Here we will study the function f (x) = e ^ x sin (x), where x ∈ [0, 2π]. a) Determine where the function is decreasing and increasing. b) Find all local maximam and minimam. Does the absolute (global) maximam / minimam have? c) Determine where f (x) curves up and down. Also find any turning points.
Answers
we are given
[tex]f(x)=e^x sin(x)[/tex]
(a)
Firstly, we will find critical numbers
so, we will find derivative
[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]
now, we can set it to 0
and then we can solve for x
we get
[tex]x=\frac{3\pi }{4} ,x=\frac{7\pi }{4}[/tex]
now, we can draw a number line and then locate these values
and then we can find sign of derivative on each intervals
increasing intervals:
[tex][0,\frac{3\pi}{4} )U(\frac{7\pi}{4} , 2\pi][/tex]
Decreasing interval:
[tex](\frac{3\pi}{4} ,\frac{7\pi}{4} )[/tex]
(b)
Local maxima:
It is the value of x where function changes from increasing to decreasing
so, local maxima is at
[tex]x=\frac{3\pi}{4}[/tex]
Local minima:
It is the value of x where function changes from decreasing to increasing
so, local minima is at
[tex]x=\frac{7\pi}{4}[/tex]
now, we will plug critical numbers and end values into original function
and we get
At x=0:
[tex]f(0)=e^0 sin(0)[/tex]
[tex]f(0)=0[/tex]
At [tex]x=\frac{3\pi}{4}[/tex]:
[tex]f(\frac{3\pi}{4})=e^{\frac{3\pi}{4}} sin(\frac{3\pi}{4})[/tex]
[tex]f(\frac{3\pi}{4})=7.46049[/tex]
At [tex]x=\frac{7\pi}{4}[/tex]:
[tex]f(\frac{7\pi}{4})=e^{\frac{7\pi}{4}} sin(\frac{7\pi}{4})[/tex]
[tex]f(\frac{7\pi}{4})=-172.640[/tex]
At [tex]x=2\pi [/tex]:
[tex]f(2\pi)=e^{2\pi} sin(2\pi )[/tex]
[tex]f(2\pi )=0[/tex]
Global maxima:
It is the largest value among them
so, we get
[tex]f(\frac{3\pi}{4})=7.46049[/tex]
Global minima:
It is the largest value among them
so, we get
[tex]f(\frac{7\pi}{4})=-172.640[/tex]
(c)
now, we can find second derivative
[tex]f'(x)=e^x sin(x)+e^x cos(x)[/tex]
[tex]f''(x)=\frac{d}{dx}\left(e^x\sin \left(x\right)+e^x\cos \left(x\right)\right)[/tex]
[tex]=\frac{d}{dx}\left(e^x\sin \left(x\right)\right)+\frac{d}{dx}\left(e^x\cos \left(x\right)\right)[/tex]
[tex]=e^x\sin \left(x\right)+\cos \left(x\right)e^x+e^x\cos \left(x\right)-e^x\sin \left(x\right)[/tex]
[tex]f''(x)=2e^x\cos \left(x\right)[/tex]
now, we can set it to 0
and then we can solve for x
[tex]f''(x)=2e^x\cos \left(x\right)=0[/tex]
so, we get
[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]
now, we can draw number line and locate these values
and then we can find sign of second derivative on each intervals
concave up intervals:
[tex][0,\frac{\pi}{2})U(\frac{3\pi}{2}, 2\pi][/tex]
Concave down intervals:
[tex](\frac{\pi}{2} ,\frac{3\pi}{2})[/tex]
Turning points:
All values of x for which concavity changes
so, we get turning points at
[tex]x=\frac{\pi}{2} ,x=\frac{3\pi}{2}[/tex]
![Here We Will Study The Function F (x) = E ^ X Sin (x), Where X [0, 2]. A) Determine Where The Function](https://i5t5.c14.e2-1.dev/c-qa-images/answers/attachments/CTvaAZFvS6pBADWnPLElvGEwmfcAaUOd.jpeg)
![Here We Will Study The Function F (x) = E ^ X Sin (x), Where X [0, 2]. A) Determine Where The Function](https://i5t5.c14.e2-1.dev/c-qa-images/answers/attachments/pd1xuc9K1JiJ9D7Z04LiDiUJmQ7MbUwA.jpeg)
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[tex]f(x) = e^x sin (x)[/tex]
To find increasing and decreasing intervals we take derivative
[tex]f'(x) = e^xsin(x)+e^x(cosx)= e^x(sinx+cosx)[/tex]
Now we set the derivative =0 and solve for x
[tex]e^x(sinx+cosx)=0[/tex]
sinx + cosx =0
divide whole equation by cos x
[tex]\frac{sinx}{cosx} + \frac{cosx}{cosx} =0[/tex]
tanx +1 =0
tanx = 1
[tex]x=\frac{3\pi }{4}[/tex] and [tex]x=\frac{7\pi}{4}[/tex]
Now we pick a number between 0 to [tex]\frac{3\pi }{4}[/tex]
Lets pick [tex]\frac{\pi }{2}[/tex]
Plug it into the derivative
[tex]f'(x) =e^{\frac{\pi }{2}}(sin(\frac{\pi}{2})+cos(\frac{\pi }{2}))[/tex]
= 4.810 is positive
So the graph of f(x) is increasing on the interval [0, [tex]x=\frac{3\pi }{4}[/tex])
Now we pick a number between [tex]\frac{7\pi}{4}[/tex] to 2pi
Lets pick [tex]\frac{11\pi}{6}[/tex]
Plug it into the derivative
[tex]f'(x) =e^{\frac{11\pi}{6}}(sin(\frac{11\pi}{6})+cos(\frac{11\pi }{6}))[/tex]
= 116 is positive
So the graph of f(x) is increasing on the interval [tex](\frac{7\pi }{4}, 2\pi)[/tex]
Increasing interval is [tex](0,\frac{3\pi }{4}) U (\frac{7\pi }{4}, 2\pi)[/tex]
Decreasing interval is [tex](\frac{3\pi}{4}, \frac{7\pi}{4})[/tex]
(b)
The graph of f(x) increases and reaches a local maximum at [tex]x=\frac{3\pi}{4}[/tex]
The graph of f(x) decreases and reaches a local minimum at [tex]x=\frac{7\pi}{4}[/tex]
(c)
f(0) = 0
[tex]f(2\pi)=0[/tex]
[tex]f(\frac{3\pi }{4})=7.46[/tex]
[tex]f(\frac{7\pi}{4})=-172.64[/tex]
Here global maximum at [tex]x=\frac{3\pi}{4}[/tex]
Here global minimum at [tex]x=\frac{7\pi}{4}[/tex]
Related Questions
If the ribbon cost .10 per foot, what is the total cost of the ribbon in dollar?
Answers
You can get 10 ft of ribbon for one dollar. What you need to do is divide 1 with .10 and you get 10 ft.
It seems like you may be missing some information, but:
[tex]Cost = .10x\\[/tex]
Where x is the number of feet.
The cost of a school banquet is $75+30n, where n is the number of people attending. What is the cost for 53 people? Plz help me :))
Answers
$1665
EXPLANATION
The relation given to you is the relation between the number of people and the cost, which can be written in a function notation as
[tex]c(n) = 75 + 30n[/tex]
You just have to plug in
[tex]n = 53[/tex]
in to the cost function and simplify.
[tex]c(n) = 75 + 30n[/tex]
[tex]c(53) = 75 + 30(53)[/tex]
[tex]c(53) = 75 + 1590[/tex]
[tex]c(53) = 1665[/tex]
Therefore the cost for 53 people is $1665
The total cost for 53 people attending the school banquet is $1,665.
What is the cost of the school banquet for 53 people?Given the parameter:
The cost of a school banquet is expressed as:
$75 + 30n, as n is the number of people attending.
To determine the cost for 53 people attending the school banquet, you can plug the value of n (which is 53) into the given cost function:
Cost = $75 + 30n
Plug in n = 53
Cost = $75 + 30( 53 )
Cost = $75 + 1590
Cost = $1,665
Therefore, the total cost will be $1,665.
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how can you do this
Answers
You add up all of the sides and the numbers that are there you pretend that they are on the other side and just add all of them up correctly and you will get your answer.
You multiply them.
4 x 4 x 3 = 48
3 x 2 x 6 = 36
the standard form of the equation of a parabola is y=x^2+4x+22. What is the vertex form of the equation?
Answers
We complete the square,
[tex]y=x^2+4x+11[/tex]
[tex]y = (x^2 + 4x + 4) + 11- 4[/tex]
[tex]y = (x+2)^2 + 7[/tex]
Answer: D
a slot machine has one to nine odds of winning a prize on any given play. what is the probability of a win?
Answers
The chance of winning is 1/9
Find the slope of the linr through the given points.
(-3,-11) and (1,1)
Answers
y2-y1 / x2-x1
1 + 11 / 1 + 3
12 / 4
3 is the slope
What does x equal if 6-4x=7x-9x-4
Answers
x= 5
Slove for x by simplifying both sides of the equation, then isolating the variable
Hey there!!
Given equation :
... 6 - 4x = 7x - 9x - 4
Combining like terms :
... 6 - 4x = - 2x - 4
Adding 4x on both sides :
... 6 = 2x - 4
Adding 4 on both sides :
... 2x = 10
Dividing by 2 on both sides :
... x = 5
Hence, the value of x is 5.
Hope my answer helps!!
I need help again PLEASE
Answers
Number 3: D
Number 4: C
What is 412 divine by 8 but in Interpret the remainder Way please help
Answers
The answer is 51 remainder 4 because 51* 4 =408 and 412 + 4 = 412
Please help answer the two questions in the photo
Answers
The given pentagon can be divided into two figures : a triangle and rectangle as shown in figure.
Let us find area of each figure separately.
Triangle:
Area of triangle is given by:
[tex]A=\frac{1}{2}*b*h[/tex]
where b=base and h=height
Height of triangle :
h=(3x+5)-(2x+1)
h=x+4
Base = 2x-2
[tex]A=\frac{1}{2}*(x+4)(2x-2)[/tex]
Area of triangle= (x-1)(x+4) = x²+3x-4
Area of rectangle:
Area of rectangle is given by:
A=l*b
[tex]A=(2x-2)(2x+1)[/tex]
Area of rectangle = 4x²-2x-2
Area of pentagon = Area of triangle + Area of rectangle
Area of pentagon = x²+3x-4 + 4x²-2x-2
Area of pentagon = 5x²+x-6
If area of pentagon is 42 cm², then solving for x,
[tex]42=5x^{2}+x-6[/tex]
[tex]5x^{2}+x-48=0[/tex]
Factorising to get x,
x=-3.2 and x=3
If we take x as negative the side will be negative, so we neglect x=-3.2
So x=3 is the answer.
Jason earns $196 each week bagging groceries at a store he saves have his have his earnings each week how much money does Jason save per week
Answers
Unclear question, have is have?
Jayson saves $98 per week because half of 196 is 98. (196 divided by 2 = 98)
The minute hand of a clock is 8 inches long and moves from 12 to 8 o’clock. How far does the tip of the minute hand move?
Answers
The minute hand is like an eight inch radius of a circle, whose circumference would equal 2 * PI * 8 = 50.265 inches. By moving to 8 o'clock, it travels 2/3 of the circumference or 50.265 * 2/3 = 33.510 inches
if the minute hand is 8 inches long, it shows the radius of the circle of the clock.
thus, the circumference of the circle (boundary)= 2πr
= 2X 3.14 X 8 ( wherein, r= radius= 8; π= 22/7 or 3.14)
= 50.27 inches.
The length between each two consecutive no.s on the clock = 50.27/12 = 4.19
Thus, the length moved n=by the tip of the minute hand= 4.19X8
= 33.44 inches
Hope that this would be correct .
The probability that an event will occur is fraction 9 over 10. Which of these best describes the likelihood of the event occurring?
Likely
Certain
Unlikely
Impossible
Answers
Answer:
Likely
Step-by-step explanation:
The answer is likely, its really close to certain but certain is 100%. Likely is the odds are for it but not confirmed.
Answer:
Likely is the answer hope this helps
Step-by-step explanation:
What does 3.12 + (-8.5) equal
Answers
3.12 + (-8.5) = 11.62
Hello there!
Answer: ⇒⇒⇒⇒⇒-5.38
Step-by-step explanation:
First, remove parenthesis.
[tex]3.12-8.5[/tex]
Then, subtract by the number.
[tex]3.12-8.5=-5.38[/tex]
[tex]=-5.38[/tex]
Hope this helps!
Thank you for posting your question at here on Brainly.
Have a great day!
-Charlie
A new bag of cat food weighs 18 pounds. At the end of each day, 0.5 pounds of food is removed to feed the cats. Find the 30th term, and explain what it represents.
Answers
The 30th term of this arithmetic sequence is 3.5 pounds. This represents the weight of the cat food bag after removing 0.5 pounds of food daily for 30 days.
Explanation:The subject of this question is mathematics, particularly, a problem related to sequences. In this case, the sequence consists of gradually diminishing weights of a bag of cat food. Initially, the bag weighs 18 pounds and then 0.5 pounds are removed daily to feed the cats.
To find the weight of the bag on the 30th day (or, in other words, the 30th term of the sequence), you would subtract half a pound for each day that has passed. This is an arithmetic sequence, where each term can be found using the formula: an = a1 + (n - 1)*d, with a1 being the first term (18 pounds), d being the common difference (-0.5 pounds), and n being the term number (30).
Substituting the known values into the formula, we get: a30 = 18 + (30 - 1)*(-0.5) = 18 - 29*0.5 = 18 - 14.5 = 3.5 pounds.
Therefore, the 30th term is 3.5 pounds. This represents the weight of the cat food bag after 30 days of removing 0.5 pounds of food daily.
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To find the 30th term of the sequence representing the weight of cat food remaining each day, we can use a formula. The 30th term represents the weight of cat food remaining after 29 days of removing 0.5 pounds each day.
Explanation:This question involves finding the 30th term of a sequence where 0.5 pounds of food is removed from an initial weight of 18 pounds every day. To find the 30th term, we can use the formula:
nth term = initial weight - (n-1) x rate of removal
Substituting the values, we have:
30th term = 18 - (30-1) x 0.5
= 18 - 29 x 0.5
= 18 - 14.5
= 3.5 pounds.
The 30th term represents the weight of cat food remaining after 29 days of removing 0.5 pounds each day.
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Which of the following represents the sum of the series below? 4+7+10+13+16+19+22+25+28+31+34+37++40
Answers
Answer:
B
Step-by-step explanation:
Edge
2x+4≥24 how do I solve this problem
Answers
The solution for the given inequality is x ≥ 10.
InequalityAn inequality is an expression mathematical that represents a non-equal relationship between a number or another algebraic expression. The solutions for inequalities can be given by: a graph in a number line or numbers.
Therefore, it is common to the use following symbols: ≤ (less than or equal to), ≥ (greater than or equal to), < (less than), and > (greater than).
The question gives the inequality 2x+4 ≥ 24. Thus, you should follow the next steps.
2x+4 ≥ 24
2x ≥ 24 -4
2x ≥ 20
x ≥ 10
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To solve the inequality 2x+4≥24, subtract 4 from both sides, simplify the expression, divide both sides by 2, and simplify again. The solution is x≥10.
Explanation:Let's solve the inequality 2x+4≥24. The first step is to isolate the term with x on one side. We can do this by subtracting 4 from both sides, which results in 2x ≥ 20. Next, we want to solve for x, so we divide both sides by 2: x ≥ 10. This means that x is greater than or equal to 10. lets solve step-by-step.
To solve the inequality 2x+4≥24, we need to isolate the variable x.
Step 1: Subtract 4 from both sides of the inequality: 2x+4-4≥24-4
Step 2: Simplify: 2x≥20
Step 3: Divide both sides of the inequality by 2: 2x/2≥20/2
Step 4: Simplify: x≥10
The solution to the inequality is x≥10. This means that any value of x that is greater than or equal to 10 satisfies the inequality.
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the graph shows the amounts of almonds in gram for different amounts of oats in cups in a granola mix. label the point (1,k) on the graph, find the value of k and explain its meaning. it's due tommarow please help!
Answers
First you need to figure out the formula for the line - this can be done using two obvious measurements in the plot (x,y): namely (0,0) and (2,50). The linear function that goes through these two points is [tex]y = 25x[/tex].
Now you can determine k (the function value for x=1) and that is [tex]k = 25\cdot1=25[/tex]
The meaning of k: you can find 25 grams of almonds in 1 cup of oat. (btw, if we were to take this literally it wouldn't make much sense - 1 cup of oat is 1 cup of oat and there is nothing else, but anyway).
Using a linear function, it is found that the value of k is 25, which means that for 1 cup of oats, 25 grams of almonds are needed.
A linear function has the following format:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change.b is the y-intercept, which is the value of y when x = 0.In this problem:
When x = 0, y = 0, thus [tex]b = 0[/tex].When x = 2, y = 50. The slope is given by change in y divided by change in x, thus:[tex]m = \frac{50 - 0}{2 - 0} = 25[/tex]
The equation is:
[tex]y = 25x[/tex]
When x = 1:
[tex]k = 25(1) = 25[/tex]
The value of k is 25, which means that for 1 cup of oats, 25 grams of almonds are needed.
The point is labeled on the sketch of the graph given below.
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Hey guys can I get some help plz thanks
Answers
What is the quotient (3x2 + 4x − 15) ÷ (x + 3)? (1 point)
Answers
Answer:
the answer is 3x-5
Step-by-step explanation:
break the expression in to groups
3x^2 + 4x -15 = (3x^2 -5x) + (9x-15)
factor out x from 3x^2 -5x: x(3x-5)
factor out 3 from 9x-15: 3(3x-5)
=x(3x-5) +3(3x-5)
factor out common terms
(x+3) (3x-5)
=((x+3) (3x-5)) / (x+3)
cancel the common factor x+3
=3x-5
The quotient for the expression is equal to 3x-5.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Break the expression into groups
3x² + 4x -15 = (3x² -5x) + (9x-15)
Factor out x from 3x^2 -5x: x(3x-5)
Factor out 3 from 9x-15: 3(3x-5)
=x(3x-5) +3(3x-5)
Factor out common terms
(x+3) (3x-5)
=((x+3) (3x-5)) / (x+3)
Cancel the common factor x+3
=3x-5
Therefore, the quotient for the expression is equal to 3x-5.
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Can u answers the rounded questions
Answers
Answer 1:
[tex]\frac{x^{2} -x+1}{x^{2} +x+1}[/tex]
Here given that, x is real that is the domain
Range of the given expression is :
[tex]\frac{1}{3} \leq y\leq 3[/tex]
Write it interval form.
[tex][\frac{1}{3},3][/tex] Option (2)
Answer 3:
[tex]\frac{11x^{2} +12x+6}{x^{2} +4x+2}[/tex]
Here domain is all real x.
Range is :
{y ∈ R : y ≤ -5 or y ≥ 3}
In interval form:
(-∞, -5] ∪ [3, ∞)
So, y can't lies between -5 to 3 Option (2)
Answer 5 :
[tex]\frac{x^{2} -3x+4}{x^{2} +3x+4}[/tex]
Here domain is :
x is real
And range is :
{y ∈ R : [tex]\frac{-1}{7}[/tex] ≤ y ≤ 7}
We see that maximum y value is 7.
So, maximum value is 7. Option (4)
Answer 6:
[tex]\sqrt{9x^{2}+6x+1 } < (2 -x)[/tex]
Solve for x .
Square both the side
9x² + 6x + 1 = 4 + x² - 4x
8x² + 10x - 3 < 0
(2x + 3)(4x - 1) < 0
2x + 3 = 0 & 4x - 1 = 0
x = [tex]\frac{-3}{2}[/tex] & x = [tex]\frac{1}{4}[/tex]
So,
[tex]\frac{-3}{2} < x < \frac{1}{4}[/tex]
x ∈ [tex](-\frac{3}{2} , \frac{1}{4} )[/tex] Option (1)
Which lines or segments are parallel? Justify your answer
Answers
B and E with C and G
The cable provider's "triple pay" package offers a land line, internet service, and cable TV for one fixed price. If you already have their cell phone service they offer an additional 12% off the price of the triple pay package. If the discounted price of the triple pay is $132, what is the price of the package without the discount? Pls help... WILL MARK BRAINLIEST!!!!!!!
Answers
let x be the price before the discount
If you get 12% off, then you only pay the remaining 88% (since 88%+12% = 100%). This means if you take 88% of the original price (x), then you get the final price (132)
In terms of an equation, we have,
88% of (original price) = final price
(88/100)*(x) = 132
0.88*x = 132
0.88*x/0.88 = 132/0.88 <--- divided both sides by 0.88
x = 150
--------------------------------------------
Answer: The price without the discount is $150
In his last game,the Rams' quarterback completed 10 out of 18 passes he threw. At this rate how many passes will he attempt if he completes 15 passes?
Answers
at this rate, he will have attempted 27 passes. we can find this by setting the problem up into a proportion: 10/18=15/?
once we solve the proportion, we get that he attempted 27 passes in order to complete 15
Final answer:
To solve for the number of passes the quarterback will attempt to complete 15 passes, we set up a proportion based on the completed 10 out of 18 passes. By cross-multiplying and solving for the unknown, we find that the quarterback would need to attempt 27 passes.
Explanation:
The question is asking us to find out how many passes the Rams' quarterback will attempt if he is to complete 15 passes, given that he completed 10 out of 18 passes in his last game. This is a proportion problem in mathematics where we set up a ratio of completed passes to attempted passes and solve for the unknown.
We know the quarterback completed 10 passes out of 18 attempts, so the ratio of completed to attempted passes is 10/18. If we want the quarterback to complete 15 passes, we can set up the proportion as:
10/18 = 15/x
where x represents the number of passes that the quarterback will attempt. To solve for x, we cross-multiply:
10(x) = 18(15)
x = (18(15))/10
x = 27
Therefore, the quarterback will have to attempt 27 passes to complete 15 passes at the same completion rate.
Check all that apply please
Answers
Answer: A & B
Step-by-step explanation:
[tex]\sqrt{5} *\sqrt{5} = \sqrt{5*5} = \sqrt{25} = 5[/tex]
Explain how you can tell that two figures are congruent ?
Answers
What does congruent mean?
Same in shape and size, can be flipped, side or turned.
Example:
We have 2 diamonds, if they are fliped, side or turned, they are congruent.
If there is a same shape but different size, it is not congruent!
Hope it helps!
you have violin lessons every forth day and singing lessons every fifth day.Today you have both lessons .In how many days will you have both lessons on the same day again?
Answers
Answer:
every 20 days
Step-by-step explanation:
-2/3(1/2)(-6/7)= answere is ?
Answers
Exact Form: 2/7
Decimal Form:0.285714 (this is also a repeating decimals)
For the equations given below, which statement is true?
-2x=14
6x=-42
A. The equations do not have the same solution because the second equation can never be obtained when multiplying the first equation by any value.
B. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −3.
C. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by 3.
D. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −4.
Answers
Answer:
B. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −3.
Statement B is true. The equations have the same solution because the second equation can be obtained by multiplying both sides of the first equation by −3.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
Equation 1;
-2x=14
Equation2;
6x=-42
Multiply equation 2 on both sides by -3.
-2x=14
-2x×3=14×3
6x= - 42
Because the second equation can be found by multiplying both sides of the first equation by 3, the equations have the same solution.
Hence, statement B is true
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LN= 6x-5 , LM= x + 7 , and MN= 3x + 20 find MN
Answers
Answer: 68
Step-by-step explanation:
LM + MN = LN
x + 7 + 3x + 20 = 6x - 5
4x + 27 = 6x - 5
-4x -4x
27 = 2x - 5
+5 +5
32 = 2x
÷2 ÷2
16 = x
MN: 3x + 20
3(16) + 20
48 + 20
68
This question is based on a principle in Mathematics called the Midpoint of a linelineline
Based on this question, the line = LNLN
To solve this question, we have the expression
LM + MN = LN
Step 1
We solve for x
Given that: LN= 6x-5 , LM= x + 7 , and MN= 3x + 20
Hence,
x + 7 + 3x + 20 = 6x - 5
Collect like terms
7 + 20 + 5 =6x - x - 3x
32 = 2x
Divide both sides by the coefficient of x = 2
32/2 = 2x/2
x = 16
The value of x = 16
Step 2
Find MN
Given that : MN= 3x + 20 and x = 16
We substitute 16 for x in MN
MN = 3(16) + 20
MN = 48 + 20
MN = 68
Therefore, the value of MN is 68.
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