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2 years ago

Simplify the following expression. (3m-4)²+8(3m-2)

Mathematics

1 answer:

Leno4ka [110]2 years ago

3 0

Step-by-step explanation:

(3m-4)² + 8(3m-2) = (3m-4)(3m-4) + 24m - 16 =

= 9m² - 3m×4 - 4×3m + 16 + 24m - 16 =

= 9m² - 24m + 16 + 24m - 16 = 9m²

so, there is seemingly something missing in your original expression.

going from 9m², the most likely solution would be 9m/4 and therefore B.

but we cannot be sure, because again, I don't know what you left out in the beginning.

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A disk with radius 3 units is inscribed in a regular hexagon. Find the approximate area of the inscribed disk using the regular

Oksi-84 [34.3K]

Answer:

The approximate are of the inscribed disk using the regular hexagon is $A=18\sqrt{3}\ units^2$

Step-by-step explanation:

we know that

we can divide the regular hexagon into 6 identical equilateral triangles

see the attached figure to better understand the problem

The approximate area of the circle is approximately the area of the six equilateral triangles

Remember that

In an equilateral triangle the interior measurement of each angle is 60 degrees

We take one triangle OAB, with O as the centre of the hexagon or circle, and AB as one side of the regular hexagon

Let

M ----> the mid-point of AB

OM ----> the perpendicular bisector of AB

x ----> the measure of angle AOM

$m\angle AOM =30^o$

In the right triangle OAM

$tan(30^o)=\frac{(a/2)}{r}=\frac{a}{2r}\\\\tan(30^o)=\frac{\sqrt{3}}{3}$

$\frac{a}{2r}=\frac{\sqrt{3}}{3}$

we have

$r=3\ units$

substitute

$\frac{a}{2(3)}=\frac{\sqrt{3}}{3}\\\\a=2\sqrt{3}\ units$

Find the area of six equilateral triangles

$A=6[\frac{1}{2}(r)(a)]$

simplify

$A=3(r)(a)$

we have

$r=3\ units\\a=2\sqrt{3}\ units$

substitute

$A=3(3)(2\sqrt{3})\\A=18\sqrt{3}\ units^2$

Therefore

The approximate are of the inscribed disk using the regular hexagon is $A=18\sqrt{3}\ units^2$

6 0

3 years ago

Which expression is equivalent to 2(a + 2b) - a - 2b?

Free_Kalibri [48]

The correct answer is D) a+2b.

Hope it helps!

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3 years ago

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mr.lumen replaced a square window with a rectangular one.The new window is 3 ft wider and 2 ft higher than the square one.it has

stira [4]

Alright, lets get started.

Suppose the original square window has the side = x feet

The new window is 3 ft wider and 2 ft higher than the square one.

Means length of the new window will be = $(x+3)$

Width of the new window will be = $(x+2)$

So the area of the new window will be = $(x+3)(x+2)$

So the area of the new window will be = $x^2 + 2x + 3x + 6$

So the area of the new window will be = $x^2 + 5x + 6$

As given in question the area of 30 square feet for the new window, hence

$x^2 + 5x + 6 = 30$

$x^2 + 5x - 24 = 0$

Factoring

$(x+8)(x-3) = 0$

x = -8 or x = 3

Side could not be negative hence

side of the original square window will be = 3 feet : Answer

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4 years ago

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Answer:

1.24

Step-by-step explanation:

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3 years ago

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3 years ago