X² + 1 = 0
=> (x+1)² - 2x = 0
=> x+1 = √(2x)
or x - √(2x) + 1 = 0
Now take y=√x
So, the equation changes to
y² - y√2 + 1 = 0
By quadratic formula, we get:-
y = [√2 ± √(2–4)]/2
or √x = (√2 ± i√2)/2 or (1 ± i)/√2 [by cancelling the √2 in numerator and denominator and ‘i' is a imaginary number with value √(-1)]
or x = [(1 ± i)²]/2
So roots are [(1+i)²]/2 and [(1 - i)²]/2
Thus we got two roots but in complex plane. If you put this values in the formula for formation of quadratic equation, that is x²+(a+b)x - ab where a and b are roots of the equation, you will get the equation
x² + 1 = 0 back again
So it’s x=1 or x=-1
Answer:
answer: 1/8
Step-by-step explanation:
because the probability of getting a nickel is 2/4 and the probability of getting a quarter is 1/4 now when I multiply them together 2/4 × 1/4 = 1/8 Hope that helps!
Answer:
A
Step-by-step explanation:
We can find the surface area of the object by adding the surface areas of each part. We have many rectangle faces to count and two triangular faces. Each has a formula for the area. We will find the area of each and then add them all together.
Triangle - 0.5 *b*h
Rectangle - b*h
<u>Triangles</u>
There are two triangles on either side. The height is 1.5. The base is 1.8.
0.5(1.5)(1.8)=1.35 meters squared
Since there are two, we will add 1.35+1.35 in our final calculation.
<u>Rectangles</u>
We will start by calculating the largest rectangle on the side. It has height of 4 and a base of 2.5 (shown above left).
4(2.5)=10
Since there are two (one we can see and one we can't), we will add 10+10 in our final calculation.
Next we calculate the top and bottom. The height is 3 and the base is 2.5 on top. But the bottom sticks out more and adds 1.8 to its base.
Top - 3(2.5)=7.5
Bottom-3(2.5+1.8)=12.9
Finally, we will calculate the front side and back(not visible) as well as the slant up front. The back side has height 4 and base 3. The front side has base 3 and height 4-1.5=2.5. The slant has base 2.3 and height 3.
Back - 4(3)=12
Front- 3(2.5)=7.5
Slant - 3(2.3)=6.9
We add all together for the total surface area: 1.35+1.35+10+10+7.5+12.9+12+7.5+6.9=69.5 meters squared.
How many facts does it take to make triangles congruent? Only 3 if they are the right three and the parts are located in the right place.
SAS where 2 sides make up one of the three angles of a triangle. The angle must between the 2 sides.
ASA where the S (side) is common to both the two given angles.
SSS where all three sides of one triangle are the same as all three sides of a second triangle. This one is my favorite. It has no exceptions.
In one very special case, you need only 2 facts, but that case is very special and it really is one of the cases above.
If you are working with a right angle triangle, you can get away with being given the hypotenuse and one of the sides. So you only need 2 facts. It is called the HL theorem. But that is a special case of SSS. The third side can be found from a^2 + b^2 = c^2.
You can also use the two sides making up the right angle but that is a special case of SAS.
Answer
There 6 parts to every triangle: 3 sides and 3 angles. If you show congruency, using any of the 3 facts above, you can conclude that the other 3 parts of the triangle are congruent as well as the three that you have.
Geometry is built on that wonderfully simple premise and it is your introduction to what makes a proof. So it's important that you understand how proving parts of congruent triangles work.