Answer:
The correct options are;
1. Definition of supplementary angles
2. m∠1 + m∠2 = m∠1 + m∠3
3. m∠2 = m∠3
4. Definition of Congruent Angles
Step-by-step explanation:
The two column proof is presented as follows;
Statement 
Reason
1. ∠1 and ∠2 are supplementary Given
∠1 and ∠3 are supplementary
2. m∠1 + m∠2 = 180° Definition of supplementary angles
m∠1 + m∠3 = 180°
3. m∠1 + m∠2 = m∠1 + m∠3 Transitive Property
4. m∠2 = m∠3 Subtraction Property of Equality
5. ∠2 ≅ ∠3 Definition of Congruent Angles
Given that angles ∠1 and ∠2 are supplementary angles and angles ∠1 and ∠3 are are also supplementary angles, then the sums of m∠1 + m∠2 and m∠1 + m∠3 are equal, therefore, ∠2 and ∠3 have equal quantitative value and therefore ∠2 = ∠3 and by definition, ∠2 ≅ ∠3.
Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question.
The upper-left coordinates on a rectangle are (−5,6) and the upper-right coordinates are (−2,6). The rectangle has a perimeter of 16units. Draw the rectangle on the coordinate plane below.
If the coordinates of the top of the triangle (breadth) is (−5,6) and (−2,6), we can calculate the breadth of the rectangle by taking the difference between the two points using the formula:
D = √(y₂-y₁)²+(x₂-x₁)²
Given x₁ = -5, y₁= 6, x₂ = -2 and y₂ = 6
D = √(6-6)²+(-2-(-5))²
D = √0²+3²
D = √9
D = 3 units
Breadth = 3 units
Given the Perimeter to be 16 units and the formula for calculating the perimeter of rectangle t be P = 2(L+B), we can get the length of the rectangle.
16 = 2(3+L)
16 = 6+2L
16-6 = 2L
2L = 10
L = 10/2
L = 5 units.
<em>Hence the length of the rectangle is 5 units and the breadth is 3 units. Find the diagram in the attachment.</em>
Answer:
-5.238- 
or
Since the exponent of the scientific notation is positive, move the decimal point 6 places to the right.
1620000
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Hope this helps :)
Answer:
37. {-1, -1}.
Step-by-step explanation:
I'll solve the first one . The other can be solved in a similar way. We can use the method of elimination.
x1 - x2 = 0
3x1 - 2x2 = -1
We can multiply the first equation by -2. We then have an equation containing + 2x2 so when we add this to the second equation the 2x2 will be eliminated
So the first equation becomes:
-2x1 + 2x2 = 0 Bring down the second equation:
3x1 - 2x2 = -1 Now adding, we get:
x1 + 0 = -1
so x1 = -1.
Now we substitute this value of x1 in the original first equation:
-1 - x2 = 0
-1 = x2
x2 = -1.
So the solution set is {-1, -1}.
If there are more than 2 equations you can use a combination of substitutions and eliminations.
