Find the product of the solutions of this equation 2x^2+26x+156=0

The length of a rectangular flower bed is 2ft longer than the width. If the area is 6ft, then what are the exact length and widt

Marizza181 [45]

Answer:

Exact dimensions:

$width=-1+\sqrt{7}$

$length=-1+\sqrt{7}+2$

$length=1+\sqrt{7}$

Approximate dimensions:

$width=1.64575ft$

$length=1.64575+2$

$length=3.64575ft$

Step-by-step explanation:

Let's assume width of rectangle is w ft

The length of a rectangular flower bed is 2ft longer than the width

so,

length =w+2

$L=w+2$

now, we can find area

$A=L\times W$

now, we can plug it

$A=(w+2)\times w$

$A=w^2+2w$

we are given area =6

so, we can set it equal

and then we can solve for w

$w^2+2w=6$

$w^2+2w-6=0$

we can use quadratic formula

$ax^2+bx+c=0$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

now, we can compare and find a,b and c

a=1 , b=2 , c=-6

$w=\frac{-2\pm \sqrt{2^2-4\cdot \:1\left(-6\right)}}{2\cdot \:1}$

$w=-1+\sqrt{7},\:w=-1-\sqrt{7}$

we know that dimension can never be negative

so, we will only consider positive value

Exact dimensions:

$width=-1+\sqrt{7}$

$length=-1+\sqrt{7}+2$

$length=1+\sqrt{7}$

Approximate dimensions:

$width=1.64575ft$

$length=1.64575+2$

$length=3.64575ft$

7 0

3 years ago

Could someplease explain the whole problem? For the first part my the answer I got was x= .618, -.618, and <img src="https://tex

algol13

9514 1404 393

Answer:

a) x = (√5 -1)/2 ≈ 0.618034

b) 1/x = (√5 +1)/2 ≈ 1.618034

Step-by-step explanation:

<u>Given</u>:

x/(1 -x) = 1/x

<u>Find</u>:

Exactly, and as a decimal approximation, ...

a) x, using the quadratic formula

b) 1/x

<u>Solution</u>:

a) We can multiply the given equation by x(1 -x) to obtain ...

x² = 1 -x

x² +x -1 = 0 . . . . . . add x-1

The coefficients for use in the quadratic formula are a=1, b=1, c=-1. The solution using the quadratic formula is ...

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-1\pm\sqrt{1^2-4\cdot1\cdot(-1)}}{2\cdot1}=\dfrac{-1\pm\sqrt{5}}{2}$

We are only interested in the positive solution, which is ...

$\boxed{x=\dfrac{\sqrt{5}-1}{2}\approx0.618034}$

__

b) The quadratic we developed in the first part can be rearranged like this:

x² +x = 1 . . . . . . add 1 to both sides

x(x +1) = 1 . . . . . factor out x

x +1 = 1/x . . . . . .divide by x

Then to find the value of 1/x, we simply need to add 1 to the value of x we have:

$\dfrac{1}{x}=\dfrac{\sqrt{5}-1}{2}+1=\dfrac{\sqrt{5}-1}{2}+\dfrac{2}{2}=\dfrac{\sqrt{5}-1+2}{2}\\\\\boxed{\dfrac{1}{x}=\dfrac{\sqrt{5}+1}{2}\approx1.618034}$

5 0

2 years ago

Plz help due today first to anser will get brainly dont steel my points plz and thx

Lina20 [59]

Answer: At the end of the year, Lorenzo will have $406

Step-by-step explanation:

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3 years ago

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PolarNik [594]

Answer:

no

Step-by-step explanation:

ask a teacher so people might lie abt the answer

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2 years ago

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Is the following true? Why or why not? 2x^3 = (2x^3)

Olin [163]

<span>2x^3 = (2x^3)
Yes it's true
Value won't change.</span>

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3 years ago

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