Given that the hall is rectangular in shape, then the shortest path that Amy must travel to reach Alice would be through the hall's diagonal.
Applying the Pythagorean theorem, with the length and width as the legs and the diagonal as the hypotenuse of the right triangle. Thus,
diagonal = √ ( 100² + 60²) = √13 600 ≈ 116.62 ft
The shortest distance, rounded off to the nearest foot, is 117 ft<span>. </span>
What you said doesn't even make sense.
I'll assume you said f(x) = -5x^2 + 4.
This is an even function.
f(-x) = f(x)
Answer:
Determine whether lines are parallel or perpendicular given their equations; Find equations of . We can begin by using point-slope form of an equation for a line. No. For two perpendicular linear functions, the product of their slopes is –1.
Step-by-step explanation:
Consider the two functions as
<span>y1(x) =3x^2 - 5x,
y2(x) = 2x^2 - x - c
The higher the value of c, father apart the two equations will be.
They will touch when the difference, i.e. y1(x)-y2(x)=x^2-4*x+c has a discriminant of 0.
This happens when D=((-4)^2-4c)=0, or when c=4.
(a)
So when c=4, the two equations will barely touch, giving a single solution, or coincident roots.
(b)
when c is greater than 4, the two curves are farther apart, thus there will be no (real) solution.
(c)
when c<4, then the two curves will cross at more than one location, giving two distinct solutions.
It will be more obvious if you plot the two curves in a graphics calculator using c=3,4, and 5.
</span>
Answer:
60%
Step-by-step explanation:
You can solve this problem by setting up a system of equations.
Let's say that the number of tickets bought by students in the first year is x, and the number bought by continuing students is y. From there, you can set it up like this:
0.4x+0.2y=160
x+y=500
Now, you can multiply the first equation by 5 on both sides to get:
2x+y=800
Subtracting the second equation from the first equation now yields:
x=300
y=200
Since 300 of the 500 tickets bought were from the first year students, and 300/500 is 0.6, 60% of the students who bought the ticket were first year students. Hope this helps!
