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3 years ago

Factor the polynomial completely

Mathematics

1 answer:

aliina [53]3 years ago

5 0

We have $2x^2-8$ .

First let us factor the 2 to obtain,

$2(x^2-4)$

We can now see clearly that the expression inside the parentheses is a difference of two squares.

We now write the 4 as 2². So that we obtain the expression,

$2(x^2-2^2)$

Recall that

$a^2-b^2=(a+b)(a-b)$

Hence our expression becomes,

$2(x+2)(x-2)$

Therefore, when factored completely,

$2x^2-8=2(x+2)(x-2)$

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How do I find the area?

nikitadnepr [17]

Answer:

The simplest (and most commonly used) area calculations are for squares and rectangles. To find the area of a rectangle, multiply its height by its width. For a square, you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.

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3 years ago

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The length of a rectangle is 5 in. more than 3 times its width. The quadratic function f(x) = x(3x + 5) represents the area of t

saveliy_v [14]

F(x)=x(3x+5)
or
f(x)=3x²+5x
Here the domain in general is: -∞<x<∞
But the length of the rectangle cannot be negative, therefore the domain is all real numbers greater than zero.

Option D is correct.

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3 years ago

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A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of

belka [17]

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==> t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348

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3 years ago

(100 Points)last one i promise lol

erik [133]

Answer:

40.35

Step-by-step explanation:

First find the discount

97 * 60%

97 *.6 = 58.2

Subtract the discount to find the new price

97-58.20 =38.80

Next find the tax

38.80 * 4%

38.80 * .04

1.55

We add the tax to the sales price

38.8+1.55

40.35

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3 years ago

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Help me please please

Anna007 [38]

Answer:

8/5 or 1.6

Step-by-step explanation:

Rise over run.

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3 years ago