If the range of the coordinate transformation (, ) = (−2,−3 +1) is (4, −2), (2, −5), (−6, 4), what is the domain?
A. (-2, 1), (-1, 2), (3, -1)
B. (-8, 7), (-4, 16), (19, -11)
C. (-8, 1), (-4, 2), (19, -1)
D. (-2, 7), (-1, 16), (3, -11)
Answers
Consider the below figure attached with this question.
Given:
The transformation is:
[tex]f(x,y)=(-2x,-3y+1)[/tex]
The range is (4,-2), (2, −5), (−6, 4).
To find:
The domain of the transformation.
Solution:
We have,
[tex]f(x,y)=(-2x,-3y+1)[/tex]
For the point (4,-2),
[tex](-2x,-3y+1)=(4,-2)[/tex]
On comparing both sides, we get
[tex]-2x=4[/tex]
[tex]x=\dfrac{4}{-2}[/tex]
[tex]x=-2[/tex]
And,
[tex]-3y+1=-2[/tex]
[tex]-3y=-2-1[/tex]
[tex]-3y=-3[/tex]
[tex]y=\dfrac{-3}{-3}[/tex]
[tex]y=1[/tex]
So, the domain of (4,-2) is (-2,1).
Similarly,
For the point (2,-5),
[tex](-2x,-3y+1)=(2,-5)[/tex]
On comparing both sides, we get [tex]x=-1,y=2[/tex]. So, the domain of (2,-5) is (-1,2).
For the point (-6,4),
[tex](-2x,-3y+1)=(-6,4)[/tex]
On comparing both sides, we get [tex]x=3,y=-1[/tex]. So, the domain of (-6,4) is (3,-1).
So, the domain of the given transformation is (-2, 1), (-1, 2), (3, -1).
Therefore, the correct option is A.
Related Questions
PLEASE HELP
The function in the table is quadratic
True
False
Answers
Answer:
True
Step-by-step explanation:
Each f(x) value increases by 5 so therefore this function would be linear
Hope you understand :)
Can someone help asap?
Answers
Answers:
sin = -5/13tan = 5/12csc = -13/5sec = -13/12cot = 12/5=============================================
Explanation:
The angle theta is between pi and 3pi/2, excluding both endpoints.
This places theta in the third quadrant (Q3) between 180 degrees and 270 degrees. The third quadrant is in the southwest.
Plot point A at the origin. 12 units to the left of this point, will be point B. So B is at (-12,0). Then five units lower is point C at (-12,-5). Refer to the diagram below. Notice how triangle ABC is a right triangle.
The angle theta will be the angle BAC, or simply angle A.
Since cos(theta) = -12/13, this indicates that
AB = -12 = adjacent
AC = 13 = hypotenuse
Technically, AB is should be positive, but I'm making it negative so that we can then say
cos(angle) = adjacent/hypotenuse
cos(theta) = AB/AC
cos(theta) = -12/13
------------------
If you apply the pythagorean theorem, you should find that BC = 5, which I'll make negative since we're below the x axis. Then we can say
sin(theta) = opposite/hypotenuse
sin(theta) = BC/AC
sin(theta) = -5/13
------------------
If you divide sine over cosine, then you'll get 5/12. The 13's cancel out. This is the value of tangent.
Or you could say
tan(theta) = opposite/adjacent
tan(theta) = BC/AB
tan(theta) = (-5)/(-12)
tan(theta) = 5/12
------------------
To find csc, aka cosecant, you apply the reciprocal to sine
sin = -5/13 which means csc = -13/5
sec, or secant, is the reciprocal of cosine
cos = -12/13 leads to sec = -13/12
and finally cotangent (cot) is the reciprocal of tangent
tan = 5/12 leads to cot = 12/5
------------------
Note: everything but tan and cot is negative in Q3.
I need help with question 9
Answers
9514 1404 393
Answer:
a) yes
b) see attached
c) see discussion
d) neither
e) increasing (2,5); decreasing (-2, 2)
Step-by-step explanation:
a) The graph passes the vertical line test, so is the graph of a function.
__
b) A table of values is attached
__
c) Generally, this sort of function would be defined piecewise:
[tex]\displaystyle f(x)=\begin{cases}-\dfrac{1}{2}x+1&\text{for }-2\le x<2\\2x-4&\text{for }2\le x \le5\end{cases}[/tex]
In the attachment, we have shown the use of the "maximum" function to define it. The effect is the same.
__
d) The function has no symmetry about the origin or the y-axis, so is neither odd nor even.
__
e) The function is increasing where the line has positive slope, on the interval (2, 5). The function is decreasing where the line has negative slope, on the interval (-2, 2).
Someone help me please
Answers
9514 1404 393
Answer:
A = (0, 1)B = (3, -2)area = 4.5 square unitsStep-by-step explanation:
Rewriting the equations to make x the subject, we have ...
x = y² -1 . . . . . [eq1]
x = 1 - y . . . . . .[eq2]
At the points of intersection, the difference will be zero.
y² -1 -(1 -y) = 0
y² +y -2 = 0
(y -1)(y +2) = 0
The y-coordinates of points A and B are 1 and -2.
The corresponding x-coordinates are ...
x = 1 -{1, -2} = {1 -1, 1+2} = {0, 3}
Then A = (0, 1) and B = (3, -2).
__
A differential of area can be written ...
(x2 -x1)dy = ((1 -y) -(y² -1))dy = (2 -y -y²)dy
Integrating this over the interval y = [-2, 1] gives the area.
[tex]\displaystyle A=\int_{-2}^1(2-y-y^2)\,dy=\left.(2y-\dfrac{1}{2}y^2-\dfrac{1}{3}y^3)\right|_{-2}^1\\\\=\left(2-\dfrac{1}{2}-\dfrac{1}{3}\right)-\left(2(-2)-\dfrac{(-2)^2}{2}-\dfrac{(-2)^3}{3}\right)=\dfrac{7}{6}+4+2-\dfrac{8}{3}\\\\=\boxed{4.5}[/tex]
The area of the shaded region is 4.5 square units.
Which solution finds the value of x in the triangle below?
A right triangle is shown. The hypotenuse has a length of 8. Another side has a length of x. The angle between the hypotenuse and the other side is 60 degrees.
Answers
Answer:
4
Step-by-step explanation:
Since this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees.
We can see that this is a 30-60-90 degree triangle.
The rules of 30-60-90 degree triangles are that the side opposite the 90 degree angle, or the hypotenuse can be measured with the variable [tex]2a[/tex]. The side opposite the 30 degree angle can be measured with [tex]a[/tex], and the side opposite the 60 degree angle will be measured with [tex]a\sqrt{3}[/tex].
We can see that 8 represents [tex]2a[/tex] because it is the hypotenuse. Since the side marked [tex]x[/tex] is separated by the hypotenuse by an angle of 60 degrees, we note that side marked [tex]x[/tex] is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked [tex]a[/tex], and since we already know that 8 is equal to [tex]2a[/tex], we realize that the side marked x is equal to [tex]a[/tex], or 4.
The value of x in the triangle is 4.
What is the Pythagorean theorem ?
The square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
It is given this is a right triangle, and one of the angles measures 60 degrees, we can conclude that the last side measures 30 degrees. By the sum of all the three interior angles of a triangle is 180 degrees
The side opposite the 90 degree angle, or the hypotenuse can be measured with the variable '2a' . The side opposite the 30 degree angle can be measured with 'a' , and the side opposite the 60 degree angle will be measured with 'a√3'.
8 represents '2a' because it is the hypotenuse. Since the side marked x is separated by the hypotenuse by an angle of 60 degrees, we note that side marked x is opposite the angle measuring 30 degrees. We note that the side opposite 30 degrees is marked 'a', and since we already know that 8 is equal to '2a', we realize that the side marked x is equal to
'a' , or 4.
2a=8
a=4
x=a=4
so, the the value of x in the triangle is 4.
Learn more about the Pythagorean theorem here:
https://brainly.com/question/24154260
#SPJ5
If Joanne can paint a room in 3 hours and her sister Angela can paint the same room in 4 hours, how long (in h) would it take Joanne and Angela to paint the room working together? Round to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
If J can paint a room in 3 hours, in 1 hour she gets [tex]\frac{1}{3}[/tex] of the job done.
If A can paint a room in 4 hours, in 1 hour she gets [tex]\frac{1}{4}[/tex] of the job done. We need to find out how long it takes them if they paint together. The equation for this is:
[tex]\frac{1}{3}+\frac{1}{4}=\frac{1}{x}[/tex] where x is the number of hours it takes them to get the job done together. Multiply everything through by 12x to get
4x + 3x = 12 so
7x = 12 and
x = 1.7 hours to get the room painted together.
How many x-intercepts are in the quadratic equation y = 7x2 − 2x − 1
Answers
Answer:
There are 2 x intercepts
Suppose X has a normal distribution with mean 10.0 and standard deviation 5.0 what is the P(2.0
Answers
Answer:
what r u answers picks
Step-by-step explanation:
cant answer with out of t
Which of the following is a polynomial
A. 1-5x^2/x
b. 11x
c. 2x^2- square root x
d. 3x^2+6x
Answers
Answer:
B and D are polynomial
Step-by-step explanation:
An algebraic expression with non-zero coefficients and variables having non-negative integers as exponents is called a polynomial.
A)
If it is [tex]1 -\frac{5x^{2}}{x }=1-5x[/tex] , then it is a polynomial.
But if it is [tex]\frac{1-5x^{2}}{x}[/tex] then it is not a polynomial
Please help me i will give Brainly
Answers
Answer:
Step-by-step explanation:
[tex]\frac{3x + 5}{2x + 7}[/tex] = 5
do cross multiplication
3x + 5 = 5(2x + 7)
3x + 5 = 10x + 35
5 - 35 = 10x - 3x
-30 = 7x
-30/7 = x
20 A
since there are 7 angles given it means that the polygon is heptagon as heptagon has 7 sides.
sum of interior angle of heptagon = (n-2)*180
(7-2)*180
5*180
900
Now ,
110 + 90 + 150 + 102 + 110 + 170 + x = 900
732 + x = 900
x = 900 - 732
x = 168 degree
20 B
since 5 angles are given it means that the polygon is pentagon as pentagon has 5 sides.
sum of interior angles of a pentagon = (n-2)*180
(5-2)*180
3*180
540 degree
Now ,
110 + 95 + 120 + 114 + x = 540
465 + x = 540
x = 540 - 465
x = 75 degree
21
let one rational number be x
according to the question,
1/7 * x = 2
x/7 = 2
do cross multiplication
x = 14
Question 1a) Suppose you sample 100 times at random with replacement from a population in which 26% of the individuals are successes. Write a Python expression that evaluates to the chance that the sample has 20 successes.
Answers
Answer:
from math import comb
n = 100
x = 20
p = 0.26
q = 0.76
print(comb(n, x)*(p**x)*(q**(n-x)))
Step-by-step explanation:
Given that :
Number of trials, n = 100
P(success), p = 26% = 0.26
P(success)' = 1 - p = 1 - 0.26 = 0.74
Chance that sample has 20 successes = x
This problem meets the condition for a binomial probability distribution :
p(x = 20)
Recall :
P(x = x) = nCx * p^x * q^(n-x)
Using python :
comb is an built in function which calculate the combination of two arguments it takes ; and returns the combination value.
** mean raised to the power and
* is used for multiplication
The Python code as per the given question is provided below.
Program explanation:
The number of trials,
100Probability of success,
20% or 0.26Size of array generated,
2000The output that shows chances of 20 success,
SProgram code:
import numpy as np
S=sum(np.random.binomial(100,0.26,2000)==20)/2000
S
Learn more about Python expression here:
https://brainly.com/question/21645017
If u get a negative answer for exponents is it correct?
Answers
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Answer:
maybe
Step-by-step explanation:
It can be. It depends on the problem.
__
The rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
Clearly, for division problems if the denominator exponent is larger, the difference 'b-c' will be negative.
__
You recall that an exponent is the way we show repeated multiplication.
x·x·x = x³
In division, like factors cancel, so ...
[tex]\dfrac{x\cdot x\cdot x}{x\cdot x}=\dfrac{x^3}{x^2}=\dfrac{x}{1}\cdot\dfrac{x\cdot x}{x\cdot x}=x^{3-2}=x^1=x[/tex]
Now, consider the same problem "upside down."
[tex]\dfrac{x\cdot x}{x\cdot x\cdot x}=\dfrac{x^2}{x^3}=\dfrac{1}{x}\cdot\dfrac{x\cdot x}{x\cdot x}=x^{2-3}=x^{-1}=\dfrac{1}{x}[/tex]
A case of 6 cost 7.5 what it the price per item
Answers
Bindi is buying pet food with a coupon for 20% off. The original price of the bag of food is $39.
Which answer gives the best estimate for the price after the discount?
$48
$19
$34
$32
Answers
.20 x 39 = 7.8
39 - 7.8 = $31.2
A boat travels 8 miles north from point A to point B. Then it moves in the direction S 40°W and reaches point Finally, it turns S 40°E and returns to point A
The total distance covered by the boat is______miles
A. 14.95
B. 18.44
C. 20.04
D. 25.88
Answers
Answer:
B.18. 44 miles
Step-by-step explanation:
We are given that
Distance between A and B=8 miles
Angle B=Angle BCQ=40 degree (Alternate interior angles)
Angle ACB=180-Angle ACP-Angle BCQ
Angle ACB=180-40-40=100 degree
In triangle ABC
Angle A+ Angle B +Angle C=180 degree using sum of angles of triangle property
Substitute the values
[tex]\angle A+40+100=180[/tex]
[tex]\angle A+140=180[/tex]
[tex]\angle A=180-140[/tex]
[tex]\angle A=40[/tex] degree
Angle A=Angle B
When two angles are equal of a triangle then the triangle is isosceles triangle.
Therefore, triangle ABC is an isosceles triangle.
[tex]\implies BC=AC [/tex]
Now, Sine law
[tex]\frac{a}{sin A}=\frac{b}{sin B}=\frac{c}{sin C}[/tex]
Using the sine law
[tex]\frac{BC}{sin 40}=\frac{AB}{sin 100}[/tex]
[tex]\frac{BC}{sin 40}=\frac{8}{sin 100}[/tex]
[tex]BC=\frac{8\times sin40}{sin 100}[/tex]
BC=5.22
AC=BC=5.22 miles
Now, total distance covered by the boat=AB+BC+AC
Total distance covered by the boat=8+5.22+5.22=18.44 miles
Hence, option B is correct.
Simplify the radical expression below square root of 5/64
A square root 5/8
B 5/64
C square root 5/64
D 5/8
Answers
Answer:
a
Step-by-step explanation:
square root distribute to numerator and denominator so both get square rooted [tex]\sqrt{5}[/tex]/8
determine the 2nd and 3rd terms of a geometric sequence of which T1 =5 and T4=40
Answers
Answer:
Second term of this sequence: [tex]10[/tex].
Third term of this sequence: [tex]20[/tex].
Step-by-step explanation:
The first step is to find the common ratio of this sequence.
In a geometric sequence, multiply one term by the common ratio to find an expression for the next term. Let [tex]r[/tex] denote the common ratio of this sequence. For this sequence:
The first term of this sequence is [tex]5[/tex]. Multiply the first term by the common ratio to find an expression for the third term: [tex]5\, r[/tex].Multiply the second term by the common ratio to find an expression for the fourth term: [tex]5\, r^{2}[/tex].Similarly, an expression for the the fourth term would be: [tex]5\, r^{3}[/tex].However, the question states that the value of the fourth term is [tex]40[/tex]. In other words, [tex]5\, r^{3} = 40[/tex].
Solve this equation for [tex]r[/tex]:
[tex]r^{3} = 8[/tex].
[tex]r = 2[/tex].
(Since the power of [tex]r[/tex] is non-even in the equation, there's no need to consider the sign of [tex]r\![/tex] when taking the cube root.)
Substitute [tex]r = 2[/tex] into the expression for the second term and the third term to find their values:
Second term: [tex]5\, r = 10[/tex].Third term: [tex]5\, r^{2} = 20[/tex].what term can you add to
[tex] \frac{5}{6} x - 4[/tex]
to make it equivalent to
[tex] \frac{1}{2} x - 4[/tex]
Answers
9514 1404 393
Answer:
-1/3x
Step-by-step explanation:
We want to find the term 'a' such that ...
(5/6x -4) + a = (1/2x -4)
Add 4-1/2x to both sides.
(5/6 -1/2)x -4 +4 +a = 0
(5/6 -3/6)x + a = 0 . . . . . . express the fractions using a common denominator
1/3x + a = 0 . . . . . . . . . . simplify the difference
a = -1/3x . . . . . . . . . . .subtract 1/3x
The term you can add to make the desired equivalent is -1/3x.
if triangle TAN has vertices T(0, 2), A(-1,3), and N(-2,-4), which of the following coordinates is N' of the dilation from the origin using the scale factor 3?
Answers
Answer:
(-6,-12)
Step-by-step explanation:
A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.
[tex] - 2 \times 3 = - 6[/tex]
[tex] - 4 \times 3 = - 12[/tex]
So our new coordinates is
(-6,-12)
Answer:
(-6,-12)
Step-by-step explanation:
A dilation makes a figure gets bigger so just multiply 3 to point N to find N prime.
So our new coordinates is
(-6,-12)
Step-by-step explanation:
Of the at-home games, what proportion of games were wins? (Note: Some answers are rounded to two decimal places
Answers
Answer:
0.33
Step-by-step explanation:
See comment for complete question
Given
[tex]H = 60\%[/tex]
[tex]W=25\%[/tex]
[tex]HW = 20\%[/tex] --- at-home wins
Required
The proportion of at-home games that were wins
This proportion is represented as:
[tex]Pr = HW : H[/tex]
Substitute values for HW and H
[tex]Pr = 20\% : 60\%[/tex]
Divide by 20%
[tex]Pr = 1 : 3[/tex]
Express as fraction
[tex]Pr = 1 /3[/tex]
[tex]Pr = 0.33[/tex]
A bag has 180 balls. the ratio of red to blue to yellow balls is 8:5:7 how many red balls are there and how many blue balls are there
Answers
Answer:
72 red
45 blue
63 yellow
Step-by-step explanation:
8+5+7= 20
180÷20= 9
red = 9*8
blue = 9*5
yellow = 9*7
13, 5, 4, 9, 7, 14, 4 The deviations are _____.
A. "5, -3, -4, 0, 1, 6, 4"
B."5, -3, -4, 1, -1, 6, -4"
C."6, -3, -4, 1, 2, 6, -4"
D."-5, 3, 4, -1, 1, 6, 4 "
Answers
Answer:
B."5, -3, -4, 1, -1, 6, -4"
Step-by-step explanation:
We are given that
13,5,4,9,7,14,4
We have to find the deviation.
Mean=[tex]\frac{sum\;of\;data}{total\;number\;of\;data}[/tex]
Using the formula
[tex]Mean,\mu=\frac{13+5+4+9+7+14+4}{7}[/tex]
[tex]Mean,\mu=\frac{56}{7}=8[/tex]
Deviation=[tex]x_i-\mu[/tex]
[tex]x_i-\mu[/tex]
13 5
5 -3
4 - 4
9 1
7 -1
14 6
4 - 4
Hence, option B is correct.
A canning factory turns out 568 tins of jam on a certain day. How many tins will be produced in 297 working days?
Answers
I am Your Crush boy you have never seen a boy like me if you will see me you will fall in my love. come zom Id- 6622308635 pas- 6UC3yE
Answers
Answer:
I don't know the answer to ur question. LOL
Answer:
stop being desperate
nobody is gonna fall in love with some desperate weirdo
equivalent fraction of 9/11
Answers
Answer:
1822
Step-by-step explanation:
The fraction 1822 is equal to 911 when reduced to lowest terms.
18
22
is equivalent to 9
11
because 9 x 2 = 18 and 11 x 2 = 22
27
33
is equivalent to 9
11
because 9 x 3 = 27 and 11 x 3 = 33
36
44
is equivalent to 9
11
because 9 x 4 = 36 and 11 x 4 = 44
Answer:
18/22
Step-by-step explanation:
You can choose any number and if you multiply the top number (numerator) and the bottom number (denominator) by that same number, the fractions are equivalent.
If you choose the number 2, then multiply 9 x 2 = 18, and 11 x 2 = 22
Or multiply by 7. Then you would get an equivalent fraction of 63/77
Domain and function
Function or not a function
Answers
Answer:
Top left: not a function
Top right: not a function
Bottom left: function
Bottom right: not a function
Step-by-step explanation:
A function is a relationship where each x value has it's own y value ( note that domain = x values and range = y values)
For the one on the top left.
S and n have more than one y value.
Because s and n have more than one y value the relation is not a function
For the one of the top right.
There x value "c" has multiple y values therefore the relation is not a function
For the one on the bottom left
Each x value has it's own y value therefore it is a function ( note that the y values can repeat. It's only the x values that can't repeat. )
For the one on the bottom right
The x value "-5" has multiple y values therefore the relation is not a function
Find the area of the figure below, formed from a triangle and a parallelogram.
144 square millimeters
120 square millimeters
72 square millimeters
96 square millimeters
Answers
total area =A1+A2+A3
A1=1/2b*h
A1=1/2*8mm*6mm
A1=24mmsquare
A2=1/2b*h
A2=1/2*8mm*6mm
A2=24mmsquare
A3=b*h
A3=8mm*6mm
A3=48mmsquare
Atotal=24mmsquare+24mmsquare+48mmsquare
Atotal=96mmsquare
A researcher designs an experiment by manipulating the following variables: temperature (low or high), illumination level (low or high), and time of testing (day or night). For a repeated measures design, how many participants would the researcher require in order to have 10 participants per condition?
Answers
Answer:
10
Step-by-step explanation:
As it could be inferred from the name, repeated measure design may be explained as experimental measures involving multiple (more than one) measures of a variable on the same observation, subject or participants which are taken at either various times or periodic intervals, different levels, different conditions. Hence, a repeated measurement taken with the same sample but under different treatment conditions. Therefore, since the measurement will be performed on a the same subjects(paired) , then the number of subjects needed will be 10. As it is this same samples that will be used for the other levels or conditions.
please answer
Find the area of the polygon.
6 cm6 cm10 cm
Answers
Answer:
Area: 360 cm
Perimeter: 44 cm
Step-by-step explanation:
To calculate the area, you must multiply the length x width.
If you need help calculating the perimeter too, just add all your lengths and widths together twice.
Using the simple spinner below what is the probability of landing on either 2, 4, or 7?
Answers
Answer:
3/10
Step-by-step explanation:
Total possibilities = 10
favourable possibilities = 3
Answer:
A
Step-by-step explanation:
There is a 1 out of 10 chance that it will land on 2.
There is a 1 out of 10 chance that it will land on 4.
There is a 1 out of 10 chance that it will land on 7.
[tex]\frac{1}{10}\cdot3=\frac{3}{10}[/tex] so the anwser is A.
