DE+EF=DF
8x+2=x+9
8x-x=9-2
7x=7
x=7/7
x=1
DF=x+9
put the value of x
DF=1+9
DF=10
When a shape is rotated, it must be rotated over a line.
<em>The square must be reflected over line </em>
<em>, for it to be mapped onto itself.</em>
<em />
<u>The points are given as:</u>
To map the square onto itself, it must be reflected over its diagonal
The diagonals of the square are: AC and BD
<u>Using AC, we have:</u>
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Start by calculating the slope (m)
So, we have:
The equation is then calculated as:
This gives:
Rewrite as:
So, the square must be reflected over line , for it to be mapped onto itself.
See attachment for square ABCD and its line of reflection.
Read more about reflections at:
brainly.com/question/1878272
Answer:
a = 66⁰
b = 33⁰
Step-by-step explanation:
Given;
∠ABC = 114⁰
To calculate a⁰;
a + 114 = 180⁰ (opposite angles of a quadrilateral are supplementary)
a = 180 - 114
a = 66⁰
To calculate b⁰;
Line AB = Line BC, thus, ∠BAC = ∠BCA
∠BAC = b, then ∠BCA = b
b + b + 114 = 180 (sum of angles in a triangle)
2b = 180 - 114
2b = 66
b = 66/2
b = 33⁰
Well first the initial fee would be the x, which is what we have to solve for. Each hour of work is $6, and she does four hours of work. This is equal to $32. The equation would look as follows...
x + 6(4) = 32
Once you have the equation start solving. Use the Pemdas method. First you have to multiply, so now the equation looks as follows...
x + 24 = 32
Now you have to get the x by itself. You do that by subtracting 24 from both sides, because what you do to one side, you do to the other. That will get you to the answer of...
x = 8
In conclusion, Carolina has an initial fee of $8.
Hope this helped.
Hello,
When we have a quadrilateral inscribed in a circle, the opposite angles add up to 180 degrees (supplementary).
Therefore, we can write and solve the following equation first with angles B and D.
3x + 9 + 2x - 4 = 180
5x + 5 = 180
5x =175
x = 35
Then, sub 35 in the expression for angle A and you will get:
2(35) + 3
70 + 3
73
Angle A is 73, that would make angle C equal to 107 degrees, because 180 - 73 = 107.
Good luck,
MrEQ
