Determine all the transformations that have happened to f(x) = (x + 4)2 + 2 compared to
f(x) = x2
Answers
Answer:
Folow the steps to learn what transformations were determined.
Step-by-step explanation:
First we would have to graph the parent function which is f(x) = x^2. Start by finding your x and y values. Find the y values by plugging in the x values into the parent function.
X Y
2 4
1 1
0 0
-1 1
-2 4
Once these points are plotted you can start determining what are the transformations. Find the difference between the parent function and f(x) = (x + 4)^2 + 2 by looking below.
Vertical Shifts:
f(x) + c moves up,
f(x) - c moves down.
Horizontal Shifts:
f(x + c) moves left,
f(x - c) moves right.
The parent function has to be transformed left 4 and up 2. In order to do this shift each point from earlier left 4 and then up 2. In conclusion you will have two functions graphed (parent function and the transformed function).
Related Questions
After a long hike in a state park, danielle decides to relax at the beach. The parking permit she purchase allows her to park at any state beach without paying again. While consulting a map, danielle notices that the closest state beach is 4 centimeters way from thepark. How far apart are the state park and the closest state beach in real life if the map uses a scale of 1 centimeter = 2 kilometers
Answers
Answer:
8 km
Step-by-step explanation:
Danielle can multiply the scale values by 4 to find the real life distance between the park and the beach.
1 cm : 2 km . . . . . given scale values
4 cm : 8 km . . . . . multiply values by 4
The state park and state beach are 8 km apart.
10.85 . ((1.7) =
answers:
1. 18.445
2. 12.55
3. 20.29
4. 1.845
Answers
Answer:
18.445
Step-by-step explanation:
Multiply
(2x² + 3x³ - 3x²-
3x - 4x-3)÷(x-2)
Answers
The simplified form of the expression \(\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}\) is \(\frac{3x^{3}-x^{2} -7x-3 }{(x-2)}\)
As per the question statement, we are provided with an expression \(\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}\).
We are supposed to simplify the above mentioned expression.
To solve this question, let us simplify the expression, part by part, i.e., first, let us consider the numerator part which is
[2x² + 3x³ - 3x² -3x -4x - 3].
Here, it is clearly visible that the numerator expression consists of terms having same same variable but with different coefficients, such as
[2x², -(3x²)] and [-(3x), -(4x)]. Therefore, we can perform the mentioned operations on the like terms and thus simplify our numerator.
\([2x^{2} +(-3x^{2} )]=(2x^{2} -3x^{2} )=-(x^{2})\\\)
And, \([(-3x) + (-4x)]=-(3x+4x)=-x(3+4)=-(7x)\).
Hence, \((2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=[+3x^{3}+(2x^{2} -3x^{2})-(3x+4x)-3]\\or, (2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=[+3x^{3}+(-x^{2} )-7x-3]\\or, (2x^{2} +3x^{3} -3x^{2} -3x-4x-3)=(+3x^{3}-x^{2}-7x-3)\\\)
And our denominator is (x - 2). Since, [2x² + 3x³ - 3x² -3x -4x - 3] does not equate to Zero for (x = 2), there (x - 2) is not a factor of the numerator, i.e., the numerator cannot be exactly divided by the denominator.
Therefore, the simplest form of our expression \(\frac{(2x^{2} +3x^{3} -3x^{2} -3x-4x-3)}{(x-2)}\) is \(\frac{3x^{3}-x^{2} -7x-3 }{(x-2)}\).
Expressions: These are mathematical statements, that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.Like Terms: Terms having the same variable.To learn more about expressions, click on the link below.
brainly.com/question/18077352
#SPJ9
Which of the following represents the function graphed? F(x)=1/2 x f(x)=x f(x)= x+2
Answers
F(x)=x
find the first four terms of the taylor series for the function 2x about the point a=1. (your answers should include the variable x when appropriate.)
Answers
The first four terms of the Taylor series for the function (2x) about the point (a=1) are (2x + 2x - 2).
What are the initial terms of the Taylor series expansion for (2x) centered at (a=1)?To find the first four terms of the Taylor series for the function (2x) about the point (a = 1), we can use the general formula for the Taylor series expansion:
\(\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \ldots\]\)
Let's calculate the first four terms:
Starting with the first term, we substitute
\(\(f(a) = f(1) = 2(1) = 2x\)\)
For the second term, we differentiate (2x) with respect to (x) to get (2), and multiply it by (x-1) to obtain (2(x-1)=2x-2).
\(\(f'(a) = \frac{d}{dx}(2x) = 2\)\)
\(\(f'(a)(x-a) = 2(x-1) = 2x - 2\)\)
Third term: \(\(f''(a) = \frac{d^2}{dx^2}(2x) = 0\)\)
Since the second derivative is zero, the third term is zero.
Fourth term:\(\(f'''(a) = \frac{d^3}{dx^3}(2x) = 0\)\)
Similarly, the fourth term is also zero.
Therefore, the first four terms of the Taylor series for the function (2x) about the point (a = 1) are:
(2x + 2x - 2)
Learn more about taylor series
brainly.com/question/31140778
#SPJ11
An internet movie rental company charges a yearly membership fee of $50 plus 1.99 per dvd rental
Answers
Answer: y= 1.99x+ 50
Equation: y=mx+b
express the number as a ratio of integers. 0.28 = 0.28282828
Answers
0.28 can be expressed as the ratio of integers 7:11.
To express 0.28 as a ratio of integers, we need to first convert the repeating decimal 0.28282828 into a fraction.
Let x = 0.28282828
Then, 100x = 28.28282828
Subtracting x from 100x, we get:
99x = 28
x = 28/99
Therefore, 0.28282828 can be expressed as the fraction 28/99.
Now, to express 0.28 as a ratio of integers, we need to simplify the fraction 28/99.
We can do this by dividing both the numerator and denominator by their greatest common factor, which is 4.
28/99 = (7*4)/(9*11) = 7/11
Therefore, 0.28 can be expressed as the ratio of integers 7:11.
In summary:
0.28 = 0.28282828 (repeating decimal)
0.28282828 = 28/99 (fraction)
28/99 can be simplified to 7/11
Therefore, 0.28 can be expressed as the ratio of integers 7:11.
Know more about ratios here:
https://brainly.com/question/12024093
#SPJ11
Harry collected data from a random sample of seventh graders at his school. Out of 25 respondents, 10 of them ride the
bus to school. Of the 150 seventh graders that attend Harry's school, how many seventh grade students should be
expected to ride the bus to school?
Answers
Answer:
10/25=×/150
x=60
so 60 students
Answer:
60
Step-by-step explanation:
because I litterly just did the test and got my answers back
When condensing a logarithm using the the product property, you combine the answers by dividing them.
Group of answer choices
True
False
When condensing a logarithm using the the power property, you move the front number to become the exponent on the log.
Group of answer choices
True
False
When condensing a logarithm using the the quotient property, you combine the answers by dividing them.
Group of answer choices
True
False
Answers
#1
log_a(bc)=log_a^b+log_a^cNot divide we multiply
False#2
logb^a=alogbYes
True#3
Yes it's reverse of first one
TrueAnswer:
False
True
True
Step-by-step explanation:
\(\textsf{Product Rule}:\quad \log_n(x)+\log_n(y)=\log_n(xy)\)
When condensing a logarithm using the product rule, you combine the answers by multiplying them.
\(\textsf{Power Rule}:\quad a \log_n(x)=\log_n(x)^a\)
When condensing a logarithm using the power rule, you move the front number to become the exponent on the log.
\(\textsf{Quotient Rule}:\quad \log_n(x)+\log_n(y)=\log_n\left(\dfrac{x}{y}\right)\)
When condensing a logarithm using the the quotient rule, you combine the answers by dividing them.
solve x2=81/16
express your answer as a fraction.
Answers
Answer:
\(x = 2 \frac{1}{4} \)
Step-by-step explanation:
\( {x}^{2} = \frac{81}{16} \)
\(x > 0\)
\(x = \sqrt{ \frac{81}{16} } \)
\(x = \frac{ \sqrt{81} }{ \sqrt{16} } = \frac{9}{4} = 2 \frac{1}{4} \)
Answer:
x^2 = 81/16
x = +√(81/16) = +9/4
Dilate point D by a scale factor of 3. what would the coordinate of D’ be (if that plane is quadrant 1)
Answers
The coordinate of D’ after the dilation is (-6, 0)
What would the coordinate of D’ after dilationFrom the question, we have the following parameters that can be used in our computation:
D = (-2, 0)
Scale factor = 3
The coordinate of D’ after the dilation is calculated as
D' = D * Scale factor
Substitute the known values in the above equation, so, we have the following representation
D' = (-2, 0) * 3
Evaluate
D' = (-6, 0)
Hence, the image is (-6, 0)
Read more about dilation at
https://brainly.com/question/3457976
#SPJ1
A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=2/3 t^3−5t^2+8t. Over the time interval 0
Answers
The maximum value of y(t) on the interval [0, 4] is y(1) = 1/3 and the minimum value is y(4) = 16/3.
To discover the most extreme and least values of y(t) over the interim [0, 4], we must begin with discovering the basic points of y(t) and after that calculate y(t) at the basic points.
To find the critical point, we need to find where the derivative of y(t) is zero or undefined. So we start by finding the derivative of y(t).
\(y'(t) = 2t^2 - 10t + 8\)
Setting y'(t) = 0 to find the location equal to zero gives:
\(2t^2 - 10t + 8 = 0\)
Simplified, it looks like this:
\(t^2 - 5t + 4 = 0\)
There is factoring:
(t - 1)(t - 4) = 0
So the critical points are t = 1 and t = 4.
Then evaluate y(t) at the critical points and the endpoints of the interval [0, 4].
y(0) = 0
y(1) = 1/3
y(4) = 16/3
A second derivative test can be used to determine if a value is the maximum or minimum. The second derivative of y(t) is
y''(t) = 4t - 10
At t = 0, y''(t) = -10, which is negative. This means that y(t) has a local maximum at t = 0.
At t = 1, y''(t) = -6, which is also negative. This means that y(t) has a local maximum at t = 1.
At t = 4, y''(t) = 6, which is positive. This means that y(t) has a local minimum at t = 4. Therefore, the maximum value of y(t) on the interval [0, 4] is y(1) = 1/3 and the minimum value is y(4) = 16/3.
The correct question is
A particle moves along the y-axis so that at time t≥0 its position is given by y(t)=2/3t^3−5t^2+8t. Over the time interval 0<t<5, for what values of t is the speed of the particle increasing?
learn more about critical point
brainly.com/question/31017064
#SPJ4
Can someone help me solve this?
Answers
The function is an exponential growth since it is increasing with time and k is positive
What is exponential growth?
Given that at t =6, P = 167075
Then;
167075 =110.8e^6k
167075/110.8 = e^6k
1507.9 = e^6k
ln(1507.9) = 6k
k = ln(1507.9)/6
k = 1.2
Thus in the year 2020;
P = 110.8e^20(1.2)
P = 2.9 * 10^12
In the year 2025;
P = 110.8e^25(1.2)
P = 1.18 * 10^15
To reach 290,000
290,000 = 110.8e^1.2t
290000/110.8 = e^1.2t
2617.3 = e^1.2t
t = ln(2617.3 )/1.2
t = 7 years
Learn more about exponential:https://brainly.com/question/28596571
#SPJ1
find the dot product and the angle between and . , question content area bottom part 1 negative 5 (simplify your answer. type an exact value, using radicals as needed.) part 2 the angle between and is 1.8. (do not round until the final answer. then round to the nearest tenth as needed.)
Answers
Rounded to the nearest tenth, the angle between the two vectors is approximately 1.8. To find the dot product between two vectors, we multiply their corresponding components and sum the results.
To find the dot product between two vectors, we multiply their corresponding components and sum the results. Let's denote the two vectors as v and w. Given that the components of v are 1 and -5, and the components of w are -5 and 0, the dot product can be calculated as follows:
v · w = (1 * -5) + (-5 * 0) = -5 + 0 = -5
Now, let's find the angle between the two vectors. The dot product can be used to find the angle using the formula:
cos(theta) = (v · w) / (||v|| * ||w||)
Where ||v|| and ||w|| represent the magnitudes (lengths) of the vectors. In this case, both vectors have a magnitude of \(\sqrt(26)\).
Substituting the values into the formula:
cos(theta) = -5 / \((\sqrt(26) * \sqrt(26))\) = -5 / 26
To find the angle theta, we can use the inverse cosine function:
theta = acos(-5 / 26)
Evaluating the expression gives:
theta ≈ 1.810
Rounded to the nearest tenth, the angle between the two vectors is approximately 1.8.
To know more about vectors visit:
https://brainly.com/question/14447709
#SPJ11
write an equation in slope -intercept form if the line has a slope of 2 and it goes through (1,-2)
Answers
The equation in slope-intercept form of the line with slope 2 that goes through the point (1,-2) is y = 2x - 4.
In the slope-intercept form, the equation of a line can be written as y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). To find the equation of a line given its slope and a point that it passes through, we can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the given values, we get y - (-2) = 2(x - 1), which simplifies to y = 2x - 4, the equation in slope-intercept form.
You can learn more about slope-intercept at
https://brainly.com/question/1884491
#SPJ11
Given f (x) = -2x+1 and g(x) =3x determine the value of f (4) + g(-1)
Answers
Answer:
-11
Step-by-step explanation:
f(4)=-2(4)+1
f(4)= -8+1
f(4)= -7
g(x)= 3(-1)
g(x) = -4
f(4)+g(-1)= -7+(-4)
-7-4
-11
hopes this helps
Answer:
-11 just took the test and that was mine
Step-by-step explanation:
Company U has 100 outlets. Half of those outlets carry Brand F. Company U allots Brand F 5 shelf facings out of the 50 facings it allots for all brands in that category. What is the percentage of category shelf facings for Brand F? (place the answer in the space below with no % sign - for example if your answer is 25%, place 25)
Answers
The percentage of category shelf facings for Brand F is 10% out of the total facings allotted for all brands in that category, based on the information provided.
To calculate the percentage of category shelf facings for Brand F, we need to determine the proportion of shelf facings allotted to Brand F out of the total facings allotted for all brands in that category.
Company U has 100 outlets, and half of those outlets carry Brand F. This means that there are 50 outlets that carry Brand F.
Out of the 50 facings allotted for all brands in that category, Company U allots Brand F 5 shelf facings.
To find the percentage, we divide the facings allotted to Brand F (5) by the total facings allotted for all brands in the category (50), and then multiply by 100 to express it as a percentage.
(5 facings / 50 facings) * 100 = 10%
Therefore, the percentage of category shelf facings for Brand F is 10%. This indicates that Brand F occupies 10% of the available shelf space in the category across Company U's outlets.
learn more about percentage here
https://brainly.com/question/33098852
#SPJ11
What the right answer
Answers
Answer:
A for the first one and c for the second
Step-by-step explanation:
sus
Answer:
a i think
Step-by-step explanation:
Write 0.00658 standard form
Answers
6.58 x 10^-3
Explanation:
Moving the decimal place till it’s in front of the 6
A given line has the equation 10x 2y=−2 . what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y=−5x 12 5x y=12 y−12=5(x−0) 5x y=−1
Answers
The equation of the line parallel to the given line and passing through the point (0, 12) is y = -5x + 12.
To find the equation of the line parallel to the given line 10x + 2y = -2 and passing through the point (0, 12), follow these
steps:
1. Find the slope of the given line by converting it to slope-intercept form (y = mx + b), where m is the slope and b is the
y-intercept:
10x + 2y = -2
2y = -10x - 2
y = -5x - 1
The slope (m) of the given line is -5.
2. Since parallel lines have the same slope, the slope of the line we're looking for is also -5.
3. Use the point-slope form (y - y1 = m(x - x1)), where m is the slope and (x1, y1) is the given point (0, 12):
y - 12 = -5(x - 0)
4. Simplify the equation to slope-intercept form (y = mx + b):
y - 12 = -5x
y = -5x + 12
So, the equation of the line parallel to the given line and passing through the point (0, 12) is y = -5x + 12.
for such more question on parallel
https://brainly.com/question/13763238
#SPJ11
For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?
Answers
Answer:For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?
Step-by-step explanation:
Multiply binomial by polynomials
Answers
In this case the answer is very simple . .
We must apply the distributive property of multiplication.
\((d^2+3)\cdot(d^2\text{ + 2d + 1) }\)\(d^2\cdot d^2+d^2(2d^{})+d^2+3(d^2\text{) + 3(2d) + 3}\)\(d^4\text{ + }2d^3+d^2+3d^2+6d+3\)\(d^4+2d^3+4d^2+6d+3^{}\)That is the solution. .
1. (5 pts) The (per hour) production function for bottles of coca-cola is q=1000K L
, where K is the number of machines and L is the number of machine supervisors. a. (2 pts) What is the RTS of the isoquant for production level q? [Use the following convention: K is expressed as a function of L b. (1 pt) Imagine the cost of operating capital is $40 per machine per hour, and labor wages are $20/ hour. What is the ratio of labor to capital cost? c. (2 pts) How much K and L should the company use to produce q units per hour at minimal cost (i.e. what is the expansion path of the firm)? What is the corresponding total cost function?
Answers
The RTS of the isoquant is 1000K, indicating the rate at which labor can be substituted for capital while maintaining constant production. The labor to capital cost ratio is 0.5. To minimize the cost of producing q units per hour, the specific value of q is needed to find the optimal combination of K and L along the expansion path, represented by the cost function C(K, L) = 40K + 20L.
The RTS (Rate of Technical Substitution) measures the rate at which one input can be substituted for another while keeping the production level constant. To determine the RTS, we need to calculate the derivative of the production function with respect to L, holding q constant.
Given the production function q = 1000KL, we can differentiate it with respect to L:
d(q)/d(L) = 1000K
Therefore, the RTS of the isoquant for production level q is 1000K.
The ratio of labor to capital cost can be calculated by dividing the labor cost by the capital cost.
Labor cost = $20/hour
Capital cost = $40/machine/hour
Ratio of labor to capital cost = Labor cost / Capital cost
= $20/hour / $40/machine/hour
= 0.5
The ratio of labor to capital cost is 0.5.
To find the combination of K and L that minimizes the cost of producing q units per hour, we need to set up the cost function and take its derivative with respect to both K and L.
Let C(K, L) be the total cost function.
The cost of capital is $40 per machine per hour, and the cost of labor is $20 per hour. Therefore, the total cost function can be expressed as:
C(K, L) = 40K + 20L
To produce q units per hour at minimal cost, we need to find the values of K and L that minimize the total cost function while satisfying the production constraint q = 1000KL.
The expansion path of the firm represents the combinations of K and L that minimize the cost at different production levels q.
Learn more about production
brainly.com/question/31859289
#SPJ11
Evaluate the expression for x = 3, y = 3, and z = 5.
12z-3y
4z-z
Enter your answer in the box.
Answers
To answer this question, simply plug in the values that represent the variables into the respective equations.
If z=5 and y =3, then 12z - 3y can be written as:
(12 × 5) - (3 × 3)
(60) - (9)
= 51
If z = 5, then the expression 4z -z can be written as:
(4 × 5) - 5
20-5
= 15
51 and 15 are your answers
find the slope. (no units needed)
Answers
Answer: 4/5
Step-by-step explanation: It is 8/10, but if you simplify it, it is 4/5.
A new television set was recently purchased for the common room in a residence hall for $520.00 including tax. If the tax rate is 4%, find the price of the television set before taxes.
Answers
Let's use the variable x to represent the price of the television set before taxes.
If the tax rate is 4%, then the original price is multiplied by 1.04, so it is equal 1.04x.
The final price is $520, so we have:
\(\begin{gathered} 1.04x=520 \\ x=\frac{520}{1.04} \\ x=500 \end{gathered}\)So the price before taxes is $500.00.
help, please, begging you
Answers
Explanation:
4x -(5.8x - 3.3)
Start by multiplying the negative sign into everything inside of the parentheses
4x -5.8x + 3.3
Now combine your like terms of x’s giving you your final result
-1.8x + 3.1
(PLEASE HELP ASAP DUE IN 1 hour) The equations of two lines are below, solve please
Answers
Line two would be Y=-3/2 +9
Take problem one the equation and move x to the other side so you would have 3y=2x+6 and divide 3 to all of them to get your answer
How many laps will Matt run in 16 minutes using the linear equation
Answers
He will run 8 laps
5/10 * 16/1 = 80/10 = 8
i need help please find the ans
you will get 15 points if you ans this
Answers
Answer:
the answer is 5 ^_^
Step-by-step explanation:
hopeee it helpss ^_^