3 hours Jeremiah has to spend riding his bike
1.1 Factoring: 4x2+9y2+16z2-6xy-12yz-8xz
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -6xy-12yz
Group 2: 16z2-8xz
Group 3: 4x2+9y2
Pull out from each group separately :
Group 1: (x+2z) • (-6y)
Group 2: (x-2z) • (-8z)
Group 3: (4x2+9y2) • (1)
Looking for common sub-expressions :
Group 1: (x+2z) • (-6y)
Group 3: (4x2+9y2) • (1)
Group 2: (x-2z) • (-8z)
Answer:
The bag costs 1500, while the umbrella cost 500
Step-by-step explanation:
Let the cost of the bag be b and the cost of the umbrella be u
Total cost is;
b + u = 2,000 •••••(i)
From the second part of the question;
b = 5u-1000 ••••••(ii)
Substitute ii into i
5u-1000 + u = 2000
6u = 2000 + 1000
6u = 3000
u = 3000/6
u = 500
To get b, substitute the value of u into equation ii
b = 5(500)-1000
b = 2500-1000
b = 1500
If you have never used a unit circle, I recommend making one.
R for the following degrees are
30*= 4((3^1/2)/2)^2
60*= 8(2^1/2)(2^1/2)^2
90*= (8((3^1/2)/2))/4
<span>Call x the distance traveled
V = x / t = 89.5 = x / t => x = 89.5t
Rest time in hours = 22min * 1 h / 60 min = 11/30 h
Total time spent on the trip = t + 11/30
=> Average speed = 77.8 = x / (t + 11/30)=> x = 77.8 (t + 11/30)
=> 89.5t = 77.8 (t + 11/30)
=> 89.5t = 77.8t + 77.8 * 11/30
=> 89.5 – 77.8t = 28.527
=> 11.7 t = 28.527
=> t = 28.527 / 11.7
=> t = 2.44 h => t + 11/30 = 2.81 h
=> x = 89.5t = 89.5 * 2.44 = 218.3 km
Answers: a) 2.81 h; b) 218.3 h
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