Answer:
(x, y) = (5, 3)
Step-by-step explanation:
You want the solution to the system of equations ...
4x -3y = 115x -9y = -2SolutionIt is convenient to subtract the second equation from 3 times the first:
3(4x -3y) -(5x -9y) = 3(11) -(-2)
12x -9y -5x +9y = 33 +2
7x = 35 . . . . . . . simplify
x = 5 . . . . . . . . . . divide by 7
4(5) -3y = 11 . . . . . substitute into the first equation
9 = 3y . . . . . . . . add 3y-11 to both sides
y = 3 . . . . . . . . divide by 3
The solution is (x, y) = (5, 3).
__
Additional comment
We find using a graphing calculator to be the easiest way to solve a pair of simultaneous equations. The attachment shows the solution is the one we found above.
The approach of "substitution" is straightforward, if error-prone. Basically, you solve one equation for either variable, then use that expression in the other equation. Here, for example, you can solve the first for x:
x = (11 +3y)/4
Then use that in the second equation:
5(11 +3y)/4 -9y = -2
5(11 +3y) -36y = -8 . . . . eliminate the denominator
55 +15y -36y = -8 . . . . . eliminate the parentheses
-21y = -63 . . . . . . . . . . . simplify, subtract 55
y = 3 . . . . . . . . . . . . divide by -21
x = (11 +3(3))/4 = 20/4 = 5 . . . . find x
In the above, we used "elimination." We took advantage of the fact that the y-coefficients were related by a factor of 3. To cancel y-terms, we need to have the equations we "add" have opposite signs for the y-terms. Here, we do that by multiplying the first by 3 (to make -9y), then subtracting the second equation (which has -9y, so will cancel). We could have subtracted 3 times the first from the second, but that would make all the resulting coefficients be negative, which we like to avoid.
Or, we could have multiplied the first equation by -3 to make the y-coefficients opposite, then added the results. (Again, that would give negative coefficients in the sum.) Planning ahead can help avoid mistakes due to minus signs.
A video game designer places an anthill at the origin of a coordinate plane. A red ant leaves the anthill and moves along a straight line to (1, 1), while a black ant leaves the anthill and moves along a straight line to (−1, −1). Next, the red ant moves to (2, 2), while the black ant moves to (−2, −2). Then the red ant moves to (3, 3), while the black ant moves to (−3, −3), and so on. Complete the explanation of why the red ant and the black ant are always the same distance from the anthill. At any given moment, the red ant's coordinates may be written as (a, a) where a > 0. The red ant's distance from the anthill is (blank) . The black ant's coordinates may be written as (−a, −a) and the black ant's distance from the anthill is (blank) . This shows that at any given moment, both ants are (blank) units from the anthill.
Answer:use calculator to divide the variables and use the countains as a providence
Step-by-step explanation:
Solve the problems. 1 Determine if each equation is true Choose True or False for each equation. a. 4.25 X 10^6 425,000 b. 6.38 X 10^9=638,000,000,000 True False True False True False True False 5.11 X 10^-2=511 d. 2.79 x 10^-4 = 0.000279
I'll mark brainlyest
Answer:
a. False
b. False
c. False
d. True
Step-by-step explanation:
a. 4.25 x 10⁶ = 425,000 (false) should be 4,250,000
b. 6.38 x 10⁹ = 638,000,000,000 (false) should be 6,380,000,000
c. 5.11 x 10⁻² = 511 (false) should be 0.0511
d. 2.79 x 10⁻⁴ = 0.000279 (true)
Answer:
True
False
False
True
Step-by-step explanation:
a local school board claims that there is a difference in the proportions of households with school-aged children that would support starting the school year a week earlier, and the proportion of households without school-aged children that would support starting the school year a week earlier. they survey a random sample of 40 households with school-aged children about whether they would support starting the school year a week earlier, and 30 households respond yes. they survey a random sample of 45 households that do not have school-aged children, and 25 respond yes. based on the 90% confidence interval, (0.03, 0.36), is there convincing evidence of a difference in the true proportions of households, those with school-aged children and those without school-aged children, who would support starting school early? there is convincing evidence because the two sample proportions are different. there is convincing evidence because the entire interval is above 0. there is not convincing evidence because if another interval with a higher confidence level is calculated, it might contain 0. there is not convincing evidence because two different sample sizes were used. in order to determine a difference, the same number of households should be selected from each population.
Based on the given information, there is convincing evidence of a difference in the proportions of households with and without school-aged children that would support starting the school year a week earlier.
Based on the 90% confidence interval given, which ranges from 0.03 to 0.36, there is convincing evidence of a difference in the true proportions of households that would support starting the school year a week earlier, between those with school-aged children and those without. This is because the interval does not include 0, which suggests that the difference is statistically significant. However, it's important to note that this conclusion is based on the specific confidence level of 90%. If a different confidence level was used, the interval could potentially contain 0, indicating that there may not be a significant difference. Therefore, it's important to consider the level of confidence when interpreting the results. Additionally, the fact that different sample sizes were used could potentially impact the validity of the results. It's generally preferred to have equal sample sizes in order to increase the accuracy of the comparison. However, in this case, the difference in sample sizes does not necessarily invalidate the results, but it should still be taken into consideration.
Learn more about proportions here
https://brainly.com/question/870035
#SPJ11
Discrete Random Variables
A discrete random variable may take on only a countable number of distinct values such as 0,1,2,3,4,...
Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete. Examples of discrete random variables include the number of children in a family, the Friday night attendance at a cinema, the number of patients in a doctor's surgery, and the number of defective light bulbs in a box of ten.
The probability distribution of a discrete random variable is a list of probabilities associated with each of its possible values. It is also sometimes called the probability function or the probability mass function.
Example'
The cumulative distribution function for the above probability distribution is calculated as follows:
The probability that \(X\) is less than or equal to is 0.1,
the probability that \(X\) is less than or equal to 2 is 0.1+0.3 = 0.4,
the probability that \(X\) is less than or equal to 3 is 0.1+0.3+0.4 = 0.8, and
the probability that \(X\) is less than or equal to 4 is 0.1+0.3+0.4+0.2 = 1.
To learn more about cumulative distribution, visit
brainly.com/question/19884447
#SPJ4
In Exercises 21–23, use determinants to find out if the matrix is invertible.22. \(\left( {\begin{aligned}{*{20}{c}}5&1&{ - 1}\\1&{ - 3}&{ - 2}\\0&5&3\end{aligned}} \right)\)
if the matrix is invertible.22. \(\left( {\begin{aligned}{*{20}{c}}5&1&{ - 1}\\1&{ - 3}&{ - 2}\\0&5&3\end{aligned}} \right)\) then, the determinant of the matrix A is -3 (non-zero), the matrix is invertible.
To determine if a matrix is invertible, we need to find its determinant. If the determinant is non-zero, the matrix is invertible. Let's calculate the determinant for the given matrix:
Matrix A = \(\begin{pmatrix} 5 & 1 & -1 \\ 1 & -3 & -2 \\ 0 & 5 & 3 \end{pmatrix}\)
Step 1: Use the first row for cofactor expansion:
Determinant(A) = 5 × Cofactor(1,1) - 1 × Cofactor(1,2) + (-1) × Cofactor(1,3)
Step 2: Calculate the cofactors:
Cofactor(1,1) = Determinant of the 2x2 matrix obtained by removing the first row and first column:
\(\begin{pmatrix} -3 & -2 \\ 5 & 3 \end{pmatrix}\)
Cofactor(1,1) = (-3)(3) - (-2)(5) = -9 + 10 = 1
Cofactor(1,2) = Determinant of the 2x2 matrix obtained by removing the first row and second column:
\(\begin{pmatrix} 1 & -2 \\ 0 & 3 \end{pmatrix}\)
Cofactor(1,2) = (1)(3) - (-2)(0) = 3
Cofactor(1,3) = Determinant of the 2x2 matrix obtained by removing the first row and third column:
\(\begin{pmatrix} 1 & -3 \\ 0 & 5 \end{pmatrix}\)
Cofactor(1,3) = (1)(5) - (-3)(0) = 5
Step 3: Substitute the cofactors back into the formula for Determinant(A):
Determinant(A) = 5 × 1 - 1 × 3 + (-1) × 5 = 5 - 3 - 5 = -3
Since the determinant of the matrix A is -3 (non-zero), the matrix is invertible.
to know more about matrix click here:
https://brainly.com/question/30389982
#SPJ11
You deposit $800 in an account that pays 8% annual interest compounded quarterly. About how
long will it take for the balance to triple?
There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 1/8. There are 56 marbles in the bag and each is equally likely to be chosen. Work out how many red marbles there must be
Answer:
7 red marbles
Step-by-step explanation:
P( red) = red marbles / total marbles = 1/8
We know there are 56 marbles
red marbles/56 = 1/8
Multiply by 56
red marbles = 1/8 *56 = 7
There are 7 red marbles
C. Solve for each quotient:
8÷5/8
I Mark brainlies
Answer:
12.8
Step-by-step explanation:
8÷5/8 is also the same as:
8 x 1/5 x 8
Proof:
the given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.
The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.
The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.
The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.
By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.
Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.
Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.
for such more question on least squares
https://brainly.com/question/3617398
#SPJ8
Question
The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.
△A ′ B ′ C ′ triangle, A, prime, B, prime, C, prime is the image of △ A B C △ABCtriangle, A, B, C under a rotation about point B BB. A A C C A ′ A ′ C ′ C ′ B B Determine the angles of rotation. Choose all answers that apply:
The rotation of the triangle that's illustrated will be a rotation of 90°.
How to illustrate the information?It should be noted that transformation is a general term for 4 specific ways that can be used to manipulate the shape and the position of a point, line, or a geometric figure. In such a case, the original shape of the object is called the pre-Image while the final shape and the position of the object is simply the image under transformation.
There are typically four common types of transformations and they're translation, rotation, reflection, as well as dilation. It should be noted that rotation about simply illustrates the transformation that takes place regarding the triangle.
For rotation, the shape rotates or turns the pre-image around the axis and there'll be no change in the size or shape of the object.
Here, the counterclockwise rotation was illustrated in the triangle ABC. Therefore, the rotation of the triangle that's illustrated will be a rotation of 90°.
In conclusion, based on the information given, the correct option is A.
Learn more about triangles on:
brainly.com/question/1058720
#SPJ1
Complete question:
Triangle ABCTriangle ABC is rotated to form △A'B'C' .
The coordinates of point A are (1, 1) , the coordinates of point B are (3, 1) , and the coordinates of point C are (1, 4) .
Which countr clockwise rotation around the origin results in the transformation of △ABC to △A'B'C' ?
Select from the drop down arrow to choose the correct rotation.
(a) rotation of 90
(b) rotation of 180
(c) rotation of 360
Find the value of x.
a
x = [?]
x
In the given circle the length of the chord marked x is
We know that the length of the chord is bisected by the perpendicular from the center of the circle.
Therefore the length of the chord is 7 × 2 = 14 units.
Again from the chord properties of a circle we know that, chords that are equidistant from the center are equal.
Since both the chords are at a distance of 9 units hence both chord lengths
Hence the length of the other chord = 14 units.
∴ x = 14
The segment of a line that joins any two points on a circle's circumference is known as the chord. It must be emphasized that its longest chord is its diameter, which runs through the center of the circle.
The circle and its chord are depicted in the diagram below. In the center of the circle, equal-length chords subtend equal angles.
To learn more about chord visit:
https://brainly.com/question/21686011
#SPJ1
One example of a mathematical model is an equation that describes the relationship between two quantities.
a. True
b. False
Answer:
True
Step-by-step explanation:
Linear equations are often used to model the relationship between the dependent variable that is affected by changes in the independent variable.
For instance, the linear function: f(x) = 2x + 3, where f(x) is the output (dependent variable) depends on the value of the input, x (independent variable).
Therefore, the correct answer is True.
in a group 20 children 60 % have blue eyes and 35 % have brown eyes how many children have brown eyes . SHOW UR WORKING OUT PLZ THANK U ❤❤❤
Answer:
7 children have brown eyes
Step-by-step explanation:
20*.35=7
Answer:
7 children have brown eyes
Step-by-step explanation:
can i get brainliest please?
The circumference would , 1 of 2. select choice . for example, a circle with a radius of 3 feet would have a circumference that is about 18 feet. when the radius doubles to 6 feet, the circumference is about , 2 of 2. select choice feet.
The circumference of the circle with a radius of 6 feet would be approximately 37.7 feet.
The circumference of a circle is the distance around the outer edge of the circle. It is the perimeter of the circle, which is the total length of the boundary that encloses the area of the circle.
The formula for the circumference of a circle is
C = 2πr
Where C is the circumference, r is the radius, and π is approximately 3.14.
If a circle has a radius of 3 feet, the circumference would be
C = 2πr
C = 2π(3)
C ≈ 18.85 feet
When the radius doubles to 6 feet, the circumference would be
C = 2πr
C = 2π(6)
C ≈ 37.7 feet
Learn more about circumference here
brainly.com/question/26605972
#SPJ4
Answer:
double, and 36
Step-by-step explanation:
Mc graw hill
Q...
Find the circumference of a circle whose diameter is 20 mm. *Plz explain your answer*
Answer:
The circumference is 62.8.
Step-by-step explanation:
Find the diameter (in this case, 20mm)Multiply the diameter by 3.14, or pi. (Pi can be a different number depending on the problem but 3.14 is the most used one)The product of the diameter multiplied by Pi is the circumference of the circle!The depth of a ship wreck is 120 feet below sea level. Which integer represents this elevation? +120 −120
Answer:
-120
Step-by-step explanation:
Answer:
YOUR ANSWER SHOULD BE -120
Step-by-step explanation:
heres why
becuase i said so
and we already asume its at 0 so if u go 120- 0 what do u get u get -120
so thats why
Help Por favor! Will mark brainliest!
Two groups of people went to see Avatar in IMAX 3‐D. The first group spent $33.00 on two adult and three children tickets. The other group spent $55.00 on five adult and two children tickets. Let x represent the cost of an adult ticket and y represent the cost of a children ticket. Answer each of the questions. Label each answer.
1) What is the equation that represents the first group spending?
2) What is the equation that represents the second group spending?
3) What is the cost for each type of ticket (the adult and the children)? Show your work.
Answer: An adult’s ticket costs $9 while a children’s ticket costs $5.
Step-by-step explanation:
1). 2x + 3y = 33
2). 5x + 2y = 55
3). I’m going to use substitution.
Isolate a variable (x):
2x + 3y = 33
2x = -3y + 33
X = (-3y + 33)/2
X = -3/2y + 33/2
Substitute and solve for y:
5x + 2y = 55
5(-3/2y + 33/2) + 2y = 55
-15/2y + 165/2 + 2y = 55
-11/2y = -55/2
Y = 5 <— children’s ticket.
Solve for x:
2x + 3y = 33
2x + 3(5) = 33
2x + 15 = 33
2x = 18
X = 9 <— adult’s ticket.
Check:
5x + 2y = 55
5(9) + 2(5) = 55
45 + 10 = 55
55 = 55
2x + 3y = 33
2(9) + 3(5) = 33
18 + 15 = 33
33 = 33
Help !!!
See question in image.
Please show workings .
Answer:
see explanation
Step-by-step explanation:
Given f(x) then the derivative f'(x) is
f'(x) = lim( h tends to 0 ) \(\frac{f(x+h)-f(x)}{h}\)
= lim( h to 0 )\(\frac{x+h+\frac{1}{x+h }-(x+\frac{1}{x} ) }{h}\)
= lim(h to 0) \(\frac{x+h+\frac{1}{x+h}-x-\frac{1}{x} }{h}\)
= (lim(h to 0) \(\frac{h+\frac{1}{x+h}-\frac{1}{x} }{h}\)
= lim( h to 0 ) \(\frac{hx(x+h)+x-(x+h)}{hx(x+h)}\)
= lim( h to 0 ) \(\frac{hx(x+h)+x-x-h}{hx(x+h)}\)
= lim(h to 0 ) \(\frac{hx(x+h)}{hx(x+h)}\) - \(\frac{h}{hx(x+h)}\)
Cancel the numerator/denominator of first fraction and h in the second
= lim ( h to 0 ) 1 - \(\frac{1}{x(x+h)}\) ( let h go to zero ), then
f'(x) = 1 - \(\frac{1}{x^2}\)
FILL IN THE BLANK. the quantitative relation between two amounts showing the number of times one value contains or is contained within the other definition. ___
Ratio is the relation between two amounts that shows the number of times one value contains within the other.
What is Ratio?
A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of vegetables contains eight tomato and six carrots, the tomato-to-carrot ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of carrots to tomato is 6:8 (or 3:4), while the proportion of tomato to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive.
Solution:
Ratio is the relation between two amounts that shows the number of times one value contains within the other.
To learn more about Ratio from the given link
https://brainly.com/question/2328454
#SPJ4
What is the answer to this question?
Answer:
If S is some point that lies between R and T, then addition RS and ST should equal RT
y = 4, RS = 27, ST = 17
RS = 6y + 3
ST = 3y + 5
RT = 44
RS + ST = RT
6y + 3 + 3y + 5 = 44
9y + 8 = 44
Combine like terms
9y = 44 - 8
Subtract 8 from both sides of the equation
9y = 36
Divide both sides of the equation by 9
y = 36/9
y = 4
Now substitute the y value in the original equation to find RS and ST
I got 27 and 17 respectively
Step-by-step explanation:
Is reverse logistics management more difficult than the management of more typical supply chain flows?
Reverse logistics management can be more challenging than the management of more typical supply chain flows. In reverse logistics, the flow of products goes in the opposite direction compared to traditional forward logistics.
It involves activities such as product returns, repairs, refurbishment, recycling, and disposal. This adds complexity to the supply chain as it requires effective coordination and management of multiple processes, including product collection, sorting, inspection, and redistribution.
There are several reasons why reverse logistics management can be more difficult. First, there is often a lack of visibility and control over the flow of returned products, which can result in inefficiencies and increased costs. Second, the nature of reverse logistics operations is typically more unpredictable and variable compared to forward logistics. Third, managing customer expectations and satisfaction during the return process is crucial, as it directly impacts customer loyalty and brand reputation.
In conclusion, reverse logistics management presents unique challenges compared to traditional supply chain flows. It requires careful planning, effective coordination, and a focus on customer satisfaction to ensure efficient and cost-effective handling of returned products. Organizations need to develop robust processes and systems to effectively manage reverse logistics and optimize their supply chain performance.
Learn more about Reverse logistics management here:
brainly.com/question/31692836
#SPJ11
prove for any real constants x and y, where y > 0 (n 7x) y = θ(n y ).
To prove that y^n = θ(n^y) for any real constants x and y, where y > 0, we need to show that y^n is both O(n^y) and Ω(n^y).
To show that y^n = O(n^y), we need to find a positive constant C and a value of n_0 such that for all n ≥ n_0, we have y^n ≤ Cn^y. We can rewrite this inequality as n^(ylog(y)) ≤ Cn^y. If we choose C = y^(y+1) and n_0 = 1, then for all n ≥ n_0, we have:
n^(ylog(y)) = n^(log(y^n)) = y^n ≤ y^(y+1) * n^y = Cn^y.
Thus, y^n = O(n^y).
To show that y^n = Ω(n^y), we need to find a positive constant C and a value of n_0 such that for all n ≥ n_0, we have y^n ≥ Cn^y. We can rewrite this inequality as (y/n)^n ≥ C. Since y > 0 and n ≥ 1, we have y/n ≥ 1, which implies (y/n)^n ≥ 1^n = 1. If we choose C = 1 and n_0 = 1, then for all n ≥ n_0, we have:
(y/n)^n ≥ 1.
Thus, y^n = Ω(n^y).
Since we have shown that y^n = O(n^y) and y^n = Ω(n^y), we can conclude that y^n = θ(n^y). Therefore, the statement is proved.
For more similar questions on probability:
brainly.com/question/13604758
#SPJ11
The local farmers market has oranges on sale for 5 for 1.80
What is the cost of one orange ?
Answer:.36 cent
1Step-by-step explanation:1.80 divided by 5
Solve the equation for y:
3 + 5y/2
= X
Answer :
y = \(\frac{2}{5} ( x - 3)\)
Step-by-step explanation:
6 + 5y = 2x
or, 5y + 6 - 6 = 2x - 6
or, 5y = 2x - 6
or, 5/5 y = 2 ( x - 3) / 5
or, y = 2/5 ( x - 3)
therefore, y = \(\frac{2}{5} ( x - 3 )\)
which structure do all embryos have early in development??
a. eyes
b. nose
c. mouth
d. tails
Answer:
D. Tails
Step-by-step explanation:
I don’t understand help
Answer:
6: (0,9)
7: ( -10, -3)
8: (-12,9)
9: (2,0)
Step-by-step explanation:
ASAP!!!! FUNCTIONS HELP
Answer:
3Step-by-step explanation:
All but first for every single x gives single y so the second, third and fourth are function
At first for x=2 we have two y (2 or -2) so this isn't function.
The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0. 40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. Is avery interpreting the probability correctly?.
Avery interpreting the Probability is wrong because 0.40 represents probability in the long run over many visits to the site
What is meant by Probability?Probability: The chance that a given event will occur. The ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes
given that the probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0. 40
Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey
Avery interpreting the Probability is wrong because 0.40 represents probability in the long run over many visits to the site
To learn more about Probability visit:
brainly.com/question/11234923
#SPJ4
Answer:
Because 0.40 represents likelihood over many visits to the site in the long term, Avery's interpretation of the probability is incorrect.
Step-by-step explanation:
What does the term probability mean?
Probability: The likelihood that a specific occurrence will take place. the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally likely outcomes that result in a specific event
Given that there is a 0. 40 percent chance that a randomly chosen website visitor will be requested to take an online survey
Avery asserts that of the following 5 site visits, 2 will be required to complete the survey.
Because 0.40 represents chance over the long term and several visits to the site, Avery's interpretation of the probability is incorrect.
Give me the slope for the following points (9, 10)
and (7,2)
The answer is
m = 4
Have a great day!!!
Answer:
4 is the slope
Step-by-step explanation:
We know this by using the slop formula, which is y2-y1/x2-x1
We just plug in the points that we know and solve from there,
Give brainliest please :3
the three angles in a traingle are 5x, 6x and 7x. work out the size of the largest angle in the triangle
Answer:
the largest angle is 70
Step-by-step explanation:
180 degrees in a triangle
180=5x+6x+7x
simplify
180=18x
x=10
7x=70
the largest angle is 70 degrees.