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3 years ago

If x^2+y^2=14 annd xy=5 find the value of (1/2x+1/2y)^2

Mathematics

1 answer:

Leviafan [203]3 years ago

4 0

Answer:

Step-by-step explanation:

$\left(\frac12x+\frac12y\right)^2=\\\\=\left[\frac12(x+y)\right]^2=\\\\=\left(\frac12\right)^2\left(x+y\right)^2=\\\\=\frac14\left(x+y\right)^2=\\\\=\frac14(x^2+2xy+y^2)=\\\\=\frac14(x^2+y^2+2xy)=\\\\=\frac14(14+2\cdot5)=\\\\=\frac14\cdot28=\\\\=7$

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Ryan and Sarah collect baseball cards. Ryan has 150 baseball cards and collects 10 cards per week. Sarah has 233 baseball cards

ICE Princess25 [194]

Answer:

About 17 weeks

Step-by-step explanation:

Given

Ryan:

$Initial = 150$

<em /> $Additional = 10$ <em> (weekly)</em>

Sarah:

$Initial = 233$

$Additional = 5$ (weekly)

Required

Determine the number of weeks they have the same cards

Represent the number of weeks with w:

For Both individuals, number of card at any given week is:

$Initial + Additional * w$

So,

For Ryan, the expression is:

$150 + 10 * w$

$150 + 10w$

For Sarah, the expression is:

$233 + 5 * w$

$233 + 5 w$

To determine the number of weeks, we have to equate both equations:

$150 + 10w= 233 + 5 w$

Collect Like Terms

$10w - 5w = 233 - 150$

$5w = 83$

Solve for w

$w = 83/5$

$w = 16.6$

16.6 implies about 17 weeks, because 16.6 approximates to 17

<em>Conclusively, Ryan and Sarah will have the same number of balls in about 17 weeks</em>

5 0

3 years ago

Two lines, C and D, are represented by the following equations: Line C: y = x + 5 Line D: y = −2x − 1 Which of the following opt

marin [14]

Answer:

The correct answer is B

Step-by-step explanation:

I know this is the answer because I took the test and got it right.

3 0

3 years ago

The product of x and y is less than or equal to 4.

timama [110]

Answer:

xy (less than or equal to sign) 4

5 0

4 years ago

Point T is on<br> SU ST=20 and TU=8<br> what is SU?

Umnica [9.8K]

SU would be 28 units because T is between S and U so you have to add ST and TU to get the length of the entire line

4 0

3 years ago

What is m∠AEB? <br> (See attachment)

aleksley [76]

Hey there,
Angle AEB + Angle CED = 180 degrees (vertically opposite angles)
(5x-10) degrees + (3x + 40) degrees = 180 degrees
5x -10 + 3x + 40 = 180 degrees
5x + 3x= 180 + 10 - 40
8x = 150
x = 150 / 8
= 18.75 degrees
Angle AEB = (18.75 x 5) - 10
=83.75 degrees.

Hope this helps ^_^

~Top

3 0

3 years ago