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3 years ago

Which number line represents the solution to the inequality x - 3 > 2

Mathematics

1 answer:

Ivahew [28]3 years ago

6 0

Answer: x > 5

Step-by-step explanation: To solve for <em>x</em> in this inequality, our goal is the same as it would be if this were an equation, to get x by itself on one side.

Since 3 is being subtracted from x, we add 3 to

both sides of the inequality to get x > 5.

When graphing x > 5, we have an open circle on 5 and the

open circle tells us that 5 is not part of our answer.

Then we draw an arrow going to the right to represent

all possible solutions to this inequality, any number greater than 5.

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3 years ago

For the point P(21, 24) and Q(26, 27) , find the distance d(P, Q) and the coordinates of the midpoint M of the segment PQ

aleksley [76]

Answer:

d(P,Q) = 5.83 units

Mid-point = (23.5,25.5)

Step-by-step explanation:

Given points are:

P(21,24) = (x1,y1)

Q(26,27) = (x2,y2)

The distance formula is given by:

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Here (x1,y1) are the coordinates of first point and (x2,y2) are coordinates of second point.

Putting the given values in the formula

$d(P,Q) = \sqrt{(26-21)^2+(27-24)^2}\\= \sqrt{(5)^2+(3)^2}\\=\sqrt{25+9}\\=\sqrt{34}$

$= 5.830952$

Rounding off: 5.83 units

The mid-point of two points is given by the formula:

$M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})$

Putting the values:

$M = (\frac{21+26}{2} , \frac{24+27}{2})\\=(\frac{47}{2} , \frac{51}{2})\\=(23.5, 25.5)$

Hence,

d(P,Q) = 5.83 units

Mid-point = (23.5,25.5)

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