rush, please answer. will UPVOTE !!
Instruction:
Solve using Laplace Transform.
Show STEP BY STEP (Use convolution if needed)
L ^-1 {4/(s^2(s+2))}
Answers
The inverse Laplace transform of 4/(s^2(s+2)) is -2 - 2t + 2e^(-2t).
To solve the given equation using Laplace Transform, we will follow these steps:
Write the given equation in the Laplace domain:
L{4/(s^2(s+2))}
Decompose the rational function into partial fractions:
4/(s^2(s+2)) = A/s + B/s^2 + C/(s+2)
To find the values of A, B, and C, we can use the method of partial fraction decomposition. Multiply both sides by the denominator and equate the numerators:
4 = A(s)(s+2) + B(s+2) + C(s^2)
Simplify and solve for A, B, and C:
4 = As^2 + 2As + 2A + Bs + 2B + Cs^2
4 = (A + C)s^2 + (2A + B)s + 2A + 2B
Comparing coefficients, we get the following equations:
A + C = 0 (coefficient of s^2)
2A + B = 0 (coefficient of s)
2A + 2B = 4 (constant term)
From the first equation, A = -C. Substituting this into the second equation gives B = -2A. Substituting these values into the third equation, we have:
2A + 2(-2A) = 4
2A - 4A = 4
-2A = 4
A = -2
From A = -2, we get C = 2.
Substituting these values back into the partial fraction decomposition, we have:
4/(s^2(s+2)) = -2/s - 2/s^2 + 2/(s+2)
Take the inverse Laplace Transform of each term using standard Laplace Transform tables:
L^-1 {-2/s} = -2
L^-1 {-2/s^2} = -2t
L^-1 {2/(s+2)} = 2e^(-2t)
Combine the inverse Laplace Transform terms:
L^-1 {4/(s^2(s+2))} = -2 - 2t + 2e^(-2t)
Therefore, the solution to the given equation using Laplace Transform is -2 - 2t + 2e^(-2t).
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Related Questions
I need help with this
Answers
Answer:
86 degrees
Step-by-step explanation:
Triangles add up to 180 degrees.
57 + 37 + x = 180
94 + x = 180
Subtract 94 from both sides.
x = 86
A box of crayons costs $1.75, including taxes. Mr. Valentino wants to purchase boxes of crayons for his class and has a $25 budget. write and inequality to solve for the number of boxes of crayons My. Valentino can purchase with his budget.
Answers
Answer:
I believe it would be 14
Step-by-step explanation:
A group of randomly selected Gamin Middle School athletes were asked to pick their favorite sport. The bar graph below shows the results of the survey. There are
414
414414 athletes at Gamin Middle School.
A bar graph where the vertical axis is labeled number of atheletes and the horizontal axis is labeled sport. Football bar extends to 15. The basketball bar extends to 9. The hockey bar extends to 10. The baseball bar extends to 8. The other bar extends to 3.
A bar graph where the vertical axis is labeled number of atheletes and the horizontal axis is labeled sport. Football bar extends to 15. The basketball bar extends to 9. The hockey bar extends to 10. The baseball bar extends to 8. The other bar extends to 3.
Based on the data, what is the most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey?
Choose 1 answer:
Choose 1 answer:
Answers
Based on the data, the most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey include the following: 4. 92.
What is a bar graph?In Mathematics, a bar graph is sometimes referred to as a bar chart and it simply refers to a type of graph that is used for the graphical representation of a population (data set), especially through the use of rectangular bars and vertical columns.
In order to determine the most reasonable estimate for the number of athletes whose favorite sport is hockey, we would have to multiply the total population size by the proportion of athletes (sample proportion) whose favorite sport is hockey:
Estimate = Population size × Sample proportion.
Estimate = 414 × 10/45
Estimate = 92 athletes.
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Complete Question:
A group of randomly selected Gamin Middle School athletes was asked to pick their favorite sport. The bar graph below shows the results of the survey. There are 414 athletes at Gamin Middle School.
Based on the data, what is the most reasonable estimate for the number of Gamin Middle School athletes whose favorite sport is hockey?
Choose 1 answer:
1. 65
2. 74
3. 83
4. 92
Low Carb Diet Supplement, Inc., has two divisions. Division A has a profit of $230,000 on sales of $2,120,000. Division B is able to make only $34,700 on sales of $381,000.
Compute the profit margins (return on sales) for each division. (Input your answers as a percent rounded to 2 decimal places.)
Division A= ______%
Division B= ______%
___________________________________________________________________________________________________________________________________________________
Polly Esther Dress Shops Inc. can open a new store that will do an annual sales volume of $1,220,400. It will turn over its assets 2.7 times per year. The profit margin on sales will be 7 percent.
What would net income and return on assets (investment) be for the year? (Input your return on assets answer as a percent rounded to 2 decimal places.)
Net Income=
Return on Assets= __________ %
Answers
The profit margins (return on sales) for each division are approximately :Division A = 10.85%,Division B = 9.11% and The calculations for the year would be:Net Income = $85,428,Return on Assets = 18.9%.
To compute the profit margins (return on sales) for each division, we divide the profit by the sales and multiply by 100 to express the result as a percentage.
For Division A:
Profit Margin = (Profit / Sales) * 100
Profit Margin = ($230,000 / $2,120,000) * 100
Profit Margin ≈ 10.85%
For Division B:
Profit Margin = (Profit / Sales) * 100
Profit Margin = ($34,700 / $381,000) * 100
Profit Margin ≈ 9.11%
To calculate the net income and return on assets for Polly Esther Dress Shops Inc., we use the given information.
Net Income = Profit Margin * Sales
Net Income = 7% * $1,220,400
Net Income = $85,428
Return on Assets = Profit Margin * Asset Turnover
Return on Assets = 7% * 2.7
Return on Assets = 18.9%
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Find the arc length of the curve on the given interval. (Round your answer to two decimal places.)
Parametric equation: x = e^-t cos t, y = e^-t sin t
Interval 0 ≤ t ≤ /2
Answers
The arc length of a curve given by parametric equations can be calculated using the formula:
\(\[S = \int_{t_1}^{t_2} \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} dt\]\)
In this case, the parametric equations are \(\(x = e^{-t} \cos t\)\) and \(\(y = e^{-t} \sin t\)\), and the interval is \(\(0 \leq t \leq \frac{\pi}{2}\)\).
To find the arc length, we need to calculate the derivatives \(\(\frac{dx}{dt}\)\) and\(\(\frac{dy}{dt}\)\):
\(\[\frac{dx}{dt} = -e^{-t} \cos t - e^{-t} \sin t\]\)
\(\[\frac{dy}{dt} = -e^{-t} \sin t + e^{-t} \cos t\]\)
Now we can substitute these derivatives into the arc length formula:
\(\[S = \int_{0}^{\frac{\pi}{2}} \sqrt{\left(-e^{-t} \cos t - e^{-t} \sin t\right)^2 + \left(-e^{-t} \sin t + e^{-t} \cos t\right)^2} dt\]\)
Simplifying and expanding the terms inside the square root, we get:
\(\[S = \int_{0}^{\frac{\pi}{2}} \sqrt{2e^{-2t}} dt\]\)
Next, we simplify the expression inside the square root:
\(\[S = \int_{0}^{\frac{\pi}{2}} e^{-t} dt\]\)
Integrating with respect to t, we have:
\(\[S = \left[-e^{-t}\right]_{0}^{\frac{\pi}{2}} \\\\= -e^{-\frac{\pi}{2}} + 1\]\)
Finally, rounding the answer to two decimal places, the arc length of the curve on the given interval is approximately 0.28 units.
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If the following figure was reflected across the x-axis, what would be the coordinates of D'?
Answers
Answer: 5, -4
Step-by-step explanation:
imagine a mirror on the x axis and just make it look symmetrical and that will help you. Its also the complete opposite of the point
WHAT IS THE TOTAL SURFACE AREA OF THE SQUARE PYRAMID???? THIS IS THE LAST QUESTION AND I ONLY HAVE 13 POINTS SO PLEASE ANSWER CORRECTLY!!!! :DD WILL GIVE BRAINLIEST AND 5 STARS AND THANKS IF YOUR RIGHT
Answers
Answer:
The answer is 203 cubed in
Step-by-step explanation:
7 x 11 = 77
77 x 2 = 154
7 x 7 = 49
154 + 49 = 203
228 million in standard form
Answers
228 million
228 000 000
The standard form of writing this is;
2.28 x 10^8
\(2.28\times10^8\)Question 9 [Total Marks 4] area А square card with sides 2x cm long has a rectangle cut out of it with side lengths 16 cm and 1.5x cm. A second piece of card is rectangular with sides 15 and 12 cm long and has a rectangle with sides (x-6) cm and (x-5) cm cut out of it. of The area of card left is the same in both cases. What is the value of x?
Answers
Given the dimensions of the square card, the cutout rectangle, the rectangular card, and its cutout rectangle, the value of \(x\) will be \(10\)
We will first calculate the leftover areas after cutting out rectangles from the first and second cards. Then we will equate the expressions for the leftover areas (since they are equal) to find the value of \(x\).
Leftover area for the first square cardSince the side of the square card is \(2x\), the area of the square card will be
\((2x)^2=4x^2\text{ cm}^2\)
The area of the rectangle cut out from the square card will be
\(16\times 1.5x=24x \text{ cm}^2\)
The leftover area after removing the rectangle from the square card will be
\((4x^2-24x)cm^2\)
Leftover area for the second cardThe second card is a \(15\) by \(12\) rectangle. Its area will be
\(15\times 12=180cm^2\)
The area of the rectangle cut from it is
\((x-5)(x-6)=(x^2-11x+30)cm^2\)
The remaining area will be
\(180-(x^2-11x+30)=(150+11x-x^2)cm^2\)
Calculating the value of xTo calculate the value of \(x\), note that the leftover areas are equal. So, we equate the expressions for the leftover areas, and solve the resulting equation for \(x\).
\(4x^2-24x=150+11x-x^2\)
rearranging, and simplifying, we get
\(x^2-7x-30=0\)
when we solve, we get
\(x=10\text{ or }x=-3\)
the only meaningful solution here is \(x=10\)
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Problems 7 through 13, determine the Taylor series about the point xo for the given function. Also determine the radius of convergence of the series. 7. sinx, Xo = 0 9. x, Xo = 1 10. x, xo =-1 13. 1 1-x' Xo = 2
15. Let y = anx". n=0
Answers
7. For sin(x) with x₀ = 0, the Taylor series is given by:
sin(x) = Σ((-1)^n * x^(2n+1))/(2n+1)!
n=0 to infinity
The radius of convergence for sin(x) is infinite.
9. For x with x₀ = 1, the Taylor series is given by:
x = Σ(x - 1)^n
n=0 to 1
The radius of convergence for this series is infinite.
10. For x with x₀ = -1, the Taylor series is given by:
x = Σ(x + 1)^n
n=0 to 1
The radius of convergence for this series is infinite.
13. For 1/(1-x) with x₀ = 2, the Taylor series is given by:
1/(1-x) = Σ(-1)^n * (x - 2)^n
n=0 to infinity
The radius of convergence for this series is 1.
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Over the past 4 years, a customer's fixed income portfolio value has dropped by 5%. During the same period, the Consumer Price Index has dropped by 2%. Based on these facts, which statement is TRUE?
Answers
The statement that is TRUE based on the given facts is that the customer's fixed income portfolio has experienced a greater decline in value than the decrease in the Consumer Price Index (CPI).
To elaborate, the customer's fixed income portfolio has dropped by 5% over the past 4 years. This means that the value of their portfolio has decreased by 5% compared to its initial value. On the other hand, the Consumer Price Index (CPI) has dropped by 2% during the same period. The CPI is a measure of inflation and represents the average change in prices of goods and services.
Since the customer's portfolio has experienced a decline of 5%, which is larger than the 2% drop in the CPI, it indicates that the value of their portfolio has decreased at a higher rate than the general decrease in prices. In other words, the purchasing power of their portfolio has been eroded to a greater extent than the overall decrease in the cost of goods and services measured by the CPI.
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ILL MARK BRAINLIEST PLEASE HELP DUE IN 10 MINS
Jessica is selling girl scout cookies and recorded how many she sold in one afternoon. She sold Thin Mints, Trefoils, and Samoas.
2a. She sold 54 boxes of Thin Mints, which was 60% of the total number she sold. How many total boxes did she sell? (3 points – 2 pts for correct answer, 1 pt for showing work)
2b. If 60% of the cookies sold were Thin Mints and 10% of the cookies sold were Samoas, how many boxes of Trefoils did she sell? (3 points – 2 pts for correct answer, 1 pt for showing work)
Answers
Answer:
Step-by-step explanation:
2a)
she sold .6 of the total
so .6*(total sold) = 54
.6x=54
x=90 boxes
2b)
.1*(total) = samoas
.1(90) =9 samoas
90 - 54 - 9 = 27 Trefoils
Answer:
A-90
B-27
Step-by-step explanation:
29
34 889
402566
500
--Key: 318-538
11. Describe the distribution of the data.
9. What is the median value?
10. What is the mean of the data? Round to the
nearest penny.
12. What percent of shoes cost more than $40?
Answers
The Percentage of shoes that cost more than $40 based on the given numbers.
11. Describe the distribution of the data:
Without additional information, it is difficult to precisely describe the distribution of the data. However, we can provide some general observations based on the provided numbers. The data appears to be a list of individual values without any clear pattern or trend. The distribution could be symmetrical, skewed, or even contain outliers. To provide a more detailed description, additional information such as the context or specific characteristics of the data would be needed.
9. What is the median value?
To find the median value, we need to arrange the data in ascending order. The given numbers are: 29, 34, 889, 402566, 500. After arranging them in ascending order, we have: 29, 34, 500, 889, 402566. Since there are five numbers, the median value will be the middle number, which in this case is 500.
10. What is the mean of the data? Round to the nearest penny.
To find the mean, we sum up all the numbers and divide by the total count. The sum of the numbers is: 29 + 34 + 889 + 402566 + 500 = 403018. Dividing this sum by the count of numbers (5), we get: 403018 / 5 = 80603.6. Rounding this to the nearest penny, the mean of the data is approximately $80603.60.
12. What percent of shoes cost more than $40?
the given data does not provide any information related to shoes or their prices. Therefore, it is not possible to determine the percentage of shoes that cost more than $40 based on the given numbers.
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Find the perimeter of the triangle below.
Round to the nearest hundredth if necessary.
Show work.
Answers
The perimeter of the triangle in the image is 15.4 units.
How to find the perimeter?The perimeter of a triangle is equal to the sum of the lengths of the 3 sides, here we can see that the lengths are:
For the base, the length is 5 units.
For the height, the length is 4 units.
Finally the hypotenuse, we can use Pythagorean's theorem to find it, we will get:
H = √(5² + 4²)
H = 6.4
Then the perimeter of the triangle is:
P = 6.4 + 4 + 5
P = 15.4
That is the perimeter.
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Given 2x - 3 = 7, what is the value of x?
Answers
Answer:
2x-3=7 /×3
2x=3+7
2x=10 /÷2
x=5
Answer:
Step-by-step explanation:
2x - 3 = 7 Add 3 to both sides
2x - 3+3 = 7 + 3 Combine
2x = 10 Divide by 2
2x/2 = 10/2 Combine
x = 5
These types of equations all follow the same pattern. The look like
ax + b = c You have to isolate the x so add b if b is minus or you subtract b if b is plus. Notice that b was minus in your question. So Add
Now you you have
ax = c - b That always happens. The x is isolated if you deal with b first. Now all you need to do is divide by a.
x = (c - b)/a
Try a couple
3x -4 = 5 The answer is 3
5x + 2 = 27 the answer is 5
what is 2 less than the square of a number ASAP
Answers
Helppppppppppppppppp
Answers
Instructions- Solve the system of equations. Type in all points of intersection for the two functions and round to the nearest tenth if necessary.
f(x) = -0.5x+2
8(x) = -5x + 3
Answers
f(×)=-0,5x+2
8(×)= -5x+3
8×= -5x+3
8-5x+3
3x+3
x6
The nearest tenth as required, the point of intersection expressed as (0.2, 2.1).
To solve the system of equations, to find the points where the two functions intersect, which means the x-values where f(x) equals g(x). Let's proceed with the solution:
f(x) = -0.5x + 2
g(x) = -5x + 3
Set f(x) equal to g(x):
-0.5x + 2 = -5x + 3
Now, let's solve for x:
Add 0.5x to both sides to eliminate the term with x on the left side:
2 = -4.5x + 3
Subtract 3 from both sides:
-1 = -4.5x
Now, divide by -4.5 to isolate x:
x = -1 / -4.5
x ≈ 0.2222
Now that we have the x-value of the point of intersection, let's find the corresponding y-value by plugging x back into either f(x) or g(x). Let's use f(x):
f(x) = -0.5x + 2
f(0.2222) = -0.5(0.2222) + 2
f(0.2222) ≈ 2.1111
So, the point of intersection is approximately (0.2222, 2.1111).
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write an equation for a line that is perpendicular to y=1/2x+6
Answers
Answer:
y= -2x+6
Step-by-step explanation:
General formula :
y=mx+c
m is the gradient
when finding when finding the perpendicular line of another line is will be the negative inverse of the gradient
The perpendicular line will have a gradient of -2 (the negative inverse of 1/2)
so
the line perpendicular to the equation y=1/2x+6
is y= -2x+6
The first-class interval in the grouped frequency distribution is 5-10. The width of the interval is:
Answers
The first-class interval in the grouped frequency distribution is 5-10. The width of the interval is 5.
The given first-class interval is 5-10. We are to find out the width of the interval.
A grouped frequency distribution can be defined as a statistical report that organizes data with non-overlapping and continuous intervals called classes. Each class interval indicates a range of values.
The width of an interval in a grouped frequency distribution can be calculated using the below formula:
width of an interval = upper limit of a class - lower limit of the same class
Given that the first-class interval in the grouped frequency distribution is 5-10;
Therefore,
Lower limit of class = 5
Upper limit of class = 10
Width of the interval can be calculated using the formula as:
Width of interval = Upper limit of a class - Lower limit of the same class = 10 - 5 = 5
Therefore, the width of the interval is 5.
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Answer pleaseeee??? Thanks
Answers
Answer:
4
Step-by-step explanation:
coefficient- a numerical or constant quantity placed before and multiplying the variable
based on info above 4 is the answer
A robot can complete 5 tasks in hour. Each task takes the same amount of time.
10
a. How long does it take the robot to complete one task?
b. How many tasks can the robot complete in one hour?
Answers
Answer:
a. 15 minutes per task
b. 5 tasks in an hour
Step-by-step explanation:
1 hour = 60 minutes
60/5 tasks = 15 minutes per task
Question 5 of 23
What is the slope-intercept equation of the line below?
A. y = 5x-2
B. y = -4/5x-2
C. y = 4/5x-2
D. y = 5x+2
Answers
The slope-intercept equation of the line below is C. y = 4/5x-2.
What is slope-intercept equation?Slope-intercept equation is a linear equation in the form of y = mx + b, where m is the slope of the line and b is the y-intercept. It can be used to graph a line on a two-dimensional plane, and is used to calculate the rate of change (rise/run) between two points on the graph.
This slope-intercept equation can be determined by analyzing the given line. By looking at the graph, we can see that the slope of the line is 4/5, which means that the coefficient of x in the equation is 4/5. Additionally, the y-intercept is at -2, so the equation is y = 4/5x-2.
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I really need help on this!!! Someone please help?
Answers
Answer:
x= 3, y= -5
Step-by-step explanation:
Answer:
(3,-4)
Step-by-step explanation:
or x = 3, y = -5
Is the set Q × Q finite, countably infinite, or uncountably
infinite?
Answers
The set Q × Q, which represents the Cartesian product of the rational numbers with themselves, is countably infinite.
The set Q × Q is countably infinite.
To understand why Q × Q is countably infinite, we need to consider the cardinality of the set. A set is countably infinite if its elements can be put into a one-to-one correspondence with the set of natural numbers (1, 2, 3, ...).
We can establish a bijection between Q × Q and the set of natural numbers by assigning each pair of rational numbers (p, q) in Q × Q a unique natural number. One way to do this is by using the Cantor pairing function, which maps two natural numbers to a unique natural number. Since Q is countable and the Cartesian product of two countable sets is countable, Q × Q is also countably infinite.
Therefore, the set Q × Q is countably infinite.
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Identify all the solutions to the following-inequality.
3(x - 3) ≤ 27
Answers
Answer: \(x \leq 12\)
Step-by-step explanation:
\(3(x-3) \leq 27\\\\x-3 \leq 9\\\\x \leq 12\)
Step-by-step explanation:
To solve the inequality 3(x - 3) ≤ 27, we can use the following steps:
Distribute the 3 on the left side of the inequality: 3x - 9 ≤ 27
Add 9 to both sides of the inequality: 3x ≤ 36
Divide both sides of the inequality by 3: x ≤ 12
Therefore, the solution to the inequality is x ≤ 12.
This solution is valid for any value of x less than or equal to 12, including 12.
Examples of values that satisfy this inequality are:
x = -6, -4, -2, 0, 2, 4, 6, 8, 10, 11, 12
x = -1, -0.5, 0.1, 4.5, 8.9, 12
Note that the solution set is a set of real numbers, that includes all x that are less or equal than 12.
What is the square root of 30?
Answers
Answer:
The square root of 30 is a decimal 5.477...
Step-by-step explanation:
The square root of 30 = 5.477 rounded up is 5.5
Consider the following system of equations: y = −x + 2 y = 3x + 1 Which description best describes the solution to the system of equations? (4 points) Group of answer choices Line y = −x + 2 intersects line y = 3x + 1. Lines y = −x + 2 and y = 3x + 1 intersect the x-axis. Lines y = −x + 2 and y = 3x + 1 intersect the y-axis. Line y = −x + 2 intersects the origin.
Answers
The answer is A) Line y = 5x + 6 intersects the line y = −x − 7.
Here, we have,
given that,
the equations are:
y = 5x + 6
y = −x − 7
so, solving the given equations ,we get,
5x + 6 = -x - 7
6x + 6 = -7
6x = -13
x = -13/6
y = 5(-13/6) + 6
y = -29/6
The solution is (-13/6, -29/6) and that tells us that the two lines do not intersect at the origin or any of the two axis.
If they intersected at the origin, then the solution should have been (0, 0).
If they intersected at the x-axis, the solution should have been (x, 0).
If the two lines intersected at the y-axis, the solution would have been (0, y).
The answer is A) Line y = 5x + 6 intersects the line y = −x − 7.
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complete question:
Consider the following system of equations: y = 5x + 6 y = −x − 7 Which description best describes the solution to the system of equations?
Line y = 5x + 6 intersects line y = −x − 7.
Lines y = 5x + 6 and y = −x − 7 intersect the x-axis.
Lines y = 5x + 6 and y = −x − 7 intersect the y-axis.
Line y = 5x + 6 intersects the origin.
If m∠BAC=(7x+1)° and m∠BCA=(5x+9)°, what is the measure of the vertex angle? Show your work to support your answer.
Answers
Answer:
128degrees
Step-by-step explanation:
Note that the given triangle ABC is an isosceles triangle with base angles equal, hence;
m∠BAC = m∠BCA
7x+1 = 5x+9
7x - 5x = 9-1
2x = 8
x = 8/2
x = 4
m∠BAC = 5x+6
m∠BAC = 5(4)+6
m∠BAC = 26 degrees
The vertex angle = 180 - (26+26)
The vertex angle = 180 - 52
The vertex angle = 128degrees
If 3r + 2s = r - 8, then r + s =
Answers
Answer:
r + s = -4
Step-by-step explanation:
3r + 2s = r - 8
3r + 2s - r = -8
2r + 2s = -8
r + s = -8/2
r + s = -4