D+100+40=180
d=180-100-40=40 (sum of all angles)
e= 100+40= 140 (exterior angle)
180-140=40
C+50+40=180
C=180-50-40= 90 (right angle)
A=50
B=180-90-50= 40
Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
Answer: xp=py
<xpa=<apy
4 right angles are formed
2(xp)=xy
<xpa and <apy are supplements.
Step-by-step explanation:
Answer:
$7.25
Step-by-step explanation:
I'm pretty sure I'm correct. Hope this helps and have a nice day!
Answer:
first option
Step-by-step explanation:
Given
| x + 4 | = 2
The absolute value function always produces a positive value but the expression inside can be positive or negative, thus
x + 4 = 2 ( subtract 4 from both sides )
x = - 2
OR
- (x + 4) = 2, distribute left side
- x - 4 = 2 ( add 4 to both sides )
- x = 6 ( multiply both sides by - 1 )
x = - 6
Thus solutions are x = - 2, x = - 6
These are represented on the graph by solid blue circles at x = - 2, x = - 6
The first option represents the solution
