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3 years ago

Simplify (3x+8)(x+1) using a table, the Distributive Property, and the FOIL

1 answer:

7 0

Foil method:
FOIL stands for
first-multiply the first term in each set of parenthesis
outer-multiply the outer term in each of the perenthesis
inner- multiply the inner term in each of the parenthesis
last- multiply the last term in each of the parenthesis
(3x+8)(x+1)
(3x*x)=3x^2
(3x*1)=3x
8*x=8x
8*1=8
thus we shall have:
3x^2+3x+8x+8
=3x^2+11x+8

Distributive property:

(3x+8)(x+1)
3x(x+1)+8(x+1)
3x^2+3x+8x+8
=3x^2+11x+8

Both methods are efficient, it all depends with the users preference

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Select and use the most direct method to solve 2x(x + 1.5) = -1. Describe and justify the methods you used to solve the quadrati

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Step-by-step explanation:

Given that,

A quadratic equation,

2x(x + 1.5) = -1

We need to solve the quadratic equation. Firstly we need to simplify the above equation to form it as $ax^2+bx+c=0$ .

So,

$2x^2+3x=-1\\\\2x^2+3x+1=0$

Here, a = 2, b = 3 and c = 1

The roots of the given equation can be given by :

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

Putting all the values we get :

$x=\dfrac{-b\pm \sqrt{b^2+4ac} }{2a}, \dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\\\\x=\dfrac{-3\pm \sqrt{3^2+4(2)(1)} }{2(2)}, \dfrac{-3\pm \sqrt{3^2-4(2)(1)} }{2(2)}\\\\x=\dfrac{-3+1}{4}, \dfrac{-3-1}{4}\\\\x=-\dfrac{1}{2}, -1$

So, the roots of the given equation is -1/2 and -1.

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3 years ago

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3 years ago

A 50 foot rope weighing a total of 32 lbs extended over a cliff that is 35 feet to the ground. A large 8 pound bucket with 19 ga

larisa86 [58]

Answer:

A function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is $W=16(50-x)+(19-\frac{x}{5})(8.3)x$ and the work to get the bucket to the top of the cliff is 3726 foot-lbs

Step-by-step explanation:

Work done to lift the rope by distance x feet:

$W_1=32(\frac{50-x}{2})$

Work done to lift the bucket by distance x feet:

$W_2=(19-\frac{x}{5})(8.3)x$

On reaching top 7 gallons of water spilled out so , on going up by x feet $\frac{7x}{35}=\frac{x}{5}$ gallons of water spilled out.

a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground:

$W=16(50-x)+(19-\frac{x}{5})(8.3)x$

Now the work to get the bucket to the top of the cliff i.e. x =35

$W=16(50-35)+(19-\frac{35}{5})(8.3)(35)$

W=3726

Hence, a function that gives the work required in foot-lbs to lift the bucket up x feet from the ground is $W=16(50-x)+(19-\frac{x}{5})(8.3)x$ and the work to get the bucket to the top of the cliff is 3726 foot-lbs

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3 years ago