Answer:
see explanation
Step-by-step explanation:
3x and 144 are adjacent angles on a straight line and sum to 180°
3x + 144 = 180 ( subtract 144 from both sides )
3x = 36 ← value of 3x
divide both sides by 3
x = 12
and
2y - 5 and 95 are vertically opposite angles and are congruent, so
2y - 5 = 95 ← value of 2y - 5
add 5 to both sides
2y = 100 ( divide both sides by 2 )
y = 50
Then
x + y = 12 + 50 = 62
Answer:
63.59
Step-by-step explanation:
If the perimeter is 32.13, that means it is equal to
2r + 2πr/4 = 32.13
Solving this for r we get 9
Now, we can find the area, which is 3.14*r^2 / 4. Assuming pi to be 3.14 again, we get 63.585. Rounding this to the nearest hundredth, we get 63.59
The minimum distance will be along a perpendicular line to the river that passes through the point (7,5)
4x+3y=12
3y=-4x+12
y=-4x/3+12/3
So a line perpendicular to the bank will be:
y=3x/4+b, and we need it to pass through (7,5) so
5=3(7)/4+b
5=21/4+b
20/4-21/4=b
-1/4=b so the perpendicular line is:
y=3x/4-1/4
So now we want to know the point where this perpendicular line meets with the river bank. When it does y=y so we can say:
(3x-1)/4=(-4x+12)/3 cross multiply
3(3x-1)=4(-4x+12)
9x-3=-16x+48
25x=51
x=51/25
x=2.04
y=(3x-1)/4
y=(3*2.04-1)/4
y=1.28
So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...
d^2=(x2-x1)^2+(y2-y1)^2
d^2=(7-2.04)^2+(5-1.28)^2
d^2=38.44
d=√38.44
d=6.2 units
Since he can run at 10 uph...
t=d/v
t=6.2/10
t=0.62 hours (37 min 12 sec)
So it will take him 0.62 hours or 37 minutes and 12 seconds for him to reach the river.
Answer:
-12
Step-by-step explanation:
<u>Step 1: Substitute</u>
ab -> -4 for a and 3 for b
(-4) * (3)
<em>-12</em>
Answer: -12
Get unknowns on one side and know on other side.
Divide both sides by -2
X= -7
