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:
Step-by-step explanation:
2 colours were taken
Answer:
$2.69
Step-by-step explanation:
The original prices of the books are $2.50, $4.95, and $6.00.
You want to buy three books that are on sale at 20% off (or 0.2 as decimal).
In total, you'll save:
Uce distributive property:
Answer:
The hummingbird beats its wings 86 400 times in one hour.
Step-by-step explanation:
There are 60 minutes in an hour. There are 60 seconds in a minute.
1h = 60m
= 60 × 60s
= 3600s
1s = 24 times
3600s = 24 × 3600
= 86 400 times
Answer:
20
Step-by-step explanation:
The first equation is 50 - 2x (because you start with $50 and subtract 2 for each 30 day period)
The second equation is 40-1.5x
Set them equal to each other: 50 - 2x = 40 - 1.5x
Solve for x:
50 - 2x = 40 - 1.5 x
+2x +2x
-----------------------
50 = 40 + 0.5 x
-40 -40
-------------------
10 = 0.5 x
20 = x
So there will be 20 30-day periods until the cards will be equal in value.
Check: After 20 periods, 50 - 2(20) = $10 left
40 - 1.5(20) = also $10 left
