1.x^2 +6x - 4 = 6x
X^2 + 6x -4 - 6x = 0
X^2 - 4 = 0
By difference of two squares :
X^2 - 4 = 0 can be written as (x-2) (x+2) = 0
(X-2)=0 therefore x= 2
(X+2)=0 therefore x= -2
2. X^2 - 8x = -6x
X^2 -8x + 6x = 0
X^2 - 2x = 0
X(X-2) = 0
X= 0, X= 2
Answer:
x = 70 degrees, red arc= 110 degrees
Step-by-step explanation:
x and 2x-30 added together is 180 degrees.
We can make an equation to find x,
x + (2x - 30) = 180
3x - 30 = 180
Add 30 to both sides to isolate x
3x = 210
By dividing both sides by 3, we get x = 70
Now we know the red arc is 2x - 30. We can plug x in because we know the value now.
2(70) - 30
140 - 30
Red Arc = 110 degrees
A reflection over the line y=x implies exchanging the x and y coordinates of a point. For example if you take a generic point (a,b) then its reflection over y=x is (b,a). Our point is (-1,3) so its reflection over y=x is the point (3,-1).
Then we have to translate it two units left. Translating a point left means that we are moving towards negative x values so we need to substract 2 from the x coordinate:
Finally we have to translate it 1 unit up towards positive y values so we have to add 1 to its y coordinate:
And these are the final coordinates. In the following picture you have the points you get after each step (from A to D) with the y=x line in blue:
Answer:
x = 10
Step-by-step explanation:
Given:
Arc LM = 13x - 10
Arc MN = 7x - 10
Required:
Solve for x
Solution:
Recall: half a circle = 180°
Therefore,
Arc LM + Arc MN = 180°
13x - 10 + 7x - 10 = 180
Add like terms
20x - 20 = 180
20x - 20 + 20 = 180 + 20
20x = 200
20x/20 = 200/20
x = 10
