Answers
Answer:
1. The negative flips the parabola upside down so there is a maximum
2. The 1/2 means there is a vertical shrink
3. -3 means the graph moves to the RIGHT 3 units (X sign always changes)
4. +12 means the graph shifts up 12 units
Step-by-step explanation:
g(x)=x^2 is the parent function. This is the most basic parabola, and transformations are added to alter the function’s lateral and vertical location and width or length.
Now that we have the parent function, let’s address the transformations done to it. Remember, when identifying transformations, remover to follow PEMDAS; act like you are inputting a value in for x and following PEMDAS to observe how the function is altered.
• Lateral shift 3 units to the right
*Remember, horizontal translations have opposite signs, so even though x is subtracted by 3, it will actually move to the right towards the positive direction.
•Reflect over the x-axis
•Shrink by a factor of 1/2
*This will produce a wide parabola
• Vertical shift up 12 units
Related Questions
(b) Each unit on the grid repreent 25 feet. Find the perimeter of the factory. Show your work
Answers
If each unit on the grid represent 25 feet, then the perimeter of the factory is 1000 feet
Each unit on the grid represent 25 feet
The length of the side w1 = 3 × 25
= 75 feet
The length of the side N1 = 13 × 25
= 325 feet
The length of the side E1 = 7 × 25
= 175 feet
The length of the side S1 = 5 × 25
= 125 feet
The length of the side W1 = 4 × 25
= 100 feet
The length of the side S2 = 8 × 25
= 200 feet
The perimeter of the factory = 75 + 325 + 175 + 125 + 100 + 200
Add the terms together
= 1000 feet
Therefore, the perimeter of the factory is 1000 feet
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the radius of the wheel on a bike is 19 inches. if the wheel is revolving at 140 revolutions per minute, what is the linear speed of the bike, in miles per hour?
Answers
Therefore, the linear speed of the wheel on a bike is approximately 0.9π miles per hour.
What is meant by linear speed?The pace at which an object travels a specific distance in a predetermined amount of time is known as linear speed. By dividing the distance traveled by the time it takes to cover that distance, it may be used to determine how rapidly an item is travelling in a straight line. For instance, if a car moves 100 meters in 10 seconds, its linear speed is 10 meters per second. Linear speed is distinct from average speed, which takes into account any variations in velocity or direction throughout the duration of a voyage. Linear speed is also distinct from tangential speed, which is the pace at which an item travels along a circular route. Physics' fundamental idea of linear speed.
How to solve?
C=2πr,
C=2π(19)=38π.
linear speed of v=(38π/60)*5280=33.6π feet per second.
final speed of v=(33.6π/3600)*60=0.9π miles per hour.
Therefore, the linear speed of the bike is approximately 0.9π miles per hour.
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A local company interested in marketing its new brand of headphones wants to know the best way to go about seeing the effectiveness of its recent advertising campaign. The company approached your Math III class for ideas, since you are studying statistics and probability right now. Using your knowledge from this module, your task is to create a new posting to explain to the company its options for soliciting the opinions of the general public. Make sure you identify the pros and cons of each possibility, and make your recommendation as to how the company should approach its market research
Answers
The subject of a random event is covered in the mathematical field of probability.
Statistics is a field of mathematics that deals with gathering, analyzing, interpreting, and presenting vast amounts of numerical data.
Given,
Probability;-
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
Statistics;-
Statistics are numerical representations of sample characteristics. One population parameter is the average income in the United States. On the other hand, a sample statistic is the average income for a sample taken from the United States. Although both figures correspond to the mean income, only one is a statistic.
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A school staff meeting had 70 teachers in attendance, 40% of whom were first-year teachers. How many first-year teachers were in the meeting?
Answers
Answer: 28.
Step-by-step explanation:
If 40% of the teachers in attendance at the school staff meeting were first-year teachers, that means 28 of the teachers in the meeting were first-year teachers.
Answer:
28
Step-by-step explanation:
We first would need to figure out what %10 of 70 is.
%10 of 70 is equal to 7.
Now that we have this answer, we can multiply 7 by 4 to get the number of teachers.
7 × 4 = 28
28 first year teachers were in the meeting.
Mike's old graphing calculator had 96 pixels across the screen.
His new calculator has 144 pixels. Find the scale factor by
which he increased his screen size.
Answers
Thus, the scale factor by which he increased his screen size is 3:2
What is scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
Given, the pixel of Mike's old calculator = 96 pixel
His new calculator has pixels = 144 pixel
Scale by which it increased = New pixels/Old pixel
= 144p/96p
= 3:2
Thus, the scale factor by which he increased his screen size is 3:2
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1. You made a decision that you are doing to take care of the animals for the Claus family so they can go to a
warmer climate for their vacation this year. They will be on vacation the months of January and February. You will
be in North Pole, Alaska caring for their Reindeer, dogs, and hanging out with some of the Elves that take care of
things.
The weather for January 2022 and February 2022 are files found with the TGA.
Find the change in temperature (from the high and low) for the first day and last day of each month. How would
you have to pack for this trip?
2. What was the hardest part for you? Explain why.
Answers
Considering the climate of the North Pole, Alaska, we have seen that the change in the Temperature is 13°F and 14 °F respectively on the 1st and last day of the month respectively.
How to calculate the change in temperature?
From records, we know that Alaska usually has an average low temperature of 9°F and an average high temperature of 22°F in January.
However In February, Alaska's temperature usually ranges from an average low temperature of 12°F to an average high temperature of 26°F.
Thus, we can find the change in Temperature:
On 1st day of January , the Change in temperature is;
ΔT = Highest Temperature - lowest temperature
ΔT = 22°F - 9°F
ΔT = 13°F
On the 1st day of February, and then the last day of January, the change in temperature is;
ΔT= Highest Temperature - lowest temperature
ΔT = 26°F - 12°F
ΔT = 14 °F.
The hardest part will be to take take care of the animals since most of the animals only require a warm, secure, as well as protected area to reside in addition to sufficient food, drink, and exercise.
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An elevator in the Seattle Space Needle can rise 100 meters
in 50 seconds, Use a model to show the elevator's rate of travel in
meters per second and in seconds per meter. Describe each rate
in words.An elevator in the Seattle Space Needle can rise 100 meters
in 50 seconds. Use a model to show the elevator's rate of travel in
meters per second and in seconds per meter. Describe each rate
in words.
Answers
The elevator's rate of travel in meters per second is 2m/s and 1/2 s/m is in seconds per meter.
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
An elevator in the Seattle Space Needle can rise 100 meters in 50 seconds,
We need to find the elevator's rate of travel in meters per second and in seconds per meter
To find in meter per second we just need to divide 100 by 50 seconds
100/50=2 m/s
To find in seconds per meter we just need to divide 50 by 100
50/100=1/2s/m
Hence, the elevator's rate of travel in meters per second is 2m/s and 1/2 s/m is in seconds per meter.
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Calculate 30% of 100 km.
Answers
Answer:30,000 meters
Step-by-step explanation:
Answer:
30km
Step-by-step explanation:
to find 10% you divide 100km by 10= 10km
to find the full 30% simply divide 10% by 3 which will give you 30km.
The price (in dollars) of a stock tracked from noon to three on a given day is shown by the function f(t) = 0.1(t - 2)3 + 6 where t is in hours. Find the rate at which the stock price was changing at one o’ clock.
Answers
The rate of increase in stock price is $ 0.10 per hour.
Calculating the Rate of increase:To calculate the rate of increase we need to know the increased amount per given time period
In this problem, we will calculate the stock price per given hour from that will calculate the rate of increase in a given situation.
Here we have
The price (in dollars) of a stock tracked from noon to three on a given day is shown by the function f(t) = 0.1(t - 2)³ + 6 where t is in hours.
Take t = 1
=> f(1) = 0.1(1 - 2)³ + 6
= 0.1(-1)³ + 6
= 0.1(-1) + 6
= - 0.1 + 6
= 5.9
Take t = 2
=> f(2) = 0.1(2 - 2)³ + 6
= 0.1(0)³ + 6
= 6
Take t = 3
=> f(3) = 0.1(3 - 2)³ + 6
= 0.1(1)³ + 6
= 0.1 + 6
= 6.1
The rate rate of increase = f(3) - f(2) = 6.1 - 6 = 0.1 ≅ $ 0.10
Therefore,
The rate of increase in stock price is $ 0.10 per hour.
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The vertices of ▲ XYZ are X (6,-5), Y (3,0), Z (-4, 9). A XYZ is translated 3 units left and 8 units up. Then, it is translated 2 units right and 6 units down. What is the final translation rule that maps the pre-image to the final image?
Answers
Answer:
After the first translation, the coordinates of the vertices of the triangle will be X (3,-13), Y (0,-8), Z (-7, 1). After the second translation, the coordinates of the vertices will be X (5,-7), Y (2,-2), Z (-5, 7).
The final translation rule that maps the pre-image to the final image is a translation of 2 units right and 6 units up. This can be written as a translation rule of the form (x, y) -> (x + 2, y + 6).
Step-by-step explanation:
After the first translation the coordinates are:
(x, y) → (x - 3, y + 8)After the second translation the coordinates are:
(x - 3, y + 8) → (x - 3 + 2, y + 8 - 6) = (x - 1, y + 2)The final translation rule is:
(x, y ) → (x - 1, y + 2)or
One unit left and 2 units up.The cubic polynomial x ^3 - 3x ^ 2 + ax + b is factor (x - 2)
(a)Find a linear relationship between a and b (b )Find the remainder when the polynomial is divided by
(a)(x-1)
(b)x-3)
Answers
Answer: Look at step-by-step explanation
Step-by-step explanation:
1) When a polynomial f(x) has a factor x - y, then f(y) = 0, hence
[tex]2^{3}[/tex] - 3 × [tex]2^{2}[/tex] + 2a + b = 0
8 - 12 + 2a + b = 0
2a + b = 4
2) When a polynomial f(x) is divided by x - y, then f(y) = the remainder, hence
(A) When divided by x - 1
[tex]1^{3}[/tex] - 3 × [tex]1^{2}[/tex] + a + b = 1 - 3 + a + b = a + b - 2
(B) When divided by x - 3
[tex]3^{3}[/tex] - 3 × [tex]3^{2}[/tex] + 3a + b = 27 - 27 + 3a + b = 3a + b
what is 42 divided by 51,860
SHOW STEPS!!!!!
Answers
The given expression can be simplified using the arithmetic operation as 0.00080987.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The given problem can be written in terms of expression as,
42 ÷ 51860
It can be solved as follows,
The number of digits in 51860 is 5 and in 42 is 2.
In order to divide the two numbers, the dividend should be greater than the divisor.
Therefore, multiply both 42 and 51860 by 10000 to obtain,
(42 × 10000) ÷ (51860 × 10000)
⇒ 420000 ÷ (51860 × 10000)
Now, first divide 420000 by 51860 to get,
420000 ÷ 51860 = 8.0987
Then, divide 8.0987 by 10000 to get,
8.0987 ÷ 10000 = 0.00080987
Hence, the required result of the given expression is 0.00080987.
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The profit a company made decreased 20% to 66 million from one year to the next. What was the profit the year before
Answers
82.5 million was the profit the year before the profit decreased 20% to 66 million from one year to the next
What does profit means ?
Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity exceeds the costs, costs, and taxes associated with maintaining that activity.
Any profits generated are returned to the company's owners, who can decide whether to keep the money for themselves, pay dividends to shareholders, or reinvest it in the company.
Entire revenue less total costs equals profit.
Companies report gross profit, operational profit, and net profit for accounting purposes (the "bottom line").
Investors are drawn to profitable businesses because these businesses either distribute their earnings as dividends to shareholders or invest them back into the business, which raises stock value.
According to the question Company lost 20% from its profit and it reached to 66 million that means
let X be the total profit of the year
X - loss percent = 66 millions
X - X (20/100) = 66 million
X-0.2X = 66 million
0.8X = 66 million
X= 66/0.8 million
X = 82.5 million
So, 82.5 million was the profit the year before
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how long is the hypotenuse?
Answers
boi
Use the model to answer the question.
a 10 by 10 grid is shown. 5 columns and 1 row are shaded.
Choose the numbers to find the product shown by the model.
0.5 × ____ = _____
Answers
The complete model will be;
⇒ 0.5 × 0.1 = 0.05
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A 10 by 10 grid is shown.
And, 5 columns and 1 row are shaded.
Now,
Since, 5 columns and 1 row are shaded.
Hence, The complete model will be;
⇒ 0.5 × 0.1 = 0.05
Thus, The complete model will be;
⇒ 0.5 × 0.1 = 0.05
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pleaseeeeeeeeeeeeeee help whats da volume
Answers
Answer:
if you want the volume of the outer cube with the other cube in it, it would be 48. if you want it without the cube its 120. the inside cube is 72.
Step-by-step explanation:
Answer:
48 mm³
Step-by-step explanation:
Outer prism:
5 mm by 4 mm by 6 mm
V = LWH = 5 × 4 × 6 mm³ = 120 mm³
Inner prism:
4 mm by 3 mm by 6 mm
V = LWH = 4 × 3 × 6 mm³ = 72 mm³
Difference:
120 mm³ - 72 mm³ = 48 mm³
Solve for x: 1 < x + 3 < 4
© 4>x>7
O 4
® -2>x>1
O -2
Answers
Answer: -2 < x < 1
Step-by-step explanation:
Jenna gets an iTunes gift card for her birthday and decides to buy some games and some music the music she likes costs $1.99 per song and the games costs $3.99 each if she buys a total of 12 items and spends $18.88 how many of each item did she buy
Answers
The number of songs and games Jenna bought is 9.5 and 2.5 respectively.
How many of each item did she buy?let
Number of songs bought = xNumber of games bought = yx + y = 12
1.99x + 3.99y = 18.88
From (1)
x = 12 - y
Substitute into (2)
1.99x + 3.99y = 18.88
1.99(12 - y) + 3.99y = 18.88
23.88 - 1.99y + 3.99y = 18.88
- 1.99y + 3.99y = 18.88 - 23.88
2y = -5
y = -5/2
y = 2.5
Substitute into (1)
x + y = 12
x + 2.5 = 12
x = 12 - 2.5
x = 9.5
Therefore, Jenna bought 9.5 songs and 2.5 games.
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Tyler made a scale drawing of an apartment. The scale of the drawing was 1 millimeter : 2 meters. The living room is 6 meters long in real life. How long is the living room in the drawing?
Answers
In the drawing, the length of the living room is 3 millimeters.
What is a scale factor?The scale factor defines a variable in a ratio of two different measurements.
Sometimes drawings of large models are represented in a scale factor of a smaller unit.
Given, Tyler made a scale drawing of an apartment. The scale of the drawing was 1 millimeter : 2 meters.
The living room is 6 meters long in real life and assuming in the drawing it is x millimeters.
∴ 1 : 2 : : x : 6.
1/2 = x/6.
x = 6/2.
x = 3.
So, In drawing it is 3 millimeters.
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On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.
(On a recent survey, students were asked if they like to fly and if they can drive. The partial results are given in the relative frequency table.)
Answers
A frequency distribution table is a tool for structuring the provided data in a way that makes sense and facilitates comprehension.
What is a frequency distribution table in math ?In our daily lives, we come across a lot of data presented as numerical values, tables, graphs, etc. This data may include statistics on the number of goals scored in football games, local temperatures, the most popular goods among pupils in a class, and so on. Data are the gathered pieces of knowledge. The frequency of an occurrence or a value is the number of times it happens. A frequency table is a collection of objects with the frequency of each item shown in the table.A frequency distribution table is a tool for structuring the provided data in a way that makes sense and facilitates comprehension.The partial results :
Likes to fly cannot drive = 0.35 - 0.12 = 0.23Row total and likes to fly = 1 - 0.4 = 0.6Does not like to fly and can drive = 0.65 - 0.37 = 0.28Does not like to fly and cannot drive = 0.40 - 0.28 = 0.12Learn more about A frequency distribution table refer to :
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Colin earned $66.00 raking leaves. If he worked 2.5 today and 3 hours yesterday, how much did he earn per hour?
Answers
66/5.5=12
$12.00/hour
solve for g:
3/4(4g+5)=6
Answers
Answer:
G = -32
Step-by-step explanation:
Please help me with this question
Answers
Answer:
D
Step-by-step explanation:
it is a regular pentagon.
so, all side lengths are equal, and also all cross connections between corners are equal.
that makes TR parallel to PQ.
and that makes SPQ an isoceles triangle (both legs are equally long). and the smaller triangle S to x to the angle to the right of x is similar to SPQ, which means they have the same angles.
so, the triangle interior angle at P = the triangle interior angle Q = y.
and they must be the same as the bottom 2 interior angles of the small triangle.
x and the angle right to x are equal too, as they are the triangle exterior (supplementary) angles to the bottom 2 interior angles of the small triangle.
we know that the sum of all angles of the internal trapezoid (PQ to x and its right neighbor) is 360.
and based on the EqualLogic found above these angles are
2×x + 2×y = 360°
x + y = 180°
Reflect GLQ across the x-axis. (PLEASE HELP!)
Answers
Answer:
Q-(1,1) L-(1,-2) G-(4,-4)
Step-by-step explanation:
becuase
PLEASE HELP!! WILL GIVE BRAINLIEST AND 25 POINTS!!
Solve for x
A. 10
B. 100
C. 64
Answers
Answer: 4
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]3^2 + x^2 = 5^2\\\\9+x^2=25\\\\x^2=16\\\\x=4[/tex]
A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad. The probability of drawing a bag with bad potatoes is less than 1. The probability of drawing a bag with good potatoes is greater than 0. What is the probability of drawing a bag with bad potatoes? what is the expected probability of the complement of the event?.
Answers
Probability of drawing bad potatoes = 0.1
The probability of drawing a bag with bad potatoes is less than 1.
The probability of drawing a bag with good potatoes is greater than 0
The probability of drawing a bag with bad potatoes as a decimal .
The probability is 20% which means 20 by hundred , which means there is a chance of being its ok.
probability of bad potatoes = 2/20
=1/10
=0.1
To find the probability of the outcomes = Number of favourable outcome / Number of total outcome.
Probability of event 1 and 2
probability of event 1 =Number of favourable outcome / Number of total outcome.
probability of event 2 = 1 -( probability of event 1)
probability of good potatoes = 1- ( probability of bad potatoes)
Probability of the given event( probability of the bad potatoes = 1-(0.1)
Thus,
Probability of the bad potatoes in the 2 of the bags are=0.9
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Gary is collecting stamps and wants to collect the same number of stamps each week. He currently has 520 stamps. He only has 6 more weeks to collect the remaining stamps that he needs for his collection. He needs a total of at least 1000 stamps before he is done. Graph the answer to the inequality.
Answers
Answer:
Step-by-step explanation:
1000-520=480
480/6=80
x+6+520=1000 (-6)
x+514=1000
x=486
Mary has 96 fliers to post around town. last week she posted 1/6 of them. this week she posted 1/4 of the remaining fliers. How many fliers has she still not posted?
Answers
Answer:
Start with 60 fliers
post 1/4 of fliers so 60*.25=15
60-15=45 left
post 1/5 of remaining so 45*.20=9
45-9=36 left
Step-by-step explanation:
Last week: (had 60) (used 1/4)= (60)(1/4)= 15. So, you used 15.
You have 60-15=45 left. This is how many you have to start the week.
This week: (had 45) (used 1/5)= (45)(1/5)= 45/5=9. So, you used 9.
This means that you have 45-9= 36 left.
Mary Still did not post 60 fliers.
Total fliers Mary was having = 96
Fliers she posted last week = 1/6 = 0.16
Fliers left with Mary after posting 1/6 part last week
= 96 x 0.16
= 16
Fliers left with Mary after the posting of 1/6 of them
= 96 - 16
= 80
Now the new remaining number of fliers with Mary = 80
Fliers she posted this week = 1/4 = 0.25
Fliers left with Mary after posting 1/4 part this week
= 80 x 0.25
= 20
Fliers left with Mary after the posting of 1/4 of them this week
= 80 - 20
= 60
Therefore, the fliers that Mary still did not post = 60
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A rideshare company charges a $3 ride fee in
addition to its meter, which is $1.50 for every mile.
Write an equation for this situation in point-slope
form for a customer who went 6 miles and paid
$12 total.
A. y 6= 3(x-12)
B. y + 6 = 1.50(x - 12)
C. y - 1.50 = 3(x-6)
D. y - 12 = 1.50(x-6)
Answers
Option D, The equation that satisfy the situation is y - 12 = 1.50(x-6).
What is Coordinate Geometry?The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.
A straight line is represented using its slope and a point on the line using point slope form. This indicates that the point slope form is used to get the equation of a line whose slope is "m" and which passes through the points (x 1, y 1). The equation of a straight line can be expressed in several ways. Point slope shape is one of them. Y - Y 1 = m(x - X 1) is the equation for the point slope form, where (x1, y1) is a randomly chosen point on the line and m is the slope of the line.
The slope of the line is 1.5
The Point through which the equation will satisfy is (6,12)
Therefore the equation of the line in Point-Slope form is
y - y1 = m ( x- x1)
⇒ y - 12 = 1.50 ( x - 6)
Option D, The equation that satisfy the situation is y - 12 = 1.50(x-6).
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Theater tickets cost $2.50 for children and $3.50 for adults. The price for 9 tickets was $29.50. How many adult tickets were purchased?
Answers
Answer:
8 is the answer