Answer:
The standard form of a circle is (x-h)^2 + (y-k)^2 = r^2 with (h,k) being the center of the circle and r being the radius. In this case the circle's equation in standard form is (x-2)^2 + (y+3)^2 = 18. Knowing this it's easy to see that the center of the circle (h,k) is (2,-3). Finally the radius is or in simplified terms, 3
Step-by-step explanation:
Answer:
Given: In triangle XYZ, , XY=13x-21 , YZ=8x-6 and XZ=x+4.
If two angles are congruent if and only if, they measure the same number of degrees.
therefore, from the given condition; .
Isosceles Triangle : An triangle with two equal sides. The angles opposite the equal sides are also equal.
Therefore, the triangle XYZ is an isosceles triangle, as the base angle and
are equal and the sides opposite to these angles are also equal i.e, XY=YZ.
Since, we have XY=YZ ,
⇒ 13x-21 =8x-6 or
13x-8x=21-6 or
5x=15
Simplify:
x=3
Therefore, the sides of an isosceles triangle are:
XY = 13x-21 = = 39-21 = 18 unit ,
YZ = 8x-6 = = 24-6 =18 unit,
and XZ = x+4 = 3+4 =7 unit.
Since, the triangle is isosceles, we draw a line from an vertex angle Y of a triangle XYZ which is perpendicular (i.e, of 90 degree angle) to opposite side meets the opposite side at its midpoint i.e, say W.
As W is the midpoint(i.e, it divide the sides into two equal halves),
XW=WZ = unit
Now, use the Pythagorean theorem, to find the altitude WY.
⇒
Substitute the value of WZ = 3.5 unit and YZ = 18 unit in above formula to calculate the length of WY;
⇒
Simplify:
or
On simplify we get;
WY=17.65 unit(approx.)
The vertex angle Y is split into two equal angles, we can find the vertex angle by finding the one of the base angle by using the fact; .
⇒
⇒ (approx) or
Therefore, the angle .
The sum of the measure of the angle in the triangle is 180 degree.
In triangle XYZ.
Since
then,
⇒
Simplify:
.
Therefore, the measure of each angle are: and
Answer:
P = 0.0215 = 2.15%
Step-by-step explanation:
First we need to convert the values of 900 and 975 to standard scores using the equation:
Where z is the standard value, x is the original value, is the mean and
is the standard deviation. So we have that:
standard value of 900:
standard value of 975:
Now, we just need to look at the standard distribution table (z-table) for the values of z = 2 and z = 3:
z = 2 -> p_2 = 0.9772
z = 3 -> p_3 = 0.9987
We want the interval between 900 and 975 hours, so we need the interval between z = 2 and z = 3, so we just need to subtract their p-values:
P = p_3 - p_2 = 0.9987 - 0.9772 = 0.0215
So the probability is 0.0215 = 2.15%