Answer:
Step-by-step explanation:
The identical arc symbols on the two angles indicates the angles are congruent. Also, these are alternate interior angles where a transversal crosses lines marked as parallel, so they are congruent:
∠A = ∠B
8x +78° = 2x +114° . . . . . substitute the given expressions
6x = 36° . . . . . . . . . . . . . subtract 2x+78° from both sides
x = 6° . . . . . . divide by 6
∠B = 2x +114° = 2·6° +114° . . . . . put the value of x into the expression
∠B = 126°
y = 3 is the line of reflection
Under a reflection in a line, corresponding points of the original and it's image should be equidistant from the line of reflection
y = 3 is the horizontal line passing through all the points with a y-coordinate of 3
A is 1 unit above and A' is 1 unit below the line
B is 3 units above and B' is 3 units below
C is 1 unit below and C' is 1 unit above
D is 1 unit below and D' is 1 unit above
The vertices of the figure and the image are all equidistant from y = 3
The answer is: t = 1
You need to separate t from everything to figure out what it is.
Step 1: Subtract 9 from both sides, so we get 7 - 2t = 5t
Step 2: Add 2t to both sides, so we get 7 = 7t.
Step 3: Divide by 7, meaning t = 1.
Next you should check your work. If we plug 1 in for t, we get 14 = 14, so the answer is correct.
Hope this helps!
11. YES. Because each x-value is only used once (no duplicate x-coordinates)
12. range is the y-values. the lowest it goes is -2 (with an open dot), then it goes to +2 (with an open dot). then there is a separate line where y = 4.
Answer: (-2, 2) U [4, 4]
13. f(-1): when x = -1, y = ??? <em>(do not count the open dot!)</em>
Answer: 1
14. f(3): when x = 3, y = ??? <em>(do not count the open dot!)</em>
Answer: 4
For this case we have that by definition of multiplication of powers of the same base, the same base is placed and the exponents are added:
So, we can rewrite the given expression as:
So, if 
:
Equality is met!
Answer:
