Answers
The simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]
How to rationalize surd functions?
Given the surd function expressed as:
[tex]\frac{\sqrt{3} +5}{\sqrt{3} - 5 }[/tex]
Multiply by the conjugate of the denominator to have:
[tex]= \frac{\sqrt{3} +5}{\sqrt{3} - 5 } \times \frac{\sqrt{3} +5}{\sqrt{3} + 5 } \\=\frac{\sqrt{9}+5\sqrt{3}+5\sqrt{3}+25 }{3-25}[/tex]
Simplify the resulting expression
[tex]\\=\frac{3+10\sqrt{3}+25 }{-22}\\=\frac{28+10\sqrt{3}}{-22} \\= \frac{14+5\sqrt{3}}{11}[/tex]
Hence the simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]
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Related Questions
A contractor records the areas, in square feet, of a small sample of houses in a neighborhood to determine data about the neighborhood. they are: 2,400; 1,750; 1,900; 2,500; 2,250; 2,100 which of the following represents the numerator in the calculation of variance and standard deviation? (225)2 (–425)2 (–275)2 (325)2 (75)2 (–75)2 = 423,750 (650)2 (–150)2 (–600)2 (250)2 (150)2 (–300)2 = 980,000 (250)2 (–400)2 (–250)2 (350)2 (100)2 (–50)2 = 420,000 what is the variance? what is the standard deviation, rounded to the nearest whole number?
Answers
Option c is the correct answer which represents the numerator in the calculation of variance and standard deviation.
What are the variance and standard deviation?In statistics, variance is a measure of the variation of data from the mean, whereas standard deviation is the measure of the normal distribution of statistical data.
A contractor records the areas, in square feet, of a small sample of houses in a neighborhood to determine data about the neighborhood.
2,400; 1,750; 1,900; 2,500; 2,250; 2,100
we need to find which of the following represents the numerator in the calculation of variance and standard deviation.
(225[tex])^{2}[/tex] + (–425[tex])^{2}[/tex]+ (–275[tex])^{2}[/tex] + (325[tex])^{2}[/tex] + (75[tex])^{2}[/tex]+ (–75[tex])^{2}[/tex] = 423,750
(650[tex])^{2}[/tex] + (–150[tex])^{2}[/tex] + (–600[tex])^{2}[/tex] + (250[tex])^{2}[/tex] + (150[tex])^{2}[/tex] + (–300[tex])^{2}[/tex] = 980,000
(250[tex])^{2}[/tex] + (–400[tex])^{2}[/tex] + (–250[tex])^{2}[/tex] + (350[tex])^{2}[/tex] + (100[tex])^{2}[/tex] + (–50[tex])^{2}[/tex] = 420,000
92416.60
The variance is 84000
The standard deviation is 290
mean = (2400+1750+1900+2500+2250+2100)/6
mean = 2150
Subtract the data values from the mean to get
2400-2150 = 250
1750-2150 = -400
1900-2150 = -250
2500-2150 = 350
2250-2150 = 100
2100-2150 = -50
The differences are 250, -400, -250, 350, 100, -50
Then you square those values and add up the squares
(250)^2 + (-400)^2 + (-250)^2 + (350)^2 + (100)^2 + (-50)^2 = 420,000
Hence, option c is the correct answer which represents the numerator in the calculation of variance and standard deviation.
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4. The method of completing the square was used to solve the equation 2x^2 - 12x + 6 = 0. Which equation is a
correct step when using this method?
A. (x - 3)^2 = 6
B. (x - 3)^2 = -6
C. (x - 3)^2 = 3
D. (x - 3)^2 = -3
Pls help
Answers
Answer: B
Step-by-step explanation: I hope it helps if not your welcome to get a tutor
The requried correct step when using the method of completing the square to solve the equation 2x² - 12x + 6 = 0 is A. (x - 3)² = 6.
What is simplification?Simplifying an expression involves eliminating unnecessary variables, components, or processes using algebraic and mathematical principles. The goal is to obtain an expression that is easier to use, manipulate, or solve.
Here,
To solve the quadratic equation 2x² - 12x + 6 = 0 using the method of completing the square, we can follow these steps:
Divide both sides by the coefficient of x^2 to make the coefficient of x² equal to 1:
x² - 6x + 3 = 0
Add and subtract the square of half the coefficient of x:
x² - 6x + 9 - 9 + 3 = 0
Factor the first three terms:
(x - 3)² - 6 = 0
Add 6 to both sides:
(x - 3)² = 6
Therefore, the correct step when using the method of completing the square to solve the equation 2x² - 12x + 6 = 0 is A. (x - 3)² = 6.
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Fernando compró un videojuego y sabe que el valor depreciado de este es de $600 luego de 12
meses de su compra y de $480 al término de 18 meses. Si el valor del sistema varía linealmente
con el tiempo, determina:
a) La ecuación que expresa la relación del valor del videojuego con su tiempo de uso.
b) El valor del videojuego cuando era nuevo.
ayudenme profavor
Answers
Usando una ecuación lineal, se encuentra que:
a) La ecuación es y = -20x + 840.
b) El valor del videojuego cuando era nuevo era de $840.
¿Qué es una función lineal?Una función lineal es modelada por:
y = mx + b
En el cual:
m es la pendiente, que es la tasa de cambio, es decir, cuánto cambia y cuando x cambia en 1.b es la intersección con y, que es el valor de y cuando x = 0, y también se puede interpretar como el valor inicial de la función.En este problema, el valor depreció $120 en 6 meses, por lo tanto la pendiente es dada por:
m = -120/6 = -20.
O sea:
y = -20x + b
Al longo de 12 meses, el valor deprecio 12 x 20 = $240. Por lo tanto, el valor inicial es dado por:
b = 600 + 240 = $840.
Y la ecuación es dada por:
y = -20x + 840.
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I need help on this
Answers
Answer:
a) 1/8
b) 8
Step-by-step explanation:
a) 1/2 x 1/2 x 1/2 = 1/8
b) since the exponent is negative it becomes positive when placed in the denominator
so 1/2 ^-1 is equal to 1/1 ÷ 1/2 which is equal to 2
therefore, (1/2)^-3 is equal to 2 x 2 x 2 or 8
The function P(x)=x^3−2x^2 is dilated by the function I(x)=P(4x).
Which function rule represents I(x)?
A.) I(x)=4x^3−8x^2
B.) I(x)=64x^3−32x^2
C.) I(x)=4x^3−2x^2
D.) I(x)=64x^3−2x^2
Answers
Answer:
Its C
Step-by-step explanation:
Why? because its C
geometry help
answer choices:
24
12
82
59
Answers
largest arc - smallest arc = 2•angle
94-70=24
24/2=A
A=12
The measure of the angle ∠A will be 12°. Then the correct option is B.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The angle formed by two secants (lines cutting a circle at two places) intersecting outside the ring is half the distance between their arc minus the closest arc.
From the diagram, the equation is given as,
∠A = (arc DE - arc BC) / 2
∠A = (94° - 70°) / 2
∠A = 24° / 2
∠A = 12°
The measure of the angle ∠A will be 12°. Then the correct option is B.
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Dakota deposited $500 in an account earning 10% interest compounded annually.
To the nearest cent, how much interest will she earn in 3 years?
Answers
Answer:
165.50
Step-by-step explanation:
yeah
Answer: 165.50
Step-by-step explanation: i had the same one and got it right
Which choice describes an equation
that has a solution set of
"All real numbers"?
3(x + 1) = 3x + 3
Answers
Answer:
Step-by-step explanation:
Remark
Choose any number at all and see what happens.
Suppose x = 8
3*(8 + 1) = 3*8 + 3
3(9) = 27
3*8 + 3 = 24 + 3 = 27
What you have shown is that the second choice is incorrect. There is at least one value that makes the equation correct (that is, both sides come to the same result.)
If choice two is false then choice one must be true since these results may give the only 2 possible results.
Question 13 options:
What is the slope of the line of the graph?
Answers
Answer:
Step-by-step explanation:
To find the slope, pick any two points fromthe line.
(2,2) & (0,-4)
x₁ = 2 & y₁ = 2
x₂ = 0 & y₂ = - 4
[tex]\boxed{Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]
[tex]\sf =\dfrac{-4-2}{0-2}\\\\\\ =\dfrac{-6}{-2}\\\\\\=3[/tex]
Slope = 3
At y-intercept x = 0.
From the graph, y-intercept = -4
Equation of the line: y = mx + b
y = 3x - 4
Can someone please help me asap ill give the most point to whoever answers first and CORRECTLY
Answers
Answer:
y+2 if this is correct can u mark me brainliest?
please help I don't know the median
Answers
Answer:8
Step-by-step explanation:
least to greatest:6,8,8,9,9
crossout the ends:6,9 and 8,9
what is left in the middle:8
Answer:
6
Step-by-step explanation:
Median is the middle of the data set which is 6.
You have several boxes with the same dimensions. They have a combined volume of 4x4-21x²-46x + 219x + 180. Determine whether the binomial below could represent the number of boxes you have.
x+3
A) Yes; x+3 divides evenly. you get 4x^3-33x^2+53x+60
B)No; x-3 does not divide evenly. You get 4x^3-33x^2+53x+60 with a remainder of 12.
C)No; x+3 divides evenly. you get 4x^3-33x^2+53x+60
Answers
Answer:
The following are the choices for this problem:A. x+4 B. x+3 C. x-5 D. 4x+3
Factoring 4x^4-21x^3-46x^2+219x+180, this will give us then the short answer of x+4.
The factor theorem states that if x-n is a factor of function f(x) = 4x^4-21^3-46^2+219x+180 then f(x) = 0.
So let us evaluate f(-4) which gives 4(256) - 21(-64) -46(16) +219(-4) + 180 = 936
Since the function f(-4) does not equate to zero, we could say that x+ 4 is not a factor.
So using x+3: f(-3) = 4(81) - 21(-27) -46(9) +219(-3) + 180 = 0, so x+3 is a factor.
Step-by-step explanation:
hope this helps if do mark brainllest
Find the image of Y(-7,4) after a dilation centered at the origin with a scale factor of -3
F= Y(-21,12)
G=Y(12,-21)
H=Y(21,-12)
J=Y(-12,21)
Answers
Answer:
H = Y (21, -12)
Step-by-step explanation:
Given
Y = (-7, 4)Dilation of -3Solving
Multiply the x-value and y-value of the coordinate by -3Y = (-7 x -3, 4 x -3)Y = (21, -12)The required image point is H=Y(21, -12)
What will happened with scale factor ?If the scale factor is given then by multiplying the scale factor with the co-ordinates gives us the image of the given point.
How to find the required image point ?Here the given point is Y(-7, 4)
After the dilation centered at origin, the scale factor is -3
∴ The x co-ordinate is (-7)×(-3)=21
& the y co-ordinate is 4×(-3)= -12
Hence the image is Y(21, -12)
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Carly has five times as many markers as camden together they have 30 markers how many markers does carly have how many markers does camden have
Answers
Answer:
carly=25 camden=5
Step-by-step explanation:
carly:camden= 5:1
5+1=6
30/6=5
carly= 5x5=25
camden=5x1=5
(1/2) (10)- (-12) -25
Answers
Answer:
-8
Step-by-step explanation:
Hey there!
(1/2)(10) - (-12) - 25
= 1/2(10) - (-12) - 25
= 5 - (-12) - 25
= 5 + 12 - 25
= 17 - 25
= -8
Therefore, your answer is: -8
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Rachel's aunt gave her $85 to spend on
school spirit items. Rachel bought 4 pens
for $0.85 each, a hoodie for $45.50, and
5 folders for $2.79 each. How much
money did she have left?
A $22.15
B $19.36
C $62.85
D $35.86
Answers
The amount Rachel has left of the amount given to her by her aunt after she makes the purchases is $22.15.
How much does Rachel have left?In order to determine the amount she would have left, determine the total value of the purchases and subtract it from the amount she was given.
Total value of the purchases = (4 x 0.85) + 45.50 + (5 x 2.79) = $62.85
Change = $85 - $62.85 = $22.15
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Solve the system of equations below. 4x+1=16 2x+30= - 2
Answers
Answer:
D. (5, 4)
Step-by-step explanation:
4x + y = 16 -----> y = 16 - 4x
2x + 3y = -2
Substitute to find x
2x + 3(16 - 4x) = -2
2x + 48 - 12x = -2
-10x = -50
x = 5
Substitute to find y
4(5) + y = 16
20 + y = 16
y = 4
Final solution: (5, 4)
Hope this helps!
Yo I need to bring up my grade bad so
-3x-9=-3y
(please show it graphed already :D)
Answers
Answer:
Step-by-step explanation:
The percentage of executives in a certain industry receiving cash signing bonuses is increasing. the percentage is given by the function b(t)= 4.891(1.331)^t. where r is the number of years since 1996. find the percentage of executives receiving signing bonuses in 2000 and in 2001.
Answers
The function b(t)= 4.891(1.331)^t is an exponential function
The percentage of executives in 2000 is 15.35The percentage of executives in 2001 is 20.43The percentage of executives in 2000The function is given as:
b(t)= 4.891(1.331)^t.
2000 is 4 years from 1996.
This means that t = 4
So, we have:
b(4)= 4.891(1.331)^4
Evaluate
b(4)= 15.35
So, the percentage of executives in 2000 is 15.35
The percentage of executives in 20012001 is 5 years from 1996.
This means that t = 5
So, we have:
b(5)= 4.891(1.331)^5
Evaluate
b(5)= 20.43
Hence, the percentage of executives in 2001 is 20.43
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heeeeeeeellllllllllllpppppppppppppp
Answers
Please help me with this math problem!! Will give brainliest!! :)
Answers
Answer:
See below
Step-by-step explanation:
From the graph :
y = -x -inf < x <=0
y = x 0<= x <= 2
y = 3 x > 2
3.873... express in p/q form
Answers
p/q formula
The theorem states that each rational solution x = p⁄q, written in lowest terms so that p and q are relatively prime, satisfies: p is an integer factor of the constant term a0, and.
Find a fraction that is bigger than ⅚, but smaller than 6/7. Show how you did it!!
Answers
16. The population density of football stadium is.57 people per square foot. If the area of the stadium is 1,750,000 ft?,
then about how many people are in the stadium?
Answers
Answer:
99750000 people
Step-by-step explanation:
1,750,000*57=99750000
The scatter plot below shows the average points scored per game by players of different ages in an adult basketball league.
Answers
The statement that describes the association between a player's age, and the average points is: C. There is a positive linear association and one outlier.
Linear association and outlierThe scatter plot shows a positive linear relationship because the points shown on the scatter plot closely look like a straight line.
We able to identify only one outlier based on the regression line because their is a distance between the point and the regression line.
Therefore there is a positive linear association and one outlier.
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timomthy began his math homework at 5:17 pm he finished at 5:49 how many minutes did he send on his math homework
Answers
Answer:
32 minutes
Step-by-step explanation:
49 - 17 = 32
Timothy spent 32 minutes on his math homework.
Answer: just count from 17 to 49 and then boom answer!!! that is if its still pm when he is done.
Q. what is the volume?
answer choices
A. 72
B. 27
C. 1.5
D. 272
Answers
Answer:
[tex]\boxed{\sf{B.\quad 27}}[/tex]Step-by-step explanation:
Use a volume formula.
Volume formula:
[tex]\Longrightarrow:\sf{V=L*W*H}[/tex]
Length: 3Width: 3Height: 3Multiply.
[tex]\sf{3*3*3=\boxed{\sf{27}}[/tex]
Therefore, the volume is 27, which is our answer.I hope this helps you! Let me know if my answer is wrong or not.
if you count the number of the cube on the sides, it’s a 3 by 3 by 3. if you multiply 3x3x3, you get 27
Through a regular hexagonal prism whose base edge is 8 cm and whose height is 12 cm, a hole in the shape of a right prism, with its end being a rhombus with diagonals 6 cm and 8 cm is drilled . Find: the total surface area of the remaining solid.
Answers
The total surface area of the remaining solid is 48(4+root3) centimeters square.
We have given that,
Through a regular hexagonal prism whose base edge is 8 cm
Whose height is 12 cm, a hole in the shape of a right prism
What is the formula for the total surface area?Total surface area=2(area of the base)+parameter of base×Height
Height=8cm
Parameter of base=12(2)=24
area of the base=6×root3/4×4^2
We use the given value in the formula
=2×6×root3/4×4^2+24×8
=48root3+192
=48(4+root3)cm^2
Therefore the total surface area of the remaining solid is 48(4+root3)cm^2.
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What is the largest whole number I could be if 9 + I is larger than 28?
Answers
Answer:
20 and greater than 20
If you add 9 and 20, you get 29, which is one greater than 28.__________________________________________________________
Questions?Ask me in the comments box.
As the number of trials increases, the __________ probability will approach the __________ probability.
Answers
Answer:
Empirical probability
And
Theoretical
hope this helps! :)
