25 POINTS PLZ ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!
2 answers:
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Answer:
Johnny will be able to reach the safe zone before the gate is closed.
Step-by-step explanation:
Given that:
Distance of Little Johnny from safe zone = 4000 feet
Time = 3 minutes
Speed = 22 mph
To find:
Will Johnny be able to reach the safe zone ?
Solution:
Johnny can only be safe if he can travel 4000 feet in 3 minutes with the given speed.
Let us try to find out, the distance that he can travel in 3 minutes at speed of 22 mph.
Let us have a look at the formula of distance traveled:
Time = 3 minutes = hrs
Speed = 22 mph
We know that 1 mile = 5280 feet
Therefore 1.1 miles = 5280 1.1 feet = 5808 feet
Distance traveled by Little Johnny is greater than 4000 feet.
Therefore Johnny will be able to reach the safe zone before the gate is closed.
1. Consider the function 
.
It is a linear function, so to draw its graph 2 points are enough:
f(4)=(3/4)*4-2=3-2=1
f(0)=(3-4)*0-2=-2
so 2 points on this line are (0, -2) and (4, 1). Check the picture 1:
2. The problem considers the inequality y>f(x)
a. the slope of the line y=ax+b is the coefficient of x, so a. In our case a=3/4, not -2
b. The graph of any linear inequality is a shaded region, not a line or a shaded line.
c. Either the part below the line, or the part above the line will be shaded since we are talking about an inequality.
Check (4, -3), picture 2, which is clearly below the line.
now here y=-3, and f(4)=(3/4)(4)-2=3-2=1, so in this region y<f(x)=(3/4)x-2
So clearly the region where the inequality holds, so the region to color, is the part above the line.
d. The line itself is not dashed, only if we have an "equal to or smaller than" or "equal to or larger than" inequality.
e. (0, 0) is in the region above the line so YES, it is a solution.
We can also check it like this: y=0, f(0)=(3/4)0-2=-2 so y>f(0)
f. The y-intercept is always f(0). In this case f(0)=-2
It is a linear function, so to draw its graph 2 points are enough:
f(4)=(3/4)*4-2=3-2=1
f(0)=(3-4)*0-2=-2
so 2 points on this line are (0, -2) and (4, 1). Check the picture 1:
2. The problem considers the inequality y>f(x)
a. the slope of the line y=ax+b is the coefficient of x, so a. In our case a=3/4, not -2
b. The graph of any linear inequality is a shaded region, not a line or a shaded line.
c. Either the part below the line, or the part above the line will be shaded since we are talking about an inequality.
Check (4, -3), picture 2, which is clearly below the line.
now here y=-3, and f(4)=(3/4)(4)-2=3-2=1, so in this region y<f(x)=(3/4)x-2
So clearly the region where the inequality holds, so the region to color, is the part above the line.
d. The line itself is not dashed, only if we have an "equal to or smaller than" or "equal to or larger than" inequality.
e. (0, 0) is in the region above the line so YES, it is a solution.
We can also check it like this: y=0, f(0)=(3/4)0-2=-2 so y>f(0)
f. The y-intercept is always f(0). In this case f(0)=-2