Given: x ∥ y
w is a transversal of x and y.

Prove: ∠4 ≅ ∠5

Parallel lines x and y are cut by transversal w. On line x where it intersects line w, 4 angles are created. Labeled clockwise, from the uppercase left: angle 2, angle 1, angle 3, angle 4. On line y where it intersects line w, 4 angles are created. Labeled clockwise, from uppercase left: angle 6, angle 5, angle 8, angle 7.
A 2-column table with 5 rows. Column 1 is labeled statements with the entries x is parallel to y, w is a transversal, angle 4 is congruent to angle 1, angle 1 is congruent to angle 5, angle 4 is congruent to angle 5. Column 2 is labeled reasons with the entries given, given, A, B, C.
Complete the two-column proof.

A

B

C

SOLUTION

For the image point A has the coordinates (-3, 6) and A' is (3, -6) so with a translation of

We see A(-3, 6) as

And B(-2, 2) as

Therefore the correct translation is

Option B is the correct answer.

The simplified expression of (-7)^2 x (-7)^5 x (-7)^-9 is (-7)^-2

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

(-7)^2 x (-7)^5 x (-7)^-9

The base of the above expression are the same

i.e. Base = -7

This means that we can apply the law of indices

When the law of indices is applied, we have the following equation:

(-7)^2 x (-7)^5 x (-7)^-9 = (-7)^(2 + 5 - 9)

Evaluate the sum in the above equation

So, we have

(-7)^2 x (-7)^5 x (-7)^-9 = (-7)^(7 - 9)

Evaluate the difference in the above equation

So, we have

(-7)^2 x (-7)^5 x (-7)^-9 = (-7)^-2

Hence, the simplified expression of the expression given as (-7)^2 x (-7)^5 x (-7)^-9 is (-7)^-2

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Answer:

a) x³

b)y⁵

Step-by-step explanation:

The right information of the circle is as follows:

The line LN is the tangent to the circle O.

Tangent to a circle is a line that touches the circle at one point.

The point where tangent meets the circle is called point of tangency.

The tangent is perpendicular to the radius of the circle, with which it intersects.

Tangent to a circle is always perpendicular to the radius.

Therefore, the correct information from the circle can be found as follows:

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Answer: A) ON is a radius of the circle

Step-by-step explanation:

The line ON starts from the midpoint of the circle showing that it is half of the distance(radius)

If 13800 adult Pacific newts made their annual migration between November 2020 and March 2021, Roughly 2/5 didn't survive the trip, then the number of newts survived crossing the road is 8280 newts

The number of adult Pacific newts made their annual migration = 13800

Roughly 2/5 didn't survive the trip

Then the number of newts didn't survive = 13800×(2/5)

= 13800×0.4

= 5520 newts

To find the number of newts survived, we have to use subtraction

The number of newts survived crossing the road = 13800-5520

= 8280 newts

Hence, If 13800 adult Pacific newts made their annual migration between November 2020 and March 2021, Roughly 2/5 didn't survive the trip, then the number of newts survived crossing the road is 8280 newts

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The set of letters in the word 'woodpecker' using the most concise method is {c, d, e, k, o, p, r, w}.

The elements (or members) of a set are enumerated in a row within curly brackets and separated by commas in the roster form; however, in the set-builder form, each element of the set is required to have only one property to be a member of the set.

Given: The word is 'woodpecker'

To write the set utilizing the listing (roster) method or the set builder notation.

The roster method or listing method exists as a method to show the elements of a set by listing the elements inside brackets.

Set builder notation exists as a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy.

The set builder notation exists not have a suitable method to list the elements of the given word.

The most concise method to list the elements of the given word, 'woodpecker', exists in the listing (roster) method.

Using the listing (roster) method,

The set of letters of the given word is {c, d, e, k, o, p, r, w}.

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Graph both equations. The coorinates of the point where the graphs intersect is the solution to the system of equations.

To graph them, notice that each equation corresponds to a line. A straight line can be drawn if two points on that line are given. Replace two different values of x into each equation to find its corresponding value of y, then, plot the coordinate pairs (x,y) to draw the lines.

First equation:

For x=2 and x=5 we have that:

Then, the points (2,1) and (5,7) belong to the line:

Second equation:

For x=0 and x=6 we have:

Then, the points (0,4) and (6,2) belong to the line:

Solution:

The lines intersect at the point (3,3).

Then, the solution for this system of equations, is:

In the picture, There is graph with a triangle SNZ. The reflected triangle of y=3 as (1,2),(5,3) and (5,5).

Given that,

In the picture, There is graph with a triangle.

The triangle is SNZ.

We have to find the reflection across y=3.

We have to draw a line on y=3.

On the line y=3,

Z point is there so it will be same that is (5,3).

Now, the point S is on (5,1)

Here, y is 1 that is 3+2=5

So, we take the reflected S point as (5,5)

Now, the point N is on (1,4)

Here, y is 4 that is 3-1=2

So, we take the reflected N point as (1,2).

Therefore, we get the reflected triangle of y=3 as (1,2),(5,3) and (5,5).

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Answer:

16%

Step-by-step explanation:

A salesperson earns a commission of $624 for selling $3900 in merchandise. Find the rate of commission:

624 is ?% of 3,900

624/3,900 = 16% of 3,900

check answer:

3,900 * 0.16 = 624

The expression for this scenario is:

Now substitute the value of t into the elevation expression above, to get the elevation reached after 3 hours.

we have

x/3=5/2

multiply in cross

2*x=3*5

2x=15

x=15/2

or

Multiply both sides by 3

3*(x/3)=3*(5/2)

x=15/2

Answer:

Step-by-step explanation:

Given two planes flying in opposite directions are 810 miles apart after 3 hours, and the first is 30 mph slower than the second, you want the speed of each plane.

Let s represent the speed of the slower plane. Then faster plane will have a speed of (s+30). The distance between the planes increases at a rate equal to the sum of their speeds. Distance is the product of speed and time, so we have ...

  distance = speed × time

  810 = (s + (s+30)) × 3

Dividing the equation by 3, we get ...

  270 = 2s +30

  240 = 2s . . . . . . subtract 30

  120 = s . . . . . . . divide by 2

  150 = s+30 . . . the speed of the faster plane

The speed of the first plane is 120 mph; the speed of the second plane is 150 mph.

The rate of the two planes flying in opposite direction was found to be

given data

The first plane is flying 30 mph slower than the second plane.

time = 3 hours

distance = 810 miles

let the rate of the faster plane be x

then rate if the slower plane will be x - 3

rate of both planes

= x + x - 30

= 2x - 30

Finding the rate of each plane

rate of both planes = total distance / total time

2x - 30 = 810 / 3

2x - 30 = 270

2x = 270 + 30

2x = 300

x = 150

Then the slower plane = 150 - 30 = 120 mph

Hence the rate of the faster plane is 150 mph and the rate of the slower plane is 120 mph

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go on play store and download symbolab it can help you

The algebraic expression for two less than the quotient of 15 and a number is 15x - 2.

What is algebraic expression ?

At least one variable and one operation must be present in an algebraic expression (addition, subtraction, multiplication, division). One such algebraic expression is 2(x + 8y).

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Answer: So the subject’s answer is Chapter 5.

Step-by-step explanation: Because there is no evidence that Armenians are smart, and in Chapter 5 people are more frustrated than kind.

The statement is (a) [tex]E_{xy}[/tex] Q(x, y); (b) -Q(x, y); (c) [tex]E_{x}[/tex] (Q(x, jeopardy) ∩ Q(x, Wheel of fortune)); (d) ∀[tex]_{y}[/tex][tex]E_{x}[/tex]Q(x, y); (e) [tex]E_{x}E_{y}[/tex](x ≠ y) (Q(x, jeopardy) ∩ Q(y, jeopardy)).

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Given that,

Q(x, y) be the statement "student x has become a contestant on quiz event y",

where the domain for x consists of all students in your major and for y consists of all quiz shows on television.

a) [tex]E_{xy}[/tex] Q(x, y)

b) -Q(x, y)

c) [tex]E_{x}[/tex] (Q(x, jeopardy) ∩ Q(x, Wheel of fortune))

d) ∀[tex]_{y}[/tex][tex]E_{x}[/tex]Q(x, y)

e)  [tex]E_{x}E_{y}[/tex](x ≠ y)(Q(x, jeopardy) ∩ Q(y, jeopardy)).

Therefore, the statements are above.

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Answer:

$1.15

Step-by-step explanation:

750 + 400 = 1,150

1/1000 * 1,150 = 1,150/1000 = $1.15 expected value of one ticket.

Since he paid more than $1.15 for the ticket he has a bad bet.

Since [tex]x[/tex] is approaching 1 from the left/below, we take the part of [tex]f(x)[/tex] that is defined over [tex]x<1[/tex], for which we have

[tex]f(x) = \dfrac{x-1}{\sqrt{x-1}}[/tex]

Since [tex]x\neq1[/tex], we can simplify this to

[tex]f(x) = \dfrac{x-1}{(x-1)^{1/2}} = (x-1)^{1/2} = \sqrt{x-1}[/tex]

and this is continuous at [tex]x=1[/tex], so we can evaluate the limit by directly substituting [tex]x[/tex].

To summarize:

[tex]\displaystyle \lim_{x\to1^-} f(x) = \lim_{x\to1} \frac{x-1}{\sqrt{x-1}} = \lim_{x\to1} \sqrt{x-1} = \sqrt{1-1} = \boxed{0}[/tex]

The most appropriate choice for expectation will be given by-

Amount of money the company expected to pay = $10400

What is expectation?

At first it is important to know about probability of an event.

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Suppose x is a random variable with the probability function f(x). suppose [tex]x_1[/tex], [tex]x_2[/tex],....., [tex]x_n[/tex] are the values corrosponding to the actual occurance of the event and [tex]p_1,[/tex] [tex]p_2,[/tex]....,[tex]p_n[/tex] be the corrosponding probabilities.

Expectation is given by the formula

[tex]p_1x_1 + p_2x_2....+p_nx_n[/tex]

Here,

Amount of money the company expected to pay =

$[tex](0 \times 0.70 +20000 \times 0.16+ 40000 \times 0.09 + 60000 \times 0.03 + 80000 \times 0.01 + 100000 \times 0.01)[/tex]

                                                                                  = $10400

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The quadratic equation in standard form that contains the points (5, - 6), (- 7, 0) and (3, 0) is y = - (1 / 4) · x² - x + 21 / 4.

Herein we find the equation of a parabola that contains a points and its x-intercepts (two real roots). According to fundamental theorem of algebra, we can derive a quadratic function with real coefficients if we know three points of the parabola. The procedure is shown below.

First, use the quadratic function in product form and substitute on all known variables to determine the lead coefficient:

y = a · (x + 7) · (x - 3)

- 6 = a · (5 + 7) · (5 - 3)

- 6 = a · 12 · 2

- 6 = 24 · a

a = - 6 / 24

a = - 1 / 4

Second, expand the quadratic function into its standard form:

y = - (1 / 4) · (x + 7) · (x - 3)

y = - (1 / 4) · (x² + 4 · x - 21)

y = - (1 / 4) · x² - x + 21 / 4

The quadratic equation in standard form is y = - (1 / 4) · x² - x + 21 / 4.

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The coordinates of the midpoint of a,b is given as;

When Seema used compatible numbers to estimate the product of (–25.31)(9.61), her estimate is A. -250.

From the information, it should be noted that Seema used compatible numbers to estimate the product of (–25.31)(9.61).

It should be noted that -25.31 when rounded will be -25.

It should be noted that 9.61 when rounded will be 10.

Therefore, the multiplication will be:

= -25 × 10

= -250.

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Seema used compatible numbers to estimate the product of (–25.31)(9.61). What was her estimate?

-250

-240

240

250

D. The function is neither above nor below its bounds.

An unbounded function is one that is not bounded. The function is referred to as being bounded (from) above by A if it has real values and f(x) A for all x in X. The function is referred to as being bounded by B (from below) if f(x) B for all x in X

A sequence is considered to be constrained if it has bounds above and below. Unbounded sequences exist when a sequence is not bounded. Because 1/n1 for all positive integers n, for instance, the sequence 1/n is confined above. Further, it

If there is an integer 2 such that for all x from the domain D(f), one has f (x) 2, we say that a real function f is bounded from below. If there is a number K such that for every x from the domain D(f), one has f (x) 2, then we say that a real function f is bounded from above.

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The variable represents time. The time in which a person runs a mile will depend on the speed of that person, and that can take almost any value, thus, here the variable is continuous.

First, when a variable is discrete and when it is continuous?

A variable is discrete if it only can take some selected values on a given interval, while a variable is continuous if it can take any value (or at least a dense set) of values in that interval.

For example, the numbers that one can roll on a dice form a discrete set, because the values can only be {1, 2, 3, 4, 5, 6}, just to given an example.

Now, in this case, the variable represents time. Time almost always is a continuous variable, in this case, the time is the time in which a person runs a mile. So that variable can take almost any value (depends on the speed of the person).

So we conclude that this is a continuous variable.

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Answer:

64 = x

Step-by-step explanation:

The angles are alternate interior angles and alternate interior angles are equal when the lines are parallel

128 = 2x

Divide each side by 2

128/2 = 2x/2

64 = x

Answer:

x = 64

Step-by-step explanation:

We know that,

If lines are parallel, the alternate angles are also equal.

Therefore,

[tex] \sf2x = 128[/tex]

Now, let us solve for x.

For that, divide both sides by 2.

[tex]x = 64[/tex]

Answer:

7 days.  

Step-by-step explanation:

139 = 202 - 9d  subtract 2002 from both sides of the equation

-63 = -9d  Divide both sides of the equation by -9

7 = d

The equation of the line with the given properties is y - 17 = 3/2(x - 18)

Linear equations are equations that have constant average rates of change.

The points are given as

(8, 17)

The slope is given as

Slope = 3/2

Calculate the slope of the points using

m = (y2 - y1)/(x2 - x1)

Where

Slope = m = 3/2

(x1, y1) = (8, 17)

So, we have

3/2 = (y - 17)/(x - 8)

Cross multiply in the above equation

So, we have

y - 17 = 3/2(x - 18)

A linear equation is represented as

y = m(x - x1) + y1

In point-slope form, we have

y - y1 = m(x - x1)

By comparing y - y1 = m(x - x1) and y - 17 = 3/2(x - 18), we can see that

y - 17 = 3/2(x - 18) is in point-slope form

Hence, the equation in point-slope form of the line that passes through the point (8, 17) is y - 17 = 3/2(x - 18)

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Answer:

Explanation:

Given the system of equations:

To