Answer:
The Proof with Figure, Statement and Reasons is given below.
Step-by-step explanation:
Given:
∠DAF ≅ ∠EBF,
DF ≅ FE
Prove:
Δ ADF ≅ Δ BFE
Proof:
Statements Reasons
a. ∠DAF ≅ ∠EBF ...........................Given
<u>48. ∠DFA ≅ ∠EFB </u>..........................Vertical Angles are congruent
DF ≅ FE ..........................<u>.49. Given</u>
50.<u> Δ ADF ≅ Δ BFE </u>.......................<u>..By Angle-Angle-Side test</u>
Answer:
x=133 y=-25
Step-by-step explanation:
I'll do both ways for you. So let's start with Substitution:
With the sub method, you have to set both equations equal to each other by setting them equal to the same variable. Since there is no coefficient in front of both x's in both equations, that variable will be easiest to solve for.
x + 2y = 83 & x + 5y = 8
Solve for x.
x = 83 - 2y & x = 8 - 5y
Once you have solved for x, set each equation equal to one another and solve for y now.
83 - 2y = 8 - 5y
Isolate all variables to one side:
83 = 8 - 3y
Now subtract the 8 to fully isolate the y variable:
75 = -3y
Divide by -3:
-25 = y Now that you have your first variable, plug it into one of the original equations and solve for x.
x + 2(-25) = 83
x - 50 = 83
x = 133
Now for the Elimination method. For this method you need to get rid of a variable by either subtracting/adding each equation together. Again, since you can subtract and x from both equations, you will be left with only the y variable to solve:
Put each equation on top of one another and subtract:
x + 2y = 83
- (x + 5y = 8)
The x's will cancel out:
(x - x) + (2y - 5y) = (83 - 8)
Simplify:
-3y = 75
Solve for y
y = -25
Then, plug y = -25 into one of the original equations:
x + 5(-25) = 8
Solve for x:
x - 125 = 8
x = 133
Hope this helps!
The numbering system we commonly use is called the decimal numbering system because it uses <u> 10 </u> symbols to represent all possible numbers.
A way of writing numbers is known as a number system.
There are the following number systems:
- Decimal number system: "Deci" meaning 10, implies that the number system consists of 10 digits or symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
- Binary number system: "Bi" meaning 2, implies that the number system consists of 2digits or symbols, namely 0, and 1.
- Octal number system: "Oct" meaning 8, implies that the number system consists of 8 digits or symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, and 8.
- Hexa-Decimal number system: "Hexa-Deci" meaning 16, implies that the number system consists of 16 symbols, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F.
Hence, we can say that the numbering system we commonly use is called the decimal numbering system because it uses <u> 10 </u> symbols to represent all possible numbers.
Learn more about number systems at
brainly.com/question/14567654
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