1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mars1129 [50]
2 years ago
13

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

Mathematics
2 answers:
yaroslaw [1]2 years ago
6 0

( 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.

aleksley [76]2 years ago
5 0

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.

You might be interested in
Mr. Nelson wants to put chicken wire around his chicken coup. He purchased 28.2 feet of chicken wire. The cost was $0.55 per foo
Shalnov [3]

Answer: $15.51

Step-by-step explanation: 28.2 times 0.55 is $15.51

6 0
2 years ago
Read 2 more answers
Find the value of the expression w^3 if w= 7=
Tasya [4]
Answer
Substitute w by 7
7^3
7x7x7 =343
3 0
2 years ago
Read 2 more answers
How to find the number of sides of a polygon when given the interior angle sum
wariber [46]

Given:

Sum of interior angle

To find:

Number of sides of a polygon

Solution:

Using sum of interior angles formula:

$S=(n-2) \times 180^{\circ}

where "S" is the sum of interior angels and "n" is the number of sides of a polygon.

Divide by 180° on both sides.

$\frac{S}{180^{\circ}}=\frac{(n-2) \times 180^{\circ}}{180^{\circ}}

Cancel common factor 180°.

$\frac{S}{180^{\circ}}=n-2

Add 2 on both sides.

$\frac{S}{180^{\circ}}+2=n-2+2

$\frac{S}{180^{\circ}}+2=n

Switch the sides.

$n=\frac{sum}{180^{\circ}}+2

Therefore number of sides of a polygon is n=\frac{sum}{180^{\circ}}+2.

3 0
3 years ago
I need to know how to determine the product of the fractions and simplify
FinnZ [79.3K]
1      3     1×3       3
--- × --- = ------ = ----
2      4      2×4      8

5       5       5×5         25
--- × ---- = --------- = -------
6       7       6×7         42

hope is understandably 

5 0
2 years ago
Solve using substitution. <br> 7x-4y=-12<br> 9x-4y=-20
MrRissso [65]

Answer:y= -4

Step-by-step explanation:

1 Solve for xx in 7x-4y=-127x−4y=−12.

x=\frac{4(y-3)}{7}

x=

7

4(y−3)

​

2 Substitute x=\frac{4(y-3)}{7}x=

7

4(y−3)

​

 into 9x-4y=-209x−4y=−20.

\frac{36(y-3)}{7}-4y=-20

7

36(y−3)

​

−4y=−20

3 Solve for yy in \frac{36(y-3)}{7}-4y=-20

7

36(y−3)

​

−4y=−20.

y=-4

y=−4

4 Substitute y=-4y=−4 into x=\frac{4(y-3)}{7}x=

7

4(y−3)

​

.

x=-4

x=−4

5 Therefore,

\begin{aligned}&x=-4\\&y=-4\end{aligned}

​

 

x=−4

y=−4

​

3 0
2 years ago
Other questions:
  • bruce rents snowmobiles to tourists. he charged $135 for 4 hours and $202.50 for 6 hours. what is the hourly rate bruce charges
    6·1 answer
  • A polynomial expression is shown below.
    12·1 answer
  • An experiment is broken up into two parts. In the first part of the experiment a penny is tossed in the air. If the coin lands o
    11·1 answer
  • Alison's car travels at 65 miles per hour. How far does she travel in 4.5 hours?
    5·1 answer
  • What’s the correct answer?
    15·2 answers
  • Find the equation of the linear function represented by the table below in slope
    5·1 answer
  • There are 24 female performers in a dance recital. The ratio of men to women is 3:4. How many men are there in the dance recital
    10·2 answers
  • Apples are cut into 8 pieces to be shared among some children. Twenty-two bags of seven apples are used. How many pieces of appl
    12·1 answer
  • NEED HELP ASAP OR I WILL FAIL WILLING TO GIVE 50 POINTS AND BRAINLIEST!
    8·2 answers
  • How do you write 8/5 as a percentage
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!