the answer to this question is
m=1
Answer: y<-x+3
Step-by-step explanation:
Slope-Intercept Form formula is y=mx+b.
1. Rearrange the variables (subtract x). x+y<3 --> y<-x+3.
2. y<-x+3 is the final answer!
Very Simple!
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The following cylinder has a volume of 20π cm3 and a height of 5 cm
What is the diameter of the cylinder? Remember, the diameter of a circle is two times its radius
Answer:
Step-by-step explanation:
To find the diameter of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
Given:
Volume = 20π cm^3
Height = 5 cm
We can rearrange the formula to solve for the radius:
radius^2 = Volume / (π * height)
radius^2 = (20π) / (π * 5)
radius^2 = 4
radius = 2
Now, we can find the diameter by multiplying the radius by 2:
diameter = 2 * radius
diameter = 2 * 2
diameter = 4
Therefore, the diameter of the cylinder is 4 cm.
Willis analyzed the following table to determine if the function it represents is linear or non-linear. First he found the differences in the y-values as 7 – 1 = 6, 17 – 7 = 10, and 31 – 17 = 14. Then he concluded that since the differences of 6, 10, and 14 are increasing by 4 each time, the function has a constant rate of change and is linear. What was Willis’s mistake?
Answer:
Step-by-step explanation:
Willis’s mistake is that he used the differences of 6, 10 and 14 instead of the differences of 7, 17 and 31. For a linear function, the y values should have a constant rate of change and not the differences.
4. The school nurse would like to compare the daily calorie consumption of some teachers to their weight. The data are given below:
The relationship between Calorie and weight is very weak and insignificant.
Relationship between VariablesComparing the relationship between Calorie and Weight using the correlation coefficient, the coefficient value obtained is 0.0086 which is very weak.
There is no obvious pattern linking an increase in calorie to Weight or decrease in association between the two variables.
Therefore, we can conclude that a very weak and insignificant relationship exists between Calorie and weight for the given data.
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Out of a pool of 26 men and 29 women what is the probability of 12 women jurors being chosen?
The probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.
To calculate the probability of selecting 12 women jurors out of a pool of 26 men and 29 women, we need to consider the total number of possible combinations and the specific combination of interest.
The total number of ways to choose 12 individuals from a pool of 55 (26 men + 29 women) is given by the combination formula:
C(55, 12) = 55! / (12! * (55-12)!) = 22579284062370.
The number of ways to choose 12 women from a pool of 29 is given by the combination formula:
C(29, 12) = 29! / (12! * (29-12)!) = 7726160.
Therefore, the probability of selecting 12 women jurors is the ratio of the number of ways to choose 12 women to the total number of possible combinations:
P(12 women jurors) = C(29, 12) / C(55, 12) ≈ 7726160 / 22579284062370 ≈ 0.000342.
Hence, the probability of 12 women jurors being chosen is approximately 0.000342 or 0.0342%.
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% of 50 = 57
Find the missing percent
A camera has a listed price $859.95 of before tax. If the sales tax rate is 9.5% , find the total cost of the camera with sales tax included.
Round your answer to the nearest cent, as necessary.
Answer:
$941.65
Step-by-step explanation:
Salex tax:We have to find the sales tax of the camera.
tax rate = 9.5%
listed price = $859.95
[tex]\sf Sales \ tax = tax \ rate * listed \ price[/tex]
= 9.5 % * 859.95
= 0.095 * 859.95
= $81.70
To find the total cost, add the sales tax to the listed price.
Total cost = 859.95 + 81.70
= $941.65
50 POINTS ANSWER THE LAST QUESTION ON THE CHART AND GIVE ME THE EQUATION FOR BRAINLIST
Answer:L*W
Step-by-step explanation:
if you look at the pattern you will see that
1. Calculate GDP at FC from the following data: GDP at MP = Rs. 2,000 billion Indirect taxes = Rs. 300 billion Subsidies = Rs. 100 billion
The GDP at FC from the following data: GDP at MP = Rs. 2,000 billion Indirect taxes = Rs. 300 billion Subsidies = Rs. 100 billion is: Rs. 1,800 billion.
What is GDP?Using this formula to determine the GDP at FC
GDP at FC = GDP at MP - Indirect taxes + Subsidies
Where:
GDP at MP (Market Price) = Rs. 2,000 billion
Indirect taxes = Rs. 300 billion
Subsidies = Rs. 100 billion
Let plug in the formula
GDP at FC = 2,000 billion - 300 billion + 100 billion
GDP at FC = 1,800 billion
Therefore the GDP at factor cost (FC) is Rs. 1,800 billion.
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In circle F with mZEFG = 70 and EF = 19 units, find the length
of arc EG. Round to the nearest hundredth.
E
F
G
Answer:
Arc EG = 23.21 units
Step-by-step explanation:
Arc length:
Arc length could be found by the below mentioned formula.
[tex]\boxed{\bf Arc \ length =\dfrac{\theta }{180}*\pi r}[/tex]
r - radius of circle = 19 units
Ф - central angle of arc = 70°
[tex]\sf arc \ EG = \dfrac{70}{180}*3.14*19\\\\[/tex]
= 23.21 units
1. At a sale on winter clothing, Cody bought two pairs of gloves and four hats for $43.00. Tor bought two pairs of gloves and two hats for
930.00. Find the prices of the hats and gloves.
(k pL.)
Let x-
Let v=
(pt.)
2. Aaliyah invested $10,000 in two mutual funds.
One of the funds rose 6% in one year, and the other rose 906 in one year. Aaliyah's investment rose a total of S684 in one vear. Find the amount she invested in each fund.
1. The price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.
2. Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.
1. Let's assume the price of a pair of gloves is represented by 'x' and the price of a hat is represented by 'y'.
From the given information, we can establish the following equations based on Cody and Tor's purchases:
Equation 1: 2x + 4y = 43.00 (Cody's purchase)
Equation 2: 2x + 2y = 30.00 (Tor's purchase)
To solve this system of equations, we can use a method like substitution or elimination.
Using the substitution method, we can rearrange Equation 2 to express x in terms of y:
2x = 30.00 - 2y
x = 15.00 - y
Now, we substitute this value of x into Equation 1:
2(15.00 - y) + 4y = 43.00
30.00 - 2y + 4y = 43.00
2y = 43.00 - 30.00
2y = 13.00
y = 6.50
Substituting this value of y back into Equation 2 to find x:
2x + 2(6.50) = 30.00
2x + 13.00 = 30.00
2x = 30.00 - 13.00
2x = 17.00
x = 8.50
Therefore, the price of a pair of gloves (x) is $8.50, and the price of a hat (y) is $6.50.
2. Let's assume Aaliyah invested an amount represented by 'x' in the mutual fund that rose 6% and an amount represented by 'y' in the mutual fund that rose 9%.
From the given information, we can establish the following equations based on the rise in investment:
Equation 1: 0.06x + 0.09y = 684 (rise in investment)
Equation 2: x + y = 10,000 (total investment)
To solve this system of equations, we can use a method like substitution or elimination.
Using the substitution method, we can rearrange Equation 2 to express x in terms of y:
x = 10,000 - y
Now, we substitute this value of x into Equation 1:
0.06(10,000 - y) + 0.09y = 684
600 - 0.06y + 0.09y = 684
0.03y = 84
y = 2800
Substituting this value of y back into Equation 2 to find x:
x + 2800 = 10,000
x = 10,000 - 2800
x = 7200
Therefore, Aaliyah invested $7,200 in the mutual fund that rose 6% and $2,800 in the mutual fund that rose 9%.
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Reema wants to build a coat rack for the front hallway. The wall is 4 feet long, and the piece of wood she has for the the rack is 28 1/4 inches long. She wants to center the coat rack on the wall. There needs to be an equal amount of space, about 7 or 8 inches, between coat hooks. The first and last hooks should be no less than 1 3/4 inches from either end of the wood. How many hooks should Reema use? What is the distance between the hooks? What is the distance of each hook from the left edge of the wood?
Reema should use 3 hooks, with a distance of 7 inches between each hook, and each hook will be positioned 5 3/8 inches from the left edge of the wood.
To determine the number of hooks Reema should use, we first need to calculate the available space on the wood for the hooks.
The total length of the wall is 4 feet, which is equivalent to 48 inches. Reema wants to center the coat rack, so she will have an equal amount of space on either side.
Therefore, each side will have (48 - 28 1/4) / 2 = 9 3/8 inches of space.
Next, we need to determine the distance between the hooks.
Reema wants about 7 or 8 inches of space between each hook.
Let's choose 7 inches for consistency.
Since there will be (n - 1) spaces between n hooks, the total space taken by the spaces will be 7 [tex]\times[/tex] (n - 1) inches.
Now, let's subtract the space taken by the spaces from the available space on the wood: 9 3/8 - 7 [tex]\times[/tex] (n - 1) = 9 3/8 - 7n + 7 inches.
Reema wants the first and last hooks to be no less than 1 3/4 inches from either end of the wood.
Therefore, we subtract twice this distance from the remaining space: 9 3/8 - 7n + 7 - 2 [tex]\times[/tex] (1 3/4) = 9 3/8 - 7n + 7 - 3 1/2 inches.
Now we have the expression 9 3/8 - 7n + 7 - 3 1/2 inches representing the remaining space.
We want this value to be greater than or equal to zero, as it should not be negative.
Simplifying the expression, we have 18 7/8 - 7n - 3 1/2 inches ≥ 0.
Now we can solve this inequality to find the range of values for n, the number of hooks.
We can then determine the distance between the hooks by dividing the remaining space by the number of spaces, and the distance of each hook from the left edge of the wood by adding the space taken by the spaces to the distance between the hooks.
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Don Arnoldo heredó una parcela de forma rectangular, en la cual el largo más el ancho mide 30 metros y la diferencia entre el largo y el ancho es de 6 metros. ¿Cuánto mide de largo y de ancho la parcela?
Por lo tanto, la parcela mide 18 metros de largo y 12 metros de ancho.
Llamemos "largo" (L) a una de las dimensiones de la parcela y "ancho" (A) a la otra dimensión.
Según la información dada, sabemos que la suma del largo y el ancho es de 30 metros:
L + A = 30 ---(1)
También se nos dice que la diferencia entre el largo y el ancho es de 6 metros:
L - A = 6 ---(2)
Podemos resolver este sistema de ecuaciones utilizando el método de sustitución o de eliminación. En este caso, resolveremos utilizando el método de sustitución.
De la ecuación (2), podemos despejar L en términos de A:
L = A + 6
Sustituyendo este valor de L en la ecuación (1), obtenemos:
(A + 6) + A = 30
2A + 6 = 30
Restamos 6 de ambos lados de la ecuación:
2A = 30 - 6
2A = 24
Dividimos ambos lados de la ecuación por 2:
A = 12
Ahora que conocemos el valor de A, podemos encontrar el valor de L sustituyendo en la ecuación (2):
L = A + 6
L = 12 + 6
L = 18
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Calculate the area of the composite figure please help me with them especially the shape and total area part please
The area of the composite figures are:
The total area of Shape A is = 115.5 in²
and, total area of Shape B is = 51ft².
Here, we have,
from the given diagram we get,
Shape A.)
Part 1: it is a rectangle,
l= 13 and w = 7
so, area = 91 in²
Part 2: it is a triangle,
b = 7 and h = 7
so, area = 1/2 *7 * 7 = 24.5 in²
So, The total area of Shape A is = 115.5 in²
now, Shape B.)
part 1 : it is a rectangle,
l=4 and w = 6
so, area = 24 ft²
part2: it is a square,
side = 3
so, area = 9 ft²
part 3: it is a trapezium,
a = 6, b = 3, h =4
so, area = 1/2 * (6+3) * 4 = 18ft²
So, total area of Shape B is = 51ft².
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whats the solutions for 2x^2-10x=0
[tex]2x^2-10x=0\\2x(x-5)=0\\2x=0 \vee x-5=0\\x=0 \vee x=5[/tex]
Answer:
Here
2x^2 - 10x = 0
2x^2 = 0 + 10x
2x^2 = 10x
x^2 = 10x ÷ 2
x^2 = 5x
2x^2 - 10x = 0
x^2 - 5x = 0
Step-by-step explanation:
first find the value of x and then put the value and slove
8. mVWY =
Segment AB and segment AD are both tangent to circle C. Find x.
Need 7-9 pls show work. Will mark you branliest
The tangent from the external point are equal, so the x value is 3 units.
7) The measure of the arc XW is 180-105=75
8) The measure of the arc VWY is 105+75+85 = 265
9) We know that, tangent from the external point are equal
In circle C, AB=AD
26=8x+2
8x=24
x=24/8
x=3 units
10) 9x-3=7x+5
9x-7x=5+3
2x=8
x=8/2
x=4
Therefore, the tangent from the external point are equal, so the x value is 3 units.
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A baking scale measures mass to the tenth of a gram, up to 650 grams. A cup of flour is placed on the scale and results in a measure of 121.8 grams. Which of the following statements is not true?
The exact mass of the cup of flour must be between 121.7 and 121.9 grams.
The cup of flour has a mass of exactly 121.8 grams.
Given the limitations of the scale, the measurement has an appropriate level of accuracy.
To the nearest gram, the cup of flour has a mass of 122 grams.
The statement "The cup of flour has a mass of exactly 121.8 grams" is not true.
Since the baking scale measures mass to the tenth of a gram, it means it can measure values such as 121.7 grams, 121.8 grams, and 121.9 grams. However, it does not have the capability to measure beyond the tenths place, so it cannot determine whether the exact mass of the cup of flour is exactly 121.8 grams. Therefore, the statement claiming an exact mass is not true.
The other statements are all true:
- The exact mass of the cup of flour must be between 121.7 and 121.9 grams because the scale can measure to the tenth of a gram.- Given the limitations of the scale, the measurement has an appropriate level of accuracy. The scale measures to the tenth of a gram, which is suitable for measuring ingredients in baking.- To the nearest gram, the cup of flour has a mass of 122 grams. Since the scale measures to the tenth of a gram, the rounded value to the nearest gram would be 122 grams.[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]
♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]
Answer:
Step-by-step explanation:
A baking scale measures mass to the tenth of a gram, up to 650 grams. A cup of flour is placed on the scale and results in a measure of 121.8 grams. [ Which of the following statements is not true? a.The exact mass of the cup of flour must be between 121.7 and 121.9 grams.
What is the value of n?
Enter your answer in the box.
n = __ cm
The value of the missing segment n using the product of intersecting chord theorem is 14cm
Using the product of intersecting chord principleThe product of the segments of two intersecting chords are equal.
The segments of the chords ;
Chord 1 = 4 and n
Chord 2 = 7 and 8
The principle can be related Mathematically thus ;
4 × n = 7 × 8
4n = 56
Divide both sides by 4
4n/4 = 56/4
n = 14
Therefore, the value of n in the question is 14cm
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¿Cuál es el valor de 6 – (3x + 1) + 2x^2, cuando x = 4?
Answer:
Para encontrar el valor de la expresión 6 - (3x + 1) + 2x^2 cuando x = 4, sustituimos el valor de x en la expresión y evaluamos:
6 - (3x + 1) + 2x^2
= 6 - (3 * 4 + 1) + 2 * 4^2
= 6 - (12 + 1) + 2 * 16
= 6 - 13 + 32
= -7 + 32
= 25
Por lo tanto, cuando x = 4, el valor de la expresión 6 - (3x + 1) + 2x^2 es igual a 25.
Step-by-step explanation:
The following cylinder has a volume of 627.8 cm3 and a height of 19.5 cm
What is the radius of the cylinder?
Use 3.14 for π and round your answer to the nearest tenth.
5.7
3.2
1.7
10.1
Answer:
Step-by-step explanation:
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
Given:
Volume = 627.8 cm^3
Height = 19.5 cm
π (pi) = 3.14
Substituting the given values into the formula:
627.8 = 3.14 * radius^2 * 19.5
Simplifying the equation:
627.8 = 60.93 * radius^2
To solve for the radius, we can divide both sides of the equation by 60.93:
radius^2 = 627.8 / 60.93
radius^2 = 10.29
Taking the square root of both sides:
radius ≈ √10.29
Rounding to the nearest tenth:
radius ≈ 3.2
Therefore, the approximate radius of the cylinder is 3.2 cm.
Answer:
3.2
Step-by-step explanation:
The volume of a cylinder is:
Vol = pi•r^2•h
Fill in what is given.
627.8 = pi•r^2•19.5
use 3.14 for pi.
627.8 = 3.14•r^2•19.5
simplify.
627.8 = 61.23r^2
divide by 61.23
10.253 = r^2
sqrt both sides
sqrt10.253 = r
3.2 = r
Mr. Chi wants to sell his house. The state he lives in charges a 3.2% sales tax on the sale of a house. The county charges a 2.6% sales tax, and the city charges a 1.8% sales tax. If Mr. Chi sells his home for $289,300, what is his total tax bill?
Answer:
To calculate Mr. Chi's total tax bill, we need to find the amount of sales tax charged by each entity and add them together.
The state sales tax on the sale of a house is 3.2%, which means Mr. Chi will owe 0.032 x $289,300 = $9,267.20 in state sales tax.
The county sales tax on the sale of a house is 2.6%, which means Mr. Chi will owe 0.026 x $289,300 = $7,520.80 in county sales tax.
The city sales tax on the sale of a house is 1.8%, which means Mr. Chi will owe 0.018 x $289,300 = $5,207.40 in city sales tax.
Therefore, Mr. Chi's total tax bill will be $9,267.20 + $7,520.80 + $5,207.40 = $21,995.40.
Based on the W2 form above, how much money did Jane Doe get to take home after taxes in 2017?
Question 9 options:
$48,500
$6,835
$50,000
$725
The amount of money that Jane Doe get to take home after taxes in 2017 is A. $48500
How to calculate the amountBased on the W-2 form above, Jane Doe's gross pay was $50,000. She had $6,835 in federal income tax withheld, $725 in state income tax withheld, and $1,000 in FICA taxes withheld. This means that her net pay was $48,500.
Net pay = Gross pay - Total taxes withheld
Net pay = $50,000 - ($6,835 + $725 + $1,000)
Net pay = $48,500
Therefore, amount of money that Jane Doe get to take home after taxes in 2017 is A. $48500
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How do i do this problem liek i have to find a side?
Answer:
[tex]\overline{LP}=77[/tex]
Step-by-step explanation:
Given [tex]\Delta LMQ\sim\Delta LNP[/tex], then [tex]\overline{LN}=\overline{LM}+\overline{MN}=8+14=22[/tex]. This will help us find [tex]\overline{LQ}[/tex] since we know the length of [tex]\overline{QP}[/tex]:
[tex]\displaystyle \frac{\overline{LM}}{\overline{LM}+\overline{MN}}=\frac{\overline{LQ}}{\overline{LQ}+\overline{QP}}\\\\\frac{8}{8+14}=\frac{\overline{LQ}}{\overline{LQ}+49}\\\\\frac{8}{22}=\frac{\overline{LQ}}{\overline{LQ}+49}\\\\8(\overline{LQ}+49)=22\overline{LQ}\\\\8\overline{LQ}+392=22\overline{LQ}\\\\392=14\overline{LQ}\\\\28=\overline{LQ}[/tex]
Therefore:
[tex]\overline{LP}=\overline{LQ}+\overline{QP}=28+49=77[/tex]
Question 5 of 10
What can you say about the y-values of the two functions f(x) = 32 - 3
and g(x) = 7x² - 3?
A. The minimum y-value of f(x) is -3.
B. The minimum y-value of g(x) is -3.
C. g(x) has the smallest possible y-value.
D. f(x) has the smallest possible y value.
SUBMIT
The minimum y-value of g(x) is -3 and g(x) has the smallest possible y-value.
The function f(x) = 32 - 3 is a constant function, as there is no variable term involving x. It simplifies to f(x) = 29.
Regardless of the value of x, the function f(x) will always have a y-value of 29.
Therefore, option A is incorrect because there is no minimum y-value for f(x); it is a constant.
g(x) = 7x² - 3 is a quadratic function in the form of ax² + bx + c, where a = 7, b = 0, and c = -3.
The coefficient a (7) is positive, indicating that the parabola opens upward.
Since there is no linear term (bx), the vertex of the parabola is located at the point (0, -3), which corresponds to the minimum y-value of the function.
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Use the table to answer the question that follows.
ROR Portfolio 1 Portfolio 2 Portfolio 3
12.6% $1,250 $950 $900
2.8% $575 $2,025 $2,350
10.4% $895 $1,185 $310
1.8% $800 $445 $1,600
−5.6% $1,775 $625 $2,780
Calculate the weighted mean of the RORs for each portfolio. Based on the results, which list shows a comparison of the overall performance of the portfolios, from best to worst?
Portfolio 1, Portfolio 2, Portfolio 3
Portfolio 3, Portfolio 2, Portfolio 1
Portfolio 2, Portfolio 3, Portfolio 1
Portfolio 2, Portfolio 1, Portfolio 3
Based on the results, the below list shows a comparison of the overall performance of the portfolios, from best to worst:
Portfolio 2, Portfolio 1, Portfolio 3
Portfolio 1:
total investment=$1250+$575+$895+$800+$1775
total investment = $5295
weighted average ROR= (12.6%*$1250/$5295 + 2.8%*$575/$5295 + 10.4%*$895/$5295 +1.8%*$800/$5295 - 5.6%*$1775/$5295)
weighted average ROR = 3.23%
Portfolio 2:
total investment = $950 + $2025 + $1185 + $445 + $625
total investment = $5230
weighted average ROR= ( 12.6%*$950/ $5230 + 2.8% *$2025/ $5230 + 10.4%*$1185/ $5230 + 1.8%* $445/ $5230 - 5.6%*$625/ $5230)
weighted average ROR = 5%
Portfolio 3:
total investment = $900 + $2350 + $310 + $1600 + $2780
total investment = $7940
weighted average ROR = ( 12.6%*$900/$7940 + 2.8% *$2,350/$7940 + 10.4%*$310/ $7940 + 1.8%* $1600 / $7940 −5.6% *$2780/$7940)
weighted average ROR = 1%
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Solve for x:
A: 3x - 7 = -19; x =
B: 2x + 3 = -11; x =
C: -3 + 1 = -26; x =
D: 6x + 3 = -15; x =
E: -9 + 7x = 33; x =
F: -2x + 8 = 4; x =
( URGENT PLEASE SOLVE !!! )
Four tiles lettered M, A, T, and H are facedown on a table. A tile is selected, the letter is recorded, the tile is replaced, and the process is repeated.
What is the theoretical probability of selecting the letter T?
The theoretical probability of selecting the letter T is 1/4.
What is probability?Probability is the possibility of happening an event.
Given the four letters M, A, T, and H.
Note that the letter T occurs 1 time, therefore, the probability of selecting the letter T is:
[tex]\sf P=\dfrac{1}{4}[/tex]
Hence, the theoretical probability of selecting the letter T is 1/4.
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Abiodun walks 5km due north,then12km due east.How far ia he from the starting point?
What is the answer pls
Mahavira wrote in detail about the idea of zero. What special characteristic did he share with Paul McCartney?
Use the given information about
to find the exact value of cos 0/2
The exact value of cos(θ/2) is:
[tex]cos(\frac{\theta }{2}) = \right-\sqrt{\frac{1}{122} }[/tex]
How to find the exact value of cos (θ/2)?To find the exact value of cos(θ/2), we can use the half-angle formula for cosine:
[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1+cos\theta}{2} }[/tex]
First, let's find the value of cos(θ) using the given information about θ:
Given:
tan(θ) = 11/60
θ lies in the 3rd quadrant (π < θ < 3π/2)
In the 3rd quadrant, both sin(θ) and cos(θ) are negative.
tan(θ) = opposite/adjacent
Also, in the 3rd quadrant, both opposite and adjacent are negative.
Thus,
opposite = -11
adjacent = -60
hypotenuse = √[(-60)² + (-11)²] (Pythagoras theorem)
hypotenuse = 61
cos(θ) = adjacent/hypotenuse
cos(θ) = -60/61
Finally, we can substitute these values into the half-angle formula for cosine:
[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1+(\frac{-60}{61})}{2} }[/tex]
[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{\frac{1}{61} }{2} }[/tex]
[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1}{122} }[/tex]
Since the cos(θ/2) is negative. Therefore, the exact value of cos(θ/2) is:
[tex]cos(\frac{\theta }{2}) = \right-\sqrt{\frac{1}{122} }[/tex]
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