All categories

2 years ago

Evaluate 4(a2 + 2b) - 2b

Mathematics

1 answer:

iogann1982 [59]2 years ago

5 0

<span>4(a^2 + 2b) - 2b
= 4a^2 + 8b - 2b
=</span> 4a^2 + 6b

You might be interested in

Round steak costs $6.95 per pound. Sara wants to buy 9.5 pounds of round steak which she estimates will cost $54. Which statemen

iren2701 [21]

Answer:

the answer is 2

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

steve gaimes is paid overtime for all time worked past 40 hours in a week. his regular time pay rate is $12 an hour and his over

Elena-2011 [213]

Answer:

40 hours

Step-by-step explanation:

47.3-40= 7.3

He worked 7.3 hours overtime meaning he worked 40 regular hours.

6 0

2 years ago

A cardboard box without a lid is to have a volume of 16,384 cm3. Find the dimensions that minimize the amount of cardboard used.

Reika [66]

Answer:

The dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

Step-by-step explanation:

Volume of the cardboard = 16,384 $cm^{3}$

The function that represents the area of the cardboard without a lid is given by

$f (x,y,z) = xy + 2xz + 2yz$ ------ (1)

Volume of the cardboard with sides x, y & z is

$xyz = 16384$

$z = \frac{16384}{xy}$

Put this value of z in equation (1) we get

$f (x,y,z) = xy + 2x(\frac{16384}{xy} ) + 2y(\frac{16384}{xy} )$

$f (x,y,z) = xy + \frac{32768}{y} + 2y(\frac{32768}{x} )$

Differentiate above equation with respect to x & y we get

$f_{x} = y - \frac{32768}{x^{2} }$

$f_{y} = x - \frac{32768}{y^{2} }$

Take $f_{x} = 0 \ and \ f_{y} = 0$

$y - \frac{32768}{x^{2} } = 0$

$y = 32768 \ x^{-2}$ ------ (2)

$x - \frac{32768}{y^{2} } = 0$

$x = 32768 \ y^{-2}$ ------- (3)

By solving equation (2) & (3) we get

$x^{3} = 32768$

x = 31 cm

From equation 2

$y = 32768 \ x^{-2}$

y = 32768 ( $31^{-2}$ )

y = 34 cm

$z = \frac{16384}{xy}$

$z = \frac{16384}{(34)(31)}$

Z = 15.54 cm

Thus the dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

6 0

2 years ago

In the Venn diagram, the blue circle represents when p is true, and the orange represents when q is true. A conjunction is true

Radda [10]

Answer:

A conjunction is true in region

✔ B <--- Answer

A disjunction is true in region(s)

✔ A, B, and C <--- Answer

A disjunction is false in region(s)

✔ D <--- Answer

Step-by-step explanation:

I took the assaignment aswell

3 0

2 years ago

Read 2 more answers

Given that $A = (\sqrt{2008}+\sqrt{2009}),$ $B = (-\sqrt{2008}-\sqrt{2009}),$ $C = (\sqrt{2008}-\sqrt{2009}),$ and $D = (\sqrt{2

kipiarov [429]

Answer:

ABCD = 0.803

Step-by-step explanation:

$A = \sqrt{2008}+\sqrt{2009} \\A = 44.81 + 44.82\\A = 89.63$

$B = -\sqrt{2008}-\sqrt{2009}\\B = -44.81 - 44.82\\B = -89.63$

$C = \sqrt{2008}-\sqrt{2009}\\C = 44.81 - 44.82\\C = - 0.01$

$D = \sqrt{2009}-\sqrt{2008}\\D = 44.82 - 44.81\\D = 0.01$

ABCD = 89.63 * (-89.63) * (-0.01) * (0.01)

ABCD = 0.803

6 0

2 years ago