Answer:
s = 71 mph, and s+9 = f = 80 mph
Step-by-step explanation:
The distances the two busses travel add up to 604 mi.
Letting f be the faster speed and s the slower. Then f = s + 9 (mph).
Then (s + 9)(mph)(4 hr) + (s)(mph)(4 hr) = 604 mi. Solve this for s:
4s + 36 + 4s = 604 mi, or 8s = 568. Finally, s = 71 mph, and s+9 = f = 80 mph.
Answer:
1/2 a bag
Step-by-step explanation:
1/2 a piece is smaller than 1/2 a bag because the bag is bigger
Answer:
3pi/4 and -pi/4
Step-by-step explanation:
We can simplify -6/6 to -1.
Therefore, this function can be simplified to arctan(-1).
Recall that the meaning of arctan is to find a value that will get the value inside the parenthesis when taken the tangent of it. In other words, tan(x) = -1.
Recall that tan(x) = sin(x)/cos(x). Now recall that sin(pi/4) and cos(pi/4) are both sqrt(2)/2, meaning that tan(pi/4) is 1. To make it -1, we can either make sin(x) -1 while keeping cos(x) 1, or the other way around.
If x is -pi/4, cos(x) will still be 1, but sin(x) will be -1, so tan(-pi/4) will be -1.
If x is 3pi/4, cos(x) will be -1, but sin(x) will still be 1, so tan(3pi/4) will be -1.
Side note: there are still infinite more answers. You can attain them by adding or subtracting 2pi as many times as you want from 3pi/4 or -pi/4 and still get an arctan of -1.
Answer:
Step-by-step explanation:
price of 1 pen= $ 2
price of 1 pencil= $1
total money spent= $12
Let the number of pen be a and number of pencil be b.
2 a + b = 12 ----------------Equation 1
We have, she bought 3 more pens than pencils
a - b = 3 ------------------ Equation 2
Equation 1 +Equation 2,
2 a + b + a - b = 12 + 3
3a = 15
a = 5
Substituting in equation
5 - b = 3
b = 2
Number pencils Ava bought = 2
Answer:
x = -6
Step-by-step explanation:
