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4 years ago

Factor by grouping:

1 answer:

3 0

The idea is to group up the terms into two groups, factor each group and then factor out the overall GCF

2x - 18 + xy - 9y
(2x - 18) + (xy - 9y)
2(x - 9) + (xy - 9y)
2(x - 9) + y(x - 9)
(2 + y)(x - 9)
(x - 9)(2 + y)

Answer: Choice B

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There is a book that is 8 inches long, 5 inches wide, and 2 inches thick what is the volume of the book?

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8 x 5 x 2 = 90
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3 years ago

A tank contains 60 kg of salt and 1000 L of water. A solution of a concentration 0.03 kg of salt per liter enters a tank at the

charle [14.2K]

Answer:

$\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg$

Step-by-step explanation:

Volume of water in the tank = 1000 L

Let y(t) denote the amount of salt in the tank at any time t.

Initially, the tank contains 60 kg of salt, therefore:

y(0)=60 kg

Rate In

A solution of concentration 0.03 kg of salt per liter enters a tank at the rate 9 L/min.

$R_{in}$ =(concentration of salt in inflow)(input rate of solution)

$=(0.03\frac{kg}{liter})( 9\frac{liter}{min})=0.27\frac{kg}{min}$

Rate Out

The solution is mixed and drains from the tank at the same rate.

Concentration, $C(t)=\dfrac{Amount}{Volume} =\dfrac{y(t)}{1000}$

$R_{out}$ =(concentration of salt in outflow)(output rate of solution)

$=\dfrac{y(t)}{1000}* 9\dfrac{liter}{min}=0.009y(t)\dfrac{kg}{min}$

Therefore, the differential equation for the amount of Salt in the Tank at any time t:

$\dfrac{dy}{dt}=R_{in}-R_{out}\\\\\dfrac{dy}{dt}=0.27-0.009y(t),$ y(0)=60kg$

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4 years ago

What variable do we use for slope? A.x B.y C.m D.b

Nady [450]

Answer:

y we use y

Step-by-step explanation:

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3 years ago

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Find the gcf of the terms of the polynomial. 45b 27 a) 3 b) 5 c) 9 d) 15

ryzh [129]

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3 years ago

The points (6, 9) and (0, 6) fall on a particular line. What is its equation in slope-intercept form?

SashulF [63]

Answer:

$y = \frac{1}{2}x + 6$

Step-by-step explanation:

$Let \ (x _1 y _ 1 ) = ( 6 , 9 ) \ and \ (x _ 2 , y _ 2 ) \ = ( 0 , 6 )\\\\$

Step 1 : Find slope, m

$slope, m = \frac{y _ 2 - y _ 1}{x_ 2 - x_ 1 } = \frac{6 - 9}{0 - 6 } = \frac{-3}{-6} = \frac{1}{2}$

Step 2 : Find the equation

$(y - y _ 1 ) = m ( x - x_ 1) \\\\( y - 9 ) = \frac{1}{2} (x - 6 ) \\\\y = \frac{1}{2}x - 3 + 9 \\\\y = \frac{1}{2}x + 6$

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3 years ago

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