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3 years ago

Fred and Victoria provide the following proofs for vertical angles to be equal.

Mathematics

2 answers:

Delvig [45]3 years ago

5 0

Both Fred and Victoria are correct.

mina [271]3 years ago

4 0

Answer:

Both Fred and Victoria's proofs are correct.

Step-by-step explanation:

Fred's proof:

angle 2 + angle 3 = 180° (t is a straight line) IT IS TRUE THAT t IS A STRAIGHT LINE

angle 1 + angle 2 = 180° (PQ is a straight line) IT IS TRUE THAT PQ IS A STRAIGHT LINE

Therefore, angle 1 + angle 2 = angle 2 + angle 3 (Transitive Property of Equality) THIS IS AN EXAMPLE OF THE TRANSITIVE PROPERTY OF EQUALITY

Hence, angle 1 = angle 3 (Subtraction Property of Equality)THIS IS AN EXAMPLE OF THE SUBTRACTION PROPERTY OF EQUALITY

Victoria's proof:

angle 1 + angle 4 = 180° (t is a straight line) TRUE

angle 1 + angle 2 =180° (PQ is a straight line) TRUE

Therefore, angle 1 + angle 2 = angle 1 + angle 4 (Transitive Property of Equality) TRUE

Hence, angle 2 = angle 4 (Subtraction Property of Equality) TRU

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Jason spent one third of his allowance going to the movies. He washed the family car and earned $7. What is weekly allowance if

mel-nik [20]

Answer:

6.66666666667

Step-by-step explanation:

so if the 7 dollars factors into allowance I am right his total allowance would be $20 one third of Twenty is 6.66666666667

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3 years ago

In geometry, how do defined terms and undefined terms relate to each other?

mart [117]

In geometry, definitions are formed using known words or terms to describe a new word. There are three words in geometry that are not formally defined. These three undefined terms are point, line and plane.

POINT (an undefined term) 
In geometry, a point has no dimension (actual size). Even though we represent a point with a dot, the point has no length, width, or thickness. A point is usually named with a capital letter. In the coordinate plane, a point is named by an ordered pair, (x,y). 

LINE (an undefined term) 
In geometry, a line has no thickness but its length extends in one dimension and goes on forever in both directions. A line is depicted to be a straight line with two arrowheads indicating that the line extends without end in two directions. A line is named by a single lowercase written letter or by two points on the line with an arrow drawn above them. 

PLANE (an undefined term) 
In geometry, a plane has no thickness but extends indefinitely in all directions. Planes are usually represented by a shape that looks like a tabletop or wall. Even though the diagram of a plane has edges, you must remember that the plane has no boundaries. A plane is named by a single letter (plane m) or by three non-collinear points (plane ABC). 

Undefined terms can be combined to define other terms. Noncollinear points, for example, are points that do not lie on the same line. A line segment is the portion of a line that includes two particular points and all points that lie between them, while a ray is the portion of a line that includes a particular point, called the end point, and all points extending infinitely to one side of the end point. 

Defined terms can be combined with each other and with undefined terms to define still more terms. An angle, for example, is a combination of two different rays or line segments that share a single end point. Similarly, a triangle is composed of three noncollinear points and the line segments that lie between them. 

Everything else builds on these and adds more information to this base. Those added things include all the theorems and other "defined" terms like parallelogram or acute angle.

8 0

3 years ago

Which is the exponential form of the expanded form shown?

Evgen [1.6K]

Answer: 4^2/5 is your main answer and pls mark me as brainiest

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Suppose that the population of the scores of all high school seniors who took the SAT Math (SAT-M) test this year follows a Norm

Vlad1618 [11]

Answer:

Confidence = $1-\alpha=1-0.01=0.99$

And then the confidence level would be given by 99%

Step-by-step explanation:

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Assuming the X follows a normal distribution

$X \sim N(\mu, \sigma)$

The distribution for the sample mean is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar x =512$ represent the sample mean

$\sigma=100$ represent the population standard deviation

n= 100 sample size selected.

The confidence interval is given by this formula:

$\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$ (1)

The marginof error for this case is given by Me=25.76. And we know that the formula for the margin of error is given by:

$Me=z_{\alpha/2} \frac{\sigma}{\sqrt{n}}$

$25.76=z_{\alpha/2} \frac{100}{\sqrt{100}}$

And we can find the critical value $z_{\alpha/2}$ like this:

$z_{\alpha/2}=\frac{25.76(\sqrt{100})}{100}=2.576$

And we know that on the right tail of the z score =2.576 we have $\alpha/2$ of the total area. We can find the area on the right of the z score using this excel code:

"=1-NORM.DIST(2.576,0,1,TRUE)" or using a table of the normal standard distribution, and we got 0.004998= $\alpha/2$ , so then $\alpha=0.00498*2=0.009995 \approx 0.01$ , and then we can find the confidence like this: