Answer:
P = 32
x = 35
Step-by-step explanation:
For the first diagram,
The two angles given are corresponding angles. Corresponding angles are equal;
So;
the first angle is a right angle triangle;
90 = 3P - 6
3P = 90 + 6
3P = 96
P = 32
For the second diagram;
The sum of those two angles is 180°
(x + 75) + 2x = 180
x + 2x + 75 = 180
3x + 75 = 180
3x = 180 - 75
3x = 105
x = 35
(3.8×10^8)×(6.9×10^5)= 2.622e^14
Question 1
Let the scale factor be k.
Then, we have the mapping
This implies that:
We equate any corresponding component find the value of the scale factor k.
6k=2
Hence the scale factor is 
Question 2:
The midpoint of any two points can be calculated using the formula;
We want to find the midpoint of (-8, 5) and (2, -2).
The midpoint is:
Hint : The product of the slopes of two lines perpendicular to each other is - 1 .
______________________________
In slope-intercept ( y = ax + b ) from of the linear equations the coefficient of x is the slope of the line.
Thus :
Slope of line a = - 14
______________________________
Suppose that the slope of line b is x according to the Hint we have :
- 14 × x = - 1
negatives simplify
14x = 1
Divide both side by 14
14x ÷ 14 = 1 ÷ 14
x = 1/14
So the slope of line b is 1/14
_____________________________
Now let's find the equation of line b by point-slope formula using the point question have us ( 2 , 6 ) :
y - y( given point ) = Slope × ( x - x ( g p ) )
y - 6 = 1/14 × ( x - 2 )
y - 6 = 1/14 x - 2/14
y - 6 = 1/14 x - 1/7
Add both sides 6
y - 6 + 6 = 1/14 x - 1/7 + 6
y = 1/14 x - 1/7 + 42/7
y = 1/14 x + 41/7
And we're done ...
Answer:
x=94º
Step-by-step explanation:
180=x+5+x-13
180=2x-8
180+8=2x
188=2x
94=x
