All categories

3 years ago

What are the steps for constructing a copy of an angle using only a compass and a straightedge?

Mathematics

1 answer:

juin [17]3 years ago

6 0

Answer:

1. Use a straightedge

2. Draw dots on the line to mark the starting point

3. Place the point of the compass on the point you made or was given

4. Extend the compass so that the pencil is on the 2nd point & make a an arc thru point B

5. Place the compass point on the starting point dot on the line and draw w/ the pencil to create an arc crossing the line.

You might be interested in

Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. Whe

Rama09 [41]

You can see how this works by thinking through what's going on.

In the first year the population declines by 3%. So the population at the end of the first year is the starting population (1200) minus the decline: 1200 minus 3% of 1200. 3% of 1200 is the same as .03 * 1200. So the population at the end of the first year is 1200 - .03 * 1200. That can be written as 1200 * (1 - .03), or 1200 * 0.97

What about the second year? The population starts at 1200 * 0.97. It declines by 3% again. But 3% of what??? The decline is based on the population at the beginning of the year, NOT based no the original population. So the decline in the second year is 0.03 * (1200 * 0.97). And just as in the first year, the population at the end of the second year is the population at the beginning of the second year minus the decline in the second year. So that's 1200 * 0.97 - 0.03 * (1200 * 0.97), which is equal to 1200 * 0.97 (1 - 0.03) = 1200 * 0.97 * 0.97 = 1200 * 0.972.

So there's a pattern. If you worked out the third year, you'd see that the population ends up as 1200 * 0.973, and it would keep going like that.

So the population after x years is 1200 * 0.97x

5 0

3 years ago

A first number plus twice a second number is 4. Twice the first number plus the second totals 20. Find the numbers

pychu [463]

Answer:

The first number is 6

The second number is -1

6+(-2)=4

6*2=12 12+(-1)=11

Step-by-step explanation:

4 0

3 years ago

A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boa

zavuch27 [327]

Law of cosine is applicable to all the triangles. The value of the angle by which the boat turns is 39.195°.

<h3>What is the law of cosine?</h3>

Law of cosine helps us to find the third side of the triangle when 2 sides and an angle are known. It is formulated as,

$c=\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}$

a, b, c is the sides of the triangle and,

$\gamma$ = angle opposite c

A.)

Given to us

A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping.

When it stopped, the boat was 18 miles from its starting point.

According to the given statements, sides and angles can be written,

a = 25 miles

b = 28 miles

c = 18 miles

$\theta = x^o$

Substitute the values,

$c=\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}$

$18=\sqrt{25^{2}+28^{2}-2(25)(28) \cdot \cos \theta}\\\\\theta = 39.195^o$

Hence, the value of the angle by which the boat turns is 39.195°.

B.)

Given to us

Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock.

The angle between 25 miles and 28 miles is x degrees.

According to the given statements, sides and angles can be written,

a = 25 miles

b = 28 miles

c = 18 miles

$\theta = x^o$

Substitute the values,

$c=\sqrt{a^{2}+b^{2}-2 a b \cdot \cos \gamma}$

$18=\sqrt{25^{2}+28^{2}-2(25)(28) \cdot \cos \theta}\\\\\theta = 39.195^o$

Hence, the value of the angle by which the boat turns is 39.195°.

Learn more about the Law of cosine:

brainly.com/question/17289163

5 0

3 years ago

What is 5,339x6 equal to in this case

BigorU [14]

32034

All I had to do was multiply. Is there more to the problem?

8 0

3 years ago

1) For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.

Gelneren [198K]

Answer:

Yes, "y" varies directly with "x".

The equation is: $y=1.375x$

Step-by-step explanation:

By definition, Direct variation equations have the following form:

$y=kx$

Where "k" is the Constant of variation.

If you solve for "k", the equation is:

$k=\frac{y}{x}$

Then, given the table provided in the exercise, you can know if "y" varies directly with "x" by finding the quotient of the correspoding values of "x" and "y":

- Dividing $y=11$ by $x=8$ you get: