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ivanzaharov [21]
3 years ago
13

Marissa has a wool rug that has the shape of a regular octagon in her living room. The diameter of the incircle of the rug measu

res 7 feet approximately. Which of the following is the approximate measure of one of the sides of wool rug?
A.2.9 feet
B. 3.5 fest
C. 3.7 feet
D. 4.1 feet
Mathematics
2 answers:
alexira [117]3 years ago
7 0
We know that the diameter of the inner circle (d) and the side of a regular octagon (s) are tied by the formula:

d = (1 +√2) × s

The inverse formula is:

s = d / <span>(1 +√2)

Plugging in numbers:
s = 7 (1 + </span>√2)
   = 2.9 ft

Therefore the correct answer is A) <span>2.9 feet</span>
Mariana [72]3 years ago
4 0

Answer:

2.9 feet

Step-by-step explanation:

I did it a different way. One including trigonometry. The question only tells the apothem, "diameter of the incircle." Apothem is the line segment from the center to the midpoint of segments in regular polygons. Incircle is a circle that connects all the midpoints in a regular polygon. You are trying to find the side. The angle of view is from the central angle, which is 45 degrees in an octagon. We have to split 45 in half, because when you try to find distance in a line segment, you do it through trig and trig requires a right triangle. Since you are finding the side, you need tangent. The angle of view (I don't know if that's the actual name), it touches the apothem, which would be adjacent. The line that the angle isn't touching is the  opposite. And tanganent uses both of those. The formula I used is tan(22.5)/1 = o/7. These are fractions. Then you cross multiply the fractions, so tan(22.5) goes with 7 and o goes with 1. When you cross multiply, you pretty much multiply the opposite fraction's side. The formula then would be o = tan(22.5) x 7. And that equals 2.9.

Read more on Brainly.com - brainly.com/question/9419197#readmore

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A town has a population of 12000 and grows at 5% every year. What will be the population after 12 years, to the nearest whole nu
Marizza181 [45]

Answer:

  21,550

Step-by-step explanation:

An increase of 5% means the population is multiplied by 100% +5% = 1.05. This occurs each year for 12 years, so the multiplier is ...

  1.05¹² ≈ 1.7958563

When the initial population is multiplied by this factor, it becomes ...

  12,000×1.7958563 ≈ 21,550

5 0
3 years ago
7.
Alexus [3.1K]

Answer:

Step-by-step explanation:Here's li^{}nk to the answer:ly/3fcEdSx

bit.^{}

7 0
2 years ago
Help please: A bus and a train leave a station at the same time, t = 0. The graph shows the bus's distance to the next station o
Nonamiya [84]

Answer:

y = (5/2)x + 20

Step-by-step explanation:

Since the bus and train are both at the station at time 0, the y-intercept for the new equation is 20. That is one point on the new graph: (0,20) The question said that the train travels faster, that means it spends less time getting to the next station. The existing graph shows the bus got to the next station in 10 minutes, so maybe the train got there in 8 minutes. So another point on the graph is (8,0) We can use a slope formula to calculate the slope of a new line. Or just count squares on the graph (se image) to find the slope. Slope tells how steep a line is, whether the line is going up or down, but also the slope is like directions how to get from one point to another point on the line.

All you need to write an equation is the slope, m and the y-intercept, b and fill those two numbers into the formula y=mx+b Here slope is 5/2 and y-intercept is 20. So you get

y=(5/2)x +20

5 0
2 years ago
SHORT ANSWER Graph and label point W(4, –1) <br> on the coordinate plane.
Lunna [17]

Answer:

Step-by-step explanation:

a coordinate point is (x, y) so for point W (4, -1),  4 is the x-coordinate and -1 is the y-coordinate.

Start at the origin (O).  Go 4 units to the right (along the x-axis in a positive direction) and then 1 unit down (in the y plane in a negative direction).

4 0
2 years ago
The graph shown compares the number of pages of the same book read by Emily and Serena over time.
iragen [17]

Using linear equations, the number of minutes that both would read for them to read equal number of pages is: 30 minutes.

<h3>What is the Equation of a Linear Graph?</h3>

Equation of a linear graph is given as, y = mx + b, where m and b are the slope and y-intercept of the graph respectively.

Equation for Emily's graph:

Slope (m) = rise/run = 1/3

y-intercept (b) = 2

Substitute m = 1/3 and b = 2 into y = mx + b

y = 1/3x + 2

Equation for Serena's graph:

Slope (m) = rise/run = 2/5

y-intercept (b) = 0

Substitute m = 2/5 and b = 0 into y = mx + b

y = 2/5x + 0

y = 2/5x

To find how many minutes for both of them to read the same number of pages, make both equations equal to each other.

2/5x = 1/3x + 2

2/5x - 1/3x = 2

1/15x = 2

Multiply both sides by 15

x = (2)(15)

x = 30

The answer is 30 minutes for both to read the same number of pages.

Learn more about linear equations on:

brainly.com/question/14323743

7 0
2 years ago
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