Answer:
3.5 miles
Step-by-step explanation:
Lydia:
3 gallons of gas = 114 miles
We want to know how many miles a friend can travel on one gallon of gas, so we divide both sides by 3
1 gallon of gas = 114/3 miles = 38 miles
Lucy:
One point is
10x corresponds to 415y
10 gallons = 415 miles
divide both sides by 10 to get one gallon on a side
1 gallon = 41.5 miles
Lydia:
38 miles = 1 gallon
Lucy:
41.5 miles = 1 gallon
For 1 gallon, the difference is 3.5 miles, with Lydia having 3.5 miles less than Lucy.
OK, this written in numbers is
But, fractions can not divide. So we need to multiply one by the reciprocal of the other. The reciprocal of a fraction is itself flipped upside down. For example, the reciprocal of 1/2 would be 2/1.
So, we will multiply 3/2 by 4/1. We know how to do this, it is simply 3/2*4=12/2=6.
So, the answer is n = 6. That would be answer c, because 6 is between 5 and 7.
Length=x
width=y
Perimeter of a rectangle=2(length)+2(width)
Therefore:
2x+2y=200
We simplify the equation dividend both sides of this equation by 2:
x+y=100
Then:
y=100-x
Area of a rectangle: length x width
We have the next inequation:
x(100-x)<900
100x-x²<900
x²-100x+900<0
We solve this inequation
1) we solve this equation:
x²-100x+900=0
x=[100⁺₋√(10000-3600)]/2=(100⁺₋80)/2
We have two solutions in this equation:
x₁=90
x₂=10
2)With these values, we make intervals:
(-∞,10)
(10,90)
(90,∞)
3)With these intervals, we check it out if the inequation works:
(-∞,10); for example; if x=0 ⇒ 0²-100(0)+900=100>0, this interval don´t work.
(10,90);f.e: if x=11; ⇒ 11²-100(11)+900=-79<0, this interval works.
(90,∞); fe; if x=91 ⇒91²-(100)91+900=81>0; this interval don´t work.
answer: the possible lengths would be the values inside of this interval:
(10,90) ft.
Answer:
EF = ~3.8
Step-by-step explanation:
Apply the sine theorem:
EF/sinD = DE/sinF
=> EF = DE*(sinD/sinF)
= 3*(sin75/sin50)
=3.78 = ~3.8
Hope this helps!
Roger speed 1/6 mile/min
Jeff speed 1/4 mile/min
Set Jeff catch Roger at x， time t
X= 1/6*t
X=1/4*（t-1）
=> 1/6*t=1/4(t-1）
4t=6t-6
t=3
X=1/2
