Answers
Answer:
Graph D
Step-by-step explanation:
Move the constant to the opposite side of the equation and group terms that include the same variable.
g(x) + 1 = x^2 + 2x
Finish the square. Remember to keep the equation balanced by using the same constants on both sides.
g(x) + 1 + 1 = x^2 + 2x + 1
g(x) + 2 = x^2 + 2x + 1
Rewrite as perfect squares
g(x) + 2 = (x + 1)^2
Equation in vertex form:
g(x) = (x + 1)^2 - 2
The vertex:
(-1, -2)
* This a minimum *
(Parabola open upward)Related Questions
Enter the correct answer in the box. Write the sum of 12√23x13 + 14√23x13 in simplest form, if x > 0.
Answers
Answer:
26x^6 sqrt 23x
Step-by-step explanation:
19
Select the correct answer.
A developer buys an empty lot to build a small house. What is the area of the lot?
Answers
Area of the plot = 193 sq.yd. , Option B is the correct answer.
What is Area ?
Area is the space occupied by a flat surface or an object .
It is measured in square units
It has wide daily life importance like in the question mentioned , a plot will be measured in area of the space.
It is given that
A developer buys an empty lot to build a small house.
area of the lot = ?
The figure is incomplete and the complete figure is attached with the answer.
To determine the area the figure needs to be divided into triangles and rectangles as shown in the figure
Area of the first triangle = (1/2) * base * height
By Calculation
base = 17 unit and height = 10 unit
= (1/2) * 17 * 10
= 17*5
=85 sq.unit
Area of the second triangle = (1/2)* 9* 8
=36 sq. unit
Area of the rectangle = base * height
base = 9 unit and height = 7 unit
Area = 9*7= 63 sq.unit
Area of the last triangle = (1/2) * 2*9
= 9 unit
The area of the plot = 85+36+63+9
Area of the plot = 193 sq.yd.
Therefore , Option B is the correct answer.
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Answer:
Step-by-step explanation:
Area of the plot = 193 sq.yd. , Option B is the correct answer.
What is Area ?
Area is the space occupied by a flat surface or an object .
It is measured in square units
It has wide daily life importance like in the question mentioned , a plot will be measured in area of the space.
It is given that
A developer buys an empty lot to build a small house.
area of the lot = ?
The figure is incomplete and the complete figure is attached with the answer.
To determine the area the figure needs to be divided into triangles and rectangles as shown in the figure
Area of the first triangle = (1/2) * base * height
By Calculation
base = 17 unit and height = 10 unit
= (1/2) * 17 * 10
= 17*5
=85 sq.unit
Area of the second triangle = (1/2)* 9* 8
=36 sq. unit
Area of the rectangle = base * height
base = 9 unit and height = 7 unit
Area = 9*7= 63 sq.unit
Area of the last triangle = (1/2) * 2*9
= 9 unit
The area of the plot = 85+36+63+9
Area of the plot = 193 sq.yd.
Therefore , Option B is the correct answer.
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3 yards 5 feet 6 inches x 7=
Answers
Answer:
1218 inches
Step-by-step explanation:
First, let's make our numbers equivalent to a certain unit. Preferably inches, since we can't turn inches into yards or feet, but we can turn yards and feet into inches.
3 yards is 9 feet, which when multiplied by 12 (12 inches in a foot) is 108.
5 feet times 12 is 60 inches.
6 inches is 6 inches.
108+60+6 is 174
Multiply all that by 7 and you get your answer of 1218 inches.
Hope this helps!
the lenghts of five boxes are shown in the table which line plot shows the data from the table
Answers
Answer:
The bottom right line plot.
Step-by-step explanation:
In the table, 9 1/4 shows up twice. This can be represented in the line plot by putting 2 x's over the 9 1/4 point.
which properties justify the steps taken to solve the system?
{2x-4y=-6
{3x+2y=-1
drag and drop the answers into the boxes to match each step
Answers
Addition property of equality
division property of equality
multiplication property of equality
associative property of equality
subtraction property of equality
simplify
substitution property of equality
Answers
Answer:
X=-1
Y=1
Step-by-step explanation:
6x-12y
-18
) 6x + 4y
-
-2
Subtract the two equations
6x - 12y - (6x + 4y) = -18 - (-2)
Determine the sign
6x- 12y - 6x- 4y
=-18 + 2
Simplify
-12y
- Ay
=-18 + 2
Solve the equation
Substitute
6×+4
-2
Solve the equation
X=
Which of the following statements describe this sequence: 3, 6, 9, 12...?
I. This is an arithmetic sequence.
II. The expression used to find the nth term would be 3n.
III. The next term in the sequence is 36.
IV. The common ratio for this sequence is 3.
O I, II, III, and IV
O I, II, and IV
II and IV
I and II
Answers
The sequence is an arithmetic sequence and the expression used to find the nth term would be 3n option fourth I and II is correct.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
We have a sequence:
3, 6, 9, 12…
First term a = 3
Common difference d = 6 - 3 = 3
This is an arithmetic sequence.
nth term of the arithmetic sequence:
a(n) = 3 + (n-1)(3)
a(n) = 3n
Plug n = 5
a(5) = 3(5) = 15
Thus, the sequence is an arithmetic sequence and the expression used to find the nth term would be 3n option fourth I and II is correct.
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ill give brainliest, help
Answers
Answer:
2 up 3 run
Step-by-step explanation:
just count the squares until u reach a part where the line touches again
logan trades 50 pennies for nickels he gets a nickel for each group of 5 pennies what equation can be used to find how many nickels logan uses
Answers
The equation that can be used to find how many nickels logan uses is: 50÷5.
Equation to find the number of nickelsGiven:
Total pennies=50
Logan got a nickel of 5 pennies=1
Hence:
Number of nickels=1÷5×50
Number of nickels=50÷5
Number of nickels=10 nickels
Therefore the equation that can be used to find how many nickels logan uses is: 50÷5.
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What is true about the solution to the system of inequities shown?
-2 -5-4-3-2-1, y≤x-1 y≤ x-3 O All values that satisfy y ≤ x-1 are solutions. All values that satisfy y ≤x-3 are solutions. O All values that satisfy either y≤ x-1 or y≤ x-3 are solutions. There are no solutions. Save and Exit Mark this and return V Next Sube
Answers
The true solution to the system of inequities shown is B; All values that satisfy [tex]y \leq \dfrac{ 1}{3}x - 3[/tex] are solutions.
What is a system of inequalities?When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalities.
A collection of inequalities for which we consider a common solution for all inequalities is called a system of inequalities.
If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true.
A set of such values is called a solution set to the considered equation or inequality.
The true solution to the system of inequities shown is B;
All values that satisfy [tex]y \leq \dfrac{ 1}{3}x - 3[/tex] are solutions.
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find the sum. 1-2+3-4+5-6+7-8...99-100
Answers
Answer:
-50
Step-by-step explanation:
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8...99 - 100
just means,
1 - 2 = -1
3 - 4 = -1
5 - 6 = - 1
7 - 8 = - 1
99 - 100 = -1
basically, -1 + -1 + -1 + -1 + ....+ -1 or -1 - 1 - 1 - 1 - ... - 1
[tex](-1)^{n}[/tex]
Treating Grandi's series as a divergent geometric series we may use the same algebraic methods that evaluate convergent geometric series to obtain a third value:
S = 1 − 1 − 1 + ..., so
1 − S = 1 − (1 − 1 − 1 ...) = 1 − 1 − 1 ... = S
1 - S = S
1 = 2*S
resulting in S = 1/2. The same conclusion results from calculating −S, subtracting the result from S, and solving 2S = 1
1/2 of the last term is 100 x 1/2 = 50
This because you are using 2 numbers per -1
example: 1 - 2 = -1 or 3 - 4 = -1 resulting in 50 of the -1 being subtracted
Find c. Give your answer in
the simplest form.
c = [?]V []
d
7V2
a
45
30
b
C
Enter the number that belongs in
the green box.
Answers
Answer:
see the attachment photo!
If R is (-4, 7) and S is (-2, 12), what is the component form of the vector R.S?
(8,84)
(2,5)
(-6, 19)
(-3,9.5)
Answers
Answer:
(2, 5)
Step-by-step explanation:
Given:
R = (-4, 7)S = (-2, 12)To find the components of [tex]\overrightarrow{RS}[/tex] we need to go from R to O and then O to S. Remember that [tex]\overrightarrow{RO}[/tex] is the negative of [tex]\overrightarrow{OR}[/tex]. Therefore:
[tex]\begin{aligned} \displaystyle \overrightarrow{RS} & =\overrightarrow{RO}+\overrightarrow{OS}\\& = \overrightarrow{OS}-\overrightarrow{OR}\\& =\binom{-2}{12}-\binom{-4}{7}\\& =\binom{2}{5}\end{aligned}[/tex]
Therefore, the component form (x, y) of the vector [tex]\overrightarrow{RS}[/tex] is (2, 5)
I need the answer please
Answers
The graphed cosine function can either be:
cos(x + pi) or cos(x - pi).
Which is the equation of the graphed function?
We know that this function is a cosine function with a phase shift, so the general form is:
f(x) = cos(x + P).
Where P is the phase shift.
In the graph we can see that when x = 0, f(0) = -1
And we know that cos(pi) = -1 = cos(-pi)
Then we must have that:
f(0) = cos(P) = -1
By what we wrote above, we know that P can be either -pi or pi (because of the parity of the cosine). Let's say that P = pi, then the cosine function is:
f(x) = cos(x + pi).
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A new computer loses 1/2 of its value every year. Which graph could represent the relationship between the year and the computer’s value?
SOMEONE HELP PLS, YOU’LL GET FREE EASY POINTS IF THE ANSWER IS RIGHT!!!!
Answers
Let's first consider: the fact that a new computer loses 1/2 of its value
⇒ third choice and fourth choice are eliminated
⇒ because of the graph project the computer's value as growing over
years
Now let's try to set up an equation:
After 1st year ⇒ Computer's value = [tex]total_.value*\frac{1}{2}[/tex]
After 2nd year ⇒ Computer's value = [tex]total_.value*\frac{1}{2}*\frac{1}{2}=total_.value*(\frac{1}{2} )^2[/tex]
After 3rd year ⇒ Computer's value =[tex]total_.value*\frac{1}{2}*\frac{1}{2}* \frac{1}{2}=total_.value*(\frac{1}{2})^3[/tex]
..... (Hopefully you see a pattern)
After x year ⇒ Computer's value = [tex]total_.value*(\frac{1}{2})^x[/tex]
Therefore, the equation is: [tex]total_.value*(\frac{1}{2})^x[/tex]
⇒that means the graph has to exponentially decreasing as it has
an exponent (meaning the function is exponential) and a base less
than 1 (meaning that the function is decreasing)
Answer: Choice (1)
Hope that helps!
Answer:
A
Step-by-step explanation:
After x year, computer's value will be (1/2)^x
So the graph has to exponentially decreasing.
Both A and B show decreasing value but B is linear. So B is incorrect
C and D show increasing value so they are both incorrect.
If you horizontally shift the square root parent function, F(x)=√x, right eight
units, what is the equation of the new function?
O A. G(x) = vx +8
OB. G(x)=√x-8
OC. G(x)=√x - 8
OD. G(x) = √√x+8
Answers
The function g(x) = √(x - 8) represents a horizontal shift of the square root parent function f(x) = √x, to the right by eight units. Option B.
To horizontally shift the square root parent function, f(x) = √x, right eight units, we need to replace x with (x - 8) in the function. This shift will move the entire graph eight units to the right.
So, the equation of the new function, let's call it g(x), will be:
g(x) = √(x - 8)
Therefore, the correct choice is g(x) = √(x - 8).
This means that for any given value of x, we substitute (x - 8) in the original square root function. The effect of this shift is that all x-values on the graph of g(x) will be eight units greater than their corresponding x-values on the graph of f(x).
For example, if we consider the point (8, 2) on the graph of f(x), after the horizontal shift, it will be located at (16, 2) on the graph of g(x). Similarly, the point (0, 0) on the graph of f(x) will shift to (8, 0) on the graph of g(x).
The function g(x) = √(x - 8) represents a horizontal shift of the square root parent function f(x) = √x, to the right by eight units. This transformation allows us to analyze and understand how the graph of the square root function is affected by horizontal shifts. SO Option B is correct.
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Jasmine played in a basketball tournament. The ratio of the number of baskets she missed during the tournament to the number of baskets she made is 3:8. If Jasmine missed 9 baskets during the tournament, how many baskets did she make? Draw a diagram to demonstrate how you found your answer.
Answers
A ratio shows us the number of times a number contains another number. The number of baskets Jasmine made is 24.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The ratio of the number of baskets she missed during the tournament to the number of baskets she made is 3:8. Therefore, we can write,
(Number of baskets Missed)/ (Number of baskets made) = 3/8
If Jasmine missed 9 baskets during the tournament, then the ratio can be rewritten as,
(Number of baskets Missed)/ (Number of baskets made) = 3/8
9 / (Number of baskets made) = 3/8
(9×8)/3 = (Number of baskets made)
Number of baskets made = 24 baskets
Hence, the number of baskets Jasmine made is 24.
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How do we calculate=
x+5/x + x+8/x-1= ?
Answers
Answer:
⇒8(x−1)=5x
⇒8x−x=5x
⇒8x−5x=8
⇒3x=8
⇒x=
3
8
Find the length of side b below using Law of Sines. Give the exact value as an expression and an approximation to the nearest tenth.
Answers
Answer:
b ≈ 7.8
Step-by-step explanation:
using the law of sines
∠ A = 180° - 105° - 40° = 180° - 145° = 35° , then
[tex]\frac{b}{sin40}[/tex] = [tex]\frac{7}{sin35}[/tex] ( cross- multiply )
b × sin35° = 7 × sin40° ( divide both sides by sin35° )
b = [tex]\frac{7sin40}{sin35}[/tex] ≈ 7.8 ( to the nearest tenth )
Sammi has $125.75 in her savings account. She deposits $25.50 into the account each month for the next 6 months.
How much is in Sammi's account at the end of the 6 months?
Enter Your answer into the box
Answers
Answer:
i think the answer is 278.75
How do you know that △STU is similar to △PQR? Complete the sentence to explain your answer.
PLEASEE I NEED HELP!! PLEASE HURRY
Answers
△STU is mapped to △PQR with center of dilation (-1.5, -1.5) and a scale factor of 2 and reflected about the x-axis.
How to interpret Dilation of Triangles?
From the given graph, we can see that;
SU is 1.5 units and the corresponding side of the dilated figure is 3 units. Thus, the scale factor of dilation is; 3/1.5 = 2
Now, we can see clearly that it is reflected about the x-axis as the x-values remain negative in △STU while the y-values are now positive in △PQR.
Lastly, we can see the dilation was with center (-1.5, -1.5)
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need help finding y-intercept and the x-intercept
Answers
Answer:
y-intercept = 1, x-intercept= -1/4
Step-by-step explanation:
Default equation of line:
y = mx+c , where m is the slope and c is the y-intercept.
So first we will find the slope from the values given in the table.
slope of line [tex]\frac{y1-y2}{x1-x2}\\= \frac{9-5}{2-1} \\= \frac{4}{1}\\ =4[/tex]
So take 1 random value of x and y from the table,
x =1 , y=5
5 = 4(1)+c
c = 5-4 = 1
so equation of line is y = 4x+1
and y intercept = 1
x intercept is the value of x when y = 0.
so given
y = 4x+1
0 = 4x+1
4x = -1
x = [tex]-\frac{1}{4}[/tex]
therefore x intercept = -1/4
simplify 1/x-10 / 9x/x2-9x-10
Answers
The simplified expression is [tex]\frac{-1}{9x} -9x - 10[/tex].
What is algebraic expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.).
Here, the given expression
[tex]\frac{1}{x}+\frac{-10x/9}{x^2}-9x-10[/tex]
[tex]\frac{1}{x}+\frac{-10}{9x}-9x-10[/tex]
[tex]\frac{9-10}{9x} -9x -10[/tex]
[tex]\frac{-1}{9x} -9x - 10[/tex]
Thus, the simplified expression is [tex]\frac{-1}{9x} -9x - 10[/tex].
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what is 232 + 88+ 61 =
Answers
Answer:
381
Step-by-step explanation:
232 + 88 = 320
320 + 61 = 381
Hope this helped and brainliest please
Given the side measurements. classify the triangle as acute, right, obtuse, or not a triangle. 11, 4, 16
Answers
Answer: not a triangle
Step-by-step explanation:
If this were to be a triangle, the shorter sides would be 11 and 4 and the longest side would be 16.
First, we should determine if it is a triangle.
Sum of shorter sides = 15 This is less than the longest side, 16, so therefore, it is not a triangle.The scale factor between two similar figures is given. The surface area and volume of the smaller figure are given. Find the surface area and volume of the larger figure.
scale factor = 2:7
SA= 8 cm²
V = 128 cm³
A) SA=98 cm², V = 5488 cm³
B) SA= 686 cm², V = 5488 cm³
C) SA= 98 cm², V = 686 cm³
D) SA=98 cm², V = 784 cm³
E) SA 14 cm². V = 112 cm³
Answers
Find the volume of the figure. Round your answer to the nearest tenth if necessary. Use 3.14 for T.
A cylinder has a radius of 7 meters and a height of 3 meters.
The volume of the cylinder is approximately
m³.
Answers
Answer:
[tex]\boxed{ \rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3} } \rm (rounded \: to \: nearest \: tenth)[/tex]
Step-by-step explanation:
Given dimensions:
Radius of the cylinder = 7 metresHeight of the cylinder = 3 metresGiven value of π :
π = 3.14To find:
The Volume of the cylinderSolution:
Here, we'll need to use the formulae of the volume of cylinder,to find it's volume.Its actually like a savior while solving these type of questions.
[tex] \pink{\star}\boxed{\rm \: Volume_{(Cylinder)} = \pi{r} {}^{2} h}\pink{\star}[/tex]
where,
π = 3.14r² = (radius)²h = heightPlug/substitute them onto the formulae,then simplify it using PEMDAS.
[We'll substitute the value of π later][tex] \rm \: Volume_{(Cylinder)} = \pi(7) {}^{2} \times 3[/tex]
[tex] \rm \: Volume_{(Cylinder)} = \pi(49)(3)[/tex]
[tex] \rm \: Volume_{(Cylinder)} = 147\pi \: [/tex]
Now substitute the value of π.[tex] \rm \: Volume_{(Cylinder)} = 147 \times 3.14[/tex]
[tex] \rm \: Volume_{(Cylinder)} = 461.58 \: {m}^{3} [/tex]
[tex] \boxed{\rm \: Volume_{(Cylinder)} \approx \: 461.6 \: {m}^{3}} \rm (rounded \: to \: nearest \: tenth) \: [/tex]
Hence, we can conclude that:
The volume of the cylinder is approximately
461.6 m³.
[tex] \rule{225pt}{2pt}[/tex]
Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following
equation.ñ
y = 2x^2 -x + 6
Answers
Answer:
(1/4, 5 7/8)
Step-by-step explanation:
The vertex is the extreme point of the graph. Here, it is a minimum.
For this quadratic function, a graphing calculator can tell you exactly what the vertex is. (No approximation is required.)
__
The graphing calculator in the attachment shows the vertex is ...
(0.25, 5.875) = (1/4, 5 7/8)
S 2. Let f(x) = x - k√x
a. Find a value of k such that the function has a critical point at x = 25.
b. Is the above critical point a local maximum, local minimum or neither? Show calculus to support your answer.
Answers
a. A critical point at x = 25 would mean f'(25) = 0 or doesn't exist. We have derivative
[tex]f(x) = x - k \sqrt x \implies f'(x) = 1 - \dfrac k{2\sqrt x}[/tex]
so that
[tex]f'(25) = 1 - \dfrac k{2\sqrt{25}} = 1 - \dfrac k{10} = 0 \implies \boxed{k=10}[/tex]
b. Taking the second derivative, we get
[tex]f''(x) = \dfrac k{4 x^{3/2}} = \dfrac5{2 x^{3/2}}[/tex]
At x = 25, the second derivative has a positive sign,
[tex]f''(25) = \dfrac 5{2 \times 25^{3/2}} = \dfrac 5{2\times5^3} = \dfrac1{50} > 0[/tex]
which means f(x) is concave upward around x = 25, so this critical point is a local minimum.
Find the area of a regular polygon with 5 sides that has a side length of 6 inches and an apothem of 9 inches.
Area = [?]in2
Answers
Answer:
see the attachment photo!
Answer: The correct answer is 135 in².
Step-by-step explanation: An area of a polygon is this:
Area = (number of sides × length of one side × apothem)/2
(5 x 6 x 9) / 2 = 135
NO LINKS!!!
Basics of Transformations
Students were asked to create true statements about transformations. Circle the names of the students who correctly completed the task. Then, unscramble the underlined letters of the circled names to answer riddle of the bottom.
Answers
Answer:
The 6 names to circle are:
LavernaAlfonsoAutumnIgnacioKathyrnLawrenceThe underlined letters from those circled names are:
RNONTUGRNWRThe letters form the phrase [tex]\underline{\text{WR}}\ \underline{\text{ON}} \ \underline{\text{G}} \ \ \ \ \ \ \underline{\text{TU}} \ \underline{\text{RN}}[/tex] or "wrong turn". The spacing is done like that in the first version to show the various subgroups of letters.
Unfortunately the mentioned riddle at the bottom is cut off, so I don't know what the riddle is.
======================================================
Explanation:
Laverna is correct because a translation is applied. "Translation" in geometry settings means "shifting up/down/left/right". In this case, triangle JKL is shifted 5 units right and 3 units up.Alfonso is correct. If a figure is labeled ABCD going in clockwise orientation, then a translation will preserve said orientation. The orientation only flips when a reflection occurs.Autumn is correct. Why? Because reflections are isometries, meaning they preserve distances and lengths and angles. In other words, the two triangles are twin clones of each other.Willa is not correct. The prime notations go on the image and NOT the preimage. In other words, the prime notations go for the "after" and not the "before". Example: triangle JKL in Laverna's diagram is the preimage, while J'K'L' is the image. JKL is "before", and J'K'L' is "after".Ignacio is correct. The figure enlarges or shrinks (depending on the scale factor if its larger than 1, or smaller than 1). The orientation stays the same. Refer to Alfonso's scenario where I mentioned the orientation flipping only when a reflection happens.Napoleon is incorrect. A reflection ALWAYS changes the orientation. Consider a triangle ABC where the motions from A to B to C goes clockwise. A reflection will flip the orientation to make A to B to C go counterclockwise. Example: Reflections over non-horizontal lines swap the positions of left vs right, which is another way to see why the orientation swaps as well.Kathyrn is correct assuming no reflection operations are done.Titus is not correct. A rotation is not the same as a reflection. Though I should point out that two reflections simplify to a rotation. The mirror lines must intersect in some way. Parallel mirror lines will have two reflections lead to a translation.Lawrence is correct. The order P,Q,R is clockwise, and so is the order P', Q', R'. A rotation preserves orientation. In this case, a 180 degree rotation has been done. The rule for that is any (x,y) point turns into (-x,-y).Here's a summary table:
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Student} & \text{Are They Correct?}\\\cline{1-2}\text{Laverna} & \textbf{Yes}\\\cline{1-2}\text{Alfonso} & \textbf{Yes}\\\cline{1-2}\text{Autumn} & \textbf{Yes}\\\cline{1-2}\text{Willa} & \text{No}\\\cline{1-2}\text{Ignacio} & \textbf{Yes}\\\cline{1-2}\text{Napoleon} & \text{No}\\\cline{1-2}\text{Kathyrn} & \textbf{Yes}\\\cline{1-2}\text{Titus} & \text{No}\\\cline{1-2}\text{Lawrence} & \textbf{Yes}\\\cline{1-2}\end{array}[/tex]
Put another way, here are the people to circle (i.e. the people who made true statements):
LavernaAlfonsoAutumnIgnacioKathyrnLawrenceIn the order presented above, the letters underlined are:
RNONTUGRNWRThrough a bit of trial and error, the letters make the phrase of:
[tex]\underline{\text{WR}}\ \underline{\text{ON}} \ \underline{\text{G}} \ \ \ \ \ \ \underline{\text{TU}} \ \underline{\text{RN}}[/tex]
I'm not sure what to do with the extra "RN". It might be a typo, or it might be the case your teacher wants you to ignore repeats like this.