The Pythagorean theorem states that a^2 + b^2 = c^2, where a and b are sides not opposite to the right angle, shown as a square. C represents the hypotenuse, or side opposite of the right angle
We see that a = 14 (it can also be b; both can be plugged in as both are adjacent and not opposite of the right angle)
c = 19; hypotenuse is opposite of right angle
14^2 + b^2 = 19^2
196 + b^2 = 361
b^2 = 361 - 196
b^2 = 165
b = square root of 165
b = 12.845
x = 12.845
Answer:
B
it goes down by $16,000 in that time frame
So,
1. Type I profits $20
2. Type II profits $30
3. Type III profits $40
4. I/day < 100
5. Type I needs 5 hrs.
6. Type II needs 10 hrs.
7. Type III needs 15 hrs.
8. Total hrs. available: 2000 hrs.
Every +5 hrs. spent yields an extra $10.
If we use 500 hrs. to make 100 Type I stereos, we will profit $2000.
If we use 500 hrs. to make 50 Type II stereos, we will profit $1500.
If we use 495 hrs. to make 33 Type III stereos, we will profit $1320.
We should use the first 500 hrs. to make Type I stereos.
We should use the last 1500 hrs. to make Type II stereos.
$2000 + $4500 = x
$6500 = x
There must be 100 Type I stereos made along with 150 Type II stereos made.
Sung drove to the mountains
s₁=speed when Sung drove to the mountains.
t=10 hour.
d=distance.
s₁=d/t
s₁=d/10 hour ⇒s₁=d/10 (1)
Sung drove home:
s₂=speed when Sung drove home.
t=7 hour
s₂=s₁+18 miles/hour
s₂=d/7 hour ⇒s₁+18 miles/h=d/7 hour ⇒ s₁+18=d/7 (2)
Whit the equations (1) and (2) make a system of equations:
s₁=d/10
s₁+18=d/7
we can solve this system of equations by substitution method.
d/10+18=d/7
least common multiple=70
7d+1260=10d
7d-10d=-1260
-3d=-1260
d=-1260/-3=420
Answer: distance= 420 miles.
