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3 years ago

10

In the straightedge and compass construction of the equilateral triangle below, which o the following reasons can you use to pro

ve that ABC = BCA?

2 answers:

Elodia [21]3 years ago

3 0

Answer:

Option 1 is the correct answer.

Step-by-step explanation:

In first circle AC ≅ AB radii of same triangle. Similarly in second circle sides AB ≅ BC radii of second circle.

Since AC ≅ AB and AB ≅ BC

Therefore AC ≅ BC ≅ AB

Since all the sides of the triangle ABC are equal therefore triangle is an equilateral triangle.

And we know in an equilateral triangle all the angles are equal so ∠ABC = ∠BCA.

Option 1 is the answer.

Oxana [17]3 years ago

3 0

Answer:

A

Step-by-step explanation:

In the figure both circles are congruence because radius AB=radius AC of one circle and radius AB = radius BC of the other circle ( radii of circles are same ). Therefore line segment AB = line segment BC= line segment AC but these are the sides of the triangle ABC. So Δ ABC is an equilateral triangle .

But we know that an equilateral Δ has three equal angles and we say that ∠ABC=∠BCA. Hence we can use the reason A, to prove the ∠ABC =∠BCA.

You might be interested in

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation

Wewaii [24]

Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

This means that $\mu = 14, \sigma = 2$

Sample of 100:

This means that $n = 100, s = \frac{2}{\sqrt{100}} = 0.2$

What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?

This is 1 subtracted by the p-value of Z when X = 14.2. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{14.2 - 14}{0.2}$

$Z = 1$

$Z = 1$ has a p-value of 0.8413.

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

6 0

3 years ago

A unit vector lies in the xy plane, at an angle of 137 degrees from the x axis, with a positive y component. What is the unit ve

Fed [463]

Answer: ( -0.731, 0.682)

Step-by-step explanation:

The unit vector is defined as a vector that points in the same direction as our vector (137 degrees from the x-axis) and has a magnitude of 1.

Knowing the angle, is really simple to do it.

First, we know that for a radius R and an angle A, the rectangular coordinates can be written as:

x = R*cos(A)

y = R*sin(A)

And if we want that the magnitude/modulus of our vector to be 1, then R = 1, and we know that A = 137°

x = 1*cos(137°) = -0.731

y = 1*sin(137°) = 0.682

Then the unit vector is: ( -0.731, 0.682)

8 0

2 years ago

If two angles in a triangle are 60° and 30°, is the third angle acute, obtuse, or right?

Sindrei [870]

Answer: Right Angle

Step-by-step explanation:

And Since The Angles Of a Trangle Add Up To 180° When You Substract 90 From It You Remain With Another 90° Which Means The Angle Is Non Other Than a right angle traingle

60° + 30° = 90°

180° - 90° = 90°

∴ 90° = Right Angle Traingle

4 0

3 years ago

I have nooooo clue, please help

Aleksandr-060686 [28]

Answer:

case a) $x^{2}=3y$ ----> open up

case b) $x^{2}=-10y$ ----> open down

case c) $y^{2}=-2x$ ----> open left

case d) $y^{2}=6x$ ----> open right

Step-by-step explanation:

we know that

1) The general equation of a vertical parabola is equal to

$y=a(x-h)^{2}+k$

where

a is a coefficient

(h,k) is the vertex

If a>0 ----> the parabola open upward and the vertex is a minimum

If a<0 ----> the parabola open downward and the vertex is a maximum

2) The general equation of a horizontal parabola is equal to

$x=a(y-k)^{2}+h$

where

a is a coefficient

(h,k) is the vertex

If a>0 ----> the parabola open to the right

If a<0 ----> the parabola open to the left

Verify each case

case a) we have

$x^{2}=3y$

so

$y=(1/3)x^{2}$

$a=(1/3)$

so

$a>0$

therefore

The parabola open up

case b) we have

$x^{2}=-10y$

so

$y=-(1/10)x^{2}$

$a=-(1/10)$

$a$

therefore

The parabola open down

case c) we have

$y^{2}=-2x$

so

$x=-(1/2)y^{2}$

$a=-(1/2)$

$a$

therefore

The parabola open to the left

case d) we have

$y^{2}=6x$

so

$x=(1/6)y^{2}$

$a=(1/6)$

$a>0$

therefore

The parabola open to the right

3 0

2 years ago

Discussion topic

Molodets [167]

Answer:

Step-by-step explanation:

More than anything else, Algebra is a procedure. It has rules and axioms which when followed produce answers to problems -- problems that may not yield anything without Algebra.

These axioms and rules are familiar to anyone who has taken a course in advanced Mathematics. So each person who knows the procedure knows also how mathematics can work. It is a universal language spoken by those trained in what it offers to the education of both the "sender" and the "receiver."

3 0

2 years ago