The equation of the parabola will be;
y = (x - 3)² + 1
What is mean by Parabola?
A parabola is a set of points in the plane which are equidistant from the directrix and focus.
Given that;
The vertex of the parabola = (3 , 1)
A parabola passes through the point (2,2).
Now,
Since, The equation of parabola in vertex form is;
y = a (x - h)² + k
Where, (h , k) are vertex of the parabola.
So, The equation of parabola with vertex (3, 1) will be;
y = a (x - 3)² + 1
And, It passes through the point (2,2).
So we substitute the value of (2, 2) in place of (x, y) as;
2 = a (2 - 3)² + 1
2 = a + 1
a = 2 - 1
a = 1
Substitute the value of a in above equation, we get;
The equation of parabola as;
y = (x - 3)² + 1
Therefore, The equation of the parabola will be;
y = (x - 3)² + 1
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Find the measure of the exterior angle.
The measure of the exterior angle is a = 54
Where is the exterior angle?
The angle formed by a polygonal side and its extended neighboring side.The angle at all between the side of a shape and a line that extends from the next side is known as the exterior angle. The result of adding the interior and outside angles is a 180° straight line. "Supplementary Angles" is what they are.the exterior angle 2a = a + 10 + 44
2a = a + 54
2a - a = 54
a = 54
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Given g (x) = 3x+5 determine x for g (-2)
Answer:
-1
Step-by-step explanation:
when you change g[×] to g[-2] , 3x+5 change to 3[-2] +5
Find the values of the constant p q and r in such that when the polynomial f(x)=x^3 +px^2+ qx+ r is divided by (x+2),(x-1),and (x-3) the remainders are respectively -48,0 and 2 hence actoreise f(x) completely
In the polynomial expression f(x) = x³ + px² + qx +r, the values of p is 1/5, q is -66/5 and r is 12.
Polynomial:
Polynomial means an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
Given,
Here we have the polynomial f(x) = x³ + px² + qx +r
And it is divisible by (x+2),(x-1),and (x-3) the remainders are respectively -48,0 and 2.
Here we need to find the value of p, q and r.
Let us consider that the equations,
x + 2 = 0 then x = -2
x - 1 = 0 then x = 1
x - 3 = 0 then x = 3.
Now, apply these values on the polynomial expression then we get,
f(-2) = (-2)³ + p(-2)² + q(-2) +r = -48
f(-2) = -8 + 4p - 2q +r = -48
f(-2) = 4p - 2q +r = -48 + 8
f(-2) = 4p - 2q + r = -40 ----------------------(1)
Apply the value of x as 1, then we get
f(1) = (1)³ + p(1)² + q(1) +r = 0
f(1) = 1 + p + q + r = 0
f(1) = p + q + r = -1 ----------------------(2)
Apply the value of x as 3, then we get
f(3) = (3)³ + p(3)² + q(3) + r = 2
f(3) = 27 + 9p + 3q + r = 2
f(3) = 9p + 3q + r = -25 ----------------------(3)
Now we have to solve the equation (2) and (1), then we get,
=> (4p -p) + (-2q - q) + (r - r) = -40 - (-1)
=> 3p -3p = -39
Divide it by 3, then we get
=> p - q = -13 ----------------------(4)
Similarly, solve equations (2) and (3), then we get,
=> (9p - p) + (3q - q) + (r - r) = -25 - (-1)
=> 8p + 2q = -24
Divide it by 2, then we get,
=> 4p + q = -12 ---------------------------(5)
Solve the equations (4) and (5), then we get,
=> (4p + p) + (q - q) = -12 - (-13)
=> 5p = 1
=> p = 1/5
Apply the value of p on equation (4), then we get the value of q as,
=> (1/5) - q = -13
=> -q = -13 -1/5
=> -q = -66/5
Apply the value of p and q on equation (2), then we get,
=> 1/5 + (-66/5) + r = -1
=> -65/5 + r = -1
=> -13 + r = -1
=> r = 12
Therefore, the value of p is 1/5, q is -66/5 and r is 12.
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Which expression is equivalent to 2x^ 2 -2x+7^ prime ?
The expression which is equivalent to; 2x² - 2x + 7 as required in the task content is; 2 (x - 0.5)² + 6.5.
Which expression is equivalent to 2x² - 2x + 7 as required in the task content?It follows from the task content that the expression which is equivalent to; 2x² - 2x + 7 is to be determined.
Therefore, since the expression whose equivalent is to be determined is; 2x² - 2x + 7; we have;
2x² - 2x + 7
By completing the square method; we have;
2(x² - x) + 7
2 {(x - 0.5)² - 0.25} + 7.
2 (x - 0.5)² - 0.5 + 7
2 (x - 0.5)² + 6.5
Therefore, the required expression which is equivalent to the given expression is; 2 (x - 0.5)² + 6.5.
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Raj has put soup into the freezer to cool down. The soups tempature started at
170 °f and decreased at a rate of 30 °f per hour.
Answer:
If the same cup of 190∘F soup is instead placed into a freezer set at 30∘F, what is the time required for the soup to cool from 190∘Fto135∘F in this situation?
3. Masani is testing 25 g of fertilizer. She of the plans to give each test plant 0.4 g fertilizer and have 8 g left over for future tests. Solve the equation 0.4n+ 8 = 25 to find the number of plants Masani car use in her
Answer:
Step-by-step explanation:
So, you have to isolate the variable. Think of it as finding how many plants she gave fertilizer to. 0.4n+8=25, when moving the 8 to the other side, it becomes negative. 0.4n=25-8. 0.4n=17. You then find the variable n. think of it as dividing 17 by 0.4 or multiplying n a certain number of times to find the number of plants.17/0.4 is 42.5. therefore, she gave 42 plants fertilizer, depending on what your teacher wanted to count. If she says round down, 42. If she wants to round up, 43. If she wants to be specific, 42.5. I would personally put the decimal.
4/7x = 28 solve for x simplify your answer as much as possible
I WILL USE CROSS MULTIPLICATION
[tex] \frac{4}{7x} = 28 \\ 4 = 28(7x) \\ 196x = 4 \\ \frac{196x}{196} = \frac{4}{196} \\ x = \frac{1}{49} [/tex]
ATTACHED IS THE SOLUTION
Answer:
16
Step-by-step explanation:
7x=28x4
7x=112
x=112/7
x=16
7/6 x 3 how to slove
The expression given: 7/6 x 3 can be calculated to get 7/2
what is multiplication?This is a basic math operation that helps to determine the product of two or more numbers.
The numbers given here include a whole number and a fraction
What is a fraction?A fraction refers to classification of numbers to be represented as having a stroke dividing the two groups of numbers.
The numbers on top is referred to as numerators while the numbers below is referred to as the denominator
in the question the fraction is 7/6: The numerator is 7 while the denominator is 6
how to solve the multiplication problem= 7/6 * 3
= 7/2
= 3.5
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show how to transform the weight function of a weighted matroid problem, where the desired optimal solution is a minimum-weight maximal independent subset, to make it a standard weighted-matroid problem. argue carefully that your transformation is correct.
To transform the weight function of weight matroid problem, there are few steps to evaluate and derive to get the desired weight expression w
We build the transformation, i.e, a new weight function, as follows: We want the elements with maximum weight to have minimum weight and. In other words, two weight functions need to be mutually opposite in this sense. Therefore, if we denote the maximum weight of all the elements with w ∗ : w ∗ = max w(x) x ∈ S we would want something along the lines of w ′ ( x ) = w ∗ − w ( x ). But in this formulation, the biggest weight element has a new weight of exactly. Since we want the weight function to be strictly positive, we finish our construction with: w ′ ( x ) := w ∗ − w ( x ) + 1, for all x ∈ S . ----------> (1)
Using equation (1) we can derive the following expression for the weight w ′
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To transform the weight function of weight matroid problem, there are few steps to evaluate and derive to get the desired weight expression w
We build the transformation,
or a new weight function, as follows:
We want the elements with maximum weight to have minimum weight a In other words, two weight functions need to be mutually opposite in this sense.
Therefore, if we denote the maximum weight of all the elements with
w ∗ : w ∗ = max w(x) x ∈ S
we would want something along the lines of w ′ ( x ) = w ∗ − w ( x ). But in this formulation, the biggest weight element has a new weight of exactly.
Since we want the weight function to be strictly positive, we finish our construction with:
w ′ ( x ) := w ∗ − w ( x ) + 1, for all x ∈ S . ----------> (1)
Using equation (1) we can derive the following expression for the weight w ′
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Hilda went hiking and used the app on her phone to track her progress. When she looked back, she discovered she had hiked up 530 feet, down 602 feet, up 1003 feet, and down 89 feet to get to the lake. What is her elevation in relation to where she started?
The elevation is 848 feet.
What is meant by elevation?The word elevation is often used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying aeroplanes or orbiting satellites, and depth is used to describe locations below the surface.
A geographical feature's elevation is determined by how high it is above the mean sea level (MSL). Accordingly, elevation is the distance between the height that corresponds to the ocean's surface and the top of the feature.
Given:
Hilda hiked up 530 feet,
down 602 feet,
up 1003 feet,
and down 89 feet to get to the lake.
Taking all similar cases together
Hiked up
= 530 + 1003
= 1533 feet
and, hiked down
=602+83
= 685
Thus, the elevation is
= 1533 - 685
= 848
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Island bank is advertising a special 1.55% APR for long -term CDs. Manny takes out a 1 year CD for $40,000. The interest is compounded daily. What will the annual percentage yield be for mannys account to the nearest hundredth of a percent .
The annual percentage yield is 1.55% for any account if the interest is compounded daily.
Given that Island bank is advertising a special 1.55% APR for long-term CDs. Manny takes out a 1 year CD for $40,000. The interest is compounded daily.
Principal (P) = $40000
Interest rate(r) = 1.55% = 0.0155
Number of periods (n) = 365
The formula for Annual Percentage Yield (APY) for an account that is compounded continuously is given as
APY = [1 + (r/n)ⁿ - 1]
Substitute the values in the formula to get
= [1 + (0.0155/365)³⁶⁵ - 1]
= [1 + 0.000042)³⁶⁵ - 1]
= [1.000042]³⁶⁵- 1
= 1.015448 - 1
= 1.55%
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x3 + 11x2 – 3x – 33 by grouping
Answer:
-3
Step-by-step explanation:
It was quite easy
Answer:
Step-by-step explanation: factor out x2
from the expression x2 (x+11) -3x-33
Factor out-3 from the expression x2 (x-+11) -3(x+11)
Factor out x+11 your solution is x2 (x+11) (x-3).
The population of a fish farm is modeled by the equation where t is time in yearsP(t) = 1250/ 2+3e ^ -0.6tpart one)part two)part three)part four)part five)
The Solution:
Given the equation that modeled the population of fish after time (t) in years as below:
[tex]p(t)=\frac{1250}{2+3e^{-0.6t}}[/tex]part 1:
We are to find the initial population of fish. This means we are to find the value of p when t = 0.
[tex]p(0)=\frac{1250}{2+3e^{-0.6(0)}}=\frac{1250}{2+3e^0}=\frac{1250}{2+3}=\frac{1250}{5}=250\text{ fish}[/tex]Part 2:
We are required to find the doubling time (t) for this population (Round the answer to the nearest tenth). This means we are to find t when P(t) = 500.
Note: double of 250 fish is 2x250 = 500 fish.
[tex]\begin{gathered} p(t)=\frac{1250}{2+3e^{-0.6t}} \\ \\ \text{Where P(t)=500, and t=?} \end{gathered}[/tex][tex]\begin{gathered} 500=\frac{1250}{2+3e^{-0.6t}} \\ \text{Cross multiplying, we get} \\ \\ 500(2+3e^{-0.6t})=1250 \\ \text{ Dividing both sides by 500, we get} \\ \\ \frac{500(2+3e^{-0.6t})}{500}=\frac{1250}{500} \end{gathered}[/tex][tex]\begin{gathered} 2+3e^{-0.6t}=2.5 \\ \text{ Collecting the like terms, we get} \\ 3e^{-0.6t}=2.5-2 \\ 3e^{-0.6t}=0.5 \end{gathered}[/tex]Dividing both sides by 3, we get
[tex]\begin{gathered} \frac{3e}{3}^{-0.6t}=\frac{0.5}{3} \\ \\ e^{-0.6t}=\frac{1}{6} \end{gathered}[/tex]Taking the natural log of both sides, we get
[tex]undefined[/tex]please I need the asnwers with explanation as soon as possible
MATH PLEASE HELP!!!
Let f(x) be given by the (large) graph to the right. On a piece of paper, graph and label each. function listed below.
y = f((1/2)x))
y=2f(2x)
y = f(2x)
original function y=f(x) is attached
y = f(2x) ⇒ Shrink the graph of function f(X) by half horizontally .
What is function and example?
A function is a type of rule that produces one output for a single input.This is represented by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.Four main categories can be used to classify various types of functions. One to one function, many to one function, onto function, one to one and into function—all based on the element.y = f((1/2)x)) ⇒ Stretch the graph of f(x) horizontally by factor 2 .
y=2f(2x) ⇒ Shrink the graph of f(X) by half horizontally .
Shrink the graph twice ( vertically) .
y = f(2x) ⇒ Shrink the graph of f(X) by half horizontally .
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What dose 10x+9-6x=-19 mean
Answer:
it algebra
Step-by-step explanation:
10x-6x=4x
Then the equation becomes
4x+9=-19
Then you subtract the 9 from -19
4x=-28
Now you have to separate the 4 from x
4x/4 and -28/4
So now you get
X=-7
after paying 5.12 salad , kamauri has 27.10
The amount of money that Kamauri has at first will be 32.22.
How to calculate the cost?From the information, it was stated that after paying 5.12 for salad, Kamauri has 27.10.
Based on the information given, the total amount of money that he had at first will be the addition of the cost of salad and the change left.
This will be illustrated as:
= 5.12 + 27.10
= 32.22
The amount is 32.22.
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After paying 5.12 for salad, Kamauri has 27.10. What was the total amount of money that he had at first?
what is the height of the candle after 7 hours
Let
y -----> candle heigh in centimeters
x ----> burning time in hours
In this problem we have the ordered pairs
(5,22.5) and (17,16.5)
step 1
Find out the slope
m=(16.5-22.5)/(17-5)
m=-6/12
m=-1/2 -----> is negative because is a decreasing function
step 2
Find out the equation in slope-intercept form
y=mx+b
we have
m=-1/2
point (5,22.5)
substitute
22.5=-(1/2)(5)+b
solve for b
b=22.5+2.5
b=25
therefore
y=-(1/2)x+25
step 3
For x=7 hours
substitute in the equation
y=-(1/2)(7)+25
y=-3.5+25
y=21.5 cm30g 25´into second please solve its optional math question please solve it carefully its my project so question is 30grade25´ into second.
Answer:
Step-by-step explanation:
30.25g=296.6511625 m/s^2
May someone please help me! I have to submit this tonight and do not know how to do it or the answer may you please help me thank you.
Which of the following is the center and radius of the circle?
x² + y2 + 10x-6y + 15 = 0
The most appropriate form for equation of circle will be given by-
Centre = (-5, 3) and radius is [tex]\sqrt{19}[/tex] units
What is equation of circle?
A round figure whose all points on the boundary maintains a fixed distance from a point known as the centre of the circle and the fixed distance is called the radius of the circle.
If radius of a circle is doubled, we will obtain the diameter of the circle.
Equation of circle
[tex](x-a)^2 + (y-b)^2 = r ^2[/tex]
where (a, b) is the centre of the circle and r is the radius of the circle.
Here,
[tex]x^2 + y^2 + 10x-6y + 15 = 0[/tex]
[tex]x^2 + 2\times x\times 5 + 5^2 -5^2 +y^2 -2\times y\times 3 + 3^2 - 3^2 + 15 = 0\\(x+5)^2 + (y-3)^2-25-9+15=0\\(x+5)^2 + (y-3)^2-19=0\\(x+5)^2 + (y-3)^2=19\\ (x+5)^2 + (y-3)^2=\sqrt{19}^2\\[/tex]
Centre = (-5, 3) and radius is [tex]\sqrt{19}[/tex] units
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a vehicle covers a distance of 524/25 kilometers on 7/8 liters of petrol. How much distance will it cover 2 liters of petrol
8.32 Km is the distance of how much it would be covered
A unit rate means a quantity at a rate of one of something.
The distance traveled with 2 liters of petrol is 47.9 km.
What is a unit rate?A unit rate means a quantity at a rate of one of something.
It is written with a denominator of one.
Example:
Man can walk 6km in 2 hours.
In one hour a man can walk 3 km.
We have,
A vehicle covers a distance of 524/25 kilometers on 7/8 liters of petrol.
This can be written as:
524/25 km = 7/8 liters
Multiply both sides by 8/7
8/7 x 524/25 km = 1 liter
23.95 km = 1 liter _____(1)
Now,
Multiply 2 on both sides of (1)
2 x 1 liter = 2 x 23.95 km
2 liter = 47.9 km
Thus,
The distance traveled with 2 liters of petrol is 47.9 km.
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17. An Uber ride costs a flat rate of $7 and you are charged $.65 per mile. What
is the algebraic expression for this situation? How much would it cost for 15
miles?
*
The suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.
What are expressions?A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation. Word illustration: The product of 8 and 3. Word illustration: The product of 8 and 3 is 11 written as 8 + 3.So, the flat rate is $7 and we're charged $0.65 per mile:
Let, 'x' be the number of miles traveled.Then the suitable expression will be:
0.65x = 7Cost if we traveled 15 miles:
So, 0.65x = y where x = 15.
0.65x = y0.65(15) = y9.75 = yIt would cost $9.75 for 15 miles.
Therefore, the suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.
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the weight of items produced by a machine is normally distributed with a mean of 7 ounces and a standard deviation of 3 ounces. what percentage of items will weigh between 4.3 and 8.65 ounces? a. 47.52%
27.80% is percentage of items .
What percentage means?
Percentage ,a comparative figure denoting one hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified.Mean = 7
standard deviation = 3 ounces
Required % = p (5.6<x < 7.1 ) × 100 = ?
z = x - μ/σ = 5.6 - 7/2
z = 7.1 - 7/2 = 0.05
∴ P(5.6 < x < 7.1 ) = p ( - 0.7 < z < 0.05 )
p( z < 0.05 ) - p ( z < - 0.7)
= 0.51994 - 0.24196 ≅ 0.2780
So, required % = 0.2780 × 100
= 27.80%
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1. Multiply.
0.7 times 100 equals what number?
A. 7
B. 70
C. 700
D. 7,000
2.Multiply.
0.13 times 10,000 equals what number?
A. 13
B. 130
C. 1,300
D. 13,000
3. Multiply.
0.63 times 0.01 equals what number?
A. 0.0063
B. 0.063
C. 0.63
D. 6.3
4. Divide.
0.37 divided by 100 equals what number?
A. 0.00037
B. 0.0037
C. 0.037
D. 0.37
5. Divide.
0.8 divided by 0.01 equals what number?
A. 8
B. 80
C. 800
D. 8,000
The various values using mathematical operations are;
1) B: 70
2) C: 1300
3) A: 0.0063
4) B: 0.0037
5) B: 80
How to use mathematical operations?
1) We want to multiply 0.7 times 100.
Now, 0.7 can be expressed as 0.7 = 7/10. Thus;
0.7 * 100 = 7/10 * 100 = 70
2) We want to multiply 0.13 by 10000.
0.13 can be expressed as;
0.13 = 13/100. Thus;
0.13 * 10000 = 13/100 * 10000 = 1300
3) We want to multiply 0.63 times 0.01.
They can be expressed as;
63/100 * 1/100 = 63/10000 = 0.0063
4) Divide 0.37 by 100.
0.37 can be expressed as 37/100. Thus;
0.37/100 = 37/100 ÷ 100
= 37/100 * 1/100 = 37/10000 = 0.0037
5) Divide 0.8 divided by 0.01.
They can be expressed as;
8/10 ÷ 1/100
= 8/10 * 100/1
= 80
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I REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(
Answer: 5.13
Step-by-step explanation:
1) Set up the equation
3.8(1.35)
2) Solve
5.13
Can someone please help me on question 42 (7th grade math) pls and thank u :)
Answer:
Answer down below!
Step-by-step explanation:
(Part a):
So we have the information that after 20 minutes, the submarine descended 480 feet.
To find how many feet it descended per minute, all we need to do is divide 480 and 20 which will give us 24
Every 1 minute, the submarine descended 24 feet.
(Part b):
Now that we have how many feet it descended per minute, we have to make an expression that goes along with it.
Our unknown variable in this case will have to have to be the feet.
We can use the letter f to express that. We can also use the letter m to express our minutes in the end
So after 24(f) = m
(Part c):
After 5 Minutes: 120 ft
After 10 Minutes: 240 ft
After 15 Minutes: 360 ft
After 18 Minutes: 432 ft
The front suspension system of a passenger car typically has coiled springs attached to the front wheels. a typical spring has a spring constant k of about 82,000 k/m
If the front suspension system of a car has coiled springs of spring constant(k) of about 82,000N/m attached to the front wheels, then the force required to compress this spring by 1.2 cms will be 984N.
As per the question statement, the front suspension system of a passenger car has coiled springs attached to the front wheels and a typical spring has a spring constant "k" of about 82,000 k/m.
We are required to calculate the force required to compress this spring by 1.2 cms
To solve this question, we will need to apply the formula to calculate the force to compress a spring, which is known as the Hooke's Law. So, as per the Hooke's Law, the force (F) required to compress a spring of spring constant (k) by "x" units, can be represented as
[F = (k * x)]
Now comparing the RHS of the Hooke's Law equation with the data provided in the question statement, we get, (k = 82000 N/m) and
(x = 0.012 m), and using these values in the Hooke's law equation, we get, the force required to compress a spring of spring constant(k) of about 82,000N/m by 1.2 cms will be (82000 * 0.012)N = 984 N.
Spring Constant: The magnitude of force required to compress or stretch a spring by unit distance, is known as it's spring constant, and it varies from spring to spring, typically being based on the constituent elements of the spring.To learn more about Spring Constants, click on the link below.
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HELP PLS! How does the graph of g(x) = (x + 2)3 − 6 compare to the parent function of f(x) = x3?
It is to be noted that the graph of g(x) = (x+2)³ -6 compares to the parent function f(x) = x³ in that g(x) is shifted 2 units to the left and 6 units down. See the explanation below.
What is a parent function?A parent function in mathematics is the simplest function in a family of functions that retains the concept of the whole family.
Here is how the transformation of a function can occur
Any change can occur during the transformation of a function.
Typically, they can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.
If the initial function is y = f(x), and the horizontal axis represents inputs and the vertical axis represents 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) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k × f(x)Horizontal stretch by a factor k: y = f(x/k)A function sets the value of one set's elements to the value of another set's specified element.
Given that the parent function is f(x)=x³, while the transformed function is g(x)=(x+2)³ - 6. Therefore, the transformation of the parent function that results in the transformed function is that g(x) is shifted 2 units to the left and 6 units down.
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The transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.
What is a function?The function is a type of relation, or rule, that maps one input to a specific single output.
A change can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.
If the initial function is y = f(x), and the horizontal axis shows the inputs and the vertical axis shows outputs, then:
Horizontal shift would be Left shift by c units; y=f(x+c) and Right shift by c units; y=f(x-c)
Vertical shift would be Up by d units; y = f(x) + d and Down by d units; y = f(x) - d
Stretching would be as Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given that the parent function is; f(x)=x³,
And the transformed function is; g(x)=(x+2)³ - 6.
Hence, the transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.
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on a certain high school athletic team, the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6. if there are 60 juniors on the team, how many students in total are on the team? a. 90 b. 140 c. 150 d. 180 e. 210
The total number of students that are on the team is e. 210 if the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6
As the ratio of freshmen to sophomores to juniors to seniors is 1:3:4:6, we can write the number of students as;
Freshmen = 1x
Sophomores = 3x
Juniors = 4x
Seniors = 6x
As the number of juniors on the team is 60, therefore;
4x = 60
To determine the value of x we divide both sides by 4;
4x/4 = 60/4
x = 15
Now the total number of students can be found by substituting the value of x;
1x + 3x + 4x + 6x
1(15) + 3(15) + 4(15) + 6(15) = 210
Hence, the total number of students on the team is 210.
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