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spayn [35]
3 years ago
10

I really need help with this

Mathematics
1 answer:
slega [8]3 years ago
8 0
Check the picture below.

the radius, so-called because if we circumscribe the triangle in a circle, that'd be the radius of the circumcircle, is 3 inches, as you see there in the picture in red.

now, bear in mind that the triangle is an equilateral one, and therefore, 180/3 = 60, meaning all its interior angles are congruently 60°.

if we run the radius of the triangle, like there, it will cut one of those interior angles in half, namely the radius is an angle bisector, and if we run a perpendicular line to the bottom side, like the dashed one there, we end up with a 30-60-90 triangle, to which we can apply the 30-60-90 rule, as you see it there.

since we know what half of a side of the triangle is, as you see it there in blue, then we can use that and plug it in at

\bf \textit{area of an equilateral triangle}\\\\
A=\cfrac{s^2\sqrt{3}}{4}~~
\begin{cases}
s=length~of\\
\qquad a~side\\
-------\\
s=\stackrel{\frac{3\sqrt{3}}{2}+\frac{3\sqrt{3}}{2}}{3\sqrt{3}}
\end{cases}\implies A=\cfrac{(3\sqrt{3})^2\sqrt{3}}{4}
\\\\\\
A=\cfrac{(3^2\sqrt{3^2})\sqrt{3}}{4}\implies A=\cfrac{(9\cdot 3)\sqrt{3}}{4}\implies A=\cfrac{27\sqrt{3}}{4}

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guajiro [1.7K]

Answer:

D is a perfect square

Step-by-step explanation:

a perfect square is a squared number that has a square root of an even number like sqrt(64) = 8 and 8 is an even number making it a perfect square

7 0
3 years ago
If Bob produces 36 or fewer items in a week, he is paid X dollars per item. If Bob produces more than 36 items in a week, he is
Greeley [361]

Answer:

How many items did Bob produce last week? 32 items.

Step-by-step explanation:

(1) Last week Bob was paid total of $480 for the items that he produced that week.

(2) This week Bob produced 2 items more than last week and was paid a total of $510 for the items that he produced this week.

a) Let's start with the simplest case:  he produced 36 or less items this week.

In this case he produced less than 36 items last week too.

So he was paid the same amount of dollar per item.

Using (1) and (2) assumptions we have:

$480+2X=$510

⇒2X=$510-$480

⇒2X=$30

⇒2X=$30/2

⇒X=$15

He was paid $15 per item.

Last week he was paid $480.

480/15= 32 items.

This week he was paid $510.

510/15=34 items.

The other cases has no solutions.

7 0
3 years ago
A study was conducted to investigate the relationship between the resale price, y (in hundreds of dollars), and the age, x (in y
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Answer:

a. $121.07

b. $60.9

C. $20.03

Step-by-step explanation:

From the equation given

Y=181.7-20.21x

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We have

y=181.7-20.21(3)

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y=121.07

The resale price after 3years is $121.07

b. To find the resale price after 6years we have, we substitute x=6 into the given equation.

We have

y=181.7-20.21(6)

y=181.7-120.72

y=60.98

The resale price after 3years is $60.98

C. To find the average decrease per year, we have

[(x=3)-(x=6)]/3

=(121.07-60.98)/3

$20.03

Hence the average annual decrease is $20.03

8 0
3 years ago
Read 2 more answers
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Answer:

$429.75

Step-by-step explanation:

First, find the tax rate on the sale of the boat:  Let r represent that rate.  Then,

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Applying this tax rate to a boat selling for $9,550:

0.045($9,550) = $429.75.  This is the amount of tax on the 2nd boat.

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