If x2 + y2 = 14 and xy = 5, find the value of (1/2 x + 1/2 y)2.

Answers

Answer 1

Answer:

(½x+½y)²=6

Step-by-step explanation:

x^2 + y^2 = 14, xy=5

(A+B)^2=A^2 +2AB+B^2... (*)

(1/2x+1/2y)^2 =(*)

(1/2x)^2 +2(1/2x)(1/2y)+(1/2y)^2 =

1/4x^2 +1/2xy+1/4y^2=

1/4(x^2 +y^2) +1/2(xy)=

1/4*14+1/2*5=

14/4+5/2=

14/4+10/4=

24/4=6

let me know if I'm wrong.

Answer 2

( 1/2x +1/2y)²

= { ( x + y )/ 2xy }²

= ( x² + 2xy + y² )/4(xy)² —(1)

As we know that x² + y² = 14 — (2)

and xy = 5 —(3)

So, substitute the value of equation 2 and 3 in equation 1,

= ( x² + 2xy + y²)/4(xy)²

=( 14 + 2*5)/(4*5²)

= 24/(4*25)

= 6/25.


Related Questions

help on this question.....

Answers

Answer:

25

Step-by-step explanation:

17 / 0.68 = 25

check your answer?

25 * 0.68 = 17

:)

Answer:

the answer is 26

Step-by-step explanation:

find the missing number so that the equation has no solutions ?x-4=4x-11

Answers

Answer:1

Step-by-step explanation:I took the test

In a patriotic bag of red, white and blue M&Ms, it is found that there are 305 M&Ms. There are three times as many red as white. The blue are five more than twice the white. How many blue M&Ms are in the package ?

A. 50
B. 75
C. 35
D. 105
E. 95 ​

Answers

Using a system of equations, it is found that the number of blue M&Ms in the package is of:

D. 105

What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Variable x: Number of red M&Ms.Variable y: Number of white M&Ms.Variable z: Number of blue M&Ms.

There are 305 M&Ms, hence:

[tex]x + y + z = 305[/tex]

There are three times as many red as white, hence:

[tex]x = 3y[/tex]

[tex]x + y + z = 305[/tex]

[tex]3y + y + z = 305[/tex]

[tex]4y + z = 305[/tex]

The blue are five more than twice the white, hence:

[tex]z = 5 + 2y[/tex]

Then:

[tex]4y + z = 305[/tex]

[tex]4y + 5 + 2y = 305[/tex]

[tex]6y = 300[/tex]

[tex]y = \frac{300}{6}[/tex]

[tex]y = 50[/tex]

[tex]z = 5 + 2y = 5 + 2(50) = 105[/tex]

Hence option D is correct.

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Sheila has investments totaling $8000 in two
accounts. The savings account pays 6% interest and the
other account is in bonds paying an interest rate of
11%. If the annual interest from the two investments
totaled $780, how much did she invest in each account?

Answers

The amount she invested in each account is:

$6,000 invested at 11%

$6,000 invested at 6%

Let x represent the amount invested at 11%

Hence:

.11x+.06(8000-x)=780

.05x+480=780

Collect like terms

.05x=300

Divide both side by .05x

x=300/.05

x=$6,000

Inconclusion the amount she invested in each account is: $6,000 invested at 11% and $6,000 invested at 6%.

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https://brainly.com/question/8553720

Joe drove 315 Thousand five hours at the same rate how many miles do you drive in 7 hours?

Answers

Answer:

441 miles

Step-by-step explanation:

1st find rate from the given

D = RT

315 = 5R

63 = R miles/hour     so,

then find distance for 7 hours

D = RT

D = 63 * 7

D = 441

Answer:

Item 3. 4 3/8

Item 4. 4/9

Item 5. 4/3

Item 6. 1/8

Item 7. 0.8

Item 8. 5.20 or 5.2 (You can choose which to put)

Item 9. 1 7/8

Item 10. A 2008=24500 2009=26000 2010=27500 2011=29000

Step-by-step explanation:

Complete the multiplication problem to find the answer.

Answers

Answer:

A

Step-by-step explanation:

Answer:

a) 39.71

Step-by-step explanation:

[tex]\sf 19=7x-2x[/tex]

Answers

Answer:

[tex]3\dfrac{4}{5}[/tex]

Step-by-step explanation:

19 = 7x - 2x

19 = (7 - 2)x

19 = 5x

Divide both side by 5

19/5 = x

[tex]x=3\dfrac{4}{5}[/tex]

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

Value of x is equal to ~

[tex] \boxed{3.8}[/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

[tex]19 = 7x - 2x[/tex]

[tex]5x = 19[/tex]

[tex]x = 19 \div 5[/tex]

[tex]x = 3.8[/tex]

A number is first increased by 20 and then doubled. The result is 2 less than 5 times the number

Answers

set up an equation:

2(x+20) = 5x - 2

Simplify:

2x +40 = 5x - 2

Add 2 to both sides:

2x + 42 = 5x

Subtract 2x from both sides:

42 = 3x

Divide both sides by 3:

x = 42/3 = 14

The number is 14

Answer:

The answer is 14

Step-by-step explanation:

1 1/3 of 15
[tex]\frac{x}{y}[/tex]

Answers

Answer:

[tex]11 \div 3 \times 15 \\ 11 \div 1 \times 5 \\ 11 \times 5 \\ = 55[/tex]

answer:
20

explanation:
1 whole of 15=15
1/3 of 15= 15/3=5
15+5=20

can someone please help me fill in the answer in the bottom.​

Answers

Answer:

Step-by-step explanation:

1) Initial water level = 30 feet

2) Rate of change = (30 - 25) / (0 - 1) = 5/(-1) = -5

5ft  per hour

3) y-intercept = 30

the person above has the correct answer

What is the x intercept of this quadratic/parabola?

Answers

Answer:

-3, 1

Step-by-step explanation:

There are actually 2 x-intercepts of the parabola. You can find them simply by looking along the x-axis and seeing where the lines of the parabola touch the axis, so -3 and 1.

Hope this helps :)

Answer:

1 and  -3

Step-by-step explanation:

At x-intercept y = 0

So, parabola intersect x-axis at two places (1 , 0) and (-3 , 0)

X-intercepts are 1 and -3

What letter comes after f

Answers

Answer:

g.....

Step-by-step explanation:

g.....

the letter is g

The letter g comes after the letter f.

What are Alphabets?

An alphabet is a set of graphs or characters used to represent the phonemic structure of a language

The english alphabets are a, b, , c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u , v, w, x, y and z.

The alphabets help to form the basis of our language and communication for a lifetime.

There are twenty six letters in the english alphabets.

As we  see the order of alphabets.

The letter g is next to the letter f.

They help to form the basis of our language and communication for a lifetime.

Hence, the letter g comes after the letter f.

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Simplify to create an equivalent expression
-5(3p+3) + 9(-7+p)
The answers are:
A)-5p-78
B)-6p-78
C)-6p-48
D)-6p+78

Answers

The answer is B. -6p-78. Pls mark brainliest.

For brainily please help

Answers

Answer: 148


A triangle = 180

So all three sides have to add up to 180.

If one side is 12 And the other is 20 you add that makes 32.

12 + 20 = 32

Now we need to find the length of the other side. 32 is two of the sides and 180 is the whole. So something + 32 = 180

32 + x = 180

To find x you subtract 32 from 180

180 - 32 = 148

Hope this helps

A tub of water drains at 3 gallons per minute. y-12=-3(x-1)

Answers

if you plot 3,12 on a graph and go move to the
left one and up one untill the x axis is zero you
will land on five. so the amount the tub started
with is 15

Need a bit of help here

Answers

Answer:

Answer 1 is 4:2 or also write as 2:1.

your friend says that there are 36 feet in 12 yards is your friend correct? explain your reasoning.

PLEASE HURRY!!​

Answers

Answer:

Yes

Step-by-step explanation:

1 yard is 3 feet. so 12 yards is 36 by 12*3

If the diagonals of a rhombus are of length 24 & 32 cm, find the altitude of the rhombus.

a) 15.8 cm
b) 14.2 cm
c) 12 cm
d) 19.2 cm​

Answers

Hello Carousel!

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

If the diagonals of a rhombus are of length 24 & 32 cm, find the altitude of the rhombus.

a) 15.8 cm

b) 14.2 cm

c) 12 cm

d) 19.2 cm

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

Please refer to the attached picture for the answers with steps included.

NOTE :-

The sides of a rhombus are equal to each other.The point of intersection of the diagonals (marked as O in the figure) forms 90° angles (which is why we used the pythagoras property to solve the question).Since 0 is the point of intersection, it's also the midpoint of the diagonals. (So, BO = ½ × BD & AO = ½ AC -- we used this to solve the question).

__________________

Hope it'll help you!

ℓu¢αzz ッ

why is this not a polynomial?
3^x - x/3 + x^3

Answers

Answer:

It is not a polynomial because the polynomial is the term given to an expression which has coefficients as well as variables with powers having a non-negative entegral value or we can say natural number. The power of the variable × here is not an integer so 3/× is not a polynomial

Step-by-step explanation:

I hope I helped you

Answer:

below

Step-by-step explanation:

-x/3 + x³ is polynomial

3ˣ IS NOT a polynomial, it makes the function be an  "exponential function", which does not fit the criteria of polynomial definition.

Un paralelogramo con una base de 13cm y una altura de 8cm, su área es de

Answers

Answer:

Step-by-step explanation:

factor the expression using the gcf 2t-10​

Answers

The GCF of 10 and 2 is 2.
So, 2(t-5).

victor want to make a book tower of height 48 cm .If the thickness of book is 12 mm ,how many books will he need to make the desire height ?​

Answers

Answer:

40

Step-by-step explanation:

1. Change 48 cm to mm, which will give you 480 mm

2. Divide 480 mm by 12 mm, that will give you 40

Therefore, Victor needs 40 books to make his desired height.

Need help ASAP please <3

the table given below shows the number of miles that teddy had been runninf over some of the past ten weeks

The number of miles that he runs per week can be represented as a linear function. What would be
the rate of change of this function in miles per week?

A) 1

B) 3

C) 6

D) 10

Answers

The answer is a because you multiple times and divided

The rate of change of this function in miles per week is 3 miles per week.

What is a expression? What is a mathematical equation?Linear function is a function whose degree is one. It is of the form -f(x) = ax + bA mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a table as shown in the question.

The rate of change in miles per week is -

(19 - 13)/(3 - 1) = (22 - 19)/(4 - 3)

6/2 = 3/1

3 = 3

3

Therefore, the rate of change of this function in miles per week is 3 miles per week.

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I need to factor this problem PLEASE HELP ASAP

Answers

Answer:

[tex] - 3x(x - 3)^{2} [/tex]

Step-by-step explanation:

[tex] - 3x^{3} + 18x - 27x[/tex]

->

[tex] - 3x( {x}^{2} - 6x + 9)[/tex]

->

[tex] - 3x(x - 3)^{2} [/tex]

[tex]\frac{2}{5}[/tex](6-5p)

Answers

Answer: -2x + 12/5

Step-by-step explanation:

the probability distribution of all possible values of the sample proportion is the

Answers

Answer: The sampling distribution of p is the probability distribution of all possible values of the sample proportion p.

Solve and graph the solution.
|4x-13| = 5x+4

Answers

Answer: x = -17

Step-by-step explanation:

4x-13=5x+4

(4x-13)+(13-5x)=(5x+4)+(13-5x)

4x-13+13-5x=5x+4+13-5x

4x-5x-13+13=5x-5x+4+13

-x=17

x=-17

Answer:

x = -1

Step-by-step explanation:

/4x-13/ = 5x + 4

4x +5x = -13 +4

9 x = -9

9x = -9

x = -1

Find the value of x within the triangle

Answers

Answer:

68.46

Step-by-step explanation:

In order to find the angle, we can use the cosine rule:

c²=a²+b²-2abCos(c)

And rearrange for Cos(c)

(please note that c in this case is x)

So,

x=Cos^(-1) (a²+b²-c²)/2ab

By substituting the values, we get x=Cos^(-1)(4²+4²-4.5^2)/2(4)(4)

=68.46

U= 1 A solution to the inequality below??

10>u

Answers

Answer:

Yes

Step-by-step explanation:

10>1

Simplify 2x2 + 3x2 + 3x

Answers

Answer:

10+3x

Step-by-step explanation:

2(2) = 4

3(2) = 6

4+6 = 10

10+3x

Answer:

Step-by-step explanation:

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