Mathematics College

Help!!!
Rationalize the denominator of;
[tex]1) \frac{1}{ \sqrt{7} } [/tex]
[tex]2) \frac{2}{ \sqrt{3} - \sqrt{2} } [/tex]
[tex]3) \frac{ \sqrt{6} + \sqrt{3} }{9 + 2 \sqrt{18} } [/tex]
​

Answers

Answer 1

Answer:

see below for explanation:-

Step-by-step explanation:

#1

[tex] \displaystyle{ \frac{1}{ \sqrt{7} } }[/tex]

[tex]\displaystyle{ \frac{1}{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{7} }{7} }[/tex]

#2

[tex]\displaystyle{ \frac{2}{ \sqrt{3} - \sqrt{2} } }[/tex]

[tex]\displaystyle{ \frac{2}{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} + \sqrt{2} } }[/tex]

[tex]\displaystyle{ \frac{2( \sqrt{3} + \sqrt{2} }{( \sqrt{3} {)}^{2} - ( \sqrt{ 2 } {)}^{2} } }[/tex]

[tex]\displaystyle{ \frac{2( \sqrt{3} + \sqrt{2} ) }{3 - 2} }[/tex]

[tex]\displaystyle{2( \sqrt{3} + \sqrt{2} )}[/tex]

#3

[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{9 + 2 \sqrt{18} } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{ 9 + 2 \sqrt{9 \times 2} } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{9 + 6 \sqrt{2} } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{3(3 + 2 \sqrt{2}) } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} + \sqrt{3} }{3(3 + 2 \sqrt{2}) } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } }[/tex]

[tex]\displaystyle{ \frac{3 \sqrt{6} - 2 \sqrt{12} + 3 \sqrt{3} - 2 \sqrt{6} }{3( {3}^{2} - (2 \sqrt{2} {)}^{2} ) } }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} - 4 \sqrt{3} + 3 \sqrt{3} }{3(9 - 8)} }[/tex]

[tex]\displaystyle{ \frac{ \sqrt{6} - \sqrt{3} }{3} }[/tex]

Related Questions

No Calculator Let gbe a twice-differentiable function. The function g and its derivatives have the properties indicated in the table above. 0 0​

Answers

Hi there!

Part D:

We can use the Taylor Polynomial expansion for a second-degree polynomial:

[tex]P_3(x) = g(c) + \frac{g'(c)}{1!}(x - c) + \frac{g''(c)}{2!}(x - c)^2[/tex]
Where c is the value that the polynomial is centered about.

We are given that:
[tex]g(c) = 1\\\\g'(c) = 0\\\\g''(x) = 2[/tex]

Therefore:
[tex]P_3(x) = 1 + \frac{0}{1}(x - 2) + \frac{2}{2!}(x - 2)^2\\\\\boxed{P_3(x) = 1 + (x - 2)^2}[/tex]

Which of the following binomials is a factor of the trinomial below?
x^2-5x-24

Answers

Answer:

(x-8) and (x+3)

Step-by-step explanation:

To find the binomials of the trinomial, we just need to factor in the trinomial.

First,

x² -5x - 24

Then split it, so the terms add to -5 and multiply to -24

x² +3x -8x - 24

Then factor x in the first part, and -8 in the second part.

x(x+3) - 8(x+3)

Factor again

(x-8)(x+3)

Answer:

Step-by-step explanation:

Factorize 24. When we add the factors, we have to get (-5) and we multiply we have to get (-24).

So, the factors are  3 and (-8)

When we add  3 +(-8) = -5  ; we multiply we get (-8)*3 =(-24)

Replace the middle terms with the factors.

x² - 5x - 24 = x² - 8x  + 3x - 24

                  = x(x - 8) + 3(x - 8)

                 = (x - 8)(x+3)

i need help finding x and y​

Answers

Answer:

x is 5 and y is 6

Step-by-step explanation

we find 2/3 factors that equal 10. 2 and 3. the only other number that can be added that equals 10 is 5. i apply the same logic to y

Answer:

Y -- 6

X -- 5

Step-by-step explanation:

we first find y by finding the side that is the longest that is parallel to y (16) we also find that two sets of fives are also parallel to y and 16 as seen in the first screenshot. Then to find the missing value we will subtract the 5 two times from 16 to find y. 16 - 5  = 11 - 5 = 6.

we do the same thing to find x, (10 - 2 = 8) (8 - 3 = 5) X = 5

Please help plsssssss

Answers

Answer:

Box 1. 2x

Box 2. -13 (1/3) or (-40/3)

Box 3. 2x

Box 4. (2/3)x

Box 5. 3

Box 6. 3

Box 7. -20

Box order left to right.

Step-by-step explanation:

(5/3)x + (1/3)x = 13 (1/3) + (8/3)x

add numberator ( top number ); keep the denominator the same ( bottom number )

Line 1. (6/3)x or 2x = 13 (1/3) + (8/3)

------------------------------------------

Line 2. -13 (1/3) = (8/3)x - 2x

-------------------------------------------

Ex. 3 × (-13) = 39 - 1 = (-40/3)

--------------------------------------------

Line 3. (-40/3) = (2/3)x

---------------------------------------------

Line 4. (3) (-40/3) = (2/3)x (3)

----------------------------------------------

               -40 = 2x

               ÷2     ÷2

Line 5.    -20 = x

-------------------------------------------------

Sorry if this is a little confusing. I hope this helped!

Step-by-step explanation:

2

-13/1/3 ; 2

2/3

3 ; 3

-40

hope it help

A square 16 cm on a side. Use this scale: Side of a
square = 2 cm.

Answers

The area of the scale drawing given the scale of the square is 64cm^2.

What is the area of the scale drawing?

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

Dimensions of the scale drawing =  original dimensions / scale of the drawing

16 cm / 2 = 8cm

Area = 8 x 8 = 64cm^2

A square 16 cm on a side. Use this scale: Side of a square = 2 cm. Find the area of the scale drawing.

To learn more about scale drawings, please check: https://brainly.com/question/26388230

.

Jennifer is a wedding planner. She set up six chairs at each table for the reception. If t represents the number of tables, which of the following expressions represents the total number of chairs that she set up?
A. 6 + t
B. t + 6
C. 6t
D. t - 6

Answers

Answer: C. 6t

Step-by-step explanation:

T is unknown, but because you are only asked for the equation to figure out the total,  you simply multiply the 6 chairs per t, or table together, 6t

Celene invierte $5,000 en un banco al 5.15% de interés anual capitalizable cada trimestre. Utiliza el interés compuesto para determinar cuál es el rendimiento porcentual anual

Answers

El monto total acumulado, capital más interés, con interés compuesto sobre un capital de $5,000.00 a una tasa de 5.15% anual compuesto 4 veces por año durante 1 año es $5,262.52.

Interés compuesto

Datos dados

Principal = $ 5000Tasa = 5,15%Tiempo = 1 año

A = P + I donde

P (principal) = $5,000.00

I (interés) = $262.52

Pasos de cálculo:

Primero, convierta R como un porcentaje a r como un decimal

r = R/100

r = 5,15/100

r = 0.0515 tasa por año,

Luego resuelve la ecuación para A

A = P(1 + r/n)^nt

A = 5000,00(1 + 0,0515/4)^(4)(1)

A = 5,000.00(1 + 0.012875)^(4)

A = $5,262.52

Obtenga más información sobre el interés compuesto aquí:

https://brainly.com/question/24924853

if julie make 18 baskets how many baskets does kari make how many baskets do they make in all

Answers

Answer:

18x

Step-by-step explanation:

j=18

k=x

18xor18

I do not understand this question

hi i need help ill give brainlyest

Answers

Answer: 48.

Step-by-step explanation: The minimum value with box and whisker plots is at the very tip of the whisker at the left side.  48 is at the the tip of the left whisker.  Therefore, that's your answer.

Hope this helps! :)

Estimate by rounding each decimal to the nearest whole number. 5.85+23.24

Answers

Answer:

Step-by-step explanation:

Cody wanted to give each of his forty-five friends an equal amount of candy. At the store he bought six hundred eighty pieces total to give to them. How many more pieces should he have bought so he didn't have any extra pieces?​

Answers

Divide total bought by number of people first:


680 / 45 = 15.111


round up to 16. Multiply 16 by 45:

45 x 16 = 720

He should have bought 720 pieces. Now by Tracy to find how many more pieces:

720 - 680 = 40

He should have bought 40 more pieces.

Karen had 200 after spending y pesos on a notebook,she bought 4 colored pens with the rest of her money,what was the price of each pen if. Y=80

I need it know

Answers

Answer:

30 pesos

Step-by-step explanation:

Given

Had 200 pesos originallyspends 'y' pesos on a notebookBought 4 colored pens with the rest of the money

Solving

Let money of the pen = x, money of notebook = y4x + y = 2004x + 80 = 2004x = 120x = 30 pesos

Rewrite the equation by completing the square. X^2-14x+40=0

Answers

Answer:

(x – 7)² – 9

Step-by-step explanation:

I hope this helps

Four less than the product of seven and a
number is seventeen. What is the number?

Answers

hello!

=============================================

First of all, let the number be u.

The product of 7 and u means you should multiply 7 times u:

[tex]\pmb{7u}[/tex]

Now, subtract 4:

[tex]\pmb{7u-4}[/tex]

This expression equals 17:

[tex]\pmb{7u-4=17}[/tex]

[tex]\rule{200}{2}[/tex]

[Now, let's Find the Value of u]

First, add 4 to both sides:

[tex]\pmb{7u=21}[/tex]

Now, divide both sides by 7:

[tex]\pmb{u=3}[/tex]

=======================================================

notes:-

Hope everything is clear; if you need any clarification /explanation, kindly let me know, and I will comment and/or edit my answer :)

(This is a multiple choice question)Suppose you are rehearsing for a dance competition and you fall and hurt your shoulder. At the hospital, they take X-rays, consult a shoulder specialist, and give you a stabilizer brace. You pay a $50 co-pay at the time of service, and the ER bills your insurance company for the rest. The total hospital bill is $3,720. The table below shows the payment structure for your health insurance policy. If the injury happened in July, what is your total paid in monthly premiums?

A. 1,050$

B. 150$

C. 900$

Answers

C is the answer your welcome

which of the following are polynomials

Answers

Answer:

I think so Option D is the correct answer

Solve the system of equations:

4x-5y=21
3x+10y= -53

Answers

Step-by-step explanation:

2× (4x-5y) = 21

3x+10y= -53

-------------------------

8x-10y = 42

3x+10y=-53

------------------------

11x= -11

{x=-1}

-----------------

3x+10y=-53

x=-1

3(-1)+10y=-53

-3+10y=-53

10y= -50

{y=5}

Sketch a graph of − 3 x − y = − 4

Answers

Answer:

Step-by-step explanation:

A rectangular shaped garden has an area of 80 square feet. The length is 5 less than twice the width. What are the dimensions of the garden?

Answers

Answer:

Width=28 1/3 Length=51 2/3

Step-by-step explanation:

1. Create an equation

x+(2x-5)=80

2. Solve

x+(2x-5)=80

3x-5=80

3x-5+5=80+5

3x/3=85/3

x=28 1/3

So, if x=28 1/3

85/3x2=170/3

56 2/3-5

So, Length=51 2/3

help me please and thank you

Answers

Answer:

m∠N = 85°

Step-by-step explanation:

Properties of a parallelogram

opposite sides are parallel and equal in lengthopposite angles are equalinterior angles that lie on the same side of the transversal are supplementary - their sum is 180°

Therefore,

m∠M + m∠N = 180°

⇒ 95° + m∠N = 180°

⇒ m∠N = 180° - 95°

⇒ m∠N = 85°

--------------------------------------------------------------------------------------

Additional calculations

m∠M = m∠P = 95°

m∠N = m∠L = 85°

MN = LP

ML = NP


Divide and simplify.

- 8/15 divided by - 3/5

A) - 3/25

B) - 4/5

C) 13/15

D) 8/9


Answers

Answer:

8/9

Step-by-step explanation:

What value in place of the question mark makes the polynomial below a perfect square trinomial?

x^2 + 24x + ?

A. 24

B. 48

C. 144

D. 12

Answers

Answer:

144

Step-by-step explanation:

[tex]x^2+24x +144\\\\=x^2 + 2\cdot 12x +12^2\\\\=(x+12)^2[/tex]

A store pays $25 for an encyclopedia. The store marks up the price by 40%. What is the amount of the mark-up?​

Answers

10%

40 divided by 100 = 0.4
25 • 0.4 = 10

NO LINKS!!

You want to make a banner that says HAPPY BIRTHDAY. You want the letters to be 3 inches high. You make a sketch of the banner with letters that are 2 inches high. The length of the phrase in your sketch is 20 inches long. What length of paper should you buy to make the banner? ​

Answers

Answer:

  30 inches

Step-by-step explanation:

Assuming the banner you want is similar to the sketch you made, the length of the banner is 10 times the letter height.

For 3-inch letters, the banner length will be 30 inches.

Answer:

30 ft

Step-by-step explanation:

**According to the image of the banner, the banner should be 3 foot high (not 3 inches)**

Create a ratio of letter height to length of phrase for the sketch and the banner.  Let x be the length of the banner.

NB There is no need to convert the measurements between inches and feet, since the letter height and length of phrase is measured in the same way for each banner.

Ratio:                      letter height : length of phrase

Sketch (in inches):                   2 : 20

Banner (in feet):                       3 : x

Equate the ratios and solve for x:

[tex]\sf \implies 2 : 20 = 3 : x[/tex]

[tex]\sf \implies \dfrac{2}{20}=\dfrac{3}{x}[/tex]

[tex]\sf \implies 2x=3 \cdot 20[/tex]

[tex]\sf \implies 2x=60[/tex]

[tex]\sf \implies x=\dfrac{60}{2}[/tex]

[tex]\sf \implies x=30[/tex]

Therefore the length of paper your should buy to make the banner is 30ft.

A model of Earth is located 7600 meters from the Globe Arena in Sweden’s solar system model. The volume of the model is approximately 3052.08 cubic centimeters. What is the length of the radius of the Earth model?

Answers

Answer:

The length of the radius of the mudel is 9 cm

Step-by-step explanation:

[tex]By\ the\ topic[/tex]

[tex]The\ volume\ of\ the\ mudel\primes\ is\ 3052.08{\rm cm}^3[/tex]

[tex]Formula\ for\ the\ volume\ of\ the\ sphere\ is[/tex]

[tex]\frac{4}{3}\pi\ r^3[/tex]

[tex]\frac{4}{3}\pi\ r^3=3052.08[/tex]

[tex]\pi\ r^3=\frac{3}{4}\times3052.08=2289.06[/tex]

[tex]\gamma3=2289.06\div\pi[/tex]

[tex]\gamma=\sqrt{\frac{2289.06}{\pi}}\approx\sqrt{\frac{2289.06}{3.14}}+\sqrt{729}[/tex]

[tex]r=9cm[/tex]

[tex]7hus,\ the\ length\ of\ the\ vadius\ of\ eanth[/tex]

[tex]mudel\ is\ 9\ cm[/tex]

[tex]Application\ of\ the\ volume\ of\ the\ spheve?[/tex]

I hope this helps you

:)

express the confidence interval 0.255 plus or minus 0.045
​

Answers

Answer:

0.255+45=0.300

or

0.255 - 0.045 = 0.210

the length of a rectagle is twice its width. if the perimeter of the rectangle is 36in, find its length and width

Answers

Answer:

6*2=12

if length is 12 half it would be 36

Answer:

width = 6in

length = 12in

Step-by-step explanation:

If we call the width x, the length has to be 2x and so...

x + 2x + x + 2x = 36 (this can be simplified to ↓)

6x = 36 (if you divide both sides by 6...)

x = 6

This means that the width of the rectangle is 6in and so the length is 12in.

Hope this helps!

Can somebody please help me thank you

Answers

Answer: <

Step-by-step explanation:

53688 < 53689

< means less than
Hence it is read as 53688 is less than 53689

Guys please help! i will mark brainliest to the right answers

Note: in order for me to mark a brainliest 2 people need to answer

Answers

Answer:

(A) :

[tex]y = - \frac{5}{2} x + 40[/tex]

(B) : it is a decreasing linear graph. this means that the amount Shikita owes is lesser by $2.50 amount each week

Step-by-step explanation:

shown in the attatchment

solve pls don't spam for marks​

Answers

1. Commutative property of addition

2. Commutative property of multiplication

the product will stay the same

Answer:

the first answer is commutative property of addition and the second answer is commutative property of multiplication

Step-by-step explanation:

hope this helps

have an awesome day -TJ

if you need anymore help just let me know

pls mark brainliest :)

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