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3 years ago

PLEASE HELP (look at pictures)

Mathematics

1 answer:

Vladimir [108]3 years ago

6 0

<h2>Answer:</h2>

This is a theorem called Converse of Alternate Exterior Angles that states that <em>if two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel</em>. Moreover, this theorem is based upon the corresponding Angles Converse Postulate that states that<em> if two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. </em>We don't need to prove this postulate, it's assume to be true. So our goal is to get corresponding angles congruent in order to use the corresponding Angles Converse Postulate,

Reason: Given

Statement: $\angle1\cong\angle2$

Reason: Def of vertical $\angle s$

Statement: $\angle1\:and\:\angle3 \ are \ vertical$

Reason: Def of vertical $\angle s$

Statement: $\angle1\cong\angle3$

Reason: Transitive Property

Statement: $\angle2\cong\angle3$

Reason: corresponding Angles Converse Postulate

Statement: $p\parallel q$

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A spinner numbered 1 through 12 is spun. Find the probability that

anastassius [24]

Answer:

$\dfrac{1}{6}$

Step-by-step explanation:

Let <em>A</em> be the event of getting an odd number.

<em>P(A)</em> be the probability of getting an odd number.

Total odd numbers here are 6 i.e. $\{1,3,5,7,9,11\}$

Here, total numbers in the game are 12 i.e $\{1,2,3,....,12\}$ .

Formula for probability of an <em>event E</em> can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

$P(A) = \dfrac{6}{12}\\\Rightarrow \dfrac{1}{2}$

Let <em>B</em> be the event of getting 11.

<em>P(B)</em> be the probability of getting 11.

Total number of possible cases is 1.

$P(B) = \dfrac{1}{12}$

$P(A \cap B)$ is the probability that we get 11 and an odd number.

Possible number of cases = 1

$P(A\cap B) = \dfrac{1}{12}$

<em>P(B/A)</em> is the probability that we get an 11 given that it is an odd number.

$P(B/A) = \dfrac{P(A \cap B)}{P(A)}\\\Rightarrow \dfrac{\dfrac{1}{12}}{\dfrac{1}{2}}\\\Rightarrow \dfrac{1}{6}$

Hence, P(B/A) = $\dfrac{1}{6}$

4 0

3 years ago

Read 2 more answers

(y - 2)2 = y2 – 6y + 4<br> Is this statement true or false?

trasher [3.6K]

<h3>Answer: False</h3>

==============================================

Explanation:

I'm assuming you meant to type out

(y-2)^2 = y^2-6y+4

This equation is not true for all real numbers because the left hand side expands out like so

(y-2)^2

(y-2)(y-2)

x(y-2) .... let x = y-2

xy-2x

y(x)-2(x)

y(y-2)-2(y-2) ... replace x with y-2

y^2-2y-2y+4

y^2-4y+4

So if the claim was (y-2)^2 = y^2-4y+4, then the claim would be true. However, the right hand side we're given doesn't match up with y^2-4y+4

--------------------------

Another approach is to pick some y value such as y = 2 to find that

(y-2)^2 = y^2-6y+4

(2-2)^2 = 2^2 - 6(2) + 4 .... plug in y = 2

0^2 = 2^2 - 6(2) + 4

0 = 4 - 6(2) + 4

0 = 4 - 12 + 4

0 = -4

We get a false statement. This is one counterexample showing the given equation is not true for all values of y.

6 0

3 years ago

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2. Find the lateral area of the pyramid to the nearest whole number.

Paladinen [302]

Answer:

What is the height of each triangle side?

Step-by-step explanation:

6 0

3 years ago

Which statement is true about the graph of the equation y=csc^-1(x)<br>

Sloan [31]

Answer:

There is a vertical asymptote at x = 0

Step-by-step explanation:

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3 years ago

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Black_prince [1.1K]

Answer:

CB= 4

Step-by-step explanation:

the triangles are in AA similarity.

AB/AD = BC/DE

4/12 = x/12

CROSS MULTIPLY;

x = 48/12

x = 4

5 0

3 years ago