How would the fraction [tex]\frac{7}{1-\sqrt{5} }[/tex] be rewritten if its denominator is rationalized using difference of squares?

Answers

Answer 1

Answer:

[tex] \frac{7 + 7 \sqrt{5} }{ - 4} [/tex]

Step-by-step explanation:

We would multiply the fraction by its conjugate

( A conjugate is a expression that has the same integer or number values but have different signs) for example

[tex]5x + 2[/tex]

and

[tex]5x - 2[/tex]

ARE Conjugates.

The conjugate of

[tex]1 - \sqrt{5} [/tex]

is

[tex]1 + \sqrt{5} [/tex]

So this means we will multiply the expression by 1 plus sqr root of 5 on the numerator and denominator.

Our new numerator will be

[tex]7 \times (1 + \sqrt{5} ) = 7 + 7 \sqrt{5} [/tex]

We can apply the difference of squares for the denominator.

[tex](x + y)(x - y) = x {}^{2} - {y}^{2} [/tex]

So our denominator will be

[tex]1 - 5 = - 4[/tex]

So our rationalized fraction will be

[tex] \frac{7 + 7 \sqrt{5} }{ - 4} [/tex]


Related Questions

what is 3/2 divided by 1/8

helppp​

Answers

Answer: 12

Step-by-step explanation:

The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.

Can any one you help me with this ?

Answers

NUE is 30° LUN is 60° EUS is 30° LUE is 90° LUS is 120°

Step-by-step explanation:

NUE is given

LUN was from the 90° angle LUE but just minus 30°

EUS is honestly a guess :/

LUE is obviously 90° as we used it earlier

LUS was the 90° plus the EUS

Which are the roots of the quadratic function f(q) = 92 – 125?

Answers

Answer:

There are no solution/no roots for f(q) = 92 - 125

The correct and best answer will be marked as brainiest

Answers

Answer:

x=10

m=3

Step-by-step explanation:

The angles are the same since the sides are the same length (isosceles triangle)

55 = 5x+5

Subtract 5

55-5 =5x+5-5

50 = 5x

Divide by 5

50/5 = 5x/5

10=x

The altitude is a perpendicular bisector so

5m-3 = 2m+6

Subtract 2m from each side

5m-3-2m = 2m+6-2m

3m-3 = 6

Add 3 to each side

3m-3 +3 =6+3

3m =9

Divide by 3

3m/3 = 9/3

m =3

Công ty T vừa đưa vào sản xuất một loại sản phẩm mới với định mức giờ máy là 2 giờ/sản phẩm. Tài liệu về sản phẩm trong năm như sau (đồng):


Chi phí nguyên vật liệu trực tiếp/sp

30.000

Chi phí nhân công trực tiếp/sp

27.000

Chi phí sản xuất chung/sp

12.000(25% là biến phí)

Bao bì/sp (ở khâu SX)

5.000

Lương quản lý và bán hàng

83.300.000

Quảng cáo

34.700.000

Chí phí khác bằng tiền

30.000.000

Vốn đầu tư bình quân

1.200 triệu

ROI mong muốn

16%

Tổng số giờ máy hoạt động cho sản xuất

40.000 giờ


Yêu cầu:

1. Hãy định giá bán theo biến phí?

2. Để sản xuất sp mới này, Cty tự chế tạo 1 chi tiết để lắp vào sản phẩm với thông tin như sau:

- Biến phí sản xuất của Chi Tiết = 40% biến phí sp

- KH TSCĐ cho việc sản xuất chi tiết là 42.000.000đ

- Chi phí quản lý chung phân bổ cho việc sản xuất chi tiết là 19.040.000đ.

Có một doanh nghiệp khác đến chào hàng chi tiết với giá chỉ bằng 70% so với giá thành cty tự sản xuất và đảm bảo đủ số lượng, chất lượng theo yêu cầu. Các phương tiện sản xuất chi tiết có thể cho thuê 13.000.000đ/năm. Cty nên tự sản xuất hay mua ngoài?

Answers

Answer:

??????

Step-by-step explanation:


x °
68°
26 °
Find the measure of x (Hint: The sum of the measures
of the angles in a triangle is 180°

Answers:

6 °
86 °
90 °
180 °

Answers

Answer:

86°

Step-by-step explanation:

180° is the sum of all angles in a triangle

The two angles given are 68° and 26°

The equation is : 180° - 68° - 26° = x°

180° - 68° - 26° = 86°

x° = 86°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

x(x-y) - y( x- y) simplify ​

Answers

Step-by-step explanation:

x²-xy-xy+y²

x²+2xy+y²

hope it helps

write seven million six hundred twenty thousand six hundred fifty in standard form?​

Answers

Answer:

7,620,650

Step-by-step explanation:

___________

Answer:

7,620,650

Step-by-step explanation:

To write in standard form, you just write the entire number out.

expand and simplify (x-2)(x+5)(2x-1)​

Answers

Answer:

simplified: 2x^3+5x^2-23x+10

Step-by-step explanation:

Please help with problem

Answers

9514 1404 393

Answer:

∠CAE ≈ 16.7°DF ≈ 5.3

Step-by-step explanation:

a) Angle CAE can be found using the tangent relation.

  tan(∠CAE) = CE/AE

  tan(∠CAE) = 6/20

  ∠CAE = arctan(6/20) ≈ 16.7°

__

b. The length of DF can be found using the law of cosines.

  DF² = FA² +DA² -2·FA·DA·cos(A)

  DF² = 14² +10² -2·14·10·cos(16.7°) ≈ 27.8086

  DF ≈ √27.8086

  DF = 5.3

Entering 38.00 into the Price of Sneakers field Entering 6.00 into the Price field Entering 3.00 into the Price of Leather field True or False: You will no

Answers

Answer:

This question seems incorrect.

Kindly take a look again and re-state it properly to enable me give the most accurate answer.

Thank you

Find x. Simplify completely.
X
9
25
x = [?]

Answers

9514 1404 393

Answer:

  x = 15

Step-by-step explanation:

In this geometry, x is the geometric mean of the segment lengths of the hypotenuse.

  x = √(9×25)

  x = 15

Sara is working on a Geometry problem in her Algebra class. The problem requires Sara to use the two quadrilaterals below to answer a list of questions.



Part A: For what one value of are the perimeters of the quadrilaterals the same? (Hint: The perimeter of a quadrilateral is the sum of its sides.)

Part B: For what one value of are the areas of the quadrilaterals the same? (Hint: The area of a quadrilateral is the product of its base and height.)

Answers

Answer:

For the perimeters, x must be equal to 2.

For the areas, it is either undefined, or something.

Step-by-step explanation:

You can first find the perimeters for both sides.

For the left shape, we add the two sides of 6 and x + 4 to get x + 10.

Then we multiply x + 10 by 2 because there are 4 sides, and we only got 2 sides.

The perimeter of the first shape is 2x + 20.

The second shape can be solved by doing the same thing by adding 2 and 3x + 4 to get 3x + 6.

3x + 6 times 2 is 6x + 12.

The second perimeter is 6x + 12.

If both sides are supposed to be equal, then we can write these two expressions we solved for like:

6x + 12 = 2x + 20.

Subtraction property of equality

6x + 12 - 12 = 2x + 20 - 12

Simplify

6x = 2x + 8

Again

6x - 2x = 2x - 2x + 8

Simplify

4x = 8

Division property of equality

4/4x = 8/4

Simplify

x = 2

So if x = 2, the perimeters will be the same.

You can confirm this by plugging it back into either equation.

For the areas, we just multiply the length and width for both shapes, so we get

6(x+4)  =  2(3x+4)

Since they are supposed to be equal.

We simplify and get

6x + 24 = 6x + 8

We know this is false and is not possible, since we can remove the 6x because it is on both sides.

We also know that 24 is not equal to 8 (who thought!)

:D

24 ≠ 8

So it is undefined or whatever you call it.

if side of square is 4.05 find its area ​

Answers

Answer:

A

16.4

please give brain list

Which set of statements shows the correct steps to find 45 percent of 75?

A.
Write 45 percent as 9 ´ 5 percent, and write 5 percent as StartFraction 1 Over 20 EndFraction. Then, find StartFraction 1 Over 20 EndFraction of 75: 75 times StartFraction 1 Over 20 EndFraction = StartFraction 75 Over 20 EndFraction = 3.75. Multiply 3.75 by 9 to get 33.75. So, 45 percent of 75 is 33.75.
B.
Write 45 percent as 9 ´ 5 percent, and write 5 percent as One-half. Then, find One-half of 75: 75 times one-half = StartFraction 75 Over 2 EndFraction = 33.75. Multiply 33.75 by 9 to get 303.75. So, 45 percent of 75 is 303.75.
C.
Write 45 percent as StartFraction 1 Over 45 EndFraction. Then, find StartFraction 1 Over 45 EndFraction of 75: 75 times StartFraction 1 Over 45 EndFraction = StartFraction 75 Over 45 EndFraction = 1.67. So, 45 percent of 75 is 1.67.
D.
Write 45 percent as StartFraction 1 Over 4.5 EndFraction. Then, find StartFraction 1 Over 4.5 EndFraction of 75: 75 times StartFraction 1 Over 4.5 EndFraction = StartFraction 75 Over 4.5 EndFraction = 16.7. So, 45 percent of 75 is 16.7.

Answers

Pls the answer is

D

Thank you

You are welcome

Answer:

d

Step-by-step explanation:

im smart

How many solutions does the nonlinear system of equations graphed below
have?
A. One
B. Four
C. Two
D. Zero

Answers

Answer:

D

Step-by-step explanation:

There is no point shared by all three graphs

URGENT PLS HELP

Given f(y)=2y^2 - 4y, and h(x)= x^2 - 1, determine f(h(x))

Answers

Answer:

f(h(x)) = 2•(x²-1)² -4•(x²-1)

Bob had 10 more cars than Paul. Paul had 15 cars.

Answers

Answer:

Bob had 25 cars

Step-by-step explanation:

10+15=25

Bob at 25 cars
explanation: paul had 15 cars bob had 10 more
15+10=25

Identify the level of measurement (nominal, ordinal, or interval-ratio) of each of the following variables: (1) How satisfied a person is with his or her employment benefits, measured as very satisfied, somewhat satisfied, neither satisfied nor dissatisfied, somewhat dissatisfied, or very dissatisfied. (2) The number of times someone has shoplifted in her or his life. (3) The number of times someone has voted in a public election measured as 0-1 times, 2-3 times, or 4 or more times. (4) The type of attomey a criminal defendant has attrial, measured as privately retained or publicly funded.

Answers

Solution :

Nominal variable

A nominal variable is defined as a variable which is used to [tex]\text{nam}e \text{ or label or categorize some particular attributes }[/tex]  which are being measured.

An ordinal variable is the one in which the order matters, but the difference between any two orders does not matter.

In interval ratio variable is defined as the variable where the difference between any two values is meaningful.

The level of measurement  for each of the following are :

1) Variables that are categorized in categories so that it is ordinal data.

2) Data scaled with the two categories her or his,  so it is a nominal data.

3) Number of votes categorized in the intervals so it is Interval type data.

4) nominal data.

at the market, a housewife bought 2 kilograms of eddoes at $5 per kilogram and 5 kilograms of chicken at $10 per kilogram. she paid that market vendor $75. how many dollar does she owe the vendor​

Answers

Answer:

The total for the housewife's purchase should be 60 dollars. So it should be the vender who owes her money. The vender owes her 15 dollars.

Step-by-step explanation:

$5 = 1kg (eddoes) meaning a total of 2kg eddos =$10

$10 = 1kg (chicken) meaning a total of 5kg chicken = $50

When added together, it'd be 60 dollars.

(I'm not sure if you maybe forgot a part of the question or only had this part)

NO LINKS OR ANSWERING WHAT YOU DON'T KNOW?

1. Suppose y varies inversely with x, and y = 25 when x = 1/5. What is the value of y when x = 5?

a. 15
b. 5
c. 25
d. 1

2. Suppose y varies inversely with x, and y = a when x = a^2. What inverse variation equation related x and y?

a. y = a^2/x
b. y = a^3/x
c. y= a^3x
d. y = ax

3. Suppose y varies inversely with x, and y = 3 when x = 1/3. What is the inverse variation equation that relates x and y?

a. y = 1/x
b. y =x
c. y = 3x
d. y = 3/x

Answers

Answer:

1. D. 1

2. B. y=a³/x

3. A. y=1/x

Step-by-step explanation:

too long to give te explanations but they're there in the attachments

¿Pueden ayudarme por favor?

Answers

Yes I can help you out 3x+4()7

For P = {5, 12, 13, 14), Q = {2, 7, 11), and R = {4, 7, 8, 11}, find PU (Q n R).

Answers

Answer:

(5 7 11 12 13 14)

Step-by-step explanation:

Q inter R = 7 and 11

So the union between p and 7 and 11 is the answer above

The quadrilateral KLMN is dilated with the center of dilation located at point M. Which statement is accurate?
1. The scale factor is 3, which means the length of the image of segment KL will be 1/3 times as long.

2. The scale factor is 1/3, which means the length of the image of segment KL will be 1/3 times as long.

3. The scale factor is 3, which means the length of the image of segment KL will be 3 times as long.

4. The scale factor is 1/3, which means the length of the image of segment KL will be 3 times as long.

Answers

Answer:

3. The scale factor is 3, which means the length of the image of segment KL will be 3 times as long.

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure. If a point A(x, y) is dilated about the center of dilation located at O(a, b), the new point is at A'[k(x - a) + a, k(y - b) + b].

Quadrilateral KLMN has vertices at K(2, 1), L(-1, -5), M(6, -5) and N(6, 1). If it is dilated by 3, about the center M(6, -5), the new points are:

K' = (3(2 - 6) + 6, 3(1 - (-5)) + (-5)) = (-6, 13)

L' = (3(-1 - 6) + 6, 3(-5 - (-5)) + (-5)) = (-15, -5)

M' = (3(6 - 6) + 6, 3(-5 - (-5)) + (-5)) = (6, -5)

N' = (3(6 - 6) + 6, 3(1 - (-5)) + (-5)) = (6, 13)

Therefore the image of segment KL will be 3 times long.

Complete the angle addition postulate for the following angle

Answers

Answer:

measurement m<GEM+m<MEO=m<GEO

Is this right?? If not please tell me the answers

Answers

yes all of these are correct

Answer:

TAMA PO

Step-by-step explanation:

Paki brainliest nadin po

Find the distance between the two points in simplest radical form. (8,−8) and (−1,−5)

Answers

Answer:

Solution given:

[tex]x_{1},y_{1}=(8,-8)[/tex]

[tex]x_{2},y_{2}=(-1,-5)[/tex]

Now

Distance between them is:

d=[tex]\sqrt{(x_{2}-x_{1})²+(y_{2}-y_{1})²}[/tex]

d=[tex]\sqrt{(-1-8)²+(-5+8)²}=3\sqrt{10}[/tex]

Distance between them is [tex]\bold{3\sqrt{10}}[/tex]

write the equation of the line shown in the graph above in slope-intercept form

Answers

y = mx + c
y= -2/3x + 1
1= c
Answer: y= -2/3x+1


Step 1: Write slope-intercept form equation

To start answering this question, it helps to write out the example equation for slope-intercept form. Let’s do this now.

y=mx+b

Keep in mine that the y represents the answer, the m represents the slope, the x represents the variable, and the b represents the y-intercept.

Step 2: Determine the y-intercept

I find that it is easiest to determine the y-intercept first. This is the b in the equation. The y-intercept can be find by looking at the y-axis, and seeing where the line intersects with the axis. In this case, it seems to be at 1. Let’s substitute this into our equation now.

y=mx+b
y=mx+1

Step 3: Determine slope

For the final thing that we need to fill in, we need to find the slope. The slope is the m in the equation, and can be found by the formula of rise/run. Choose any two points, and see how far they are from each other up and down (rise), as well as left and right (run).
For the sake of this problem, we will work with (0,1) and (-3,3). There is a difference in the rise of 2 and in the run of 3. This makes the rise/ run be 2/3. Let’s substitute this now.

y=mx+1
y= 2/3x+1

The slope will also need to be negative since the line on the graph descends. Let’s change this to a negative now.

y= -2/3x+1


This is your answer. Hope this helps! Comment below for more questions.

Select the correct answer from the drop-down menu.
The measure of the angle between the two sides of the roof is approximately
A. 95.8
B. 91.2
C. 92.9

Answers

i think it’s B 91.2

The time that it takes to fold 1,000 origami cranes varies inversely with the number of people folding the cranes. If a class of 25 students work together to fold the 1,000 cranes, it will take 3 hours. Write an equation to show the relationship between time (t) and the number of people (n) folding cranes.
ASAP!!!!

Answers

Answer:

t = [tex]\frac{75}{n}[/tex]

Step-by-step explanation:

Use the inverse variation equation, y = [tex]\frac{k}{x}[/tex]

Replace y with t, and replace x with n, since those are the variables in this situation:

t = [tex]\frac{k}{n}[/tex]

Plug in 3 as t and 25 as n, and solve for k:

3 = [tex]\frac{k}{25}[/tex]

75 = k

Create the equation by plugging in 75 as k:

t = [tex]\frac{75}{n}[/tex]

So, the equation is t = [tex]\frac{75}{n}[/tex]

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Which sentence uses the underlinedvocabulary word incorrectly?A. Ben had no scruples when it came to "borrowing"someone else's books or computer.B. Jerry and Kay took a nominal bus into town sothey could attend the celebration.C. There was a radiance in her countenance thatbrought the audience to its feet with amazement. The lengths of nails produced in a factory are normally distributed with a mean of 6.13 centimeters and a standard deviation of 0.06 centimeters. Find the two lengths that separate the top 7% and the bottom 7%. These lengths could serve as limits used to identify which nails should be rejected. What change would increase the amount of solid solute able to be dissolved in liquid water? Decreasing rate of stirringDecreasing surface areaIncreasing pressureIncreasing temperature QUESTION 1Identify whether the following sentence is complete or a fragment. To ride a bicycle.1. complete2. fragment Translate this sentence into an equation.The difference of Malik's height and 11 is 44Use the variable m to represent Malik's height. Recall how the sorceress's twinbrother converts blueberries byadding 9 to the number ofblueberries given to him and thendoubling it. Find the output if he isgiven zero blueberries.The wizard returns blueberries. You buy a 12-year 10% annual coupon bond at par value, $1,000. You sell the bond 3 years later for $1,100. What is your total rate of return over this 3-year period? Hellocan u help me with a essay about for a brand namePlz help me asap Hich US region is the most important for agriculture and mining? A. the Rocky Mountains B. the Coastal Plains C. the Great Basin D. the Great Plains Please select the best answer from the choices provided A B C D Your friend was injured in an accident, and the insurance company has offered him the choice of $25,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity Mes parents sont .. banqueA) laB) enC) l' In September, Jeanette Company purchased materials costing $34,400 and incurred direct labor cost of $22,100. Manufacturing overhead totaled $58,000 for the month. Information on inventories was as follows: September 1 September 30 Materials $10,300 $9,800 Work in process 6,500 7,400 Finished goods 3,630 2,970 What was the cost of direct materials used in production for the month of September? a. $34,900 b. $33,900 c. $35,300 d. $33,500 You are a chemist working in your laboratory. In your storage closet you have acabinet that holds only samples of pure elements, no compounds. While looking for asample of lithium (LI), you notice that the label on one bottle has worn off. The room isat normal temperature. The contents of the bottle are liquid and do not look metallic.What element should you relabel the bottle as?A.HeliumB.BromineC.Arsenic D.Chlorine The volume of air inside a rubber ball with radius r can be found using the function V(r)= 4/3pier^3 what does V(5/7) represent? Which method correctly solves the equation using the distributive property?Negative 0.2 (x minus 4) = negative 1.7Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x minus 4 = negative 1.7. Negative 0.2 x = 2.3. x = negative 11.5.Negative 0.2 (x minus 4) = negative 1.7. x minus 4 = 0.34. x = 4.34.Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x + 0.8 = negative 1.7. Negative 0.2 x = negative 2.5. x = 12.5.Negative 0.2 (x minus 4) = negative 1.7. Negative 0.2 x minus 0.8 = negative 1.7. Negative 0.2 x = negative 0.9. x = 4.5. A paddleboat can move at a speed of 4 km/h in still water. The boat is paddled 12 km downstream in a river in the same time it takes to go 6 km upstream. What is the speed of the river? Find the area of the region that is enclosed between the curves y = x2 andy = x + 6. a british citizen who supported social reform in the victorian era would most likely call the government to discuss cybersecurity in today's current situation 4c = 3c + 4 my answer : 4c = 4 - 3c 4c = 1c c = 4/1 c= 4 just checking, Is this Correct?