Consider the parallelogram shown below.
The lengths of the sides are a and b.
The lengths of the diagonals are 2x and 2y.
Because the diagonals are both congruent and perpendicular, therefore there are two right triangles as shown.
Note that x = y.
Because x = y, each right triangle is isosceles and has the angles 90°, 45° and 45°.
From the Pythagorean theorem,
For one right triangle,
a² = x² + y² = x² + x² = 2x².
For the other right triangle,
b² = y² + x² = x² + x² = 2x²
Therefore
a² = b²
a = b
It follows that all sides of the parallelogram are equal and each angle is
45+45 = 90°
Therefore the parallelogram is a square.
Answer:
Z=-2
This value means that the score of Rachel 550 it's 2 deviations below the mean of the population 
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
represent the population mean for the Graduate Record Exam (GRE)
represent the population standard deviation for Graduate Record Exam (GRE)
2) Solution to the problem
Let X the random variable that represent the Graduate Record Exam (GRE) of a population, and for this case we know the distribution for X is given by:
Where and
We want to find the z score for a score of 550. And in order to do this we need to apply the formula for the z score given by:
If we apply this formula to our probability we got this:
So the answer for our case would be Z=-2
This value means that the score of Rachel 550 it's 2 deviations below the mean of the population
slope = (25-4)/(30-10)
slope = 21/20
slope =21/20
using point slope form
y-y1 = m(x-x1)
y-4 = 21/20 (x-10)
y = 21/20x -21/2 +4
y = 21/20 x -21/2 +8/2
y = 21/20x -13/2
let x=40
y = 21/20 (40) -13/2
y = 42-13/2
y = 35.5 games
If we round the slope to 1
slope =1
using point slope form
y-y1 = m(x-x1)
y-4 = 1 (x-10)
y = 1x -10 +4
y = x -6
let x=40
y = 40-6
y = 34 games
Hey!
-----------------------------------------------
Solution:
= (-18) - (4)
= -18 - 4
= -22
When you subtract a positive to a negative number the end result will always be negative.
-----------------------------------------------
Answer:
B. 22
-----------------------------------------------
Hope This Helped! Good Luck!
1. Line l; point P not on l.( Take a line I and mark point P outside it or on the line.So from point P there are infinite number of lines out of which only one line is parallel to line I. Suppose you are taking point P on line I, from that point P also infinite number of lines can be drawn but only one line will be coincident or parallel to line I.
2. Plane R is parallel to plane S; Plane T cuts planes R and S.(Imagine you are sitting inside a room ,consider two walls opposite to each other as two planes R and S and floor on which you are sitting as third plane T ,so R and S are parallel and plane T is cutting them so in this case their lines of intersect .But this is not possible in each and every case, suppose R and S planes are parallel to each other and Plane T cuts them like two faces of a building and third plane T is stairs or suppose it is in slanting position i.e not parallel to R and S so in this case also lines of intersection will be parallel.
3. △ABC with midpoints M and N.( As you know if we take a triangle ABC ,the mid points of sides AB and AC being M and N, so the line joining the mid point of two sides of a triangle is parallel to third side and is half of it.
4.Point B is between points A and C.( Take a line segment AC. Mark any point B anywhere on the line segment AC. Three possibilities arises
(i) AB > BC (ii) AB < BC (iii) AB = BC
Since A, B,C are collinear .So in each case 
