Answer:
- no real solutions
- 2 complex solutions
Step-by-step explanation:
The equation can be rearranged to vertex form:
x^2 -4x = -5 . . . . . . . . . subtract 4x
x^2 -4x +4 = -5 +4 . . . . add 4
(x -2)^2 = -1 . . . . . . . . . show the left side as a square
x -2 = ±√-1 = ±i . . . . . . take the square root; the right side is imaginary
x = 2 ± i . . . . . . . . . . . . . add 2. These are the complex solutions.
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<em>Comment on the question</em>
Every 2nd degree polynomial equation has two solutions. They may be real, complex, or (real and) identical. That is, there may be 0, 1, or 2 real solutions. This equation has 0 real solutions, because they are both complex.
To create an area that is 1.5 m^2 in size, you will need to make use of a total of 27 triangles.
<h3>How many triangles are needed to compose a region that is 1.5 square meters?</h3>
A square that has a size of one square meter is divided into nine smaller squares that are similar to each other. Each of the little squares is divided into two triangles that are similar to one another.
There are nine smaller squares contained inside one square meter, since 1 square meter may be broken down into nine identical smaller squares. Each of the little squares is divided into two triangles that are similar to one another. 9 smaller squares may be broken down into the following:
9*2=18 (shows identical triangles)
Hence, 1 square meter is decomposed into 18 identical triangles.
We need to find the number of triangles needed to compose a region that is square meters
where
m^2 = 1.5 m^2
Where
1 m^2 = 18 identical triangles.
1.5 m^2 = 1.5 * 18
1.5 m^2 = 27 identical triangles.
In conclusion, To create an area that is 1.5 m^2 in size, you will need to make use of a total of 27 triangles.
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Answer:
1. AB ~= DF
2. Definition of Congruent
3. Reflexive Property of Congruency
4 BD=BD
6. AB+BD=AD; DF+BD=BF
7. Substitution Property of Equality
8. Definition of Congruent
Step-by-step explanation:
1. The given always goes first, and that's the first reason, so AB ~= DF must be the first statement (that should be the congruency symbol).
2. The definition of congruent is that if they are congruent then they are equal. Since that statement made two congruent lines equal, it must be the definition.
3. The reflexive property means something is congruent to itself, and BDis BD, therefore it is the reflexive property.
4. Remember if something is congruent then it is equal.
6. The segment addition postulate states that if we are given two points on a line segment, then AB+AC=AC.
7. In this statement AD was substituted for DF+BD. This can be done because of AB=DF and BD=BD as aforementioned.
8. If two things are congruent then they are equal by definition of congruency.
