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4 years ago

If the farmer has 116 feet of fencing, what are the dimensions of the region with the largest area?

Mathematics

2 answers:

Kruka [31]4 years ago

8 0

Answer:29 ft by 58 ft

Step-by-step explanation:

Savatey [412]4 years ago

3 0

Yes ye yuh na Lyin bru u cappin

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If α , β are roots of x2 + 5x + a =0 and 2α + 5β = -1 then α is equal to _____?

ELEN [110]

9514 1404 393

Answer:

-8

Step-by-step explanation:

If α and β are roots of x^2 +5x +a = 0, then we must have ...

(x -α)(x -β) = x^2 +5x +a

x^2 -(α+b)x +αβ = x^2 +5x +a

Then ...

α + β = -5

Together with the other relation between the roots, we have a system of equations in α and β.

Using the above to write an expression for β, we get ...

β = -α -5

Substituting this into the given relation, we have an equation for α:

2α +5(-α -5) = -1

-3α -25 = -1 . . . . . . eliminate parentheses

-24 = 3α . . . . . . . . add 3α +1

-8 = α

The root α is equal to -8.

3 0

4 years ago

It takes four minutes to fill a bathtub if the hot and cold water taps are both on and the stopper is in. It takes six minutes t

bekas [8.4K]

Answer:

12 minutes

Step-by-step explanation:

Since it takes 4 minutes to fill the bathtub with both taps on and stopper is in then for each minute the 2 taps can fill up to a quarter (1/4) of the tub:

Similarly, it takes 6 minutes to drain the tub with both taps off and the stopper is out. This means for each minute the stopper can drain one sixth (1/6) of the tub.

Therefore, when both taps are on and the stopper is out, then for each minutes, the amount of water remaining in the tub is the water flowing in minus the water draining out

$\frac{1}{4} - \frac{1}{6} = \frac{3}{12} - \frac{2}{12} = \frac{1}{12}tub$

So for each minute, one twelveth of the tub is filled, for the tub to be completely filled in, it would take 12 minutes

3 0

3 years ago

Please help if you can

White raven [17]

Answer:

Lets solve it

4x-3 <5

4x<5+3

4x<8

x<8/4

x<2

So yes, two is a solution

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

60/8+X + 60/8-X = 16

Anuta_ua [19.1K]

Answer:

Step-by-step explanation:

$Domain:\\8+x\neq0\ \wedge\ 8-x\neq0\\\boxed{D:x\neq-8\ \wedge\ x\neq8}\\\\\dfrac{60}{8+x}+\dfrac{60}{8-x}=16\\\\\dfrac{60(8-x)}{(8+x)(8-x)}+\dfrac{60(8+x)}{(8+x)(8-x)}=16\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\\dfrac{60(8-x)+60(8+x)}{8^2-x^2}=16\qquad\text{use the distributive property}\\\\\dfrac{(60)(8)+(60)(-x)+(60)(8)+(60)(x)}{64-x^2}=16\\\\\dfrac{480-60x+480+60x}{64-x^2}=16\qquad\text{combine like terms}\\\\\dfrac{(480+480)+(-60x+60x)}{64-x^2}=16\\\\\dfrac{960}{64-x^2}=16$

$\dfrac{960}{64-x^2}=\dfrac{16}{1}\qquad\text{cross multiply}\\\\16(64-x^2)=(960)(1)\qquad\text{use the distributive property}\\\\(16)(64)+(16)(-x^2)=960\\\\1024-16x^2=960\qquad\text{subtract 1024 from both sides}\\\\1024-1024-16x^2=960-1024\\\\-16x^2=-64\qquad\text{divide both sides by (-16)}\\\\\dfrac{-16x^2}{-16}=\dfrac{-64}{-16}\\\\x^2=4\to x=\pm\sqrt4\\\\x=\pm2\in D$

3 0

4 years ago

Estimate the quotient: 1628 ÷ 8 and its NOT 203

nexus9112 [7]

204 i rounded up from 203.5

4 0

3 years ago

Read 2 more answers