Left parenthesis 5 plus 2 square root of 6 right parenthesis squared = a plus b square root of 6 then the value of a and b are

Answers

Answer 1

Answer:

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.

Step-by-step explanation:

The statement is equivalent to the following mathematic expression:

[tex]\left(5 + 2\sqrt{2})^{2} = a + b\cdot \sqrt{6}[/tex] (1)

By definition of the perfect square trinomial:

[tex]25 + 20\cdot \sqrt{2} + 8 = a + b\cdot \sqrt{6}[/tex]

[tex]33 + 20\sqrt{2} = a + b\cdot \sqrt{6}[/tex]

And by direct comparison we have the following system:

[tex]a = 33[/tex] (2)

[tex]b\cdot \sqrt{6} = 20\sqrt{2}[/tex] (3)

By (3), we solve for [tex]b[/tex]:

[tex]b = \frac{20}{\sqrt{3}}[/tex]

[tex]b = \frac{20\sqrt{3}}{3}[/tex]

The values of [tex]a[/tex] and [tex]b[/tex] are [tex]33[/tex] and [tex]\frac{20\sqrt{3}}{3}[/tex], respectively.


Related Questions

I need to show my work but I don’t know how to do these can someone help me??

Answers

Use cymath.com it shows the steps to copy

Find the volume of the cone.
Either enter an exact answer in terms of π or use 3.14 for π and round your final answer to the nearest hundredth.

Answers

Answer:37.68

Step-by-step explanation:

Do yk the anwser to my question?

Solve for x in the triangle round your answer to the nearest tenth
PLZ HELP ASAP I WILL MARK BRAINLIEST

Answers

Answer:

Step-by-step explanation:

Answer:

x = 9.32

Step-by-step explanation:

For a right angles triangles , we can use trigonometry equations :-

In this case , we need to use sine equation in perpendicular :

sin θ = opposite side / hypotenuse

sin 58° = x / 11

x = sin 58 ° × 11

x = 0.84 × 11

x = 9.32852906

Round nearest tenth = 9.32

How do the perimeters of the triangles compare? Original: height-18, slant-30, length-24 Scaled: height-6, slant-10, length-8 A) the scaled triangles perimeter is 3x's larger than the original triangles perimeter. B) the scaled triangles perimeter is 6x's smaller than the original triangles perimeter C) the scaled triangles perimeter is 1/9 the size of the original triangles perimeter D) the scaled triangles perimeter is 1/3 the size of the original triangles perimeter

Answers

Answer:

D) the scaled triangles perimeter is 1/3 the size of the original triangles perimeter

Step-by-step explanation:

Given

Original:

[tex]Height = 18, Slant = 30, Length =24[/tex]

Scaled:

[tex]Height =6, Slant=10, Length=8[/tex]

Looking at the dimension of both triangles, The relationship between the original and the scaled copy is:

[tex]Scaled = \frac{1}{3} * Original[/tex]

Hence, the perimeter is:

[tex]Perimeter (Scaled) = \frac{1}{3} * Perimeter (Original)[/tex]

Jeremy’s car travels 26 miles per gallon of gas (g). If the distance traveled (d) can be given by a function, what is the input of this function?

Answers

You can put this solution on YOUR website!
Jeremy’s car travels 26 miles per gallon of gas (g). If the distance traveled (d) can be given by a function, what is the input of this function?
---------

x/6 + 12 = 6
Please help me

Answers

Answer:

[tex]x=-36[/tex]

Step-by-step explanation:

[tex]\frac{x}{6} +12=6[/tex]

[tex]\frac{-36}{6} +12=6[/tex]

[tex]-6+12=6[/tex]

Hence, x = -36

Answer:

X = -36

Step-by-step explanation:

x/6 + 12 = 6

-12         = -12

x/6 = -6

(6) = (6)

 x = -36

A parabola is defined by the equation x2 = 3/4 y. In which direction will the parabola open?

Answers

I’m pretty sure it’s positive so a upward one that looks like :u

Find the distance from point P to RQ

Answers

Answer:

option A : about 2.8 units

Step-by-step explanation:

To find the distance from P to RQ , Find the distance from ( 1 , 1) to (3 , 3).

 [tex]Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

                 [tex]= \sqrt{(3-1)^2 + (3-1)^2}\\\\= \sqrt{2^2 + 2^2 }\\\\= \sqrt{4 + 4 }\\\\= \sqrt{8}\\\\=2\sqrt{2}[/tex]

                 = 2.83 units

Answer:

A

Step-by-step explanation:

Remark

The distance you want is the point P to the (3,3). Then two lines meet as these two do, the shortest distance is the right angle distance. And that is how distance is defined.

Formula

d = sqrt( (x2 - x1)^2 + (y2 - y1)^2  )

Givens

x2 = 1

x1 = 3

y2 = 1

y1 = 3

Solution

d = sqrt( (1 - 3)^2 + (1  - 3)^2 )

d = sqrt( (-2)^2 + (-2)^2 )

d = sqrt ( 4 + 4)

d = sqrt(8)

d = 2√2

d = 2.8

The length of the triangle for the pool table is the twice the sum of 5 and a number. If the rack is equilateral, what is the perimeter, in inches, of the triangle?​

Answers

Answer:  

30 + 6x inches

Step-by-step explanation:  

Let the required number be x

If the length of the triangle for the pool table is twice the sum of 5 and a number

L = 2(5+x)

L = 10+2x

Since the triangle is quadrilateral, this means that all sides are equal

Perimeter = 3L

Perimeter = 3(10+2x)

Perimeter = 30+6x

Hence the perimeter, in inches, of the triangle is 30 + 6x inches

The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of service means an increase of $0.50 per hour. So, employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour. Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00. Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour. And, employees of at least nine years, but less than twelve years receive an increase of $2.00. Write a function to represent this scenario. Which graph represents this wage increase for x < 12? ​

Answers

你有國際觀年內開通農委會可歌可泣欸哭哭哭哭我是很懊惱與農會選舉口號欸人民卻是誰肯欸哭鬧我口口聲聲可輕鬆過關你有國際觀年內開通農委會可歌可泣欸哭哭哭哭我是很懊惱與農會選舉口號欸人民卻是誰肯欸哭鬧我口口聲聲可輕鬆過關你有國際觀年內開通農委會可歌可泣欸哭哭哭哭我是很懊惱與農會選舉口號欸人民卻是誰肯欸哭鬧我口口聲聲可輕鬆過關你有國際觀年內開通農委會可歌可泣欸哭哭哭哭我是很懊惱與農會選舉口號欸人民卻是誰肯欸哭鬧我口口聲聲可輕鬆過關 $$

The solution is Option C.

The graph which represents the inequality equation is

f ( x ) = { 0.50 , if x < 3

             1       , if 3 ≤ x < 6

             1.50  , if 6 ≤ x < 9

             2.00 , if 9 ≤ x < 12 }

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the number of years be = x

Let the increment in wages be = y

Now , the equation will be

For the employees that have been with the company for less than three years can expect to receive an increase of $0.50 per hour

So , the inequality equation is x < 3 , f ( x ) = 0.50

Employees that have been with the company for at least three years, but less than six years can expect an increase of $1.00

So , the inequality equation is 3 ≤ x < 6 , f ( x ) = 1

Employees that have been with the company for at six years, but less than nine years, receive an increase of $1.50 per hour

So , the inequality equation is 6 ≤ x < 9 , f ( x ) = 1.50

Employees of at least nine years, but less than twelve years receive an increase of $2.00

So , the inequality equation is 9 ≤ x < 12 , f ( x ) = 2

Therefore , the graph which represents the solution is Option C.

Hence , the inequality equation is 9 ≤ x < 12 , f ( x ) = 2

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ2

There were 60 7th grade students last year in CHAMPS. This year, there are 48 7th grade students. What is the percent decrease from last year to this year?

Answers

20%

Hope this helps! :)

______________

Brainliest goes to whoever answers correctly I have other questions if you want more points

Answers

Answer:

C

Step-by-step explanation:

Find the graph that shows temperatures decreasing. Two of the graphs show that it's decreasing; C and D. When something is in a constant rate, it is going to be a straight line (doesn't mean it can't be slanted!). Therefore it is C.

Jack had 3bags of golf balls with b balls in each bag; then his friend gave him 6 more golf balls. How many golf balls does Jack have now?

Answers

Answer:

3(b+2)balls

Step-by-step explanation:

Given data

number of bags of golf balls= 3

number of balls in each bag=b

total number of balls in all three bags= 3b

His friend gave him 6 more= 3b+6

Hence the total balls is = 3b+6

= 3(b+2)balls

Use the following list of balances for Paul's Guitar Shop to answer the following question. Guitar Sales 24,800, Depreciation expense 2,000, Wage expense 10,950, Rent 500, Music Lesson Revenue 3,000, Interest expense 500, Supplies expense 500, Utilities expense 400. What is the TOTAL value of EXPENSES? *

Answers

Answer:

The Total Value of Expenses is $14,350

Step-by-step explanation:

AMOUNT

Depreciation Expense $ 2,000

Wage Expense $ 10,950

Interest Expense $ 500

Supplies Expense $ 500

Utility Expense $ 400

TOTAL $ 14,350

the graphs of f(x) =-2x and g(x)=(1/2)^z are shown

Answers

Answer:

f(x)-3x+5 and g(x)=4+5 is it true ?Step-by-step explanation:

what is a kite? what are its properties? what is its use in our daily life?

Answers

Answer:

Well, in geometry, the properties would be that the angles produced by the intersection of the diagonals are right angles. A kite is basically entertainment, made by cloth and string

A kite is a four sided shape. Like an elongated rectangle.a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. In contrast, a parallelogram also has two pairs of equal-length sides, but they are opposite to each other instead of being adjacent. Kite quadrilaterals are named for the wind-blown, flying kites, which often have this shape and which are in turn named for a bird. Kites are also known as deltoids, but the word "deltoid" may also refer to a deltoid curve, an unrelated geometric object.Kites have been used for human flight, military applications, science and meteorology, photography, lifting radio antennas, generating power, aerodynamics experiments, and much more.

URGENT: Graph y = cosx for -3\pi/2 <= x <= -pi/2

What is the largest value in the range?


A. -1

B. 0

C. 1/2

D. 1

Answers

I’m pretty sure it’s d

Please help me with this geometry question

Answers

Answer:

2) 40

Step-by-step explanation:

the perimeter of Rhombus =

4 × (√(12/2)²+(16/2)² )

= 4× (√6²+8²)

= 4× (√100)

= 4×10

= 40

Q) 4 × (√(12/2)²+(16/2)² )

→ 4 × (√6²+8²)

→ 4 × (√100)

→ 4 × 10

→ 40 is the perimeter of rhombus.

What is the solution to the inequality 5.25 - b 2 6.52
+
+→
5
-5 -4 -3 -2 -1 0
1
2
3
4
OH ++
-5 -4 -3 -2 -1 0 1 2
+
3
+
4
5
OA
-5 -4 -3 -2 -1 0 1
2
3 4 5
-5 -4 -3 -2 -1 0 1 2 3 3 4 4 5

Answers

Answer:

1st option

Step-by-step explanation:

Solving the inequality

5.25 - b ≥ 6.5 ( subtract 5.25 from both sides )

- b ≥ 1.25

Divide both sides by - 1, reversing the symbol as a result of dividing by a negative quantity.

b ≤ - 1.25

Since less than or equal to the number line will have a solid circle at - 1.25 and the arrow pointing left.

The solution is represented on the first diagram

Find the sale price of an $18 item after a 50% discount.

Answers

Rewrite 50% as a decimal : 0.50

Multiply the price by 0.50:

18 x 0.50 = 9

The sale price is $9

Answer:

$9

Step-by-step explanation:

price of an item=$18

discount=50%

sale price =? (be x)

sale price= original price -discount% of original price

x=$18 -50/100 * $18

x=$1800-$900/100

=$900/100

=$9

therefore sale price of an item is $9.

*Brainliest* What is the value of X?

or how do I solve this equation?

Answers

Answer:

x = 6

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360

69+111+12x-3 +111 = 360

Combine like terms

12x+288=360

Subtract 288 from each side

12x+288-288 = 360-288

12x = 72

Divide by 12

12x/12 = 72/12

x = 6

Answer:

x = 6

Step-by-step explanation:

All angles together equal 360

Us this to set up your formula

360 = 111 + 111 + 69 + 12x-3

360 = 288 + 12 x

360 - 288 = 12x

72 = 12x

72/12 = x

6 = x

You could also use the fact that angle t and r are equal to set your formula up as

69 = 12x-3

69+3=12x

72=12x

72/12=x

6=x

Consider the graph of the function f(x)=2x.
Which statement describes a key feature of
function g if g(x) = 2f(x)? Answers:
A. y-intercept at (0,2)
B. y-intercept at (2,0)
C. horizontal asymptote of y = -2
D. horizontal asymptote of y = 2

Answers

Given:

The parent function is:

[tex]f(x)=2^x[/tex]

The other function is:

[tex]g(x)=2f(x)[/tex]

To find:

The statement that describes a key feature of function g.

Solution:

We have,

[tex]f(x)=2^x[/tex]

[tex]g(x)=2f(x)[/tex]

Using these two functions, we get

[tex]g(x)=2(2)^x[/tex]

Putting [tex]x=0[/tex], we get

[tex]g(x)=2(2)^{(0)}[/tex]

[tex]g(x)=2(1)[/tex]

[tex]g(x)=2[/tex]

The y-intercept of the function g at (0,2). So, option A is correct and option B is incorrect.

We know that [tex]g(x)\to 0[/tex] as [tex]x\to -\infty[/tex] and it will never intersect the line [tex]y=0[/tex]. It means the horizontal asymptote of the function g is

Therefore, the correct option is A.

Answer:

A

Step-by-step explanation:

Write the equation of the line in slope-intercept form

Answers

Answer:

y = 4/1 + 0

Step-by-step explanation:

we rise 4 units up and move 1 unit to the right

and the y intercept is 0 because its exactly in the center of x and y axis

Find k if (x+1) 2x^3+kx^2+1

Answers

Question:

Find k if (x+1) is a factor of 2x³ + kx² + 1

Answer:

k = 1

Step-by-step explanation:

The factor of a polynomial F(x) is another polynomial that divides evenly into F(x). For example, x + 3 is a factor of the polynomial x² - 9.

This is because;

i. x² - 9 can be written as (x - 3)(x + 3) which shows that both (x - 3) and (x + 3) are factors.

ii. If x = -3 is substituted into the polynomial x² - 9, the result gives zero. i.e

=> (-3)² - 9

=> (9) - 9 = 0

Therefore, if (x + a) is a factor of a polynomial, substituting x = -a into the polynomial should result to zero. This also means that, if x - a is a factor of a polynomial, substituting x = a into the polynomial should give zero.

From the question

Given polynomial: 2x³ + kx² + 1

Given factor: x + 1.

Since x + 1 is a factor of the polynomial, substituting x = -1 into the polynomial should give zero and from there we can calculate the value of k. i.e

2(-1)³ + k(-1)² + 1 = 0

2(-1) + k(1) + 1 = 0

-2 + k + 1 = 0

k - 1 = 0

k = 1

Therefore the value of k is 1.

Lin buys a candle that is 9 inches tall and burns down x inches per minute. She wants to let the candle burn for 7 minutes until it is less than 6 inches tall. 9 − 7x < 6 Solve the inequality that represents the story. If the variable is on the left, what is the sign?

Answers

Answer:

+ or > depending on what you mean exactly

Step-by-step explanation:

-7x<6-9

-7x<-3

x>3 (remember to flip the sigh)

the sign is the > symbol , or positive, not sure what you mean really

What is the definition of exponential growth?

Any help out there

Answers

Answer:

Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.

Answer:

The answer is probably B. If not it might be C.

Step-by-step explanation:

Exponential growth is growth that becomes more and more rapid. I hope this helps :).

74 + -28 =[find the difference and put the sign of big number]

Answers

Answer:

It should be 74+(-28) as 2 signs can bit be put together.

74+(-28)

=74-28 (sign only changes when there is (minus) before it

=48

We are not putting a minius (-) as 74 is digger that 28 and it has plus (+) before it.

I HOPE IT HELPS

HAVE A GREAT DAY

[tex]#Liliflim✌[/tex]

Solve this plz for god sake ​

Answers

Answer:

AB = 8.66 m

Step-by-step explanation:

Here, we want to get the length AB

What we have is a right triangle

so to get the length AB, we are going to use the appropriate trigonometric ratio

From the question, AB faces the given angle and that makes it the opposite

AC faces the right angle and that makes it the hypotenuse

The relationship between the hypotenuse and the opposite can be defined by the sine

the sine of an angle is the ratio of the length of the opposite to the hypotenuse

so, we have it that;

sine 60 = AB/10

AB = 10 * sine 60

AB = 8.66 m

Drag the numbers to label the points plotted on the number line.

Answers

Answer:

First Box: -10/5

Second Box = -1.25

Third Box = -0.5

Fourth Box = 0.75

Fifth Box = 3/2

Step-by-step explanation:

NOTE: I AM SAYING THIS FROM LEFT TO RIGHT

Answer:

The first box should be -[tex]\frac{10}{5}[/tex] ;

The 2nd box should be -1.25 ;

The 3d box should be -0.5 ;

The 4th box should be 0.75 ;

The 5th box should be 3/2 which is the last box left.

The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the y-variable, and what is the solution for this system?

Answers

The question is incomplete, the complete question is:

The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the y-variable, and what is the solution for this system?

x + 3y = 42

2x − y = 14

A: Multiply the second equation by -3. The solution is x = 12, y = 9.

B: Multiply the second equation by -2. The solution is x = 12, y = 10.

C: Multiply the second equation by 2. The solution is x = 15, y = 9

D: Multiply the second equation by 3. The solution is x = 12, y = 10

Answer: The correct option is D.

Step-by-step explanation:

The elimination method is a technique wherein we eliminate the coefficient of any one variable.

The given equations are:

x + 3y = 42

2x − y = 14

We multiply the second equation by (3) and the equations formed are:

x + 3y = 42

6x − 3y = 42

The final equation after eliminating the y-term becomes:

7x = 84

x = 12

Putting value of 'x' in any of the original equation, we get:

⇒ 12 + 3y = 42

⇒ 3y = 30

⇒ y = 10

Hence, the correct option is D.

Other Questions
since fighting alqueda have president bush and obama exceeded their war powers authority since aumf 2001? A manufacturer claims that the mean lifetime,u , of its light bulbs is 51 months. The standard deviation of these lifetimes is 7 months. Sixty bulbs are selected at random, and their mean lifetime is found to be 53 months. Can we conclude, at the 0.1 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 51 months?Perform a two-tailed test. Then fill in the table below.Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)the null hypothesis:The alternative hypotehsis:The type of test statistic (choose Z, t, Chi-square, or F)The value of the test statistic (round to at least three decimal places:Can we conclude that the mean lifetime of the bulbs made by this manufacture differ from 51 months? Which womens suffrage leaders led the Seneca Falls Convention?A.Susan B. Anthony and Carrie Chapman CattB.Alice Paul and Lucy BurnsC.Elizabeth Cady Stanton and Lucretia MottD.Woodrow Wilson and Susan B. Anthony What is the significance of the Battle of Yorktown?A. The British won the warB. It led to the start of peace negotiationsC. It completely ended fighting in North AmericaD. It caused France to join the war As were well aware, vending machines are used to sell snacks and beverages, whereas newspapers are sold out of a box that allows anyone to take more than one paper. How does the concept of diminishing marginal utility explain the different distribution techniques for newspapers vs. snacks and beverages? Identify two additional examples of an item whose diminishing marginal utility is high. Remember: Marginal utility is the change in total utility that results from a one-unit increase in the quantity of a good consumed; diminishing marginal utility is the general tendency for marginal utility to decrease as the quantity of a good consumed increases. The viscid silk produced by the European garden spider (Araneus diadematus) has a resilience of 0.35. If 10.0 J of work are done on the silk to stretch it out, how many Joules of work are released as thermal energy as it relaxes? Read this excerpt from a letter to the city council:Dear city council members:The city has proposed limiting library hours in order tosave money. I understand that the city budget is beingchallenged at the moment, but no good will come ofdenying children access to the library after school.Children go to the library to learn and to get help with theirhomework. As a single parent, I rely on the library as anaffordable place where I know my kids will be safe. Of allthe programs to cut, the library should not be your firstchoice.Which statement best describes the authors point of view?A. The city should encourage better childcare optionsB. The city should find another way to save moneyC. The city should stop ignoring voters' opinions about librariesD. The city should expand library hours. How have you incorporated your artistic preferences into your final piece? what does this question mean Please help (add work/reasoning if you can) Using the formation of formaldehyde as a model, comment on photosynthesis and the formation of sugars using what we know about entropy and free energy. A bicycle has a listed price of 593.98 before tax. If the sales tax rate is 9.5%, find the total cost of the bicycle with sales tax included. Round your answer to the nearest cent, as necessary. Which is an emotional benefit experienced by people who practice abstinence PLEASE HELP ME WITH THIS ONE QUESTION The half-life of Barium-139 is 4.96 x 10^3 seconds. A sample contains 3.21 x 10^17 nuclei. What is the decay constant for this decay?A) 1.67 x 10^-4 s^-1B) 5.43 x 10^-4 s^-1C) 1.40 x 10^-4 s^-1D) 2.22 x 10^-4 s^-1 Identifying a Proportional Relationship in a TableWhich takle represents a proportional relationship?xy4*.09y852127182026122860841820 What is the value of y?O A. 36O B. 72C. 54O D. 1080 C. Lee los siguientes comentarios que la Srta. Palma les hace a sus estudiantes durantela clase de ecologa. Subraya la palabra entre parntesis ms apropiada para completarcada oracin.1. Todos debemos (proteger / resolver / eliminar) el medio ambiente. La (paz / Luna /Tierra) es nuestra casa.2. Una manera de proteger la naturaleza es luchar contra la (destruccin / contaminacin /fuente) del aire. Para eso es importante (mejorar / reducir / eliminar) el nmero decoches que (se juntan / luchan / funcionan) con gasolina y producir ms coches queusen electricidad,3. Es cierto que la luz (contaminada / solar / pura) es una (fuente / manera / planta) de(medio ambiente naturaleza/ energa).4. Adems, debemos conservar nuestros fuentes / bosques / maneras). Las (plantascontaminaciones / maneras) y los rboles son una parte importante de la energa /naturaleza destruccin).5. En la escuela vamos a instalar un sistema de (contaminacin / aire acondicionadoextincin) nuevo Es bueno porque ser ms (grave / contaminado / econmico) que elque tenemos ahora, WILL GIVE BRAINLIST TO CORRECT ANSWER Two of the three points of the cell theory are listed below. All new cells come from preexisting ones. Cells are the basic units of life.Which of the following is the third point of the cell theory?O A. All living cells are surrounded by a rigid cell wall.O B. All living things have many cells.O C. All living cells have a nucleus.D. All living things are made of at least one cell. plzz help me with the correct ans find x nd interest for a loanTo pay for an $18,900 truck, Joe made a down payment of $3600 and took out a loan for the rest. On the loan, he paid monthly payments of $338.67 for 4years. What does "increase local sustainability" mean?