In circle D with the measure of minor aré CE = 162 degrees, find m of CFE
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SOLUTION
Step 1: Make a more comprehensive sketch of the question.
The measure of CFE is 81 degrees.
Related Questions
If the statement is true, type true in the space provided. If it is false, replace the underlined word(s) with the word(s) that will make the statement true.
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The sum and difference of two simple quadratic surds are said to be conjugate surds to each other.
In general, the following surds are conjugate to each other:
[tex](x\sqrt{a}+y\sqrt{b})\text{ and \lparen}x\sqrt{a}-y\sqrt{b})[/tex]Therefore, the conjugate of the surd:
[tex](5-\sqrt{7})[/tex]will be:
[tex](5+\sqrt{7})[/tex]The statement is true.
Draw a figure to use for numbers 13 - 15. Points A. B. and C are collinear and Bis the midpoint of AC. 13. If AB = 3x - 8 and BC = x + 4, find the length of AB 14. If BC = 6x - 7 and AB = 5x + 1. find the length of AC 15. If AB = 8x + 11 and BC = 12x - 1. find the length of BCAnswer 13
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13.
Given:
AB = 3x - 8, BC = x + 4
A, B and C are collinear
B is a midpoint of AC
Since B is the midpoint, we can write:
[tex]\text{length of AB = Length of BC}[/tex]Hence, we have:
[tex]3x\text{ - 8 = x + 4}[/tex]Solving for x:
[tex]\begin{gathered} \text{Collect like terms} \\ 3x\text{ -x = 4 + 8} \\ 2x\text{ = 12} \\ \text{Divide both sides by 2} \\ x\text{ = 6} \end{gathered}[/tex]Hence, the length of AB is:
[tex]\begin{gathered} =\text{ 3x - 8} \\ =\text{ 3}\times\text{ 6 -8} \\ =\text{ 18 -8} \\ =\text{ 10} \end{gathered}[/tex]Answer:
The length of AB is 10 unit
Factor the Expression. If the expression cannot be factored, say so. 8.) x^2 - 4x - 12
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To factor an expression of the form:
[tex]x^2+bx+c[/tex]we find two numbers B and C that fulfills the following properties:
[tex]\begin{gathered} B+C=b \\ BC=c \end{gathered}[/tex]In this case we have b=-4 and c=-12. We can choose B=-6 and C=2. Then we write the expression as:
[tex]x^2-4x-12=x^2-6x+2x-12[/tex]and we factor the common factors in the first two and last terms:
[tex]\begin{gathered} x^2-4x-12=x^2-6x+2x-12 \\ =x(x-6)+2(x-6) \\ =(x+2)(x-6) \end{gathered}[/tex]Therefore:
[tex]x^2-4x-12=(x+2)(x-6)[/tex]Allison earned a score of 150 on Exam A that had a mean of 100 and a standard deviation of 25. She is about to take Exam B that has a mean of 200 and a standard deviation of 40. How well must Allison score on Exam B in order to do equivalently well as she did on Exam A? Assume that scores on each exam are normally distributed.
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Allison must score 280 on Exam B to do equivalently well as she did on Exam A
Explanations:Note that:
[tex]\begin{gathered} z-\text{score = }\frac{x-\mu}{\sigma} \\ \text{where }\mu\text{ represents the mean} \\ \sigma\text{ represents the standard deviation} \end{gathered}[/tex][tex]\begin{gathered} \text{For Exam A:} \\ x\text{ = 150} \\ \mu\text{ = 100} \\ \sigma\text{ = 25} \\ z-\text{score = }\frac{150-100}{25} \\ z-\text{score = 2} \end{gathered}[/tex]Since we want Allison to perform similarly in Exam A and Exam B, their z-scores will be the same
Therefore for exam B:
[tex]\begin{gathered} \mu\text{ = 200} \\ \sigma\text{ = 40} \\ z-\text{score = 2} \\ z-\text{score = }\frac{x-\mu}{\sigma} \\ 2\text{ = }\frac{x-200}{40} \\ 2(40)\text{ = x - 200} \\ 80\text{ = x - 200} \\ 80\text{ + 200 = x} \\ x\text{ = 280} \end{gathered}[/tex]Allison must score 280 on Exam B to do equivalently well as she did on Exam A
Reflected over the x-axis , horizontal shrink of 1/2, translated 7 down.
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Given:
Reflected over the x-axis, horizontal shrink of 1/2, translated 7 down.
The parent function is y=|x|.
[tex]\begin{gathered} \text{reflected over x-axis=-f(x)} \\ \text{horizontal shrink=f(}\frac{x}{b}\text{)} \\ \text{translation to the down=f(x)-d} \end{gathered}[/tex]The function becomes,
[tex]y=-|2x|-7[/tex]Answer:
[tex]y=-|2x|-7[/tex]Not a timed or graded assignment. Quick answer = amazing review :)
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The question is given to be:
[tex]\sqrt[]{\frac{64}{100}}[/tex]Recall the rule:
[tex]\sqrt[]{\frac{a}{b}}=\frac{\sqrt[]{a}}{\sqrt[]{b}}[/tex]Therefore, the expression becomes:
[tex]\sqrt[]{\frac{64}{100}}=\frac{\sqrt[]{64}}{\sqrt[]{100}}[/tex]Recall that:
[tex]\begin{gathered} 8\times8=64,\therefore\sqrt[]{64}=8 \\ \text{and} \\ 10\times10=100,\therefore\sqrt[]{100}=10 \end{gathered}[/tex]Hence, the expression becomes:
[tex]\frac{\sqrt[]{64}}{\sqrt[]{100}}=\frac{8}{10}[/tex]Dividing through by 2, we have:
[tex]\frac{8}{10}=\frac{4}{5}[/tex]Therefore, the answer is:
[tex]\sqrt[]{\frac{64}{100}}=\frac{4}{5}[/tex]When you are on the 2nd step of factoring this trinomial,you should be listing the factors of?
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Given:
The trinomial equation is given as,
[tex]3v^2-4v-7[/tex]The objective is to choose the correct value for which the factors are to be obtained for factorization.
Explanation:
From the step 1, to perform the factorization the values of a and c has to be multiplied.
Then in step 2, the factors need to be calculated for the product of a and c.
Product of a and c :
The product of a and c will be,
[tex]a\times c=3\times7=21[/tex]Thus, factors are to be listed for the number 21.
Hence, option (1) is the correct answer.
Subway wants to know how their customers feel about their food quality and service. When each customer pays for their food, the Subway employee hands them their receipt and tells them that they have a chance to win $500 if they go on line and answer a few questions about the restaurant. a) Experimentb) Observational Studyc) None of thesed) Survey
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From the question, we were told that a subway company decides to reward their customers if they go online and answer a few questions about the restaurant.
We are to determine what the process means.
The general view, examination, or description of something or someone in most cases for a reward is known as a survey.
So since subway wants its customers to go online and answer some question about the restaurant and get a reward, then it is a survey.
So, the process that was carried out is a survey.
Therefore, the correct option is D, which is survey.
√121 = ?
i need help
Answers
Answer:
11 and -11. Usually you only want the positive form
Step-by-step explanation:
[tex]\sqrt{121}[/tex] is asking what number times itself is 121? 11
11 x 11 = 121
-11 x -11 = 121
2. State two (2) values of θ (theta) to the nearest degree forsin θ = − 0. 966
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To find a value of θ theta given a value of sin(θ) we must use the arcsin function, it receives a value of an sin as argument and returns the value of the angle θ. Then we must use a calculator and input
[tex]\begin{gathered} \theta=\arcsin\left(x\right) \\ \\ \theta=\arcsin(-0.966) \\ \\ \theta=−75 \end{gathered}[/tex]The result is already rounded to the nearest degree. Therefore, one value of θ that satisfies sin θ = −0.966 is θ= -75°
Now to find the other value we will look at the symmetry in the trigonometric circle:
Then, the other value of theta will be
[tex]\begin{gathered} \theta_2=-75°-30° \\ \\ \theta_2=105° \end{gathered}[/tex]Final answer:
[tex]\begin{gathered} \theta=-75° \\ \theta_2=-105° \end{gathered}[/tex]Using the Distributive Property, which of the following expressions are equivalent to 7 x 6? Select all that apply. A. (6 x 7)+(6 x 7)
B. (5×6) + (2 × 6)
C. (7 x 6) + (1 x 6)
D. (7 x 6) + (2 x 6)
E. (2 x 6)+(5 x 6)
Answers
By using the Distributive Property, the equivalent expression to 6 x 7 is option (B) (5 x 6) + (2 x 6) and option (E) (2 x 6) + (5 x 6).
Distributive property:
The distributive Property defines that when a factor is multiplied by the addition of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation.
This property can be stated symbolically as:
A ( B+ C) = (A x B) + (A x C)
Where A, B and C are three different values.
Given,
Here we have the expression 7 x 6.
Now, we need to find the equivalent expression by using the distributive expression.
AS per the definition of distributive property,
First we have o identify in which term is got separated,
Here they separated the term 7.
So, there three way for dividing it,
They are,
6 + 1 = 7
2 + 5 = 7
3 + 4 = 7
Based on these, we have two way to write the expression,
one is,
(5 x 6) + (2 x 6)
Another way is,
(2 x 6) + (5 x 6)
So, the correct options are option (B) and (E).
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the probability that DeAndre missed at least 1 day of school in a given week is
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Probability that Deandre missed at least 1 day is;
[tex]Pr(x\ge1)=Pr(1)+Pr(2)+Pr(3)+Pr(4)+Pr(5)[/tex]Write out the values of each probability and sum them
[tex]\begin{gathered} Pr(x\ge1)=0.25+0.18+0.34+0.12+0.04 \\ =0.93 \end{gathered}[/tex]Hence,
The probability that Deandre missed at least 1 day is 0.93
Which of the equations below could be the equation of this parabola?
10-
(0,0)
Vertex
-10
O A. y--/2²2
O B. x=2²
O c. y-1/2x²
O D. x=-12²
10
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The equation of this parabola is Y = -1/2 X². So option C is correct.
What is an Equation ?An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
Given that,
The graph of parabola,
the vertex (0, 0)
Y - 0 = 4a (X - 0)²
Y = 4aX²
It can be seen in the graph it is downward parabola so value a should be less than zero
So possible equation could be Y = -1/2 X²
Hence, the equation is Y = -1/2 X²
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Isaiah is a plumber. One day he receives a house call from a potential customer in a differentcity. The distance on a map between his home and the customer's home is 8 inches. What isthe actual distance between Isaiah's home and the customer's home if the scale of the map is1 inch = 1 mile?
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Given:
The distance on a map between his home and the customer's home, D=8 inches.
In the map, 1 inch=1 mile.
The actual distance between Isaiah's home and the customer's home is,
[tex]\begin{gathered} \text{Actual distance=8 inches}\times\frac{1\text{ mile}}{1\text{ inch}} \\ =8\text{ miles} \end{gathered}[/tex]Therefore, the actual distance between Isaiah's home and the customer's home is 8 miles.
Find f(-4) and f(3) for the following funxripnf(x)=3x
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Given the function:
[tex]f(x)=3x[/tex]• You need to substitute this value of "x" into the function:
[tex]x=-4[/tex]And then evaluate, in order to find:
[tex]f(-4)[/tex]You get:
[tex]f(-4)=3(-4)[/tex][tex]f(-4)=-12[/tex]Remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]• Substitute this value of "x" into the function:
[tex]x=3[/tex]Then:
[tex]f(3)=3(3)[/tex]Evaluate, in order to find:
[tex]f(3)[/tex]You get:
[tex]f(3)=9[/tex]Hence, the answer is:
[tex]\begin{gathered} f(-4)=-12 \\ f(3)=9 \end{gathered}[/tex]An athlete runs at a speed of 9 miles per hour. If one lap is 349 yards, how many laps does he run in 22 minutes
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The athlete will cover 17 yards in 22 minutes of his running.
What is unitary method?The unitary method is a method in which you find the value of a single unit and then the value of a required number of units.
Given is an athlete who runs at a speed of 9 miles per hour and one lap is 349 yards.
We will use the unit conversions to solve the given problem.
The speed of the athlete is 9 mph. We can write it as -
9 mph = (9 x 1760) yards per hour = 15840 yards per hour.
15840 yards per hour = (15840/60) yards per minute = 264 yards per min.
Total yards covered in 22 minutes = 22 x 264 = 5808 yards
one lap is equivalent to 349 yards.
1 yard is equivalent to (1/349) laps
5808 yards are equivalent to (5808/349) or 16.6 yards or approximately 17 yards.
Therefore, the athlete will cover 17 yards in 22 minutes of his running.
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Given that the shape below is a rectangle, we know that the diagonals, lines AD and CB, are ____.
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The given information is the shape is a rectangle.
About the diagonals of rectangles, there are two known properties:
- The diagonals of a rectangle bisect each other
- Both diagonals have the same length
Then, the answer is option C. They have the same length
A triangular road sign has a base of 30 inches and a height of 40 inches. What is it’s area?
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Answer:
600ft
Step-by-step explanation:
Because a triangle is half of a rectangle, the area can be found by taking the base times height and dividing by 2.
A = (b * h)/2
A = (40 * 30)/2
A = 1200/2
A = 600ft
good night I will send a picture of work
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In the form of the equation
S = m D + b
S represented on the y-axis
D represented on the x-axis
The independent is x
The dependent is y
Then D is the independent
S is the dependent
let us find the correct answer
a washer and dryer cost 1001 combined the washer costs 51 more the than the dryer how much does the dryer cost
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we can write equations from the statements
a washer and dryer cost 1001 combined
[tex]w+d=1001[/tex]where w is the price of the washer and d the price of the dryer
the washer costs 51 more the than the dryer
[tex]w=51+d[/tex]then we can replace the value of w from the second equation to the first equation
[tex]\begin{gathered} (51+d)+d=1001 \\ 51+d+d=1001 \\ 51+2d=1001 \end{gathered}[/tex]and solve for d
[tex]\begin{gathered} 2d=1001-51 \\ 2d=950 \\ d=\frac{950}{2} \\ \\ d=475 \end{gathered}[/tex]the cost of the dryer was $475
What is the slope of the line that passes through (5,4) and (7,10)a.3b. -3 C. 2D.-2
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To find a slope of a line we need two points, so we will do it as follows.
[tex]m=\frac{\Delta y}{\Delta x}=\frac{10-4}{7-5}=\frac{6}{2}=3[/tex]Therefore it is (a) the slope is 3.
Answer:
a.3
Step-by-step explanation:
To find the slope, use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 10-4)/(7-5)
= 6/2
= 3
the discriminant equation How many real solution 4x^2-8x+10=-x^2-5 have?
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Answer:
0 real solutions
Explanation:
First, we need to transform the equation into the form:
[tex]ax^2+bx+c=0[/tex]So, the initial equation is equivalent to:
[tex]\begin{gathered} 4x^2-8x+10=-x^2-5 \\ 4x^2-8x+10+x^2+5=-x^2-5+x^2+5 \\ 5x^2-8x+15=0 \end{gathered}[/tex]Now, the discriminant can be calculated as:
[tex]b^2-4ac[/tex]If the discriminant is greater than 0, the equation has 2 real solutions.
If the discriminant is equal to 0, the equation has 1 real solution
If the discriminant is less than 0, the equation has 0 real solutions
So, in this case, a is 5, b is -8 and c is 15. Then, the discriminant is equal to:
[tex](-8)^2-4\cdot5\cdot15=84-300=-236[/tex]Since the discriminant is less than zero, the equation has 0 real solutions
D is the midpoint of AC, BA ≅BC and ∠EDA ≅ ∠FDC. Prove ΔAED ≅ ΔCFD
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We are asked to prove that triangles AED and CFD are congruent. To do that we will prove that we can use the ASA (Angle Side Angle) rule of congruency.
First, we are given that D is a midpoint of segment AC, therefore:
[tex]\bar{AD}=\bar{AC}[/tex]Also, we are given that:
[tex]\bar{BA}=\bar{BC}[/tex]This means that triangle ABC is an isosceles triangle and therefore, its base angles are equal. This means that:
[tex]\angle BAC=\angle BCA[/tex]And, since we are given that angles EDA and FDC are equal, then by ASA we can conclude that:
[tex]\Delta AED\cong\Delta CFD[/tex]when taking a 19 question multiple choice test ,where each question has 3 possible answers ,it would be unusual to get or more questions correct by guessing alone consider "unusual " to be more than two standard deviations away from expected.
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we have that
You have 1 in 3 probability of guessing the correct answer for a single question
you have 19 opportunities to guess
so
19*(1/3)=19/3=18/3+1/3=6 1/3
therefore
would be unusual to get 7 or more questions correct by guessing alone
Given the focus and directrix shown on the graph, what is the vertex form of the equation of the parabola?
[tex]x\ =\ \frac{1}{10}(y\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
[tex]x\ =\ 10(y\ +\ 3)^2\ +\ \frac{3}{2}[/tex]
[tex]x\ =\ \textrm{-}\frac{1}{10}(y\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
[tex]y\ =\ \frac{1}{10}(x\ -\ 3)^2\ -\ \frac{3}{2}[/tex]
Answers
The vertex-form equation of the parabola is given as follows:
y = 1/10(y - 3)² - 3/2.
What is the equation of a horizontal parabola?An horizontal parabola of vertex (h,k) is modeled as follows:
x = (1/4p)(y - k)² + h.
In which:
The directrix is x = h - p.The focus is (h + p, k).In the context of this problem, we have that:
The directrix is x = -4.The focus is: (1,3), hence k = 3.A system of equations is built for h and p as follows:
h - p = -4.h + p = 1.Hence:
2h = -3
h = -3/2.
p = 1 + 3/2 = 2.5.
Then the equation is:
y = 1/10(y - 3)² - 3/2. (first option).
Missing informationThe graph is given by the image at the end of the answer.
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question given below slove the following equations for r4al x and y .
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S={(-24,7/3)}
1) When we're dealing with Complex Numbers we can rewrite this expression:
[tex](3+4i)^2-2(x-yi)=x+yi[/tex]Considering that their real and their imaginary parts can be taken as equal, so:
[tex]\begin{gathered} (3+4i)^2-2(x-yi)=x+yi \\ (3+4i)^2-2(x-iy) \\ 9+24i+16i^2+2x+2yi \\ \end{gathered}[/tex]2) Rewrite that into the Standard form for complex numbers y= ax +bi combining like terms:
[tex]\begin{gathered} 9+24i-16+2x+2yi \\ (-7-2x)+i(24+2y)\text{ = x+ iy} \\ \end{gathered}[/tex]Finally writing those two expressions as a System of equations we have:
[tex]\begin{gathered} \begin{cases}-7-2x=\text{ x} \\ 24+2y=y\end{cases} \\ -7-2x=x\Rightarrow-7=2x+x\Rightarrow3x=7\Rightarrow\frac{3x}{3}=\frac{7}{3} \\ 24+2y=y\Rightarrow24=-2y+y\Rightarrow-y=24\Rightarrow y=-24 \\ S=\mleft\lbrace(\frac{7}{3},-24)\mright\rbrace \end{gathered}[/tex]3) Hence, the answer is S={(-24,7/3)}
Chase and his brother want to improve their personal information for when they startapplying to colleges of their choice. To accomplish this they decide to help the SalvationArmy with delivering hot meals to senior citizens. About a month ago, they decided tokeep track of how many successful deliveries they have each completed. As of today,Chase has successfully delivered 18 out of the 30 meals to senior citizens.Part AHow many more meals would Chase have to deliver in a row in order to have a 75%successful delivery record? Justify your answer.Part BHow many more meals would Chase have to deliver in a row in order to have a 90%successful delivery record? Justify your answer.PartAfter successfully delivering 18 out of 30 meals would Chase ever be able to reach a100% successful delivery record? Explain why or why not.
Answers
Part A.
Chase has successfully delivered 18 out of the 30 meals to senior citizens.
We have to calculate how many more meals (lets call it x) she has to deliver to have a 75% successful delivery record.
In order to do that, (18+x) meals have te be delivered successfully out of (30+x), and the successful meals (18+x) divided by (30+x) has to be 0.75:
[tex]\begin{gathered} \frac{18+x}{30+x}=0.75 \\ 18+x=0.75(30+x) \\ 18+x=22.5+0.75x \\ x-0.75x=22.5-18 \\ 0.25x=4.5 \\ x=\frac{4.5}{0.25} \\ x=18 \end{gathered}[/tex]Chase has to deliver 18 more meals successfully in order to have a 75% success delivery record.
Part B.
We apply the same analysis but we replace 0.75 with 0.9 as the delivery record.
[tex]\begin{gathered} \frac{18+x}{30+x}=0.9 \\ 18+x=0.9(30+x) \\ 18+x=27+0.9x \\ (1-0.9)x=27-18 \\ 0.1x=9 \\ x=\frac{9}{0.1} \\ x=90 \end{gathered}[/tex]Chase has to deliver 90 more meals successfully in order to have a 90% success delivery record.
Part C.
She won't be able to achieve 100% successful delivery record. We can prove it mathematically, but we already know as there are 12 meals that weren't successfully delivered, so we can get close to 100% but it can't never be reached.
Mathematically we have:
[tex]\begin{gathered} \frac{18+x}{30+x}=1 \\ 18+x=30+x \\ x-x=30-18 \\ 0=12 \end{gathered}[/tex]This solution is not valid, so there is no valid solution for x.
Function f is defined by f(x) = 2x – 7 and g is defined by g(x) = 5*
Answers
Answer
f(3) = -1, f(2) = -3, f(1) = -5, f(0) = -7, f(-1) = -9
g(3) = 125, g(2) = 25, g(1) = 5, g(0) = 1, g(-1) = 0.2
Step-by-step explanation:
Given the following functions
f(x) =2x - 7
g(x) = 5^x
find f(3), f(2), f(1), f(0), and f(-1)
for the first function
f(x) = 2x - 7
f(3) means substitute x = 3 into the function
f(3) = 2(3) - 7
f(3) = 6 - 7
f(3) =-1
f(2), let x = 2
f(2) = 2(2) - 7
f(2) = 4 - 7
f(2) =-3
f(1) = 2(1) - 7
f(1) = 2 - 7
f(1) =-5
f(0) = 2(0) - 7
f(0) =0 - 7
f(0) = -7
f(-1) = 2(-1) - 7
f(-1) = -2 - 7
f(-1) = -9
g(x) = 5^x
find g(3), g(2), g(1), g(0), and g(-1)
g(3), substitute x = 3
g(3) = 5^3
g(3) = 5 x 5 x 5
g(3) = 125
g(2) = 5^2
g(2) = 5 x 5
g(2) = 25
g(1) = 5^1
g(1) = 5
g(0) = 5^0
any number raised to the power of zero = 1
g(0) = 1
g(-1) = 5^-1
g(-1) = 1/5
g(-1) = 0.2
Can you please help me with 44Please use all 3 forms such as :up/down, as_,_ and limits
Answers
Given:
[tex]h(x)=(x-1)^3(x+3)^2[/tex]The x-intercepts of the given polynomial are
[tex]x-\text{intercepts }=1\text{ (multiplicity 3) and -3 (multiplicity 2)}[/tex]Substitute x=0 in h(x) to find y-intercepts.
[tex]\text{ y-intercepts =}(-1)^3(3)^2=-9[/tex][tex]\lim _{x\to-\infty}h(x)=\lim _{x\to-\infty}(x-1)^3(x+3)^2=-\infty[/tex][tex]as\text{ x}\rightarrow-\infty,\text{ h(x)}\rightarrow-\infty[/tex][tex]\lim _{x\to\infty}h(x)=\lim _{x\to\infty}(x-1)^3(x+3)^2=\infty[/tex][tex]as\text{ x}\rightarrow\infty,\text{ h(x)}\rightarrow\infty[/tex]The graph of the given polynomial h(x) is
The degree of the polynomial is 6=even and the leading coefficient=1=positive.
Both ends of the graph point up.
End behaviour is
up/up.
I need help figuring out how to solve the length
Answers
We have the parallel sides of the rectangle are equal, therefore:
[tex]\begin{gathered} RS=QP=4x+3 \\ \text{and} \\ SP=RQ=5x \end{gathered}[/tex]The perimeter is the sum of all sides, then:
[tex]RS+QP+SP+RQ=222[/tex]Substitute the given data:
[tex](4x+3)+(4x+3)+5x+5x=222[/tex]And solve for x:
[tex]\begin{gathered} 4x+3+4x+3+5x+5x=222 \\ 18x+6=222 \\ 18x+6-6=222-6 \\ 18x=216 \\ \frac{18x}{18}=\frac{216}{18} \\ x=12 \end{gathered}[/tex]Next, we find the length of side RS:
[tex]RS=4x+3=4(12)+3=48+3=51[/tex]Answer: RS = 51 units
