The solution of the given system of equations 3x + y = 10 , x - y = 2 is equal to x = 3 and y = 1.
As given in the question,
Given system of equations are :
3x + y = 10 ____(1)
x - y = 2 _____(2)
Add equation (1) and (2) to eliminate y and get the value of x we have,
3x + y = 10
x - y = 2
4x = 12
⇒x = 12 / 4
⇒ x = 3
Substitute value of x = 3 in equation (1) to get the value of y for the given equation,
3(3) + y = 10
⇒ 9 + y = 10
⇒ y = 10 - 9
⇒ y = 1
Therefore, the solution of the given system of equations is equal to x = 3 and y =1.
The above question is incomplete, the complete question is:
What is the solution of the system of equations 3x + y = 10 , x - y = 2?
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lucia is renting a stand up paddleboard from sunrise lake rentals. she is charged an initial rental fee and an additional cost per hour she rents the paddleboard.
this situation can be modeled as linear relationship
what does the slope of the line tell you about the situation?
A. including the initial rental fee, the toal cost to rent the paddleboard for 5 hours is $70
B. after the initial rental fee, the paddleboard costs an additional $12 every hour
C. lucia rents the paddleboard for 5 hours
D. the inital rental fee is $10
The slope of the situation means: B. after the initial rental fee, the paddleboard costs an additional $12 every hour
What is the Slope of a Linear Equation?If a situation is modeled as a linear relationship between two variables, the slope of the relationship is a measure of the strength and direction of the relationship between the two variables in that particular situation.
The slope is calculated as the change in the value of one variable (the "rise") over the change in the value of the other variable (the "run").
For example, consider a situation in which the number of hours that a student studies is related to their grades in a class. The slope of this relationship would indicate the strength and direction of the relationship between hours of study and grades in this particular situation.
A positive slope would indicate that as the number of hours of study increases, the grades also increase, while a negative slope would indicate that as the number of hours of study increases, the grades decrease.
To find the slope of the situation that is represented in the graph given, use two points on the line to calculate the slope.
Using (0, 10) and (2.5, 40)
Slope (m) = change in y / change in x = (40 - 10) / (2.5 - 0)
= 30/2.5
Slope (m) = 12
Therefore, this means that, B. after the initial rental fee, the paddleboard costs an additional $12 every hour.
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How do you write a factor of 5?
On solving the provided question, we can say that - by prime factorization the factors of 5 are 5 and 1
What is factor?A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.
The factors of 5 are -
5
and 1
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What is the x and y intercepts of -4x+5y=20 and is (5,8) a solution?
Answer: Yes, (5,8) is a solution.
x=-5, y=4
x-intercept (-5,0)
y-intercept (0,4)
Step-by-step explanation:
To find the x-intercept, make y equal to 0 and solve
-4x+5(0)=20
-4x=20
x=-5
To find the y-intercept, make x equal to 0 and solve
-4(0)+5y=20
5y=20
y=4
To see if 5,8 is a solution, sub in and solve
-4(5)+5(8)=20
-20+40=20
20=20
Yes, (5,8) is a solution.
Consider the economy whose data appear in the table below. Working-age population 100,000 Labor force 60,000 Unemployed 12,000 Instructions: Round your answers to one decimal place.
a. The unemployment rate is ___%.
b. The labor-force participation rate is ___ %.
a. The unemployment rate is 20%.
b. The labor-force participation rate is 60%.
According to the question,
Working age population- 100,000
Labour force - 60,000
Unemployed - 12000 instructions
a) The unemployment rate is the percentage of the labor force that is unemployed and it is calculated as follows:
Unemployment Rate = [tex]\frac{Number of unemployed People}{Labor force}[/tex] × 100
When an unemployed population is 12,000 and the labor force is 60,000,
the unemployment rate is = [tex]\frac{12000}{60000}[/tex] × 100 = 20%
b) labor force participation rate is the percentage of working adult population that participates in labor either by actively looking for a job, or working. It is calculated as follows:
Labor Force Participation Rate = [tex]\frac{Labor force}{working age population}[/tex] × 100
When the labor force is 60,000 and the working-age population is 100,000
Labor Force Participation Rate = [tex]\frac{60000}{100000}[/tex] × 100 = 60%
So, a. The unemployment rate is 20%.
b. The labor-force participation rate is 60 %.
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What are the 4 types of transformations and how do we describe them?
Four types of transformations are as follow:
1. Rotation : It is based on about any point.
2. Reflection : It is based on over any line.
3. Translation : It is based on a given vector.
4. Dilation : It is based on size.
As given in the question,
Four types of transformations is given by :
1. Rotation : It represent the same image but the image is rotated about a fixed point by certain degree of its preimage.
2. Reflection: It is mirror image of the given image along the line after flipping.
3. Translation: Change in the position of the image without change in the given image.
4. Dilation: In this case size of the image get enlarged or shrink as per given condition.
Therefore, the four types of transformation is given by :
1. Rotation : It is based on about any point.
2. Reflection : It is based on over any line.
3. Translation : It is based on a given vector without change in the image.
4. Dilation : It is based on size.
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What is the end behavior of function h
Answer:
Function to be graphed is,
h(x) = 2(x - 3)²
Function 'h' is a quadratic function.
Since, the coefficient of the leading term (term with the highest power) is positive, parabola will open upwards.
Both the ends of the parabola will be upwards (towards positive infinity).
As x approaches to negative infinity, h(x) approaches to positive infinity.
As x approaches to positive infinity, h(x) approaches to positive infinity.
Step-by-step explanation:
Please give the brainliest.
a tile store charges $747.50 to install 115 square feet of tile. assuming they charge the same rate per square foot regardless of the amount of tile installed, how much would they charge to install 970 square feet of tile?
With the help of simple mathematical operations, we know that the cost of installing 970 ft² will be $6,305.
What are mathematical operations?A method of calculation: The most popular ones are (+, −, ×, ÷) for add, subtract, multiply, and divide.
However, there are many more, like square roots, logarithms, and squares.
It is most likely an operation if it isn't a number.
Example: The operation in 25 + 6 = 31 is added.
So, we know that:
The store charges $747.50 to install 115 ft² of tiles.
Then, the amount that will come to install 970 ft² tiles:?
Cost of installing 1 ft² of tiles:
747.50/115
$6.5
So, the cost of installing 1 ft² of tiles: is $6.5.
Now, the cost of installing 970 ft² tiles will be:
6.5 × 970
$6,305
Therefore, with the help of simple mathematical operations, we know that the cost of installing 970 ft² will be $6,305.
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write the equation of the line that is parallel to the graph of 3x-y=5 whose y-intercept is (0,4)
Answer:
3x -y = -4
Step-by-step explanation:
You want the equation of the line parallel to 3x-y=5 through point (0, 4).
Parallel lineThe equation for the parallel will differ only in the constant. To find the new constant, use the given point coordinates for x and y.
3x -y = 3(0) -(4) = -4
The equation of the line is ...
3x -y = -4
What is the factor of x² 11x 18?
On solving the provided question we can say that, - the factors of the given equations [tex]x^2 -11x +18[/tex] are - x= 2 and x = 9
What is factor?A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.
[tex]x^2 -11x +18[/tex]
(x-2)(x-9)
x= 2 and x = 9
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Andy bought 300 shares of a corporation that manufactures kitchen cabinets. He
bought the stock years ago for x dollars. He recently sold this stock for y dollars.
Express his capital gain as a percent of the original purchase price algebraically.
The equation for capital gain as a percent of the original purchase price will be equal to a = (y - x)/x × 100.
What is an expression?If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.
The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. A mathematical operation like reduction, addition, multiplication, or division is used to include terms in an expression.
As per the given information in the question,
Use the equation for capital gain,
Let the selling price be y and the purchase price is x dollars.
Capital gain = Selling price - Purchase
Substitute the values,
Capital gain = y - x
Now, let's find out the percent increase.
Let's assume that 'a' is the percent increase.
So, the equation will be,
(a)(x) = y - x
ax = y - x
Divide both sides by x.
(ax)/x = (y - x)/x
a = (y - x)/x
Multiply the equation by 100 to show in percentage form,
a = (y - x)/x × 100
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What is discontinuity example?
Example of discontinuity in mathematical function is given by :
f(x) = ( x - 1 )/ ( x - 2) at x = 2.
Discontinuous function is defined as:
A function is said to be discontinuous if its left hand side limit is not equal to right hand side limit.It does not show the continuity of a function.Example of discontinuous function is given by :f(x) = ( x - 1 ) / ( x - 2 )
When x = 2 function does not defined .
Hence it is not continuous at x = 2.
Therefore, the example of the discontinuity in mathematics function is f(x) = ( x - 1 )/ ( x - 2) at x = 2.
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The graph of the equation y = x^2 − x − 6 is shown below
For what value or values of x is y=0?
x=−2 and x=3
x=2 and x=−3
x=−6 only
x=−2 only
For the equation y=0, there is much less math involved. This is because, no matter what, for any value of x, y must always be equal to zero.
What does y-intercept 0 mean?This is so because the y-intercept occurs at x = 0. X = 0, mx = 0, and Y = B at this point. When y = 0, we solve the equation for x to determine the x-intercept. The line crosses the x-axis at y=0,
Is the Y axis at Y = 0?You can mistakenly think of the line y = 0 as the y-axis, be aware of this. It's not right. Simply put, the line y=0 indicates that the y coordinate is always 0 for all locations (x, y) in the x-y plane, indicating that the line y=0 represents the x-axis.
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When Deema begins her drive, she is 400 mi from home. She drives at an average rate of 50 mph until she gets home. Draw a graph to represent this situation?
The linear function to model the problem is written in slope-intercept form as y = -50x + 400
Linear FunctionA linear function is of the form f(x) = mx + b where 'm' and 'b' are real numbers. Isn't it looking like the slope-intercept form of a line which is expressed as y = mx + b
m = slope of lineb = y-interceptIn the question given, we can model a linear function to represent this.
Let x represent the distance covered.
The function can be written as;
f(x) = -50x + 400
This function represents the distance left till she gets home
Plotting this on a graph, we would have a straight line intercpeting the x-axis at (8, 0) and the y- axis at (0, 400)
Kindly find attached graph below.
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What is the equation of the line that passes through (2, -1) and is perpendicular to the line 1 whose equation is y=-1/2
x+4?
Answer:
Step-by-step explanation:
The point-slope form of the equation of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
So, the equation for this problem, let
[tex](x_1,y_1)=(2,-1)[/tex]
then,
[tex]y-(-1)=m(x-2)\\y+1=m(x-2)[/tex]
If line (a) is perpendicular to line (b), then [tex]m_b[/tex] is equal to [tex]-\frac{1}{m_a}[/tex]. For this problem, let
[tex]m_a=-\frac{1}{2}[/tex] and [tex]m_b=2[/tex]
So,
[tex]y+1=(2)(x-2)\\y+1=2x-4\\(y+1)-1=(2x-4)-1\\y=2x-5[/tex]
find k so that a and b will be orthogonal
Answer:
k = -5
Step-by-step explanation:
The scalar product of vectors a and b is zero when the vectors are orthogonal (perpendicular):
[tex]\boxed{\begin{aligned}\vec a \cdot \vec b & = |a||b| \cos \theta\\& = |a||b| \cos 90^{\circ}\\& = 0 \end{aligned}}[/tex]
[tex]\textsf{Therefore, $\vec a$\; and \;$\vec b$\; are orthogonal when\; $\vec a\cdot \vec b=0$}[/tex]
Given:
a = ⟨2, -2⟩b = ⟨−5, k⟩Substitute the given vectors into the formula and solve for k:
[tex]\implies \langle 2, -2 \rangle \cdot \langle-5, k \rangle=0[/tex]
[tex]\implies (2)(-5) +(-2)(k)=0[/tex]
[tex]\implies -10-2k=0[/tex]
[tex]\implies 2k=-10[/tex]
[tex]\implies k=-5[/tex]
New customers with Verizon pay a flat rate installation fee plus $45.00 per month for the
service. If after nine months, Mr. Burns paid $565, write and solve a linear equation to determine
how much he would pay after one year.
He would pay $160 after one year if the installation fee per month is $45.
What is meant by installation fee?The cost of installing something. charge - the cost of a good or service; "the admittance charge" Based on the Farlex clipart collection and WordNet 3.0. Installation can be divided into two major categories: physical and virtual. While a virtual installation relates to the installation of software, a physical installation concerns the installation of tangible items like computer hard drives, wires, modems, and so on.
Simple installation entails unpacking and plugging the appliance into the main electrical outlet. This excludes mounting on brackets, reinstalling in fixed units, or connecting to the gas or water.
Installment fee per month=$45
For 9 months,
9×45=405
Total fees=Installation+405
Installation+405=$565
Let the installation be x then,
x+405=565
x=565-405
x=$160
Therefore, he would pay $160 after one year if the installation fee per month is $45.
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How do you write more than 3 in math?
The way to write 'more than 3' is >3.
We have to find a way to write "more than 3" in a mathematical form.
The greater-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the right, >, has been found in documents dated as far back as 1631. In mathematical writing, the greater-than sign is typically placed between two values being compared and signifies that the first number is greater than the second number.
Examples of typical usage include 1.5 > 1 and 1 > −2. The less-than sign and greater-than sign always "point" to the smaller number. Since the development of computer programming languages, the greater-than sign and the less-than sign have been repurposed for a range of uses and operations.
We can use this mathematical symbol here, in order to denote "more than 3" mathematically.
> 3 denotes that a number is more than 3.
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Examples of typical usage include 1.5 > 1 and 1 > −2. The less-than sign and greater-than sign always "point" to the smaller number. Since the development of computer programming languages, the greater-than sign and the less-than sign have been repurposed for a range of uses and operations.
We can use this mathematical symbol here, in order to denote "more than 3" mathematically.
> 3 denotes that a number is more than 3.
Hazel and Tom travel the same 18 km route.
Hazel starts at 9. 00 am and walks at a constant speed of 4. 8 km/h
Tom starts at 9. 39 am and runs at a constant speed.
Tom overtakes Hazel at 10. 15 am
At what time does Tom finish the route?
Answer:
11:27 am.
Step-by-step explanation:
The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked
1.25 * 4.8
= 6 km.
So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes
= 0.6 hrs.
So, Tom's speed is 6/0.6 = 10 km/hr.
,
and Tom will take 18/10 = 1.8 hours to finish the route,
= 1 hr 48 minutes
So he finishes the route at
9:39 + 1:48
= 11:27 am.
13a ^2+14-17a-12a ^2+12a+6a-a^ 2
(A) a-14
(B) a+14
(C) -9a^2+14
(D) -9a^2-5a-14.
Answer:
B
Step-by-step explanation:
13a ^2+14-17a-12a ^2+12a+6a-a^ 2
=14-17a+12a+6a
=14+a or a+14
Hi can someone fully answer the question down below
Answer:
x= -10
Step-by-step explanation:
since its > not ≥, your only answer would be -10.
at the point -6, it would be =
when x= -10,
[tex]\frac{-10+3}{6}[/tex]>[tex]\frac{-10}{4}[/tex]+1
-7/6>-3/2
which is correct
How can I grow my height?
It is estimated that around 80% of the final height is determined by hereditary factors. Several environmental factors, also including nutrition and exercise, frequently account for the remaining portion.
Explain the meaning of the term height?A variety of factors affect your overall height.
1. Consume a diet rich in fresh, fruits, and vegetables.
proteins from whole grains.
2. Use caution when using supplements:
Few situations call for the use of supplements to help children grow taller and elderly persons stop shrinking.
3. Get the appropriate amount of rest:
On occasion skipping sleep won't have a long-term impact on your height. However, issues could arise if you consistently clock less than the advised amount during adolescence.
4. Keep moving:
Regular exercise has a lot of advantages. It aids you in maintaining a healthy weight, strengthens the muscles and bones, and encourages the synthesis of HGH.
5. Take care of your posture:
You could appear shorter than they actually are if you have poor posture.
Additionally, slouching or slumping over time might change your actual height.
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A rectangle has a height of 1 1/4 inches and a base of 5/6 inches. What is the area of the rectangle?
Work out the area of this shape.
3cm
4cm
7cm
6cm
Answer: the area of the shape=25.5 cm²
Step-by-step explanation:
This shape is composed of a rectangle and a trapezoid
The area of the rectangle= 3(4)
The area of the rectangle= 12 cm²
[tex]\displaystyle\\The\ area\ of\ the\ trapezoid=\frac{3+6}{2} (7-4)\\\\The\ area\ of\ the\ trapezoid=\frac{9}{2} (3)\\\\The\ area\ of\ the\ trapezoid=4.5(3)\\\\The\ area\ of\ the\ trapezoid=13.5 \ cm^2[/tex]
The area of the shape=12+13.5
The area of the shape=25.5 cm²
What is a multiple of 32?
32, 64, 96,...... are the multiples of the 32.
What are mathematical operations?Calculate the answer using a math operator is referred to as a mathematical operation.
Basic mathematical operations are addition, multiplication, subtraction and division.
The given term is 32,
To find the multiple of 32,
Multiply 32 which natural numbers 1, 2, 3, 4, 5.....
32 x 1 = 32.
32 x 2 = 64
32 x 3 = 96
and so on...
Since, there are infinite multiples of 32.
So, 32, 64, 96,.... are the multiples of 32.
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Franklin Middle School's spring concert is next week. The music teacher chose students from the choir and the orchestra to perform solos. There are 25 choir students, and 5 of them have a solo. There are 20 orchestra students, and 4 of them have a solo. Do the two groups have the same ratio of students with a solo to total students?
For the choir, the ratio is 1/5 and for the orchestra, the ratio is also 1/5, then yes, the two groups have the same ratio
Do the two groups have the same ratio?
Here we just need to compute the two ratios, to do that, we need to take the quotient between the number of students with a solo and the total number of students.
For the choir, there are 25 students and 5 with a solo, so the ratio is:
5/25 = 1/5
For the orchestra, there are 20 students and 4 of them have a solo, so the ratio is:
4/20 = 1/5
So yes, both groups have the same ratio of students with a solo to total students.
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Choose an equivalent system of equations to the following system: (1 point) fx + gy = h qx + ry = s.
5Fx+5Gy=5H Qx +Ry=S is a system of equations that is equivalent to the following system.
An equivalent system of equations is a system of equations that has the same solutions as the original system, but the coefficients of the variables may be different.
To determine which of the given systems is equivalent to the original system, you need to solve each system and see if they have the same solutions.
The original system is:
Fx + Gy = H
Qx + Ry = S
The solution to this system can be found by either graphing the equations or using substitution or elimination methods.
If we solve each of the other systems in the same way, we find that the system that is equivalent to the original system is:
C. 5Fx + 5Gy = 5H
Qx + Ry = S
This is because all of the other systems have different coefficients for the variables, and therefore will not have the same solutions as the original system.
The complete question is;-
Choose an equivalent system of equations to the following system:
Fx + Gy = H
Qx + Ry = S
A. 5Fx + 5Gy = 5H
Qx − Ry = S
B. 5Fx + Gy = 5H
Qx + 5Ry = S
C.5Fx + 5Gy = 5H
Qx + Ry = S
D. Fx + 5Gy = 5H
Qx + Ry = S
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A wheelchair ramp is 20 feet long. It rises 5.1 feet above the ground. What is its angle of inclination (angle of elevation), to the nearest degree
Answer:
θ = 15°
Step-by-step explanation:
The wheelchair ramp creates a right triangle figure. Look at the image I have attached to this response to see the figure.
⭐ What is the "angle of inclination"?
The angle of inclination is the base angle adjacent to the 90-degrees. The angle of inclination is often denoted as θ.
To solve for the angle of inclination, θ, we have to use the inverse of a trigonometric function.
⭐ What trigonometric function do we use?
Look at the side lengths you are given. Are they opposite of θ? Are they adjacent to θ? Are they the hypotenuse of the triangle? Whatever combination of 2 side lengths you have, see what trigonometric function uses those 2 side lengths.
We are given the side length opposite of θ and a side length that is the hypotenuse of the triangle. Therefore, we are going to use the sine function.
⭐ What is the sine function?
sin(θ) = opposite/hypotenuse
Now, we are going to create an equation of the wheelchair ramp using the sine function.
sin(θ) = 5.1/20
Next, find the inverse of the equation. Here is the inverse of the sine function:[tex]sin^{-1} (opposite/hypotenuse) =[/tex]
Let's substitute the opposite and hypotenuse into the inverse of the sine function and solve using a scientific calculator. Make sure to round to the nearest degree.
[tex]sin^{-1}(5.1/20) =[/tex]
∴ [tex]sin^{-1}(5.1/20)[/tex] ≈ 15°
What property of congruence is illustrated in the statement if ∠A ≅ ∠B then ∠B ≅ ∠A?
The property of congruence illustrated in the statement is the transitive property.
The transitive property states that if A is congruent to B and B is congruent to C, then A is congruent to C. In other words, if two things are congruent to a third thing, they are also congruent to each other.
In the statement "If AB ≅ DE, EF ≅ DE then AB ≅ EF," AB is congruent to DE, and EF is congruent to DE, so AB must also be congruent to EF according to the transitive property.
The other properties you listed are not applicable in this case. The symmetric property states that if A is congruent to B, then B is congruent to A. The reflexive property states that every object is congruent to itself. And multiplication is not a property of congruence.
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The question is -
What property of congruence is illustrated in the statement? If AB ≅ DE, EF ≅ DE then AB ≅ EF.
a. Symmetric
c. Reflexive
b. Transitive
d. Multiplication
After researching many different shoes, chris narrows down his choice to these two. Which shoes are the best deal?.
Based on the information provided, it appears that the Air Slammers might be the best deal for Chris if his primary concern is getting the best price.
If Chris' primary concern is getting the best price, then the Air Slammers might be the best deal for him based on the information provided. It is important to note, however, that other factors might also be important in the decision-making process, such as the durability of the shoes and any preferences or personal preferences Chris might have.
It is also possible that the Hyper-Dunks might offer other benefits, such as better performance or more comfort, that could make them a more attractive option for Chris even if they are more expensive. Ultimately, the best deal depends on what is most important to Chris and how he weighs the different factors in the decision-making process.
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The sides of a triangle are given by
(3x2 − y2);(4x2−7xy+4y)and (−3x+7xy+8y2)
3x2 − y2;4x2−7xy+4yand (−3x+7xy+8y2)
.
Find its perimeter.
Answer:
Here is the answer
Step-by-step explanation:
To find the perimeter of a triangle, we need to add up the lengths of all three sides. In this case, the sides of the triangle are given by the expressions 3x2 - y2, 4x2 - 7xy + 4y, and -3x + 7xy + 8y2.
To find the perimeter, we can simply add up these three expressions:
Perimeter = 3x2 - y2 + 4x2 - 7xy + 4y - 3x + 7xy + 8y2
= 7x2 - 3xy + 12y
This is the perimeter of the triangle. Note that the perimeter is a scalar quantity, not a vector, so it does not have a direction associated with it.