Answer: g(x) = (1/3)*(-x)^2 + 3.
Step-by-step explanation:
Let's define all the transformations in a general way,
A vertical contraction/dilation of a scale factor a is written as:
g(x) = a*f(x)
where if a > 1, it is a dilation.
if 0 < a < 1, it is a contraction.
A reflection in the y-axis changes the value of the x-component and leaves the y-component invariable, then this transformation is written as:
g(x) = f(-x).
A translation of A units up (A positive) is written as:
g(x) = f(x) + A.
Then for this case we have:
A dilation with scale factor 1/3.
g(x) = (1/3)*f(x)
A reflection over the y-axis.
g(x) = (1/3)*f(-x)
A translation of 3 units up.
g(x) = (1/3)*f(-x) + 3
(in that order, remember that the order in which you applly the transformations matters)
Then g(x) = (1/3)*f(-x) + 3
and f(x) = x^2, so we can replace that in the equation for g(x)
g(x) = (1/3)*(-x)^2 + 3.
Transformation involves changing the position of a function.
The rule for g is: [tex]\mathbf{g(x) = \frac 13(x - 3)^2}[/tex]
The parent function is given as:
[tex]\mathbf{f(x) = x^2}[/tex]
The rule of vertical shrink by a factor of 1/3 is:
[tex]\mathbf{(x,y) \to (x,\frac 13y)}[/tex]
So, we have:
[tex]\mathbf{f'(x) = \frac 13x^2}[/tex]
The rule of reflection across the y-axis is:
[tex]\mathbf{(x,y) \to (-x,y)}[/tex]
So, we have:
[tex]\mathbf{f''(x) = \frac 13(-x)^2}[/tex]
[tex]\mathbf{f''(x) = \frac 13x^2}[/tex]
The rule of translation 3 units right is:
[tex]\mathbf{(x,y) \to (x - 3,y)}[/tex]
So, we have:
[tex]\mathbf{g(x) = \frac 13(x - 3)^2}[/tex]
Hence, the rule for g is: [tex]\mathbf{g(x) = \frac 13(x - 3)^2}[/tex]
Read more about transformations at:
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Q.3)
Find the mean absolute deviation of the fulfilled items on Sherrie's registry. $29, $58, $15, $129,
A. 19
B. 54.7
114
D. 32.67
47
Simplify
52
4 10
55
RE
5
421
56
127
153
How many inches combined 1/2 1/3 1/6 1/2 1/8 1:4
Answer:
Imperial Units
155/8 Inches (fraction)
15.625 Inches
1.302083 Feet
Metric Units
396.875 Millimeters
39.6875 Centimeters
0.396875 Meters
For a party, you buy 4 3/8 lbs of salt water taffy. If 150 people are attending, how much salt water taffy does each person get?
Answer:
Step-by-step explanation
150 divided by 4 3/8 = 34.2
Pls help thanks
.............
Answer:
Can you re-take the picture? It's too shaky then I can help you :)
If Luke can now mow 10 yards in 5 hours, how many lawns can he mow in 8 hours?
Answer:
Step-by-step explanation:
10 yards in 5 hours is 2 yards an hour
8*2=16 yards in 8 hours
Answer:
16 yards
Step-by-step explanation:
he would mow 2 yards an hour in 5 hours because 2 x 5 = 10 so if you use 2 it would be 16
$7.80(1 + 0.055)=
Your answer
Answer:
$8.229
Step-by-step explanation:
do whats in the paranthese first: 1 + 0.055 = 1.055
when a number is next to another number you multiply: 7.80(1.055) which is 7.80 x 1.055 = 8.229
A rope 160m in length is cut into 5 equal lengths. How long is each length of rope?
Answer:32m
Step-by-step explanation:
So you would have to divide 160 and 5 and it would equal 32
Jessica counted 26 heartbeats in 20 seconds. How many times will her heart beat in 1 minute? WILL GIVE BRAINLIEST!!!!!!!
Answer:
78
Step-by-step explanation:
multiply 26 by 3 because 60÷20=3
Answer: 78
Step-by-step explanation: 20x3=60 and there is 60 secs in a minute
and 26x3=78
So the answer is 78 heartbeats in a min
20 PTS! Is the answer h=2.7?
Answer:
Yes your right
Step-by-step explanation:
Five hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.
18–24 25–34 35–55 55 and over Total
Liked Crunchicles 39 66 10 86 201
Disliked Crunchicles 27 19 38 95 179
No Preference 24 37 35 24 120
Total 90 122 83 205 500
One consumer from the survey is selected at random. Use reduced fractions for your responses to each of the following questions.
What is the probability that the consumer is 18–24 years of age, given that they dislike Crunchicles?
Answer:
The probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles is 0.151.
Step-by-step explanation:
The age groups and preferences are given as follows:
18 - 24 25 - 34 35 - 55 55 and over Total
Liked Crunchicles 39 66 10 86 201
Disliked Crunchicles 27 19 38 95 179
No Preference 24 37 35 24 120
Total 90 122 83 205 500
One consumer from the survey is selected at random.
Compute the probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles as follows:
[tex]P(18-24|DC)=\frac{P(18-24\cap DC)}{P(DC)}[/tex]
[tex]=\frac{n(18-24\cap DC)}{n(DC)}\\\\=\frac{27}{179}\\\\=0.15084\\\\\approx 0.151[/tex]
Thus, the probability that the consumer is 18 - 24 years of age, given that they dislike Crunchicles is 0.151.
Determine whether the planes are parallel, perpendicular, or neither.8x + 8y + 8z = 1, 8x − 8y + 8z = 1 parallel perpendicular neither Correct: Your answer is correct.If neither, find the angle between them. (Round your answer to one decimal place. If the planes are parallel or perpendicular, enter PARALLEL or PERPENDICULAR, respectively.)
Answer:
The answer is "[tex]\bold{\theta= 70.53^{\circ}}[/tex]"
Step-by-step explanation:
The given value:
[tex]8x+8y+8z = 1\ and \ 8x-8y+8z = 1[/tex]
When the normal vectors are in the plane:
[tex]n_1 = < 8,8,8 > \ and \ n_2 = < 8, -8, 8>:[/tex]
Because the two variables really aren't proportional to each other and the wings are not parallel.
Let us just find that two vectors' dot product.
[tex]n_1 \cdot n_2 =<8,8,8> < 8,—8,8>\\\\ = 64-64+ 64 \\\\ = 64 \neq 0[/tex]
Therefore, we won't find that angle between both the given planes as parallel.
[tex]\cos \theta = \frac{n_1 \cdot n_2}{|n_1||n_2|}\\\\\cos \theta =\frac{64}{\sqrt{192} \sqrt{192}}\\\\\cos \theta =\frac{64}{8\sqrt{3} 8\sqrt{3}}\\\\\cos \theta = \frac{1}{3}\\\\ \theta = 70.53^{\circ}[/tex]
It is required to know the orientation of one plane relative to the other.
The angle between the planes is 70.5°.
PlanesThe given planes are
8x + 8y + 8z = 1
8x − 8y + 8z = 1
Parallel
[tex]\dfrac{8}{8}=\dfrac{8}{-8}=\dfrac{8}{8}\\\Rightarrow 1\neq -1\neq 1[/tex]
The planes are not parallel.
Perpendicular
[tex]8\times 8+8\times -8+8\times8=64\neq 0[/tex]
The planes are not perpendicular as dot product is not 0.
Finding angle
[tex]\theta=\cos^{-1}\dfrac{8\times 8+8\times -8+8\times8}{\sqrt{8^2+8^2+8^2}\sqrt{8^2+(-8)^2+8^2}}\\\Rightarrow \theta=\cos^{-1}\dfrac{1}{3}\\\Rightarrow \theta=70.53^{\circ}[/tex]
Learn more about planes:
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Find the value of the expression: 1/3√.81-1
Answer:
1/6
Step-by-step explanation:
1/3÷by.81_81_1 and =1/6according to the calculator :^)
A book costs $4.75 plus sales tax. After sales tax, the book is $5.13. What is the approximate sales tax rate?
Answer:
Step-by-step explanation:
5.13 - 4.75 = 0.38
4.75 / 0.38 = 12.5
There are 2 value's in a game. one of them is Pancake, the other is waffle. Pancakes are worth 1.5x a waffle. I have 10 waffles, how much Pancake value do I have?
Answer:
Approximately 6.67 pancakes.
Step-by-step explanation:
We can write an equation that relates the two items.
Let P represent Pancake and let W represent Waffle.
Pancakes are worth 1.5 times a Waffle. Therefore:
[tex]W=1.5P[/tex]
To find the Pancake value for 10 Waffles, we can substitute 10 for W and solve for P. Therefore:
[tex]\begin{aligned} W&=1.5P \\ 10&=1.5P \\ 6.\overline{6}&=P \end{aligned}[/tex]
Hence, 10 Waffles equates to approximately 6.67 pancakes.
Pls help with this problem
Answer:
A.
Step-by-step explanation:
set a proportion
75 x
--- = ----
1.5 2.25
2.25 times 75
168.75
divide it by 1.5
337.5
337 one half
What is the area of the figure?
Answer: 17.5 square yards
================================================
Work Shown:
base = 5 yards
height = 7 yards
The base and height are always perpendicular to one another
area of triangle = 0.5*(base)*(height)
area of triangle = 0.5*(5)*(7)
area of triangle = 17.5 square yards
The other values aren't used. They're likely thrown in as a distraction.
In the 2015 NFL season, the Philadelphia Eagles won 7 games, the New York Giants won 6 games, and the Houston Texans won 9 games. Select whether each statement is true or false.
Answer:
dey r all true
Step-by-step explanation:
A cab company charges $4 per cab ride, plus an additional $2 per mile driven. Write an equation that shows the relationship between the distance x and the cost y. Write your answer as an equation with y first, followed by an equals sign.
Answer:
y = 2x + 4
Step-by-step explanation:
So, the cab company charges a flat fee of $4 per cab ride, meaning 4 has no variables in the equation. Now, x is the distance, and the cab company charges $2 per mile driven. Per mile driven is a distance unit, so the x goes with the 2. From that, you can get that the cost is equal to 4 dollars plus 2x (2 times the distance in miles). This is y = 2x+4.
Find the general solution for the differential equation (dy)/(dx) + 3y = 18
Y=
Answer:
[tex]y=-e^{-3x-c_1}+6[/tex]
Step-by-step explanation:
[tex]\frac{dy}{dx}+3y=18\\\\\mathrm{Substitute\quad }\frac{dy}{dx}\mathrm{\:with\:}y'\:\\\\y'\:+3y=18\\\\Rewrite\\\\\frac{1}{6-y}y'\:=3\\\\Solve \::\frac{1}{6-y}y'\:=3\\\\-In(6-y)=3x+c_1\\\\Isolate\:y\\\\\\y=-e^{-3x-c_1}+6[/tex]
Which decimal number is equal to 3/18 ?
A. 0.167
B. 0.16¯
C. 0.16¯¯¯¯
D. 0.167¯¯¯¯¯
Answer:
Second option
Step-by-step explanation:
In order to find the answer to this question you have to divide the numerator into the denominator remembering that whole numbers have a secret decimal point to the right of itself.
[tex]\frac{3}{18}[/tex]
[tex]\frac{3}{18} =3\div18[/tex]
[tex]3\div18=0.16666666666[/tex]
= 0.16666666666 or 0.16 repeating
Hope this helps.
Please help me! The question is in the screenshot below.
PLEASE HELP ASAP WILL MARK BRAINLEIST
Answer:
x = 85°, y = 30°
Step-by-step explanation:
40° + x + 55° = 180°
x + 95° = 180°
x = 85°
85° + 65° + y = 180°
150° + y = 180°
y = 30°
Appreciate if sum one could give me help
Answer:
okay so
Step-by-step explanation:
A and B together means straight
C is curved or somthing like curved bc
its not like a circle i would so Horizontical or Vertical
If a couple has 3 children, what is the probability of all three children being girls? Justify.
Answer:
The probability of all three children being girls will Be: 1/8
Step-by-step explanation:
The couple has 3 children.
We have to determine the probability of all three children being girls.
As we know that for each child, the probability of being a girl is ' [tex]\frac{1}{2}[/tex] ' as is the probability of being a boy is ' [tex]\frac{1}{2}[/tex] '.
so for there to be all girls, the probability will be:
P ( all girls) = 1/2 × 1/2 × 1/2 = 1/8
Therefore, the probability of all three children being girls will Be: 1/8
need some help please
Answer:
Ariel ate the most .
Step-by-step explanation:
hope this helps you.
Answer:
dan
Step-by-step explanation:
find the common denomanator= 28
dan 6/7 to the common denomanator is 24/28
ariel 3/4 is 21/28
15 POINTS IF U ANSWER CORRECT
Max ran 5 miles on Thursday. One mile is equal to 5,280 feet. Which proportion can be used to determine how many feet, x, Max ran on Thursday?
Answer:
x/5 = 5280/1
Step-by-step explanation:
this is a proportion set up and then cross multiple. You will get your answer for x. Which is 26, 400 feet.
Work out the mean data for 9.7,4.5,1.9,8,6.6
Step-by-step explanation:
im not really sure about this but I think it's 6.1
The weights in a weighted mean can be relative frequencies
Answer:
WHAT IS THIS QUESTION ABOUT?
Step-by-step explanation:
Solve the inequality for x:
4x - 28 > 16
We have:
4x - 28 > 16
Add 28 to both sides:[tex]4x-28+28>16+28[/tex]
Simplify:4x > 44
Divide both sides by 4:[tex]\dfrac{4x}{4}>\dfrac{44}{4}[/tex]
Simplify:[tex]\boxed{x>11}[/tex]
[tex]\begin{bmatrix}\mathrm{Solution:}\:&\:x>11\:\\ \:\mathrm{Interval\:Notation:}&\:\left(11,\:\infty \:\right)\end{bmatrix}[/tex]