which expression is equivalent to 9^36/9^3 ? A) 1/9^12 B) 9^33 C) 9^12 D) 9^39
Answers
Answer:
[tex]\huge\boxed{\dfrac{9^{36}}{9^3}=9^{33}\to\mathbb{B)}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ \dfrac{a^n}{a^m}=a^{n-m},\ \text{for}\ a\neq0.\\\\\text{We have}\ \dfrac{9^{36}}{9^3}=9^{36-3}=9^{33}[/tex]
Over the last three evenings, Lucy received a total of 107 phone calls at the call center. The second evening, she received 3 times as many calls as the third evening. The first evening, she received 7 more calls than the third evening. How many phone calls did she receive each evening?
Answers
Answer:
1st evening = 7 + 20 = 27 calls
2nd evening = 3 (20 ) = 60 call
3rd evening = 20 calls
Step-by-step explanation:
total calls for the last three evenings = 107 phone calls
2nd evening = 3x as many calls as the 3rd evening
1st evening = 7 more calls than the 3rd evening.
find:
how many calls did she receive each evening?
let T (total) = 107
let x = 3rd evening.
let 2nd = 3x
let 1st = (7 + x)
T = 1st + 2nd + 3rd
107 = (7 + x) + 3x + x
107 - 7 = 5x
100 = 5x
x = 100 / 5
x = 20
therefore,
1st evening = 7 + 20 = 27 calls
2nd evening = 3 (20 ) = 60 call
3rd evening = 20 calls
Answer:
1st = 27 calls
2nd = 60 call
3rd = 20 calls
Step-by-step explanation:
total calls = 107 phone calls
2nd = 3x
1st = 7 + 3x
T (total) = 107
T = 1st + 2nd + 3rd
107 = (7 + x) + 3x + x
107 - 7 = 5x
100 = 5x
x = 100 / 5
x = 20
so,
1st = 7 + 20 = 27 calls
2nd = 3 (20 ) = 60 call
3rd = 20 calls
5x - 10 less than it equal to 20
Answers
5x-10 = 20
5x=20+10
5x=30
x= 6