Answer:
x = 24 , y = 19
Step-by-step explanation:
(2x + 13) and 47 + 3x are same- side interior angles and sum to 180° , so
2x + 13 + 47 + 3x = 180 , that is
5x + 60 = 180 ( subtract 60 from both sides )
5x = 120 ( divide both sides by 5 )
x = 24
Then 3x = 3 × 24 = 72
5y - 23 and 3x are corresponding angles and are congruent , then
5y - 23 = 72 ( add 23 to both sides )
5y = 95 ( divide both sides by 5 )
y = 19
Answer:
(1,1)
Step-by-step explanation:
The choices are not visible, however are unnecessary to solve this problem.
Given y = 3x - 2 and y = -2x + 3
[Set them equal to each other]
3x - 2 = -2x + 3
[Find x]
3x + 2x - 2 = 3
3x + 2x = 5
5x = 5
x = 1
[Plug x = 1 to both equations to check and find y]
y = 3x - 2
y = 3(1) - 2 = 3 - 2 = 1
y = -2x + 3
y = -2(1) + 3 = -2 + 3 = 1
Both are equal to y = 1 when x = 1
The point is then: (1,1)
To take out terms outside the radical we need to divide the power of the term by the index of the radical; the quotient will be the power of the term outside the radical, and the remainder will be the power of the term inside the radical.
First, lets factor 8:
Now we can divide the power of the term, 3, by the index of the radical 2:

= 1 with a remainder of 1
Next, lets do the same for our second term

:

= 3 with a remainder of 1
Again, lets do the same for our third term

:

with no remainder, so this term will come out completely.
Finally, lets take our terms out of the radical:

We can conclude that the correct answer is the third one.