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Determine the cubic function obtained from the parent function y=x^3 after each sequence of transformations.
a reflection across the x-axis; a translation 1 unit up; and a translation 2 units right
Answer:
-(y+3)=(x-2)^3
Step-by-step explanation:
Transformed function B is f' ( x ) = - ( x - 2 )³ + 1
The transformed function is given by y = - ( x - 2 )³ + 1
How does the transformation of a function happen?
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be denoted as A
Now , the value of A is
y = x³
Let the transformed function be denoted as B
Now , the value of B is calculated by
Step 1 :
A reflection across the x-axis
So , the function changes to g ( x ) = -x³
Step 2 :
A translation 1 unit up
Up by d units: y = f(x) + d
So , the function changes to h ( x ) = -x³ + 1
Step 3 :
A translation of 2 units right
Right shift by c units: y=f(x-c)
So , the function changes to f' ( x ) = - ( x - 2 )³ + 1
Therefore , the value of B is f' ( x ) = - ( x - 2 )³ + 1
Hence , the transformed function B is f' ( x ) = - ( x - 2 )³ + 1
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6. Here are some lengths, widths, and areas of a garden whose perimeter is
40 feet. (Lesson 6-1)
. Complete the table with the missing
measurements.
b. What lengths and widths do you think will produce
the largest possible area? Explain how you know.
Length
4
8
10
12
14
16
Width
(ft)
16
12
Area
(sq ft)
64
96
64
If the length of the garden is 8 feet and width is 12 feet then the area of the garden be 96 [tex]feet^{2}[/tex], if the length of garden is 12 and the area of the garden is 96 [tex]feet^{2}[/tex],then the width be 8 feet, if the length of garden is 16 feet and the area is 64 [tex]feet^{2}[/tex], then the width of garden be 4 feet and the length and breadth which produce largest area are 8 feet and 12 feet and they can be interchanged.
Given a table of various combinations of length and breadth of garden.
We are required to fill the blanks and find the length and widths which produce largest area.
Length Width Area
4 16 64
8 12 96
10
12 8 96
14
16 4 64
The bold values were the blanks. The blanks which is not filled cannot be filled because we need atleast two values whether they will be length and breadth , breadth and area or length and area. The largest area is 96 [tex]feet^{2}[/tex]. The length and breadth are 8 feet and 12 feet. They can be interchanged because we have two such combinations.
Hence if the length of the garden is 8 feet and width is 12 feet then the area of the garden be 96 [tex]feet^{2}[/tex], if the length of garden is 12 and the area of the garden is 96 [tex]feet^{2}[/tex],then the width be 8 feet, if the length of garden is 16 feet and the area is 64 [tex]feet^{2}[/tex], then the width of garden be 4 feet and the length and breadth which produce largest area are 8 feet and 12 feet and they can be interchanged.
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Question is incomplete. It should include the attached picture.
Suppose you borrow $680 for a term of three years at simple interest and 3.94% APR. Determine the total (principal plus interest) you must pay back on the loan.
The total amount that we need to pay back after the end of 3 years with principal amount as $ 680 and simple interest as 3.94 % will be $ 760.376.
We are given that:
Principal amount = P = $ 680
Time period = t = 3 years
Simple interest rate = r = 3.94 %
We know that, the formula for simple interest is given by:
SI = P × r × t
SI = 680 × 3.94 % × 3
SI = 80.376
Amount will become:
Amount = $ 680 + $ 80.376
Amount = $ 760.376
Therefore, we get that, the total amount that we need to pay back after the end of 3 years with principal amount as $ 680 and simple interest as 3.94 % will be $ 760.376.
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Simplify this expression 3(2x-6)+x.
Answer:
7x-18
Step-by-step explanation:
3(2x-6)+x
multiply 3*2 to get 6x
then 3 *-6 = -18
then you have an extra x which you simply add to the 6x to get 7x
To determine the number of trout in a lake, a conservationist catches 94 trout, tags them and throws them back into the lake. Later, 30 trout are caught; 10 of them are tagged. How many trout would the conservationist expect to be in the lake?
1. You borrow P200,000 and promise to pay back P212,000 at the end of 1year. Compute the interest rate.
2. JPIA invested P10 million to buy a tract of land and plant some young pine trees. The trees can be harvested in 5 years at which time JPIA plans to sell the forest at an expected price of P15 million. What is JPIA’s expected rate of return?
3. While I was a student at USC, I borrowed P200,000 in student loans at an annual interest rate of 5%. If I repay P50,000 per year, then how long will it take me to repay the loan?
4. A mortgage company offers to lend you $85,000; the loan calls for the payments of $8,273.59 at the end of each year for 30 years. What interest rate is the mortgage company charging you?
Round off your answer up to four decimal places.
The interest on the P200,000 is borrowed is 6.0000% rounded to 4 decimal places.
What is the future value of amount borrowed now?
The future value of borrowed is the initial loan plus the interest over the 1 year period that would be repaid to the lender when the matures in 1 year
FV=PV*(1+r)^N
FV=loan repayment=212,000
PV=initial loan=200,000
r=rate of interest=unknown
N=duration of loan=1
212000=200,000*(1+r)^1
212000=200,000*(1+r)
212000/200,000=1+r
1.06=1+r
r=1.06-1
r=6.0000%
15=10*(1+r)^5
15/10=(1+r)^5
1.5=(1+r)^5
1.5=(1.5)^1
(1.5)^1=(1+r)^5
divide indexes on both sides by 5
(1.5)^(1/5)=1+r
r=(1.5)^(1/5)-1
r=8.4472%
Using a financial calculator, we can determine the number of years it takes to repay the loan
I/Y=annual interest rate=5(without the % sign)
PMT=50000(annual payment)
PV=loan amount=-200000
FV=future value which is not applicable in this instance
CPT(press compute)
N= 4.5735 years
N=number of years of repayment=30
PMT=8273.59(annual payment)
PV=loan amount=-85000
FV=future value which is not applicable in this instance
CPT(press compute)
I/Y=9.0000%
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GUYS PLEASE HELPPPP (and dont take the points pls)
Answer:
12.9
Step-by-step explanation:
Let's understand this,
Angle of elevation is 30° and the is standing perpendicularly, we have to find the distance from the branch to the mouse.
According to question,
cosine or cos thita = Base/Hypotenuse
Cos 30° = 15/H
0.86 = 15/H
H = 0.86 × 15
H = 12.9 (Round off 13)
Hope it helps!
Max has $17 in a fund he is creating to save for a bike. He adds $6 per week of his babysitting
earnings to the fund. If his weekly fund balance is represented by an arithmetic sequence, find
the 27th term.
The 27th term is $173.
In an arithmetic progression the difference between the two consecutive terms is same.
Here it is given that the first term of the AP which is represented by a is $17.
And Max adds $6 after every week in his fund so the common difference d is $6.
We know the general expression to find the nth term of an AP is
= a+(n-1)d
Here we have to find the 27th term. so the value of n will be 27.
Now the 27th term of the AP = 17+(27-1)6
= 17+156
= $ 173
The balance in the fund after 27th week will be $173.
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Maci is paid biweekly and earns $1500 each paycheck. What is his yearly salary?
Find the measure of θ. (to the nearest tenth) A) 28.8° B) 33.4° C) 61.2° D) 63.4°
Answer:A:28.8
Step-by-step explanation:
Answer: 28.8
Step-by-step explanation:
Which of the following is a non-prime factor of 70?
Company XYZ has created a neutral (useless) product to help college students make it to class on time. The company runs 40
studies with a confidence level of 95% Even if the product is useless, it would on average produce one study showing the
predict was beneficial, one study showing it was harmfut and thirty eight inconclusive studies (38 is 95% of 40) XYZ then
uses the one beneficial study to promote their new product.
Identity the misuse of statistical data by Company XYZ.
Loaded questions
Data manipulation
Overgeneralization
D
Discarding untavorable data
Ki
Answer: Discarding unfavorable data
Step-by-step explanation:
When companies discard data that will not support the narrative that they are trying to push, this is rightfully called, Discarding Unfavorable Data. There is a higher likelihood of this happening when the company does not publish all of the data the research showed.
Tobacco companies are an example of companies that do this. In cases where they hope to show that the relationship between cancer and tobacco smoking is minimal, they would show the very few examples that supports this.
The area of a rectangular field is 8320 square yards . the width is 65 yards . how long is the field? dont forget to include units in your answer!!
The measure of length of the rectangular field is 128 yards.
Given that, the area of a rectangular field is 8320 square yards. The width is 65 yards.
We need to find measure the length of the rectangular field.
What is the area of a rectangle?The area of a rectangle (A) is the product of its length 'a' and width or breadth 'b'. So, the area of the rectangle = (a × b) square units.
Now, 8320 = 65 × b
⇒b=128 yards
Therefore, the measure of length of the rectangular field is 128 yards.
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Select the correct answer.
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) - 3?
A.
It is the graph of f(x) translated 3 units to the left.
B.
It is the graph of f(x) translated 3 units down.
C.
It is the graph of f(x) where the slope is decreased by 3.
D.
It is the graph of f(x) translated 3 units up.
Answer:
It is B
Step-by-step explanation:
It is the graph of f (x) reflected about the x-axis and shrunk vertically by a factor of 10.
Answer:
B.
It is the graph of f(x) translated 3 units down.
Step-by-step explanation:
Write the equation of the line in point-slope, slope-intercept, and standard form.
38. Line passing through points (-4, 2) and (0,3)
A bag contains 4 red marbles, 3 blue marbles, and 7 green marbles. If a marble is randomly selected from the bag, find
the probability that a blue marble will be drawn.
a.
b.
1
3
1
OC
OD
C. 1
7
Mark this and return
d.
Please select the best answer from the choices provided
3
14
NEED HELP ASAP
Answer:
3/14
Step-by-step explanation:
4 + 3 + 7 = 14
The blue marbles are 3,
So the probability will be total blue ÷ total marble
3 / 14 which is D
An 80-foot diameter reservoir currently holds 825,000 gallons of water. What is the depth of water in this reservoir, measured in feet?
Answer:
Step-by-step explanation:
d=80 ft
r=80/2=40 ft
volume of cylinder=π r²h,where h is height or depth of cylinder.
π×40²×h=825,000
πh=825,000/40²=4125/8
h=4125/(8π)≈164.1285≈164.13 ft
The depth of water in the reservoir is approximately 21.92 feet.
To find the depth of water in the reservoir, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Where:
Volume is the total volume of water in the reservoir (in gallons),
π (pi) is a mathematical constant approximately equal to 3.14159,
r is the radius of the reservoir (half of the diameter), and
h is the depth of water in the reservoir (in feet).
Given:
Diameter = 80 feet
Volume = 825,000 gallons
We first need to calculate the radius (r) of the reservoir:
Radius (r) = Diameter / 2 = 80 feet / 2 = 40 feet
Now, we can convert the volume from gallons to cubic feet because we need the measurements to b²e in consistent units:
1 gallon ≈ 0.13368 cubic feet
Volume (in cubic feet) = 825,000 gallons * 0.13368 cubic feet/gallon ≈ 110,127 cubic feet
Now, we can find the depth (h) using the formula:
110,127 cubic feet = π * (40 feet)² * h
Solving for h:
h = 110,127 cubic feet / (π * 40 feet)² ≈ 110,127 cubic feet / 5026.5482 square feet ≈ 21.92 feet
Therefore, the depth of water in the reservoir is approximately 21.92 feet.
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Please I need the answer
Answer:
Angle A is 62 degrees
Step-by-step explanation:
2x + 4 + x - 1 = 90 is the equation. Simplified it is 3x + 3 = 90. Solving the equation would make x = 29. Then, plug in x for each equation. Angle A is 62 degrees and Angle B is 28.
[(1.7×106)÷(2.63×105)]+7.33
Answer:
[(1.7×106)÷(2.63×105)]+7.33
=7.9825439073
I HOPE IT HELP YOU
triangle LMN is reflected about line y=3
where is point M on the transformed triangle?
A.(3,6)
B.(9,6)
C.(-3,-6)
D.(-3,0)
please answer it I need it for a test pls help
Answer:
the correct answer is: c (-3,-6)
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Which statement is true about the graph of a quadratic function on the left?
A.the axis of symmetry is x=-3
B.the range is y > 0
C.the y-intercept is at 2
D.the vertex (-1,-3)
The true statement for the given graph is the vertex is (-1, -3).
What is a parabola?A parabola is a curve where any point is at an equal distance from: a fixed point called the focus, and the fixed straight line called the directrix.
Given is a graph of a parabola, we need to determine the correct statements for the graph,
The graph is having the axis of symmetry at x = -1, so the first option is wrong.
The range y is y < 0, so the second option is also wrong,
There is no y-intercept.
Lastly, the vertex is at (-1, -3) therefore this option is correct.
Hence, the true statement for the given graph is the vertex is (-1, -3).
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PLEASE HELP!!!!!!!!!!!!!
Which of the following relationships represents a function?
A.
x -1 6 2 6
y 15 13 15 14
B.
x -1 6 -1 10
y 15 15 21 14
C.
x -1 6 1 10
y 15 13 21 15
D.
x -1 6 1 1
y 15 13 15 14
Answer:
the answer is c
Step-by-step explanation:
because it doesn't repeat the same number for example if it was two -1s it wouldn't be a function but positive and negative are different so yeah
what is the slope-intercept of? 3x-2y = -16
Answer:x intercept: (-16/3 ,0) y intercept: (0,8). bascially: (-16/3,8)
Step-by-step explanation:
What is the sum of three hundredths plus two?
Answer:
2.03
Step-by-step explanation:
The bakery sells each cake for $120. Last year, the bakery sold 98 cakes. How much money did the bakery earn selling cakes?
Answer:
The bakery earned $11760 by selling cakes
Step-by-step explanation:
Cost of 1 cake = $120
Bakery sold cakes = 98
We need to find how much money did the bakery earn selling cakes?
We are given cost of 1 cake, if we multiply cost of 1 cake by 98 we can get cost of 98 cakes. Solving:
Cost of 1 cake = 120
Cost of 98 cakes = 120 x 98
= 11760
So, The bakery earned $11760 by selling cakes
3 angles added to a 180ﾟ one angle has mingle has the measure of 7X plus 8 angle 2 has a measure of 2X plus 9 and angle 3 has a meter of 10X plus 5 given that some of the angles is a 180ﾟ what is the measure of angle 1
Answer:
66 or 65.82
Step-by-step explanation:
check on the phrasing of the question but i assume would be this 7x+8+2x+9+10x+5=180
19x=157
x=8.26
8.26x7 +8=65.82
For 6 consecutive days, Alejandro studied for 5 minutes more each day than he did the previous day. Which best represents the change in the amount of time that Alejandro studied on the first day to the amount of time he studied on the last day? –30 minutes –11 minutes 11 minutes 30 minutes
Answer:
it is on ed it is 30
Step-by-step explanation:
Answer:
30 minutes
Step-by-step explanation:
ASAP WILL GIVE BRAINLIEST
Answer:
jo
Step-by-step explanation:
I believe a proportion will form a parabola because it a proportion. It is x and y value which are different. The numbers that come together will form a direct and good parobla
Please I need help with this
Answer:
I believe it would be 8
Step-by-step explanation:
Step-by-step explanation:
it should be 8 but the calculation is not coming yet.....
Noah bought 15 baseball cards for $9.00. Assuming that each baseball card costs the same amount, answer the following questions.How much will 30 baseball cards cost?
Answer:
270 dollars
Step-by-step explanation: