What transformations change the graph F(x) to the graph g(x)
f(x) = 3x^2
G(x) = 9x^2-4
A. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated DOWN 4 units
B. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated UP 4 units
C. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/3 and translated up 4 units
Final answer:
The transformation from f(x) = 3x^2 to g(x) = 9x^2 - 4 includes a vertical stretch by a factor of 3 followed by a vertical translation down by 4 units.
Explanation:
The transformations that change the graph f(x) = 3x2 to the graph g(x) = 9x2 - 4 involve two steps:
A vertical stretch by a factor of 3, which is achieved by multiplying the original function f(x) by 3, yielding 9x2. This transformation changes the original coefficient (3) in front of x2 to a new coefficient (9).
A vertical translation down by 4 units, which is represented by subtracting 4 from the result of the stretch transformation.
Therefore, the correct answer to the student's question is:
A. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated DOWN 4 units.
Why must bowhunters use broadhead points when hunting big game?
Bowhunters use broadhead points when hunting big game for their greater cutting surface, penetration, lethality, blood trails, terminal performance, and ethical considerations.
We have,
Bowhunters use broadhead points when hunting big game for several reasons:
- Greater Cutting Surface
Broadhead points have a larger cutting surface area compared to target or field points.
This increased surface area allows for more effective cutting and penetration, which is essential when hunting big game animals that have tough hides, muscles, and bones.
- Penetration and Lethality:
Big game animals often require deep penetration to reach vital organs for an ethical and humane kill.
Broadheads are designed to maximize penetration by creating large wound channels and causing significant tissue damage.
This helps ensure quick and effective kills, minimizing suffering for the animal.
- Blood Trails
- Terminal Performance
- Ethical Considerations
Thus,
Bowhunters use broadhead points when hunting big game for their greater cutting surface, penetration, lethality, blood trails, terminal performance, and ethical considerations.
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Rhett decides to build a square room for his movie and music collection. If the area of the room is 9x^2 − 6x + 1 square feet, what is the length of one side of the room?
(3x + 1) feet
(9x − 1) feet
(3x − 1) feet
(9x + 1) feet
If point P is at the center of the circle, and the length of equals 12 inches, which is the length of AP?
a)4.5 inches
b)6 inches
c)9 inches
d)12 inches
an angle with measure between 90 and 180 is called
An angle with measure between 90° and 180° is called obtuse angle.
The definition of an obtuse angle in geometry states that an angle whose measure is greater than 90° and less than 180° is called an obtuse angle.
So, if the angle measure between 90 degree and 180 degree is obtuse angle.
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Find the side of a square whose diagonal is of the given measure. Given = 12 square root 2ft.
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Which statement is true about the function f(x)=-√-x
a.The domain of the function is all negative real numbers.
b.The range of the function is all positive real numbers.
c.The domain and range of the function have opposite signs.
d.The domain and range of the function are the same.
Answer: D.The domain and range of the function are the same.
Step-by-step explanation: Given function f(x)=-√-x.
The given function is a square root function and we have minus sign in front of x inside square root.
A square root always defined for positive values or 0.
In order to get a positive number or 0 inside square root, let us solve the inequality:
[tex]-x\geq 0[/tex]
On dividing both sides by -1, the inequality sign would get flip and we get
Domain: [tex]x \leq 0.[/tex]We can see that we have a negative sign in front of square root. So, the value of f(x) would be always a negative number or 0.
Therefore, range would also be :[tex]x \leq 0.[/tex].Therefore, correct option is D option.Answer:
hi thereee, the answer to this question is
d. the domain and range of the function are the same
hope this helps :)
have a good day!
Step-by-step explanation:
i just took the test
A dentist had some fish in a fish tank. The dentist added 43 more fish to the fish tank. Now there are 66 fish in the fish tank. How many fish were in the fish tank before the dentist added more?
___fish
Answer:
The dentist had 23 fish before she added 43
Step-by-step explanation:
Find the length of both arc AB and arc APB, where
MATH HELP!
Kristen's gross annual income is $47,208. She is paid semimonthly and has 6% deducted from her paychecks for her 403(b). Her employer matches her deduction, up to 5%. How much is deposited into Kirsten's 403(b) each payday?
$98.35
$118.02
$196.70
$216.37
The amount deposited into Kristen's each payday is is 216.37
Kristen's gross annual income is $47,208.
What is the meaning of semimonthly?Twice a month
semimonthly per year means
12(2)=24
She paid semimonthly,
47,208 / 24 = 1967
6% deducted from her paychecks then,
1967 * 0.06 = 118.02
Her employer matches her deduction, up to 5% then,
1967 * 0.05 = 98.35
The amount deposited into Kristen's each payday is
118.02 + 98.35 = 216.37
Therefore,the amount deposited into Kristen's each payday is is 216.37
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Help me in this plz plz
What is the GCF of the terms of 8x3 − 12x2 + 4x?
(35 points) Fred played golf and for the past 5 times had a score of 72, 79, 73, 81, and 70. What was his average score? A. 75 B. 77 C. 85 D. 375
The average score of Fred is 75.
What is the average value?The common cost of a characteristic over language is described to be crucial of the feature divided by way of the period of the interval.
calculation:-
a score of 72, 79, 73, 81, and 70.
nu,ber of times = 5
total score = 72+79+ 73+ 81+ 70.
= 375
average score = 375/5
= 75
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Carlo wants to join gym.the total gym offers three options for the membership. Option1:pay as you go.pay only $6 each time You work out. Option2: Regular Deal. Pay $50 a month and $2 each time you workout.
I need help please with these two questions.
1. What is the volume of this sphere? (First Picture)
8π cm³
16π cm³
27π cm³
36π cm³
2. What is the volume of this sphere? (Second Picture)
Use 3.14 for pi and round to the nearest hundredth when necessary.
615.44 cm³
2461.76 cm³
11,488.21 cm³
91,905.71 cm³
Answer:
(1) Volume of a sphere is [tex]36 \pi\ cm^{3}[/tex] .
(2)volume of the sphere is 11488.21 cm³ .
Step-by-step explanation:
Formula
[tex]Volume\ of\ a\ sphere = \frac{4}{3} \pi r^{3}[/tex]
Where r is the radius of the sphere .
Part First
As given the radius of the circle is 3cm .
Putting values in the formula
[tex]Volume\ of\ a\ sphere = \frac{4\times 3\times 3\times 3}{3} \pi[/tex]
[tex]Volume\ of\ a\ sphere = \frac{108}{3} \pi[/tex]
[tex]Volume\ of\ a\ sphere = 36 \pi\ cm^{3}[/tex]
Therefore the volume of a sphere is [tex]36 \pi\ cm^{3}[/tex] .
Second Part
As given
Diameter of the sphere is 28 cm .
[tex]Radius (r) = \frac{Diameter}{2}[/tex]
[tex]Radius (r) = \frac{28}{2}[/tex]
[tex]Radius (r) = 14\ cm[/tex]
[tex]\pi = 3.14[/tex]
Putting all the values in the formula
[tex]Volume\ of\ a\ sphere = \frac{4}{3}\times 3.14\times 14\times 14\times 14[/tex]
[tex]Volume\ of\ a\ sphere = \frac{4\times 3.14\times 14\times 14\times 14}{3}[/tex]
[tex]Volume\ of\ a\ sphere = \frac{34464.64}{3}[/tex]
[tex]Volume\ of\ a\ sphere =11488.21\ cm^{3}[/tex]
Therefore the volume of the sphere is 11488.21 cm³ .
1. The volume of the sphere is 16π cubic centimeters, which matches option B.
2. The correct answer for the volume of the second sphere is:
C. 11,488.21 [tex]cm^3[/tex]
1. For the sphere shown in the image with a diameter of 3 cm, the correct choice for its volume is:
B. 16π cm³
To calculate the volume of a sphere, we use the formula:
V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] r^3
Where r is the radius of the sphere.
Given:
- Diameter of the sphere = 3 cm
- Therefore, radius (r) = 3/2 = 1.5 cm
Substituting in the formula:
V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] (1.5)^3
V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] 3.375
V = 4 [tex]\times[/tex] π [tex]\times[/tex] 3.375/3
V = 16π cm³
So the volume of the sphere is 16π cubic centimeters, which matches option B.
2.For the second sphere shown with a diameter of 28 cm, to calculate its volume using π = 3.14 and rounding to the nearest hundredth, we follow these steps:
1) Find the radius by dividing the diameter by 2:
Radius = 28 cm / 2 = 14 cm
2) Use the formula for sphere volume: V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] r^3
Substituting the values:
V = (4/3) [tex]\times[/tex] 3.14 [tex]\times[/tex] (14 cm)^3
V = (4/3) [tex]\times[/tex] 3.14 [tex]\times[/tex] 2744
V = 11,488.53 cm^3
3) Rounding to the nearest hundredth as instructed:
V = 11,488.53 cm^3 rounds to 11,488.21 cm^3
Therefore, the correct answer for the volume of the second sphere is:
C. 11,488.21 [tex]cm^3[/tex]
The correct question is:
1. What is the volume of this sphere? (First Picture)
A. 8π cm³
B. 16π cm³
C. 27π cm³
D. 36π cm³
2. What is the volume of this sphere? (Second Picture)
Use 3.14 for pi and round to the nearest hundredth when necessary.
A. 615.44 cm³
B. 2461.76 cm³
C. 11,488.21 cm³
D. 91,905.71 cm³
In which way do REITs resemble mutual friends
REITs resemble mutual funds in that they both allow investors to pool their money to invest in a diversified portfolio. REITs consist of a variety of real estate properties, while mutual funds consist of stocks or bonds. Both provide individuals with an opportunity to invest in a professionally managed portfolio.
Explanation:REITs (Real Estate Investment Trusts) resemble mutual funds in that they both allow investors to pool their money together to invest in a diversified portfolio. Just as mutual funds consist of a variety of stocks or bonds from different companies, REITs consist of a variety of real estate properties such as office buildings, apartments, and shopping centers. Investors buy shares of a REIT and receive a return based on the performance of the real estate portfolio as a whole. Both REITs and mutual funds provide individuals with an opportunity to invest in a professionally managed portfolio without having to directly invest in individual stocks or properties.
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How would you solve this?
miss parks wrote 4 statement to the board and asked the class which one was true. Which statement is true?
A)3 and 2/3 x 4/5 is greater than 3 and 2/3
B)1 and 7/8 x 2 and 1/3 is greater than 2 and 1/3
C)1 and 7/8 x 8/8 is less than 2 and 5/6
D)2 and 3/8 x 4 is less than 4
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True or false ? A car taking a turn at a constant speed is accelerating.
Item 20The width of a rectangular room is 60% of its length. The length of the room is 10 feet. What is the area of the room?
If ΔMNO ≅ ΔPQR, which of the following can you conclude as being true? I'LL MARK BRAINLIEST !!!!
Answer:
NO=QR
Step-by-step explanation:
Mr burn's class is taking
a. field trip to the planetarium. The trip will cost $27 for each student. There are 18 students in his class.Use compatible numbers to estimate the total cost of field trip
Answer:
600
Step-by-step explanation:
The answer is 600
Choose the correct simplification of (7x3y3)2.
14x6y6
49x5y5
49x6y6
14x5y5
The correct simplification of (7x3y3)2 = 49x6y6
What is simplification?Simplification is defined as the removal of parentheses in an algebraic expressions in such a way that it would be understood.
From the expression given,
(7x3y3)2 = 2 × 7x × 3y × 3
= 49x6y6
Therefore, the correct simplification of (7x3y3)2 = 49x6y6
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Choose the option that correctly completes the statement.
The sum of the measures of the interior angles of a quadrilateral is _____ degrees.
270
180
90
360
Answer:
D. 360 degrees.
Step-by-step explanation:
We have been given an incomplete statement. We are asked to complete the given statement using provided options.
Statement:
The sum of the measures of the interior angles of a quadrilateral is _____ degrees.
We know that a quadrilateral is a polygon with 4 vertices.
We can divide a quadrilateral into two triangles by drawing a diagonal. We know that sum of three angles of a triangle is equal to 180 degrees, so sum of angles of two triangles would be 360 degrees.
Therefore, the sum of the measures of the interior angles of a quadrilateral is 360 degrees and option D is the correct choice.
Help please.....!!!!!
A rectangular auditorium seats 1344 people. The number of seats in each rows exceeds the number of rows by 20. Find the number of seats in each row
To solve this problem, we must first set up an equation. We are told that the total number of seats in the auditorium is 1344. We are also told that the number of seats in each row exceeds the number of rows by 20.
Let's denote the number of rows as x. Therefore, the number of seats per row is x + 20 (as it exceeds the number of rows by 20). Setting up an equation would be as follows:
x * (x + 20) = 1344
This equation states that the number of rows times the number of seats per row equals the total number of seats.
Solving this equation requires finding the roots of a quadratic equation. We set it up as a quadratic equation ax² + bx + c = 0. Here, a = 1, b = 20, and c = -1344.
Solving a quadratic equation gives us two possible solutions, but in our case, we disregard the negative value, as the number of rows cannot be negative. So, we take the maximum of the two roots.
Solving this equation gives us x = 28.0, which represents the number of rows.
Finally, to find the number of seats in each row, we remember that it exceeds the number of rows by 20. So, we add 20 to the number of rows.
28.0 + 20 = 48.0
So, there are 48 seats in each row.
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Four sides of a octagon each measure 12 cm. The perimeter of the octagon is 70 cm. What is the length of each remaining side, if each remaining side has the same length?
Answer:
It would be 5.5 cm
Step-by-step explanation:
The combined average weight of an okapi and a llama is 450450450 kilograms. The average weight of 333 llamas is 190190190 kilograms more than the average weight of one okapi. On average, how much does an okapi weigh, and how much does a llama weigh?
Llama's weight will be 160kg and Okami's weight will be 290kg.
What is an average?An average is one number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group.
The weight for both will be calculated as below:-
x= Okapi weight
y= Llama weight
There are 2 equations to be written:
1) 450kg is equal to the weight of one Okapi and one Llama.
450kg= x + y
2) The weight of 3 llamas is equal to the weight of one Okapi plus 190kg.
3y=190kg + x
Solve for one variable in one equation and substitute the answer in the other equation.
450kg= x + y
Subtract y from both sides.
450-y =x
Substitute (450-y) in the second equation in place of x to solve for y.
3y=190kg + x
3y=190 + (450-y)
3y=640 -y
Add y to both sides.
4y=640
Divide both sides by 4.
y=160kg Llama weight
Substitute 160kg in either equation to solve for x.
3y=190kg + x
3(160)=190 + x
480=190 + x
Subtract both sides by 190.
290= x
x= 290kg Okapi weight
Therefore, Llama's weight will be 160kg and Okami's weight will be 290kg.
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