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3 years ago

12

to get a certain shade of green paint, Melissa decides to mix 3 gallons of blue paint with 2 gallons of yellow paint. How much b

lue paint does Melissa need for each gallon of yellow paint

1 answer:

maw [93]3 years ago

3 0

Melissa will need 1.5 gallons of blue paint for each gallon of yellow paint.

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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.

Let segment $\sf CH$ be a height on side $\sf AB$ . Since this triangle is equilateral, the size of each internal angle will be $\sf 60^\circ$ . The length of segment

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

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:

$\displaystyle 6 \times 25\sqrt{3} = 150\sqrt{3}$ .

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

Refer to the first diagram. The length of each side of these equilateral triangles is the same as the radius of the circle. Since the length of one such side is $10$ inches, the radius of this circle will also be $10$ inches.

The area (in square inches) of a circle of radius $10$ inches is:

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

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

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

3 0

3 years ago

1. Josefina ha pintado 2/4 de una pared y su hermano<br>  ¿Cuánto han pintado entre los dos?

Irina18 [472]

Answer 67+67=6886

Step-by-step explanation:

8 0

3 years ago

Brainliest!!!<br><br> pls help

Vanyuwa [196]

Answer:

31.6

Step-by-step explanation:

38+29+16+42+33 = 158

158÷5 = 31.6

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3 years ago

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Suppose your school costs for this term were $4780 and financial aid covered 3/4 of that amount. How much did financial aid cove

Alexandra [31]

Answer: Amount covered by financial aid=$3,585

Amount left that you have to pay =$1,195

Step-by-step explanation:

School cost for the term = $4780

Amount covered by financial aid = 3/4 of $4780

= 3/4 x 4780

Amount left that you have to pay=School cost for the term -Amount covered by financial aid

= $4,780 - $3,585

Amount left that you have to pay =$1,195

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3 years ago

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Tema [17]

Answer:

1. not possible, 2. a. 65 b. 115 c.115

Step-by-step explanation:

def. sup. <

vertical angles post.

corresponding angles thm.

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3 years ago

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