What are the steps for using a compass and straightedge to construct an equilateral triangle?

Drag the steps and drop them in order from start to finish.

Construct a point at one of the two intersection points of circle E and circle F and label this point G

.Construct ​ EG¯¯¯¯¯ ​ and ​ FG¯¯¯¯¯​ .

Construct ​ EF¯¯¯¯¯​

.Construct a circle with point E as the center and a circle with point F as the center with each circle having radius EF .

Answer: 3.200 x 10^7h

Step-by-step explanation:

Correct answer on K12

Answer: L greater than 31

Step-by-step explanation:

Trevor is swimming laps to raise at over 100 dollars for the local food bank. He earns $1.85 per lap and has already swum 23 laps.

This means that the total amount that he has raised is number of laps that he has swum × the amount he earns per lap. Therefore,

Amount that he has already raised

= 1.85 × 23 = $42.55

100 - 42.55 = 57.45

He still needs to raise an amount greater than $57.45

To raise this amount, he needs to swim more laps. Number of laps that he needs to swim will be

57.45/1.85 = 31.05

Approximately 31 laps

Let the number of laps that he needs to swim be L

The inequality to show how many more laps Trevor needs to swim in order to raise more than $100 will be

L greater than 31

To solve this question, we have to:

Doing this, we get that the length of the base is 10 cm and the length of the legs is 20 cm.

Isosceles triangle:

In an isosceles triangle, two sides have the same measure. An example is given by the picture at the end of this answer.

Perimeter:

The perimeter of a polygon, in this case a triangle, is the sum of all it's sides.

In this question:

Then, the equation is:

[tex]l + l + \frac{l}{2} = 50[/tex]

[tex]2l + \frac{l}{2} = 50[/tex]

[tex]\frac{4l + l}{2} = 50[/tex]

[tex]5l = 100[/tex]

[tex]l = \frac{100}{5}[/tex]

[tex]l = 20[/tex]

Thus:

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Answer:

Obtuse and Isosceles

:) Apex

The triangle in the image can be classified as follows:

The correct options will be

Right [ F] : One of the angles is 90 degrees.

Isosceles [ D]: Two of the sides are equal (the two shorter sides).

We can see from the triangle that two of the angles measure 41 degrees each and the third angle is 98 degrees. The sum of the angles in a triangle is 180 degrees, and since 41 + 41 + 98 = 180, we know that the triangle is valid.

Right triangles can also be isosceles (in fact, there is a specific type of right triangle called a 45-45-90 triangle). So, this triangle qualifies for both classifications.

The triangle cannot be classified as:

Acute [ B]: Acute triangles have all angles less than 90 degrees.

Obtuse [ A]: Obtuse triangles have one angle greater than 90 degrees.

Equilateral [ E]: Equilateral triangles have all three sides equal.

The complete question is: Classify the following triangle.Check all that apply.

To factor the quadratic x^2 + 3x + 2, it can be written as (x + 1)(x + 2). The concept of infinity over infinity (∞/∞) is an indeterminate form in limits and usually requires further techniques to evaluate.

To factor x^2 + 3x + 2, you want to find two numbers that both add up to +3 (the coefficient of x) and multiply to +2 (the constant term). These numbers are +1 and +2. Thus, you can express the quadratic equation as a product of two binomials:

x^2 + 3x + 2 = (x + 1)(x + 2).

As for the concept of limits like ∞/∞, it commonly arises when evaluating the behavior of functions as the variable approaches infinity. It represents an indeterminate form which requires further algebraic manipulation or techniques such as L'Hôpital's rule to find a meaningful limit.

Answer:

A) The term 7p represents the cost for 7 packs of pencils.

Step-by-step explanation:

Have a good day ^.^

To solve a physics problem, make a list of known variables, solve the equation for the unknown, substitute known values with correct units into the equation, and check if the solution is reasonable.

Steps to Solve a Physics Problem

When attempting to solve a physics problem, it is essential to follow a structured approach to reach a solution successfully. Here is a step-by-step method to guide you:

Some problems may require several steps or the use of multiple equations to find the solution. Always keep in mind the physical principles to guide your problem-solving process.

Answer:

c=6 and d=2 makes the equation true

Step-by-step explanation:

[tex]\sqrt[3]{162x^cy^5} = 3x^2y(\sqrt[3]{6y^d})[/tex]

plug in c=2  and check

[tex]\sqrt[3]{162x^2y^5}[/tex]

We cannot simplify cuberoot (x^2)

So c=2 does not works

Lets try with c=6 and d=2

[tex]\sqrt[3]{162x^6y^5}[/tex]

Cuberoot(x^6) = x^2

cuberoot (y^5)= ycuberoot (y^2)

[tex]\sqrt[3]{162x^6y^5} = 3x^2y(\sqrt[3]{6y^2})[/tex]

So c=6 and d=2 makes the equation true

Answer:

300 meters

Step-by-step explanation:

The altitude divides the equilateral triangle into two congruent 30-60-90 triangles. The altitude is the long leg whose length is

300

 meters.

The value of x is 70 degrees. This is obtained by solving the equation formed from the definition of complementary angles (the sum of the angles is 90 degrees).

In mathematics, two angles are said to be complementary if the sum of their measures is 90 degrees. In this case, the two angles in question have measures of 15 degrees and (x+5) degrees. Therefore, we can create an equation by adding the two measures and setting the sum equal to 90.

So, 15 + (x+5) = 90.

Solving for x, we first combine like terms, yielding x + 20 = 90. Then we simply subtract 20 from both sides of the equation to obtain the value for x. So, x = 90 - 20 = 70 degrees.

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The answer would be B, which, in other words, would also be 5/8, 3/4, 7/9.

Answer:A

Step-by-step explanation:

The standard deviation of the snowfall in Chillyville, when the snowfall exceeds 60 inches in 15 percent of the years, is 5 inches.

The question is about finding the standard deviation of the normally distributed data for snowfall in Chillyville. From the given problem, we have the mean (μ) as 55 inches and the given probability for snowfall exceeding 60 inches is 15% or 0.15 which happens to correspond to 1 - 0.85 = 0.15 in the standard normal distribution. This places it in the 85th percentile of the standard normal distribution, which corresponds to a Z-score of about 1.

From the Z-score formula Z = (X - μ)/σ, where X is the data point, μ is the mean and σ is the standard deviation, we can substitute the known values: 1 = (60 - 55)/σ . Solving it gives σ = 60 - 55, which implies the standard deviation is 5 inches.

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Answer:

80%

Step-by-step explanation:

If 60% of the class passed the second exam and only 48% passed the first your solution would have to be of the 48%. Therefore 0.48/0.60=0.8/1.0=80%

Answer:

64

Step-by-step explanation:

Pairs: (1,64), (2, 32), (4, 16), (8, 8)

Note: 8 only counts as 1 factor (not 2)

Factors: 1, 2, 4, 8, 16, 32, 64

count them and you get 7 factors

Answer:

ITS C  

y -1 =  1/2 ( x -5)

The equation represents a line that passes through (5, 1) and has a slope of 1/2 is given by (A) y - 5 = 1/2 (x-1).

The tangent value of the angle formed between a straight line and positive x-axis is called the Slope of that straight line.

If the slope of a line is m and the line is satisfied by point (a,b) then the equation of the line is given by,

y - b = m (x - a)

Here in the problem it is given that the slope is 1/2 and line passes thorugh (5,1).

So, a = 5, b = 1, m = 1/2

Hence the equation of the straight line is given by,

y - 5 = 1/2 (x - 1)

Hence the correct option is (A)

Your question is incomplete.Please find the missing content here:

Which equation represents a line that passes through (5, 1) and has a slope of 1/2 ?

?y – 5 = 1/2(x –1)

?y – 5 = 1/2(x –1)y – 1/2 = 5(x –1)

?y – 5 = 1/2(x –1)y – 1/2 = 5(x –1)y – 1 = 1/2(x –5)

?y – 5 = 1/2(x –1)y – 1/2 = 5(x –1)y – 1 = 1/2(x –5)y – 1 = 5|x-1/2|

Learn more about Slope here -

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The value of a = (p + n) / m.

To isolate a in the given equation am - n = p, follow these steps:

Start with the original equation: am - n = p.

Add n to both sides of the equation to eliminate n from the left-hand side:
am - n + n = p + n
am = p + n.

Next, divide both sides of the equation by m to solve for a:
(am) / m​ = (p + n) / m
a = (p + n) / m

Therefore, a = (p + n) / m is the solution to the equation.

Final answer:

Advanced calculus covers computational aspects and applications of calculus in multiple dimensions, while real analysis focuses on the theoretical fundamentals, such as rigorous development of the real number system and proof-based examination of limits and continuity.

Explanation:

The difference between advanced calculus and real analysis lies in the focus and depth of the subjects. Advanced calculus, also known as calculus III in some curricula, typically extends the study of calculus to multiple dimensions, covering topics such as partial derivatives, multiple integrals, and vector calculus. It focuses more on the computational aspects and applications of calculus.

Real analysis, on the other hand, delves deeper into the theoretical underpinnings of calculus and analysis. It deals with the rigorous development of the real number system, sequences and series, continuity, differentiation, integration, and convergence. Real analysis puts a strong emphasis on proof and logical reasoning, providing a foundation for the truth and logic behind the mathematics used in calculus.

While both subjects are mathematically advanced, real analysis is considered to be more abstract and is often a stepping stone for further study in pure mathematics. Familiarity with calculus is often a prerequisite before studying real analysis as it lays the groundwork for the more complex theoretical concepts.