The solutions of the given system of Equations are (5/2, 41/2).
What are the Solutions of Equations:The set of values for each variable in a system of linear equations is referred to as the solution set.
The intersection or meeting points of the lines or planes used to illustrate the linear equations are also known as the solutions.
The elimination method is one way of resolving a system of linear equations. To obtain the equation in one variable using this technique, simply add or subtract the equations.
Here we have
y = 9x-2 --- (1)
y = 7x+3 --- (2)
From (1) and (2)
=> 9x - 2 = 7x + 3
=> 9x - 7x = 3 + 2
=> 2x = 5
=> x = 5/2
Substitute x = 5/2 in (1)
=> y = 9(5/2) - 2
=> y = (45/2) - 2
=> y = (45 - 4)/2
=> y = 41/2
Therefore,
The solutions of given system of Equations are (5/2, 41/2).
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A hand soap container proudly boasts 30% more for the same price as their regular
container. The larger bottle has 9.75 ounces of soap. What is the original amount of
soap before the 30% increase?
Answer:
6.825 ounces
Step-by-step explanation:
9.75 x 0.3 = 2.925
9.75 - 2.925 = 6.825
Question 1 (1 point)
A bacteria culture started with 200 bacteria at 2 p.m. After 1 hour, the population
has grown to 240 bacteria. Assume the population grows exponentially.
1. Find an explicit formula the gives the number of bacteria n hours after 2 p.m.
2. Use your formula to find the number of bacteria at 9 p.m. Round your answer
to nearest integer.
Hello, Elyna. ,
The formula would be:
200+200x=b
Step-by-step formula:
1.) x equals hours, whereas b equals bacteria.
2.) There are 24 hours in one day.
3.) 24*5= 120
4.) Connect it.
5.) 200+200(120)= 6.) 24200= 5 bacterium days
Hope I could help.
Pls answer its for my finall
The non-real complex number is [tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex].
We have,
To find a non-real complex number,
What is not a real number?
Real numbers include rational numbers like positive and negative integers, fractions, and irrational numbers. Now, which numbers are not real numbers? The numbers that are neither rational nor irrational are non-real numbers, like, √-1, 2 + 3i, and -i.
A non-real complex number is an imaginary number containing negative numbers in the root.
Here,
[tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex]
In this option, it includes the negative term that is in the root so this is imaginary, therefore, the answer is "Option B".
Hence, the non-real complex number is [tex]\frac{8}{3} + \sqrt{-\frac{7}{3}}[/tex].
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- Frank has a gas can with 5 gallons of gas.
If he uses 0.36 gallons each time he cuts the
grass, how many times can he cut the grass?
Suppose an investigator has data on the amount of shelf space x devoted to display of a particular product and sales revenue y for that product. The investigator may wish to fit a model for which the true regression line passes through (0, 0). The appropriate model is Y ¼ b1x + e. Assume that (x1, y1), . . ., (xn, yn) are observed pairs generated from this model, and derive the least squares estimator of b1. [Hint: Write the sum of squared deviations as a function of b1, a trial value, and use calculus to find the minimizing value of b1.]
Hence, the least square estimator is obtained when you substitute [tex]y_i[/tex] with [tex]Y_i[/tex] is
[tex]\beta _1=\frac{\sum_{i=1}^{n}x_iY_i}{\sum_{i=1}^{n}x_i^2}[/tex]
What is the line of regression?
A regression line indicates a linear relationship between the dependent variables on the y-axis and the independent variables on the x-axis.
Here given that,
Suppose an investigator has data on the amount of shelf space [tex]x[/tex] devoted to display of a particular product and sales revenue [tex]y[/tex] for that product.
The investigator may wish to fit a model for which the true regression line passes through [tex](0, 0)[/tex]. The appropriate model is [tex]Y=\beta x+E[/tex]
Assume that[tex](x_1, y_1), . . ., (x_n, y_n)[/tex] are observed pairs generated from this model, and derive the least squares estimator of [tex]b_1[/tex].
Here, our motive is to minimize the function
[tex]f(b_1)=[/tex][tex]\sum_{i=1}^{n}(y_i-b_1x_i)^2[/tex]
Now,
[tex]f`(b_1)=0\\\\f`(b_1)=2\sum{i=1}^{n}(y_i-b_1x_i).(-x_i)\\\\[/tex]
So, the least square estimate [tex]b_1[/tex] is
[tex]\sum_{i=1}^{n}x_iy_i=b_1\sum_{i=1}^{n}x_i^2[/tex]
Hence, the least square estimator is obtained when you substitute [tex]y_i[/tex] with [tex]Y_i[/tex] is
[tex]\beta _1=\frac{\sum_{i=1}^{n}x_iY_i}{\sum_{i=1}^{n}x_i^2}[/tex].
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Corey has $89 go to shopping T shirt cost $12.50 each corey wants to buy some T shirt and have at least $14 for lunch
Answer:
6 shirts you can buy and still have $14 dollars for lunch.
Step-by-step explanation:
So let's do 89-14=75. So since we just took out the cost of the lunch it should be a lot easier to solve now.
s=shirts
So 75=12.50s
75/12.50=6
So Corey can buy 6 shirts.
I hope this helps!!!
Value: 10
Which of the following equations represent exponential functions?
f(x)=2x²-3x+1
g(x)=0.875*
h(x)=1.75x+2
j(x)=1095.6-2x
Answer:
The first one, due to the x being raised to the power of 2
Step-by-step explanation:
What is the solution set of the equation( 6/m)+2 = (m+3)/(m−1)?
Solution set of the equation is -3,-1, and 2 by simplifying the equation we get m³+2m²-5m-6 = 0
What is equation ?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Mathematical algebraic equations typically have one or more variables.
Given equation is: (6/m)+2 = (m+3)(m-1)
multiply with m both sides,
⇒6+2m = m(m²+2m-3)
⇒m³+2m²-3m = 6+2m
So we get,
m³+2m²-5m-6 = 0
Solving we get, m = -3, m = -1, m = 2 as solution of given equation.
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write an equivalent expression for 1/2(X+8)
x/2 + 4 is an equivalent expression .
What is an expression in maths?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
This mathematical operation may be addition, subtraction, multiplication, or division. An expression's structure is as follows: Number/variable, Math Operator, Number/Variable is an expression.
An expression in mathematics is made up of a mixture of variables, numbers, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases.
= 1/2(X+8)
= x/2 + 8/2
= x/2 + 4
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Graph the line with slope −2 and y-intercept −4
Can you also mark the two points on the graph.
Answer:
Below
Step-by-step explanation:
See image below:
Chloe is older than her brother, Michael, and she never lets him forget it! When Michael is y
years old, Chloe is y + 2.5 years old. Right now Michael is 9.5 years old.
How old is Chloe?
Write your answer as a whole number or decimal.
Answer: Chloe is 12 years old
y + 2.5
y = 9.5
9.5 + 2.5 = 12
Ten friends want to play a game. They must be divided into thee teams with three people in each team and one field judge. In how many ways can they do it?
Answer: 840 ways
Step-by-step explanation:
[tex]\displaystyle\\C_{10}^1*C_9^3=\\\\\frac{10!}{(10-1)!1!} *\frac{9!}{(9-3)!3!}=\\\\\frac{9!10}{9!1} *\frac{6!*7*8*9}{6!*1*2*3}=\\\\10*\frac{7*8*9}{2*3} =\\\\10*84=\\\\840\ ways[/tex]
Answer: 840 ways
mark me BRAINLIEST
Step-by-step explanation:
Look at the grid below.
a) What equation best represents the red line on the grid below?
b) What equation best represents the blue line on the grid below?
c) Find and list two co-ordinates on the red line
d) Find and list two co-ordinates on the blue line
a) The linear function that best represents the red line is given as follows: y = -4x + 4.
b) The linear function that best represents the blue line is given as follows: y = x - 2.
c) Two coordinates of the red line are given as follows: (0,4) and (1,0).
d) The coordinates of the blue line are given as follows: (0,-2) and (2,0).
What are the linear functions?The slope-intercept definition used to define a linear function from it's graph is given as follows:
y = mx + b.
In which the coefficients are listed as follows:
m is the slope, representing by how much y changes when x is increased by one.b is the y-intercept, representing the value of y when the graph of the function crosses the y-axis.For the red line, two points are given as follows:
(0,4) and (1,0)
Hence the parameters are of:
b = 4, a when x = 0, y = 4.m = -4, as when x increases by one, y decays by 4.Thus the equation is of:
y = -4x + 4.
For the blue line, the equation is of:
y = x - 2.
As:
When x = 0, y = -2.When x increases by 2, y also increases by 2, hence the slope is of m = 2/2 = 1.More can be learned about linear functions at https://brainly.com/question/24808124
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The correct solution set for -7x>_56
Answer:
Answer in image
Step-by-step explanation:
A hiker maintains an average speed of 3 3 /4 km/h. How many kilometers will the hiker walk in 5 hours.
average speed = 3 3/4 km/h
In order to find how many kilometers the hiker will walk in 5 hours, you'll need to multiply the average speed by the hiker's hours.
[tex]3\dfrac{3}{4} \times5[/tex]
[tex]=\fbox{18.75 km}[/tex]
choose an equivalent expression for [(2/3)^4 (2/3)^3]^2
By using exponent properties, we will find the equivalent expression:
[(2/3)^4*(2/3)^3]^2 = (2/3)^14
How to find an equivalent expression?There are two exponent properties that we can use here, these are:
a^x*a^y = a^{x + y}
(a^x)^y = a^{x*y}
Now we have the expression:
[(2/3)^4 (2/3)^3]^2
If we use the first property, we can rewrite the expression as:
[(2/3)^4 (2/3)^3]^2 = [(2/3)^{4 + 3}]^2
[(2/3)^{4 + 3}]^2 = [(2/3)^7]^2
Now we can use the second property to get:
[(2/3)^7]^2 = (2/3)^{7*2} = (2/3)^14
That is the equivalent expression.
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For each of these relations on the set (1,2,3,4), decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive. a) {(2,2), (2,3), (2,4), (3,2), (3,3), (3,4)) b) {(1,1), (1,2), (2,1), (2,2). (3,3), (4,4)} c) {(2,4), (4,2)) d) {(1,2), (2,3), (3,4)} e) {(1,1), (2,2), (3,3), (4,4)} f) {(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)}
Relations on the set (1,2,3,4), decide whether it is reflexive, whether it is symmetric, whether it is anti symmetric, and whether it is transitive.
Given :
a )
= { ( 2, 2 ),( 2, 3 ),( 2, 4 ),( 3, 2 ),( 3, 3 ) ,( 3, 4 ) }
Not reflexive because we do not have (1, 1), (3, 3), and (4, 4).
Not symmetric because while we we have (3, 4), we do not have (4, 3).
Not anti symmetric because we have both (2, 3) and (3, 2).
Transitive because if we have (a, b) in this relation, then a will be either 2 or 3. Then (2, c)
b )
{(1, 1),(1, 2),(2, 1),(2, 2),(3, 3),(4, 4)}
Reflexive because (a, a) is in the relation for all a = 1, 2, 3, 4.
Symmetric because for every (a, b), we have a (b, a).
Not antisymmetric because we have (1, 2) and (2, 1).
Transitive because while we have (1, 2) and (2, 1), we also have (1, 1) and (2, 2) in the relation.
c )
{(2, 4),(4, 2)}
Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.
Symmetric because for every (a, b), we have a (b, a).
Not antisymmetric because we have both (2, 4) and (4, 2).
Not transitive because we are missing (2, 2) and (4, 4)
d )
{(1, 2),(2, 3),(3, 4)}
Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.
Not symmetric because we do not have (2, 1),(3, 2), and (4, 3).
Antisymmetric because for every (a, b), we do not have a (b, a).
Not transitive because we do not have (1, 3) for (1, 2) and (2, 3)
e )
{(1, 1),(2, 2),(3, 3),(4, 4)}
Reflexive because we have (a, a) for every a = 1, 2, 3, 4.
Symmetric because we do not have a case where (a, b) and a 6= b.
Antisymmetric because we do not have a case where (a, b) and a 6= b.
Transitive because we can satisfy (a, b) and (b, c) when a = b = c.
f )
{(1, 3),(1, 4),(2, 3),(2, 4),(3, 1),(3, 4)}
Not reflexive because we do not have (a, a) for all a = 1, 2, 3, 4.
Not symmetric because the relation does not contain (4, 1), (3, 2), (4, 2), and (4, 3).
Not antisymmetric because we have (1, 3) and (3, 1).
Not transitive because we do not have (2, 1) for (2, 3) and (3, 1).
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what is
m=-(4+m)+2
thank you
The value of m in the equation m=-(4+m)+2 is -1.
How are linear equations solved step-by-step?
Clear decimals or fractions.Remove parentheses from each side of the equation and combine similar phrases to make it simpler.Remove the variable term from the equation's other side.Divide each side of the equation to find the solution.Verify your response.One of the easiest methods for resolving a system of linear equations is graphing. Simply plot each equation as a line on a graph and identify the point or points where the lines converge to find the value. These equations are simple to graph because they are already expressed in slope-intercept form.
m = -(4+m)+2
m = -4 -m + 2
m = -2 - m
m + m = -2
2m = -2
m = -1
Hence, the value of m in equation m=-(4+m)+2 is -1.
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What is the mean of the temperatures?
19°C
22°C
30°C
45°C
answers
A.19°C
B.29°C
C.45°C
D.116°C
The mean of the temperatures is 29°C, which corresponds to answer B.
Step-by-step explanation:1. Add all the values together.For convenience reasons we are going to avoid the use of the Celsius symbol (°C) during the calculations.
[tex]19+22+30+45=116[/tex]
2. Count the amount of given values.There are 4 values of temperature.
3. Divide the total of the sum by the amount of given values.[tex]\frac{116}{4}=29[/tex]
4. Conclude.The mean of the temperatures is 29°C, which corresponds to answer B.
The Sugar Sweet company is going to transport its sugar to the market. It will cost $7500 to rent trucks, and it will cost an additional $175 for each ton of sugar transported.
Let C represent the total cost ( in dollars) and let s represent the amount of sugar (in tons) transported. Write an equation to find the total cost to transport 12 tons of sugar.
The total cost to transport 12 tons of sugar is $9600.
Whet is the equation to find the total cost to transport 12 tons of sugar?From the information, Sugar Sweet company is going to transport its sugar to the market. It will cost $7500 to rent trucks, and it will cost an additional $175 for each ton of sugar transported.
Let C represent the total cost ( in dollars)
Let s represent the amount of sugar.
The equation to find the total cost to transport 12 tons of sugar will be:
C = 7500 + (175 × s)
C = 7500 + 175s
C = 7500 + (175 × 12)
C = 7500 + 2100
C = 9600
The cost is $9600.
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Find the volume of a sphere with a radius of 10 ft. Use 3.14 for . You may round to the nearest hundredth when necessary.
A) 4186.67ft3
B) 5712.86ft3
C) 6578.24ft3
D) 2473.58ft3
Volume of sphere is 4186.67 ft³ with a radius 10 ft.
Define volume of sphere.The capacity of a sphere is its volume. It is the area that the sphere occupies. Cubic measurements of a sphere's volume include m3, cm3, in3, etc. The sphere has a round, three-dimensional shape. Its shape is determined by three axes: the x, y, and z axes. A sphere's volume is equal to 4/3 r³, where r is the sphere's radius. Using Archimedes' principle, one may determine volume, a fixed quantity. In accordance with Archimedes, the amount of water displaced if a solid sphere is dropped into a container of water will be equal to the volume of the sphere.
Given
Radius of sphere = 10 ft
Volume of sphere
4/3πr³
4/3 × 3.14 × 10³
4/3 × 3.14 × 1000
4/3 × 3140
4186.67 ft³
Volume of sphere is 4186.67 ft³ with a radius 10 ft.
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The box plot below represents some data set. What is the interquartile range (IQR) of the data? 0, 25, 50, 75, 100
The box plot indicates that the interquartile range (IQR) of the data 0, 25, 50, 75, and 100 is 100.
What is the interquartile range?Find the median (middle value) of the bottom half and upper half of the data before calculating the interquartile range (IQR). Quartile 1 (Q1) and Quartile 3 are these values (Q3). The IQR represents the variation between Q3 and Q1. We use the median to summarize a typical value rather than the mean when a data collection contains outliers or extreme values. The interquartile range, which is the difference between the first and third quartiles, is a statistic that is frequently used to summarize variability in data sets with outliers.
Here,
The first and third quartiles would need to be located initially. Then, to obtain the IQR, you would divide the third quartile by the first.
IQR, in my opinion, is 100.
The interquartile range (IQR) of the data 0, 25, 50, 75, 100 will be 100 by the given box plot.
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A rectangular box of sand measures 4 inches by 12 inches by 16 inches. When resting on its smallest face, the level of the sand is 4 inches from the top of the box. How many inches from the bottom of the box will the sand level reach when the box is placed on its largest face?
The level of the sand in the box when the box is placed at the largest face will be 3 inches.
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
Volume has units of cube example meter³,cm³, etc.
The volume of the cube = side³.
The volume of sand when placed on a small face (4 x 12) will be as follows,
Volume = 4 x 12 x (16 - 4) = 4 x 12 x 12
When the box was kept at the largest face (16 x 12) the volume was still the same.
Let's say it goes up to h.
h x 16 x 12 = 4 x 12 x 12
h = 12/4 = 3 inches
Hence "The level of the sand in the box when the box is placed at the largest face will be 3 inches".
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Jon, Mona and Weber went to the local craft store to purchase supplies for making decorations for the upcoming dance at the high school. Jon purchased 2 sheets of craft paper, 4 boxes of markers and 5 glue sticks. His bill, before taxes was $36. Mona spent $32 when she bought 6 sheets of craft paper, 4 boxes of markers and 2 glue sticks. Weber, purchases totaled $16 when he bought 3 sheets of craft paper, 2 boxes of markers and 1 glue stick. Determine the unit cost of craft paper, marker and glue stick.
We have "No Solutions" or "Infinite Solutions" case.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
let the unit cost of Craft paper be x.
let the unit cost of boxes of markers be y.
let the unit cost of glue sticks be z.
So, the system of equations are
2x+ 4y + 5z= 36
6x+ 4y +2 z = 32
3x+ 2y+ z= 16
Now, solving the above three equation we get using Matrix method
All determinants are zero we have "No Solutions" or "Infinite Solutions" case.
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A sequence of positive numbers is defined by
given that a1=2
find a2 and a3 leaving your answer in a surd form
The values of a2 and a3 that satisfy the sequence [tex]a_{n+1}[/tex] = [tex]\sqrt{a_{n} ^{2} + 3 }[/tex] are [tex]\sqrt{7}[/tex] and [tex]\sqrt{10}[/tex]
What is a sequence?
A sequence is an arrangement of any objects or a set of numbers in a particular order followed by some rule. If a1, a2, a3, a4 etc. denote the terms of a sequence, then 1,2,3,4 denotes the position of the term.
the rule of the sequence is [tex]a_{n+1}[/tex] = [tex]\sqrt{a_{n} ^{2} + 3 }[/tex] when n = 1
[tex]a_{2}[/tex] = [tex]\sqrt{a_{1} ^{2} + 3 }[/tex] but [tex]a_{1}[/tex] = 2
[tex]a_{2}[/tex] = [tex]\sqrt{(2) ^{2} + 3 }[/tex]
[tex]a_{2}[/tex] = [tex]\sqrt{7}[/tex]
when n = 2
[tex]a_{3}[/tex] = [tex]\sqrt{a_{2} ^{2} + 3 }[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{a_{2} ^{2} + 3 }[/tex] but [tex]a_{2}[/tex] = [tex]\sqrt{7}[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{(\sqrt{7}) ^{2} + 3 }[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{7 + 3}[/tex]
[tex]a_{3}[/tex] = [tex]\sqrt{10}[/tex]
In conclusion [tex]a_{2}[/tex] and [tex]a_{3}[/tex] are [tex]\sqrt{7}[/tex] and [tex]\sqrt{10}[/tex] respectively.
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What amount will reduce the amount due on an invoice of $ 9410.25 by $ 842 if the terms of the invoice are 5/10, n/30 and the payment was made during the discount period?
The required amount of $799.90 will reduce the amount by $842.
Given that,
The amount will reduce the amount due on an invoice of $ 9410.25 by $ 842 if the terms of the invoice are 5/10, n/30 and the payment was made during the discount period is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
For 5/10 and n /30
The discount would be 5% if paid in the 30-day span,
Amount = amount invoiced [1 - 5%/100]
Amount = $842[0.95]
Amount = $799.9
Thus, the required amount of $799.90 will reduce the amount by $842.
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Kala bought 6 CDs that were each the same price. Including sales tax, she paid a total of $97.20. Each CD had a tax of $1.30. What was the price of each CD before tax?
Answer:
Step-by-step explanation:
The total tax Kala paid on the CDs was $1.30/CD * 6 CDs = $1.3*6=7.80.The total cost of the CDs before tax was $97.20 - $7.80 = $97.2-7.8=89.40.The price of each CD before tax was $89.40 / 6 CDs = $89.4/6=14.90/CD. Answer: 14.90.
Compute mean for list of values and return mean for python
Python is a dynamic, high-level, free open source, and interpreted programming language.
What are basics of Python?So let's begin by looking at them:Properties. Python is implicitly and dynamically typed, so you do not have to declare variables. ...Data types. Let's move ahead to data types. ...Strings. Let's move on to strings. ...Flow control statements. ...Functions. ...Classes. ...Exceptions. ...File I/O.Python 3 was used for the above code.Each function in the above code is defined starting with the keyword def, the name of the function (mean, median, mode, main) and a pair of parentheses containing the parameter.The various defined functions in the module are saved as stats.py in the text editor.#definition of "median" function
def median(list):
#checking median condition to make sure the list returns zero if empty
if len(list) == 0:
return 0
#sort the list
list.sort()
#find middle element
mid = len(list) / 2
#check the condition
if len(list) % 2 == 1:
return list[mid]
else:
return (list[mid] + list[mid - 1]) / 2
#definition of "mean" function
def mean(list):
#checking mean condition to make sure the list returns zero if empty
if len(list) == 0:
return 0
#sort the list
list.sort()
#set the value
total = 0
#initiate a for loop
for num in list:
#then we calculate the total
total += num
#return the value
return total/ len(list)
#definition of "mode" function
def mode(list):
#checking mode condition to make sure the list returns zero if empty
if len(list) == 0:
return 0
#declare the variable
num_Dictionary = {}
#check the condition
for digit in list:
num = num_Dictionary.get(digit, None)
if num == None:
num_Dictionary[digit] = 1
else:
num_Dictionary[digit] = num + 1
#getting the maximum value
max_Value = max(num_Dictionary.values())
mode_List = []
for k in num_Dictionary:
if num_Dictionary[k] == max_Value:
mode_List.append(k)
return mode_List
#definition of main function
def main():
#set the list
num_list = [7, 4, 8, 10, 9]
#call the "mean" function with a parameter
print ("Mean of the given list: ", mean(num_list))
#call the "mode" function with a parameter
print ("Mode of the given list:", mode(num_list))
#call the "median" function with a parameter
print ("Median of the given list:", median(num_list))
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I need help , Polygon ABCDE is reflected across the line x = -2. Graph and label the image A’B’C’D’E’. Is m/_ A = m/_ A’ Explain.
point A' is the contracted point of A. The coordinate of point A is (-4,4) and coordinate of point A' is (-2,4) as per the given question and available figure.
what is dilation?The extension or contraction of image or figure based on a scale factor is called dilation. In this way, an image is transformed from one position to another.
what is scale factor?Scale factor is defined as the ratio of original image and transformed image.
As stated in the question, the polygon ABCDE is contracted and moved to a shape A'B'C'D'E'. The coordinate of point A is (-4,4) and point A' is (-2,4) as shown in figure. Angle A is equal to angle A' that means the shape of polygon was not changed.
hence, A'B'C'D'E' is the reflected image of ABCDE
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f(x)=3x square + x f(-5)
Answer:
If you need the answer as f by simplifying both sides of the equation and then isolating the variable, the answer would be:
[tex]xf=\frac{3x^2}{5}-\frac{f(x)}{5}[/tex]
Or, if you need to evaluate the function itself, the answer would be:
[tex]f(x)=3x^2-5xf[/tex]