Answer:
p = 35
Step-by-step explanation:
Complementary angles sum to 90°
Sum the 2 given angles and equate to 90, that is
20 + 2p = 90 ( subtract 20 from both sides )
2p = 70 ( divide both sides by 2 )
p = 35
The first equation, 8x - 9y = - 23
Obtain the equation in slope- intercept form
y = mx + c ( m is the slope and c the y-intercept )
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (
, 3) and (x₂, y₂ ) = (- 4, - 1 )
m =
= (- 4)/-
= 
partial equation is y =
x + c
to find c substitute either of the 2 points into the partial equation
using (- 4, - 1 ), then
- 1 = -
+ c ⇒ c = 
y =
x +
← in slope- intercept form
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
rearrange the slope- intercept equation into this form
multiply through by 9
9y = 8x + 23 ( subtract 9y and 23 from both sides )
8x - 9y = - 23 in standard form
Distribute 6 thru the parenthesis=
198 pie plus 6 pie
Factor out the perfect square=
Pie 3 to the second power times 22 plus 7 pie 6
Calculate the square root =
3 pie 22 plus 7 pie 6
Which equals to 31.2177
Answer:
12.1
Step-by-step explanation:
Triangle:
A = 3 x 9 x 1/2 = 13.5
Large rectangle (center):
A = 9 x 12 = 108
Medium rectangle:
A = 4 x 6 = 24
Small rectangle (bottom):
A = 4 x 2 = 8
Figure:
A = 13.5 + 108 + 24 + 8 = 153.5 square feet
Hope this helps! :)