Answers
Answer:
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
Step-by-step explanation:
The graph of function f(x) is the parent function.
(Parent functions are the simplest form of a given family of functions).
The graph of g(x) is related to the graph of f(x) by a series of transformations. To determine the series of transformations, work out the steps of how to go from f(x) to g(x).
Transformations
For a > 0
[tex]\begin{aligned} y =a\:f(x) \implies & f(x) \: \textsf{stretched/compressed vertically by a factor of }\:a \\& \textsf{If }a > 1 \textsf{ it is stretched by a factor of}\: a\\& \textsf{If }0 < a < 1 \textsf{ it is compressed by a factor of}\: a \end{aligned}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
Parent function:
[tex]f(x)=x^3[/tex]
Step 1
Multiply the parent function by 6:
[tex]\implies 6f(x)=6x^3[/tex]
Therefore, this is a vertical stretch by a factor of 6.
Step 2
Now make the function negative:
[tex]\implies -6f(x)=-6x^3[/tex]
Therefore, this is a reflection in the x-axis.
Step 3
Finally, add 2 to the function:
[tex]\implies -6f(x)+2=-6x^3+2[/tex]
Therefore, the function has been translated 2 units up.
Conclusion
Function g(x) is function f(x) vertically stretched by a factor of 6, reflected in the x-axis, and translated 2 units up.
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Related Questions
Which is the correct classification of StartRoot 18 EndRoot?
irrational number, non-repeating decimal
irrational number, terminating decimal
rational number, terminating decimal
rational number, non-repeating decimal
Answers
The correct classification for √18 is an irrational number, non-repeating decimal.
The correct classification of √18 is an irrational number.An irrational number is a number that cannot be expressed as a fraction (ratio) of two integers and cannot be written as a terminating or repeating decimal.
√18 cannot be simplified to a fraction, and when expressed as a decimal, it is a non-repeating decimal that continues indefinitely without a pattern.
Therefore, the correct classification for √18 is an irrational number, non-repeating decimal.The number √18 is the square root of 18. An irrational number is a number that cannot be expressed as a fraction of two integers (a/b) where a and b are integers and b is not equal to zero.
When we calculate the square root of 18, we find that it is approximately 4.24264. However, this decimal representation continues indefinitely without repeating or terminating. It does not settle into a pattern of digits that repeats infinitely like a rational number or terminate after a finite number of decimal places.
Since √18 cannot be expressed as a fraction and its decimal representation is non-repeating and non-terminating, it falls under the category of an irrational number.
Therefore, the correct classification of √18 is an irrational number, specifically a non-repeating decimal.
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A woman when working with her takes 2 hours to complete the housework, and takes 3 hours when working alone How long would it take the daughter to complete the housework if working alone?
A) 6 hours
B) 2 hours
C) 4 hours
D) 9 hours
E) 0 hours
Answers
Answer:
6 hours for daughter alone Answer A
Step-by-step explanation:
Rate of mom to clean one house = 1 house /3 hrs = 1/3
rate of daughter = 1/x
Now find the time to clean one house with their combined rates for one house
1 / (1/3 + 1/x ) = 2 hrs
1/3 + 1/x = 1/ 2
x + 3 = 3/2 x
3 = 1/2 x
x = 6 hrs daughter alone
please do draw the answer
please needed fast. (^^)
Answers
Answer:
hope it helps.good day
in case you don't understand anywhere feel free to ask
Evaluate 21 + (-3c) when c=-2
Answers
27
Solution:
Substitute c with -221 + ( -3 ) ( -2 )
Simplify21 + 6
27
Therefore, The answer is 27.
Which table has greater constant of proportionality?
Answers
The table with greater proportionality is table 3.
What is constant proportionality?The constant of proportionality is the ratio between two directly proportional quantities.
As, the constant proportionality is
k= y/x
For table 1,
k = 1/1 = 2/2 =1
For table 2,
k = 6/1= 12/2 = 2
For table 3,
k = 5/1 = 10/2 = 5
For table 4,
k = 4/1 = 8/2 = 4
Hence, table 3 is with greater proportionality.
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Attached is a document that I need help on, please help!!!
Answers
The ratio of the median weekly earnings is 3 : 5
The ratio of the median weekly earningsFrom the graph, we have the median weekly earnings to be:
High school diploma = $750Bachelor's degree = $1250So, the ratio is:
Ratio = $750 : $1250
Simplify
Ratio = 3 : 5
Hence, the ratio of the median weekly earnings is 3 : 5
The ratio of the area of the red rectangle to the blue rectangle in graph A?
In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
Both rectangles have a width of 1 unit.
So, we have:
Ratio = 3 * 1: 5 * 1
Simplify
Ratio = 3 : 5
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5
The ratio of the area of the red rectangle to the blue rectangle in graph B?In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
The red rectangle has a width of 3 units, while the blue has 5 units as its width
So, we have:
Ratio = 3 * 3 : 5 * 5
Simplify
Ratio = 9 : 25
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25
The ratio of the volume of the red cube to the blue cube in graph C?
In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
The red rectangle has a width of 3 units, while the blue has 5 units as its width.
Since the base are squares, we have:
Ratio = 3 * 3 * 3 : 5 * 5 * 5
Simplify
Ratio = 27 : 125
Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125
The most misleading graph
The most misleading graph is graph B.
This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale
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A certain aircraft can fly 1330 miles with the wind in 5 hours and travel
the same distance against the wind in 7 hours. What is the speed of the
wind?
Answers
distance = 1330 ; time = 5 hrs ; rate = d/t = 1330/5 = 266 mph
---------------------------
Upwind DATA:
distance = 1330 ; time = 7 hrs ; rate = d/t = 1330/7 = 190 mph
---------------------------
Equations:
p + w = 266
P - w = 190
-------------
Subtract 2nd equ. from 1st to get:
2w = 76
w = 38 mph (speed of the wind)
Answer 38mph
Help please I need it now!
Answers
Answer: [tex]\sum^{7}_{n=1} (-2+9n)[/tex]
Step-by-step explanation:
This is an arithmetic series with first term 7 and common difference 9, so the general formula for the nth term of the sequence is [tex]7+9(n-1)=7+9n-9=-2+9n[/tex].
The sequence has 7 terms, so the sigma notation is:
[tex]\sum^{7}_{n=1} (-2+9n)[/tex]
What is the base area of Box 3? x2 + x
edge
Answers
The expression of base area of box will be 4x + x²
The area of a a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. Basically, the area formula is the product of the rectangle's length and width.
Given,
Length = 4+x
width = x
height = x²+1
We have to find the expression of base area of box
Given the length, width, and height
The formula for area of rectangle is as follow:
Area of rectangle = length x width
Area of rectangle = (4+x) x (x)
Area of rectangle = 4x + x²
Hence the expression of base area of box will be 4x + x²
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Select all the correct answers. Function g is a transformation of the parent exponential function. Which statements are true about function g? A Linear graph function where red line g intercepts y-axis at (0, 4) and passes through (minus 10, 3) and (3, 10) Function g is positive over the interval . The domain of function g is . Function g has a y-intercept of . Function g decreasing over the interval . Function g is 4 units above function f. The range of function g is .
Answers
The correct statements are:
Function g has a y-intercept of (0,4)
The range of the function g is (3, ∞).
The function g is positive over the interval (-∞ , ∞ ).
The parent function i.e. exponential function is defined by:
y=f(x)=aˣ
From the graph given below,
1. The graph of the function g is 3 units above the graph of the parent exponential function. as the parent exponential function aˣ cuts the y-axis at (0,1) and the child transformed function cut at (0,4) for which g is 4-1=3 units above the parent function
2. The domain of the function is set of all the inputs for which function is defined. From the graph of function g, it is clear tha the domain of the function is (-∞ , ∞ ) as the domain of the parent exponential function is also (-∞ , ∞ ).
3. The y-intercept is the point at which function cut the y-axis. Graph of function g cut the y-axis at (0, 4). Therefore, Function g has the y-intercept at (0,4).
4. From the graph it is clear that Function g increases over the interval (-∞, 0) .
5. The range of the function is the output values of the function. From the graph, it is observed that the range of function g is (3, ∞). as its minimum value is 3 then the maximum value is ∞.
6. As, the graph of function g is drawn above the x-axis. Therefore, Function g lies completely on +ve y-axis, so function g is positive over the interval (-∞ , ∞ ).
Therefore The correct statements are:
Function g has a y-intercept of (0,4)
The range of the function g is (3, ∞).
The function g is positive over the interval (-∞ , ∞ ).
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Covert 3/7into a percent
Answers
Answer:
42.86%
Step-by-step explanation:
Our percent fraction is 42.857142857143/100, which means that 37 as a percentage is 42.86%
Here we are going to show you step by step how to convert the fraction 3/7 to a percentage.
In the fraction 3/7, 3 is the numerator and 7 is the denominator.
First, we are going to divide the numerator by the denominator. Therefore, we are going to divide 3 by 7.
3 ÷ 7 = 0.428571A percentage shows a number as a proportion of one hundred.
Now we are going to multiply 0.72 by 100 to get the percentage.
0.428571 x 100 = 42.86Therefore, the answer to 3/7 percent is
42.86%Note: If necessary, we round to the nearest hundred.
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
în doi saci sunt 182 kg de grâu dacă din primul sac ar lua 36 kg de grâu și sar pune în al doilea sac atunci ambii saci ar conține cantități egale de grâu ce cantitate de grâu este în fiecare sac
Answers
Answer:
a = 127 kg
b = 55 kg
Step-by-step explanation:
a + b = 182
a - 36 = b + 36
+ 36 + 36
a = b + 72
(a) + b = 182
(b + 72) + b = 182
2b + 72 = 182
-72 -72
2b = 110
÷2 ÷2
b = 55
a + (b) = 182
a + (55) = 182
- 55 - 55
a = 127
{127 - 36 = 91}
{55 + 36 = 91}
{91 + 91 = 182}
Given the function f(x) = -0.5|2x + 2 + 1, for what
values of x is f(x) = 6?
x = 6, x = -5
x = 5, x = -5
x= 7, x=-6
Ono solution
DONE
Answers
Answer:
Step-by-step explanation:
56565656565656565656565
Similar Polygons
Not quite sure how to get this question.
Answers
Answer:
No
Step-by-step explanation:
We know that the 3-4-5 and 9-12-15 right triangles are similar. If you add 6 units to the length of each side of both of these triangles, you obtain 9-10-11 and 15-18-21 triangles, which are not similar since 9/15 is not equal to 10/18.
Transform each graph as specified below.
Answers
Answer:
Transcribed image text: Transform each graph as specified below. (a) The graph of y=f(x) is shown. Graph y=2f(x). (b) the graph of y=g(x) is shown. Graph y=g(2x).
Please answer this and I will give u a cookie ;)
Answers
Answer:
m∠BAC = 40°
Step-by-step explanation:
Note that line BD passes through A, so ∠BAC and ∠CAD form a linear pair. By the Linear Pair Postulate, ∠BAC and ∠CAD are supplementary angles, and by definition their measures add to 180°:
m∠BAC + m∠CAD = 180°
Since the diagram gives us that m∠CAD = 140°, we can substitute and solve:
Starting supplementary angles definition equation ...
m∠BAC + m∠CAD = 180°
Substituting the known value of m∠CAD ...
m∠BAC + (140°) = 180°
Subtracting 140° from both sides of the equation...
(m∠BAC + 140°) - 140° = (180°) - 140°
Simplifying/evaluating...
m∠BAC = 40°
Express 10/4 as a mixed fraction
Answers
Hey there!
10/4
≈ 10 ÷ 2 / 4 ÷ 2
≈ 5/2
≈ 2 1/2
Therefore, your answer should be:
2 1/2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
what fraction is 2500 of 3600
Answers
Answer:
25/36
Step-by-step explanation:
put 2500 over 3600 and remove the 0's to simplify it
Suppose you are designing a cardboard box that must have a volume of 27 cubic feet. The cost of the cardboard is $0.21 per square foot.
The material in each box will cost $____
Answers
find 7x +y when x=7 and y=1
Answers
Answer:
7x+y
7(7)+1
49+1
50
Step-by-step explanation:
please mark me as brainlest
Answer:
7x + y
x=7 y=1
7(7) + 1
49 + 1
= 50
What would the slope of a line be if it were parallel to the line: y = 1 / 3x - 5 ?
Answers
Answer:
Parallel lines have the same slope, so the slope would be 1/3. It would need a different y intercept though or it would be the same line.
A fingernail grows about 0.1 mm, day. How much does a fingermail grow in 45 days ? 90 days?
Answers
Answer:
- In 45 days = 4,5mm ; In 90 days = 9mm
Step-by-step explanation:
in 45 days = 0,1 * 45 = 4,5 mm ; in 90 days = 0,1 * 90 = 9mm
Help I’m stuck on this question! Please help.
Answers
Answer: 20
Step-by-step explanation:
A and B have 57+79-42=94 distinct elements in total.
This means that 114-94=20 elements are in neither A nor B.
Which of the following points lies on the graph of the function y = 2*3^x? a. (1, 0) c. (3, 6) b. (2, 9) d. (0, 2) Please select the best answer from the choices provided A B C D
Answers
The point which lies on the graph of the given function is; Choice D; (0, 2).
Which of the following points lies on the graph of the function y = 2*3^x?The point which lies on the graph of the given function; y = 2*3^x is it's y-intercept. The y-intercept which corresponds to the value of y when variable X is set to zero.
Hence, y = 2*3^0;
y = 2 ×1 = 2.
Hence, the point is; (0,2).
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The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?
Answers
The number of cars that have passed through the intersection after 7 wrecks is 1/5 cars
Direct variationNumber of wrecks = wNumber of cars = cw = k × c
31 = k × 1,085
31 = 1,085k
k = 1085/31
k = 35
If w = 7
w = k × c
7 = 35 × c
7 = 35c
c = 7/35
c = 1/5 car
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Two dice are thrown. Determine the probability of obtaining a score of at least 4.
Answers
11/36 would be the probability of getting 4 , when two dice are thrown simultaneously.
As there are 6 faces of die,
So Probability of Not getting four in one dice = [tex]5/6[/tex]
As both events are mutually exclusive, the probability of not getting four in two dice = [tex](5/6) * (5/6) = 25/36[/tex]
So probability of getting at least one four is = [tex]1-(25/36) = 11/36[/tex]
So probability = [tex]11/36[/tex]
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use interval notation to express the following: the set of all numbers greater than or equal to 5 and less than or equal to 7
Answers
[5, +∞) ∪ (-∞,7] is the notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7.
We need to use interval notation to express the set of all numbers greater than or equal to 5 and less than or equal to 7.
What is a set?A set is a mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Let x belong to the set of real numbers (R)
Now, x≥5 and x≤7.
So, x≥5⇒[5, +∞) and x≤7⇒(-∞,7]
Therefore, the notation will be [5, +∞) ∪ (-∞,7].
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A. 0 m/s
B. -0.17 m/s
C. 12 m/s
D. 0.17 m/s
Answers
Answer:
0 m/s
Step-by-step explanation:
-2y = x + 6 Graph A On a coordinate plane, a line goes through (negative 6, 0) and (1, negative 3). Graph B On a coordinate plane, a line goes through (0, 3) and (2, 4). Graph C On a coordinate plane, a line goes through (0, 3) and (2, 2). Graph D On a coordinate plane, a line goes through (0, negative 3) and (6, 0). a. Graph A c. Graph C b. Graph B d. Graph D Please select the best answer from the choices provided
Answers
On a coordinate plane, a line goes through (negative 3, 0) and (0, negative 6).
The graph for the first equation of a system is shown in orange. The second equation is: 3y+30=6x
What is the solution to the system?
A. (2, –10)
B. (1, –8)
C. (–2, –14)
D. (2, –6)
Answer: 4.9/5
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Answer:
B. (1,-8)
Step-by-step explanation:
Slope of the first one:
(-6-0)/(0--3) = -6/3 = -2
y = -2x - 6
3y + 30 = 6x
y + 10 = 2x
-2x - 6 + 10 = 2x
4 = 4x
x = 1
y = -2(1) - 6
y = -8
A movie theater offers three types of tickets: child, student, and adult. Ticket sales for two movies are shown in the table.
Ticket Type
Child Student Adult Total
Movie Title The Ransom 12 38 70 100
Space Force 34 42 56 132
Total 46 80 126 232
What proportion of tickets sold were adult tickets?
0.4310
0.5431
0.5556
0.7000
Answers
Answer:
(b) 0.5431
Step-by-step explanation:
The proportion of adult tickets sold is the ratio of the total number of adult tickets sold to the total number of tickets sold. Those totals are found on the bottom line of the table.
__
proportion = (adult tickets)/(total tickets) = 126/232 ≈ 0.5431
Approximately 0.5431 of the tickets sold were adult tickets.
Answer:
B) 0.5431
Step-by-step explanation:
edge 2023