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bixtya [17]
3 years ago
10

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:

<h2>              7</h2>

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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Tema [17]

Answer:  The required probability of event B is P(B) = 0.37.

Step-by-step explanation:  For two events A and B, we are given the following probabilities :

P(A) = 0.34,    P(A ∩ B) = 0.27   and   P(A ∪ B) = 0.44.

We are to find the probability of event B, P(B) = ?

From the laws of probability, we have

P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow 0.44=0.34+P(B)-0.27\\\\\Rightarrow 0.44=0.07+P(B)\\\\\Rightarrow P(B)=0.44-0.07\\\\\Rightarrow P(B)=0.37.

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Answer:

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Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

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  • b is the y-intercept

Given the lines

y = 2/3 x -3       --- Line 1

y = -3/2x +2      --- Line 2

<u>The slope of line 1</u>

y = 2/3 x -3       --- Line 1

By comparing with the slope-intercept form of the line equation

The slope of line 1 is: m₁ = 2/3

<u>The slope of line 2</u>

y = -3/2x +2      --- Line 2

By comparing with the slope-intercept y = mx+b form of the line equation

The slope of line 2 is: m₂ = -3/2

We know that when two lines are perpendicular, the product of their slopes is -1.

Let us check the product of two slopes m₁ and m₂

m₁ × m₂ = (2/3)(-3/2 )

m₁ × m₂ = -1

Thus, the product of the slopes of lines is -1.

i.e. m₁ × m₂ = -1

Thus, the lines are perpendicular.

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