EXPLANATION:
1.We must locate the points that the exercise gives us in the Cartesian plane.
2.The figure that it gives us must be moved 3 units to the left and then 2 units up.
3.To correctly translate a figure, we must add the units that the exercise indicates and towards the correct direction, if it tells us that to the left is towards the negative axis, then each of the points given in the exercise we will transfer 3 units towards the left and then add each of the points two units up, then we see that the triangle takes new coordinates for the points.
4.The new coordinates for point E are (3,6)
The supplementary angle would be 180 degrees, and the other angle would be 92.2 degrees
Step-by-step explanation:
We can write this word problem as two variables. Let us assume that:
x = Natalie's age
y = Fred's age
The first part of the word problem is that "If you add Natalie's age and Fred's age, the result is 39." Therefore:
Natalie's age + Fred's age = 39
x + y = 39
This will be our first equation. The second equation can be derived from the statement that "If you add Fred's age to 4 times Natalie's age, the result is 78." Therefore:
(4 times Natalie's age) + Fred's age = 78
4x + y = 78
We can now form a system of equations and solve for both x and y:
The simplest way to solve would be using the Substitution method, as seen here:
x + y = 39
y = 39 - x
4x + y = 78
4x + (39 - x) = 78
3x + 39 = 78
3x = 39
x = 13
x + y = 39
13 + y = 39
y = 26
Remember that x = Natalie's age and y = Fred's age. Therefore, Natalie's age is 13 years old and Fred's age is 26 years old.
8953.7 is the answer to this
