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3 years ago

Factor 60 – 36w to identify the equivalent expressions.

Mathematics

1 answer:

gtnhenbr [62]3 years ago

5 0

Answer:

Step-by-step explanation:

60 – 36w = 6(10 - 6w),

4(15 - 9w)

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3 years ago

If we inscribe a circle such that it is touching all six corners of a regular hexagon of side 10 inches, what is the area of the

Brrunno [24]

Answer:

$\left(100\pi - 150\sqrt{3}\right)$ square inches.

Step-by-step explanation:

<h3>Area of the Inscribed Hexagon</h3>

Refer to the first diagram attached. This inscribed regular hexagon can be split into six equilateral triangles. The length of each side of these triangle will be $10$ inches (same as the length of each side of the regular hexagon.)

Refer to the second attachment for one of these equilateral triangles.

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$\displaystyle 10\, \sin\left(60^\circ\right) = 10 \times \frac{\sqrt{3}}{2} = 5\sqrt{3}$ .

The area (in square inches) of this equilateral triangle will be:

$\begin{aligned}&\frac{1}{2} \times \text{Base} \times\text{Height} \\ &= \frac{1}{2} \times 10 \times 5\sqrt{3}= 25\sqrt{3} \end{aligned}$ .

Note that the inscribed hexagon in this question is made up of six equilateral triangles like this one. Therefore, the area (in square inches) of this hexagon will be:

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<h3>Area of of the circle that is not covered</h3>

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$\pi \times (\text{radius})^2 = \pi \times 10^2 = 100\pi$ .

The area (in square inches) of the circle that the hexagon did not cover would be:

$\begin{aligned}&\text{Area of circle} - \text{Area of hexagon} \\ &= 100\pi - 150\sqrt{3}\end{aligned}$ .

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3 years ago

Twice x, plus 4, is the same as -6.

BARSIC [14]

Start by writing what is said:
2x + 4 = -6
From there just solve for x:

Subtract 4 from both sides
2x + 4 - 4 = -6 - 4
2x = -10

Divide by 2 to get x by itself
2x/2 = -10/2
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