Provide the reasons for the following proof.
The figure shows triangle W X Y with a segment X Z drawn from vertex X to point Z on side W Y.
Given: Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y
Prove: triangle W X Z is congruent to triangle Y X Z
Statements Reasons
1.Segment W X is congruent to Segment X Y and segment X Z bisects angle W X Y 1. Given.
2. angle W X Z is congruent to angle Y X Z 2. Definition of an angle bisector.
3. Segment X Z is congruent to segment X Z. 3. _____________
4. triangle W X Z is congruent to triangle Y X Z 4. _____________
A. Reflexive Property of congruent to; SSS
B. Symmetric Property of congruent to; SSS
C. Reflexive Property of congruent to; SAS
D. Symmetric Property of congruent to; SAS

SOMEONE HELP! PLEASE!

The measure of ∠EFJ is 60°. Option B is the correct option.

What is a linear pair?

When two lines cross at one point, a linear pair of angles are created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as supplementary angles.

∠EFG is a linear pair of angle.

This means ∠E F G = 180°

Given that ∠J F K = 90° and ∠E F J = 2∠K F G.

∠E F G is the sum of angles ∠E F J, ∠J F K  and ∠K F G

∠E F G = ∠E F J + ∠J F K + ∠K F G

Now putting the value of ∠E F G, ∠J F K

180° = ∠E F J +  90° + ∠K F G

Again putting ∠K F G = 1/2∠E F J:

180° = ∠E F J +  90° + 1/2∠E F J

180° -  90° = 3/2 ∠E F J

90° = 3/2 ∠E F J

∠E F J = 90° ×(2/3)

∠E F J = 60°.

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Therefore , the solution of the given problem of triangle comes out to be tangent angle ∠B = 41/9 .

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

Here,

Given :

=> B = 8

=> S = 40

Tangent :

=> Angle ∠A = 40/9

For tangent ∠B:

=> Angle ∠B = 41/9

Therefore , the solution of the given problem of triangle comes out to be tangent angle ∠B = 41/9 .

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The probability that the two bills together will be worth at least 30 dollars is, 4/7

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

Given that,

Marya has 3 bills worth 10 dollars each

4 bills worth 20 dollars each

she chooses two of these bills at random

the probability that the two bills together worth at least 30 dollars =?

So,  total possible combinations  (10, 10, 10, 20, 20, 20, 20) = ⁷C₂ = 21

favorable combinations = ³C₁ × ⁴C₁ = 12

Probability = 12/21

Probability = 4/7

Hence, the probability is 4/7

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The function operations are given as follows:

The addition of functions is done combining the like terms, hence:

(f + g)(x) = f(x) + g(x)

(f + g)(x) = x² - 1 + 7 - 3x - x²

(f + g)(x) = -3x + 6.

The multiplication of the functions is done multiplying the terms and then combining the like terms, as follows:

hf(x) = (2x - 1)(x² - 1)

hf(x) = 2x³ - x² - 2x + 1.

The quotient of the functions is quite straightforward, we just replace their definitions, as follows:

(f/h)(x) = (x² - 1)/(2x - 1)

The subtraction of the functions is similar to the addition, combining the like terms, as follows:

(g - f)(x) = 7 - 3x - x² - (x² - 1)

(g - f)(x) = 7 - 3x - x² - x² + 1

(g - f)(x) = -2x² - 3x + 8.

(h - g)(x) = 2x - 1 - (7 - 3x - x²)

(h - g)(x) = 2x - 1 - 7 + 3x + x²

(h - g)(x) = x² + 5x - 8.

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Based on the given figure, we refer to angle a as the length of the side opposite to the angle θ, b as the length of the side adjacent to the angle θ and c as the length of the hypotenuse.

A right triangle is composed by two sides, that form a right angle = angle of 90º between them, plus the hypotenuse, which is the segment connecting these two sides.

The angles are classified as adjacent and opposite as follows:

The problem is given by the image presented at the end of the answer.

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The function is being transformed with a dilation of scale factor of 3 and an upward vertical shift of 4.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given is a function under some transformations, 3 h(x) + 4 ;

If we consider h(x) as a parent function, then the result after the transformation is 3h(x)+4,

We see that, it is being multiplied by 3, we know that if a function is being multiplied by a number greater than 1 in transformation then it is dilated by a scale factor of the number, hence, the function is being dilated by a scale factor of 3.

Also, we see, here is an addition of 4, we know that, when function is added by a certain number then in the transformed function the function is shifted vertically and addition mean it shifted vertically upwards, sine, 4 is added to the function it means, the function is shifted 4 unit vertically upwards.

Hence, the function is being transformed with a dilation of scale factor of 3 and an upward vertical shift of 4.

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Answer:

2670 feet

Step-by-step explanation:

x = [tex]\frac{19341}{tan14}[/tex]

The fraction form of the given decimal number [tex]8.3 \overline3[/tex] is 75/90.

Any number with a decimal point in between the full amount and the fractional portion is said to be decimal. These two components of the decimal are separated by the point. It is known as a decimal point as a result the figures following the decimal point are always less than one.

We can covert every decimal number into fractions as follows

Here we have

[tex]8.3 \overline3 = 10F[/tex]  ---- (1)

[tex]- 0.8\overline3 = - F[/tex]  ---- (2)    

Subtract (2) from (1)

=> [tex]8.3 \overline3 - 0.8\overline3 = 10F - F[/tex]  

=> 7.5 = 9F

=> F = 7.5/9

=> F = 75/90    [ Multiplied by 10 on both sides ]

Therefore,

The fraction form of the given decimal number [tex]8.3 \overline3[/tex] is 75/90.

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When a number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.

The sample space describing all possible outcomes is {1, 2, 3, 4, 5, 6}

Then outcomes for the event of rolling an even number. {2, 4, 6}

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to foretell the likelihood of many events.

In probability, sample space refers to the list of all potential outcomes of an experiment. Regardless of the number of ways an event could occur, each potential result is represented by a single point in the sample space.

The sample space is the numbers from 1 to 6 while event of rolling an even number is 3/6 = 1/2

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Based on the given derivative function, the function f is decreasing for a < x < b, because f'(x) < 0 for a < x < b (A).

The given derivative function is the first derivative of function f(x), where:

f'(x) = x² - (a+b) x + ab = (x - a) (x - b)

a < b

Since the first derivative function f'(x) is still in the form of x²  function, we can deduce that the original function f(x) has 2 extreme points, the maximum and the minimum. Those extreme points are (x = a) and (x = b).

However we cannot determine which one is the maximum point and which is the minimum one. We need to do another derivative work and check the second derivative function for each extreme points relevant to zero (0).

f'(x) = x²  - (a+b) x + ab

f''(x) = 2x - (a+b)

(x = a)

f''(a) = 2(a) - (a+b)

f''(a) = 2a - a - b

f''(a) = a - b < 0 --> because a < b

(x = b)

f''(b) = 2(b) - (a+b)

f''(b) = 2b - a - b

f''(b) = b - a > 0 --> because a < b

Based on the second derivative function, we can define that (x = a) is the maximum point because f''(a) < 0 and (x = b) is the minimum point because f''(b) > 0. Then the value of f(x) between a < x < b should be on a downward slope.

However wee need to reconfirm this statement by choosing one set of random number that meet the rules of a < x < b. For this time, we use:

a = 1

b = 3

x = 2

Then:

f'(x) = x² - (1 + 3) x + (1) (3)

f'(x) = x²  - 4x + 4

(x = 2)

f'(2) = (2)²  - 4(2) + 3

f'(2) = 4 - 8 + 3

f'(2) = -1 < 0 --> supported statement A

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The number of square inches of fabric that Alicia would need to create the logo is equal to 141.135 square inches.

Based on the information provided, we can logically deduce that a mathematical expression that represents the number of square inches of fabric that Alicia would need to create the logo is given by:

s . s + 0.5s . s

where:

s represents the length of the side of the square in inches.

By simplifying the mathematical expression, we have the following:

Number of square inches of fabric = s² + 0.5s²

Substituting the given parameters into the mathematical expression, we have the following;

Number of square inches of fabric = 9.7² + 0.5(9.7)²

Number of square inches of fabric = 94.09 + 0.5(94.09)

Number of square inches of fabric = 94.09 + 47.045

Number of square inches of fabric = 141.135 square inches.

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Complete Question:

Alicia, a graphic designer, is designing a new logo for a company. The logo will contain a square and a triangle. The triangle’s base and height will be the same length as the side of the square. Alicia wants to use fabric to create the shapes to use during her presentation to the company. The expression s · s + 0.5s · s represents the number of square inches of fabric she will need to create the logo, where s is the length of the side of the square in inches.

If a side of the square is 9.7 inches long, how many square inches of fabric will Alicia need?

Answer: The summer monsoon rains are a crucial source of rainfall for India, bringing in 80% of the country's annual rainfall. These rains are essential for the country's agriculture as they provide the necessary water for crops to grow and thrive. The monsoon season typically runs from June to September, and the amount of rainfall received during this time period can greatly impact the success of the agricultural season. With the majority of the rainfall coming during this season, farmers and agricultural experts closely monitor the monsoon forecast to ensure that enough rainfall is received to support the crops. Without the summer monsoon rains, the agricultural production of the country would be greatly impacted and the livelihoods of many farmers would be at risk.

Step-by-step explanation:

The p-value of the test hypothesis for each case is given as follows:

b) n = 9: 0.1151.

i. n = 25: 0.0228.

ii. n = 100: 0.

iii. When the sample size increases, the test statistic also increases, and hence the p-value decreases.

Before obtaining the p-value, the first step is obtaining the test statistic for the test.

The z-distribution is used, as the standard deviation for the population is known, and the equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which the parameters are given as follows:

The fixed parameters for this problem are given as follows:

[tex]\overline{x} = 52, \mu = 50, \sigma = 5[/tex]

Hence, for n = 9, the test statistic is given as follows:

z = (52 - 50)/(5/3)

z = 1.2.

We have a right-tailed test, as we are testing if the mean is greater than a value, hence the p-value is of 1 subtracted by the p-value of z = 1.2, that is:

1 - 0.8849 = 0.1151.

With n = 25, we have that:

z = (52 - 50)/(5/5)

z = 2.

z = 2 has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

With n = 100, we have that:

z = (52 - 50)/(5/10)

z = 4.

z = 4 has a p-value of 1.

1 - 1 = 0.

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Answer:

Slope =y2−y1/2−x1 =4−81+3=−1

Answer:

y = 4/5x + 3

Step-by-step explanation:

The equation y + 1 = 4/5(x + 5) can be solved by first isolating the y variable on one side of the equation. To do this, we'll first distribute the 4/5 across the parenthesis:

y + 1 = 4/5x + 4

Next, we'll subtract 1 from both sides of the equation:

y = 4/5x + 3

This is the equation in standard form, with the y variable on the left side and the x variable on the right side, and the constants added and subtracted.

Please find attached the drawing, created with MS Word, of the image of the triangle following the reflection across the mirror surface.

1) The object and the image are equidistant from the mirror

2) The object and the image following the reflection across a plane mirror are have the same side lengths and are therefore congruent

3) The image of the triangle is upright, and virtual and inverted from left to right

The laws of reflection are;

1) The angle made by the incident ray and the normal line (the angle of incidence) is equal to the angle made by reflected ray and the normal line

2) The incident ray, the reflected ray and the normal are coplanar

3) The incident ray is on the other side of the normal with regards to the refracted ray

1) The distance of the points on the object from the mirror are the same as the distance of the corresponding point from on the image from the mirror

2) A reflection of an object across a plane mirror is a rigid transformation such that the size of the object and the size of the image are the same.

Therefore, ΔABC ≅ ΔA'B'C'

3) The coordinates of the image formed following the  reflection of a point (x, y) across the y-axis is; (-x, y)

The y-coordinate remains the same, and the x-coordinates changes from positive to negative, and the location of the object on the left of the y-axis, produces an image on the right of the y-axis. Therefore

Therefore, the image is upright and inverted from right to left

The image of the triangle cannot be played on the screen, therefore, the image is virtual

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The graph that shows that y is less than or equal to 3x - 4 is plotted and attached

The graph is plotted by forming a table of value, then tracing eaching point in the table and marking the points of intersection of the x and y

The points intersections later joined with a line

The table of value is formed for x = -2, 0, and2

y ≤ 3x - 4

for x = -2, y ≤ 3 * -2 - 4 = -10

for x = 0, y ≤ 3 * 0 - 4 = -4

for x = 2, y ≤ 3 * 2 - 4 = 2

table of value

x      y

-2    -10

0     -4

2      2

The graph is attached, the line is a solid line since the inequality is less than or "equal to". The shading is below because it is less than

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Answer:

[tex]\frac{10}{7}x^4[/tex]

Step-by-step explanation:

There is an exponent rule which essentially states: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

All this is doing is essentially cancelling out the terms, since you can think of it as: [tex]\frac{x^a}{x^b}\implies \frac{x*x*x...\text{ "a" amount of times}}{x*x*x...\text{"b" amount of times}}[/tex], and if you recall, multiplication and division cancel. So we cancel out "b" amount of x's, leaving us with "a - b" amount of x's. Which can also be expressed as: [tex]x^{a-b}[/tex]

We can use this logic to solve our problem: [tex]\frac{20x^6}{14x^2}[/tex], here we can separate this into two different fractions: [tex]\frac{20}{14}*\frac{x^6}{x^2}[/tex] and we can use basic division on the left side and our exponent rule on the right side. This gives us the following:  [tex]\frac{10}{7}x^{6-2}\implies \frac{10}{7}x^4[/tex] which is our solution!

The Casey's rectangular array that is 1,167 units long and 7 units wide has an area of  

The formula for the area of a rectangle is the product of length and wide. This is written mathematically as

= length * wideness

In the problem the rectangular array made by Casey has a the following dimensions

length = 1167 units

wide = 7 units

Area of rectangle = length * wideness

substituting the values

Area of rectangle = 1167 * 7

Area of rectangle = 8169 square units

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I preserve shape but not size.

My image and pre-image will be similar.

I am created by using a scale factor that is less than one.

I am Dilation (decrease).

What is scale factor?

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller).

The points given are -

1. I preserve shape but not size.

2. My image and pre-image will be similar.

3. I am created by using a scale factor that is less than one.

During dilation if the scale factor is between 0 and 1, then the image shrinks.

The new image will be same but smaller in size than the original image.

The size of the image decreases from its original size but the shape remains the same.

Therefore, this is known as dilation (decrease).

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let's firstly convert the mixed fractions to improper fractions and then sum them up.

[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} ~\hfill \stackrel{mixed}{2\frac{2}{5}} \implies \cfrac{2\cdot 5+2}{5} \implies \stackrel{improper}{\cfrac{12}{5}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{equal sides}}{x+x}~~ + ~~\stackrel{\textit{third side}}{\left( x+\cfrac{4}{3} \right)} ~~ = ~~\stackrel{perimeter}{\cfrac{12}{5}}\implies 3x+\cfrac{4}{3}=\cfrac{12}{5}[/tex]

[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{15}}{15\left( 3x+\cfrac{4}{3} \right)=15\left( \cfrac{12}{5} \right)}\implies 45x+20=36\implies 45x=16 \\\\\\ \stackrel{\textit{equal sides}}{\boxed{x=\cfrac{16}{45}}}\hspace{10em}x+\cfrac{4}{3}\implies \cfrac{16}{45}+\cfrac{4}{3}\implies \stackrel{\textit{third side}}{\boxed{\cfrac{76}{45}}}[/tex]

The total number of relations in the set s = {1,2,3} is given as follows:

9.

The total number of relations in a set is given by the cardinality of the square of the set.

The square of a set is composed by all the possible pairs that can be formed with the elements in the set.

The set for this problem is defined as follows:

s = {1, 2, 3}.

The set has a cardinality of 3, as it has 3 elements, hence the cardinality of the square of the set is given as follows:

3² = 9.

Which is the total number of relations in the set.

These relations are all the ordered pairs with elements of s, hence:

Relations = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}

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Answer:

Step-by-step explanation:

y2-y2/x2-x1

The maximum score that can be in the bottom 5% of scores is 2.64

The middle 90% of scores lie between 2.88 and 4.56.

(a) To find the maximum score that can be in the bottom 5% of scores, we need to find the score that corresponds to the 5th percentile of the normal distribution.

Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28. To convert this back to the original scale, we can use the formula:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

x= 2.64

(b)

To find the range of scores that the middle 90% of scores lie between, we need to find the 5th and 95th percentiles of the normal distribution.

Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28 and the 95th percentile corresponds to a standard normal score of 1.28. To convert these back to the original scale, we can use the formula:

x = mu + z * sigma

Where

Plugging in the values, we get:

x = 3.6 + (-1.28) * 0.75

= 2.88 for the 5th percentile

x = 3.6 + 1.28 * 0.75

= 4.56 for the 95th percentile

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Answer:

top right graph

Step-by-step explanation:

5y=-10x+20

y=-2x+4

Answer: 40 years old.

Step-by-step explanation:

Let man's age = a

Let son's age = b

Since a man is 4 times as old as his son, therefore

a= 4b

In 5 years, he will only be 3 times as old as his son, therefore

a+5=3(b+5)

Apply substitution method :

4b+5=3b+15

b=10

a=40

the number of students going

$12.50 is the cost of the STUDENT ticket, so that knocks 2 answers down then, would you times the total by 12.5 to get the actual cost. no so it has to be the number of students going

Answer:

31=3+x

31=-3+x

28=x

28/7

$4

Each Candy bar cost $4 each

Step-by-step explanation: