Answer:
65 square units
Step-by-step explanation:
Assuming point O refers to the origin, the segment OA has slope ...
m = Δy/Δx = 5/1 = 5
Then the slope of the perpendicular line AP will be the negative reciprocal of this, -1/5.
The x-intercept of the line through (1, 5) with slope -1/5 can be found by setting y=0 in the point-slope equation for that line:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
0 -5 = (-1/5)(x -1)
25 = x -1 . . . . . . . multiply by -5
x = 26 . . . . . . . add 1
This means ΔOAP has a base length (OP) of 26 units and an altitude of 5 units. Its area is given by the formula ...
A = 1/2bh
A = 1/2(26)(5) = 65 . . . . square units
Triangle OAP has an area of 65 square units.
Answer: -21 + -18t
Step-by-step explanation:
-3(7+6t)
-3 x 7= -21
-3 x 6t= 18t
Let's begin by putting together some equations:
Seth has charges $39 and then $13 per hour. Since "hour" is our variable, let's write that as $13h where h = the number of hours.
Seth = 39 + 13h, $39 plus $13 times the number of hours
Malcolm charges $55 and then $11 per hour. So:
Malcolm = 55 + 11h, $55 plus $11 times the number of hours
Our goal is to find out how many hours both have to work before they charge the same amount. So let's set our Seth and Malcolm equations equal to one another.
39 + 13h = 55 + 11h, because we want to solve for h to see the number of hours.
First let's subtract 39 from each side:
(39 + 13h) - 39 = (55 + 11h) - 39
13h = 16 + 11h
Now let's subtract 11h from each side:
(13h) - 11h = (16 + 11h) - 11h
2h = 16
Simplify and solve for h by dividing each side by two:
(2h)/2 = (16)/2
h = 8
So Malcolm and Seth would have to work for 8 hours before both earn the same amount. After 8 hours, Seth would earn more than Malcolm. Before 8 hours, Malcolm would earn more than Seth.
Hello!
The sum of the intern angles of a triangle is 180°. If an angle is obtuse (bigger than 90°), the sum of the others must be less than 90 degrees. Letter a).
Hugs!
