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777dan777 [17]
3 years ago
15

Find the area of the regular 30-gon with radius 10 mm.

Mathematics
1 answer:
Irina-Kira [14]3 years ago
4 0

Answer:

This polygon is comprised of 30 congruent triangles, each with a central angle of 12°  

And using trig, each has an area of......

(1/2)(20)^2 sin(12°) = 41.5823381636 sq ft

So, 30 times this = 1247.470144908 sq ft  = 1247.5 sq ft  (rounded to the nearest tenth)

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- 4x + 8y = 20<br> ----4x + 2y = -30
snow_tiger [21]

Answer:

40

Step-by-step explanation:

5 0
3 years ago
A school bought pens, each costing $1, and pencils, each costing $0.5. The cost of the whole purchase was $220. How many pens an
Mkey [24]

Answer:

  • <u>120 pens and 200 pencils.</u>

<u></u>

Explanation:

You can set a system of two equations.

<u>1. Variables</u>

<u />

  • x: number of pens
  • y: number of pencils

<u>2. Cost</u>

  • <em>each pen costs</em> $1, then x pens costs: x
  • <em>each pencil costs</em> $0.5, then y pencil costs: 0.5y

  • Then, the total cost is: x + 0.5y

  • The cost of the whole purchase was $ 220, then the first equation is:

          x + 0.5y = 220 ↔ equation (1)

<u>3. </u><em><u>There were 80 more pencils than pens</u></em>

Then:

  pencils  =      80   +   pens

       ↓                               ↓

       y        =      80   +      x        ↔ equation (2)

<u>4. Solve the system</u>

i) Substitute the equation (2) into the equation (1):

  • x + 0.5(80 + x) = 220

ii) Solve

  • x + 40 + 0.5x = 220
  • 1.5x = 180
  • x = 180/1.5
  • x = 120 pens

iii) Substitute x = 120 into the equation (2)

  • y = 80 + 120
  • y = 200 pencils

Solution: 120 pens and 200 pencils ← answer

6 0
2 years ago
PQRS is a trapezoid with a right angle. What are the coordinates of S
Brrunno [24]

Answer: (a, 0)

<u>Step-by-step explanation:</u>

Notice that S is on the x-axis, therefore the y-coordinate is "0".

Notice that S has the same x-value of R. The x-value of R is "a".

8 0
3 years ago
Quick!
MAVERICK [17]

Answer:

y=-x-2

Step-by-step explanation:

To find the slope of the line, you can use the slope formula. I did this with (-3,1) and (2,-4) to get: (1+4)/(-3-2). This ends up as -5/5, which simplifies to -1.

next I plugged in the slope and one point into the line equation: y=mx+b. I plugged in (-4)=(-1)(2)+b. This equated to b=-2.

Check Work:

The equation -4=(-1)(2)-2 is true

The equation 1=(-1)(-3)-2 is true

5 0
3 years ago
Which expression is equivalent to 2(x + 7) - 2(9x - 0.4)?
Black_prince [1.1K]

Answer:

-16x+14.8

Step-by-step explanation:

2(x+7)-2(9x-0.4)

2x+14-18x+0.8

-2x+14-18x+0.8

14-16x+0.8

14+0.8-16x

14.8+-16x

8 0
2 years ago
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