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Bas_tet [7]
3 years ago
8

Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of angles. What is a reasonable conjecture

for Kathryn to make by recognizing a pattern and using inductive reasoning? When a pair of lines intersect, the vertical angles are acute. When a pair of lines intersect, all of the angles formed are right angles. When a pair of lines intersect, the vertical angles are congruent. When a pair of lines intersect, all of the angles formed are congruent.

Mathematics
2 answers:
icang [17]3 years ago
8 0
<h2>Answer:</h2>

The reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning is:

  When a pair of lines intersect, the vertical angles are congruent.

<h2>Step-by-step explanation:</h2>

The vertical angles are the opposite angles that are formed by the intersection of two lines. They are also known as Vertically opposite angles.

<em>We know that when a pair of lines intersect then the vertical angles are always congruent.</em>

However the measure of the angles may be acute or obtuse or right angle.

The same could be seen with the help of the figure attached to the answer.

denis23 [38]3 years ago
3 0
<span>Inductive reasoning is that when two lines intersect you will always have a pair of congruent angles considering an exception when all the angles are congruent. According to this,
1) Vertical angles (or opposite angles) are congruent. In this case, vertical angles could be acute or obtuse depending on the position of the lines.

2) The second case is the exception when all the angles are equal. It means that the lines are perpendicular.

3) Again back to the first case, vertical angles are equal or congruent in other words.

4) And again back to the second case when the lines are perpendicular, then all the angles that formed are equal to each other.

You can observe all the cases in the picture attached below.</span>

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Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work.
skad [1K]

5-2x2=-15

Two solutions were found :

                  x = ± √10 = ± 3.1623

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    5-2*x^2-(-15)=0

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (5 -  2x2) -  -15  = 0

Step  2  :

Step  3  :

Pulling out like terms :

3.1     Pull out like factors :

  20 - 2x2  =   -2 • (x2 - 10)

Trying to factor as a Difference of Squares :

3.2      Factoring:  x2 - 10

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 10 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step  3  :

 -2 • (x2 - 10)  = 0

Step  4  :

Equations which are never true :

4.1      Solve :    -2   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.2      Solve  :    x2-10 = 0

Add  10  to both sides of the equation :

                     x2 = 10

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ 10  

The equation has two real solutions  

These solutions are  x = ± √10 = ± 3.1623  

Two solutions were found :

                  x = ± √10 = ± 3.1623

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