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Andru [333]
3 years ago
10

the polynomial function i (t)=-0.1t^2+1.6t represents the yearly income (or loss) form a real estate investment where t is time

in years. after what year does income begin to decline
Mathematics
1 answer:
Natali [406]3 years ago
6 0
Factor out 0.1t (t + 16)
t + 16 = 0
Subtract 16 from both sides
t = -16
After 16 years the income begins to decline
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Answer:

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Let the equation if the line be y = mx + c

since the line is parallel to y = -2x - 8, their gradients/slope must be the same (aka m = -2)

sub (-4, 3):

3 = -2(-4) + c

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therefore, the equation of the line is y = -2x - 5

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Find the equation of the line through the point (–2, –2) that is perpendicular to the line y = 2x – 1.
lawyer [7]

Hi student, let me help you out!

.....................................................................................................

---------------------------------------------

<h3>Part 1.</h3>

Perpendicular lines have slopes that are <u>opposite inverses </u>of each other.

The opposite inverse of 2 is \mathrm{-\cfrac{1}{2}}.

Now let's stick in this number into the equation \mathrm{y=mx+b}:

\mathrm{y=-\cfrac{1}{2}x+b}.  Let's carry out several operations to determine the y intercept.

First, let's stick in -2 for x and y (Do you remember that the line passes through (-2,-2)? We're given that piece of information.)

\mathrm{-2=-\cfrac{1}{2}\times(-2)+b}.

You are probably thinking, "Why did you do that and just complicate things?" Wait for it! ^-^

Upon simplifying this, we obtain: \mathrm{-2=1+b}. See, it's nice and smooth now.

One last operation remains. We need to subtract 1 from both sides: \mathrm{-3=b}.

∴, the equation of the line is: \mathrm{\underline{\boxed{y=-\cfrac{1}{2}-3}}}

Hope this helped you out, ask in comments if any queries arise.

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Step-by-step explanation:

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