4. Use the triangle congruence postulates to prove congruence.
Part I: Fill in the blanks to name each triangle congruence postulate.
a. SSS:
b. SAS:
c. ASA:
AAS:
In the triangle

56 sets of pictures she can post on her wall

It is given that alyssa's favorite tennis team has 8 players on them. She has taken a picture with every single athlete individually and wants to post some of the pictures on her wall. But she only wants to post 3 pictures on her wall.

For this we hve to use factorials. In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. The factorial of n also equals the product of n with the next smaller factorial: For example, The value of 0! is 1, according to the convention for an empty product.

So it will be - [tex]\frac{8!}{3!(8-3)!}[/tex] as this is the formula for combination

This will be 56.

Thus, 56 sets of pictures she can post on her wall

From both percentages, you can see that 0.735 is less than 3/4, hence the expression that 0.735 > 3/4 is FALSE

The number given are in form of fractions and decimals. In order to determine which is true, we will convert the decimals and fractions to percentages.

For option B

0.735 = 0.735 * 100

0.735 = 73.5%

For the fraction 3/4

3/4 * 100 = 75%

From both percentages, you can see that 0.735 is less than 3/4, hence the expression that 0.735 > 3/4 is FALSE

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Answer:

refer to the above attachment

The solution to the equations 2x + 3y = 3, x – 2y = 5 using substitution method is y = -1 and x = 3 respectively.

2x + 3y = 3

x – 2y = 5

from equation (2)

x = 5 + 2y

Substitute x = 5 + 2y into equation (1)

2x + 3y = 3

2(5 + 2y) + 3y = 3

10 + 4y + 3y = 3

10 + 7y = 3

7y = 3 - 10

7y = -7

y = -7/7

y = -1

Substitute y = -1 into (2)

x – 2y = 5

x - 2(-1) = 5

x + 2 = 5

x = 5 - 2

x = 3

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After completing their trade, Store Owner A has 0 puzzles and 10 puppets, and Store Owner B has 30 puzzles and 0 puppets.

Here,

Let's assume the two toy store owners are Store Owner A and Store Owner B.

Before the trade, Store Owner A has 30 puzzles and 0 puppets, and Store Owner B has 0 puzzles and 10 puppets.

They agree to trade 30 puzzles for 10 puppets at a rate of 3 puzzles for each puppet.

So, for every 3 puzzles, Store Owner A will receive 1 puppet.

Store Owner A gives away 30 puzzles and receives 30 / 3 = 10 puppets.

After the trade, Store Owner A has 0 puzzles and 10 puppets.

Store Owner B gives away 10 puppets and receives 10 * 3 = 30 puzzles.

After the trade, Store Owner B has 30 puzzles and 0 puppets.

So, after completing their trade, Store Owner A has 0 puzzles and 10 puppets, and Store Owner B has 30 puzzles and 0 puppets.

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Answer: $67.20

Step-by-step explanation: i got it right

Mike has to spend $67.20 on his remodeling project.

Explanation:

6 ft = (4 + x) ft

4+x = 6

   x = 6-4 = 2

Area 1:

S1 = 2 × (4+2)

    = 2 × 6

    = 12 ft²

Area 2:

S2 = 2 × (4+2)

     = 2 × 6

     = 12 ft²

The area of his kitchen is S1 + S2 = 12 + 12 = 24ft²

               = 24 × 2.80

               = $67.20

The image is given below for the area of the house.

Word problems normally include mathematical modeling questions, in which data and facts approximately a sure machine is given and a scholar is required to increase a model. as an instance: Jane had $five.00, then spent $2.00. How tons does she have now?

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Answer:

21.1

Step-by-step explanation:

sin 49 = x / 28

0.75470958 = x/28

x = 21.1

Answer:

x=18.4

y=35

Step-by-step explanation:

So to solve for x, you're going to use one of the six trigonometric functions (you really only need to use the three main ones, sin, cos, and tan, to solve these problems). In this case you know the adjacent of the angle 49 degrees, and the hypotenuse. There is a trigonometric function which is defined as: [tex]\frac{adjacent}{hypotenuse}=cos(\theta)[/tex]. So let's plug in the known values:

[tex]cos(49) = \frac{x}{28}[/tex]

Multiply both sides by 28

[tex]cos(49) * 28 = x\\[/tex]

Calculate cos(49) using a calculator (make sure it's in degree mode):

[tex]0.656 * 28 \approx x[/tex]

[tex]18.4 \approx x[/tex]

So the second problem, you need to use the inverse of one of the trigonometric function, which essentially takes what f(x) is, and returns x. So in this case we're looking for a trigonometric function that is defined using the opposite and adjacent side, which tan is. [tex]tan(\theta)=\frac{opposite}{adajcent}[/tex]. In this case opposite=19, and adjacent=27. So plug in the known values:

[tex]tan(y)=\frac{19}{27}[/tex]

Apply the inverse of tan to both sides

[tex]y=tan^{-1}(\frac{19}{27})[/tex]

Calculate inverse of tan of 19/27 using a calculator:

[tex]y\approx35[/tex]

Answer:

a= 79° because they are in the position of co interior and b°is 101 it's self because of VOA

Answer:

x=7/9

Step-by-step explanation:

- Rewrite as x = 0.77777

- Setup another equation:

10x = 7.7777

x = 0.7777

- Substract and get to :

9x = 7

- Finally, solve for X

x = 7/9

Answer:

188

Step-by-step explanation:

1 - Multiply the numbers

4 * 11 * 5 * 28 + 4

44 + 5 * 28 + 4

2 - Multiply the numbers

44 + 5 * 28 + 4

44 + 140 + 4

3 - Add the numbers

44 + 140 + 4

188

ANSWER: >> 188

Diving the length AB into equal parts gives;

[tex]D→\left (4 \:,4.5\right) [/tex]

[tex]E→\left (5 \:,4.75\right) [/tex]

[tex]H→\left (8 \:,5.5\right) [/tex]

[tex]I →\left (9 \:,5.75\right) [/tex]

The number of equal parts obtained by counting are 8

Coordinates of point A is (2, 4)

Coordinates of point B is (10, 6)

Therefore;

Coordinates of point C is

[tex]\mathbf{ \left (2 + \frac{10 - 2}{8},\: 4 + \frac{6 - 4}{8}\right) }= \left (3 \:, 4.25\right) [/tex]

Coordinates of point D are;

[tex]\mathbf{\left (2 + \frac{10 - 2}{4} \: , 4 + \frac{6 - 4}{4}\right) }= \left (4 \:,4.5\right) [/tex]

Coordinates of point E are;

[tex]\mathbf{\left (2 + \frac{8 \times 3}{8} \: , 4 + \frac{2 \times 3}{8}\right)} = \left (5 \:,4.75\right) [/tex]

Coordinates of point F are;

[tex] \mathbf{\left (2 + \frac{8 \times 4}{8} \: , 4 + \frac{2 \times 4}{8}\right)} = \left (6 \:,5\right) [/tex]

Coordinates of point H are;

[tex]\mathbf{\left (2 + \frac{8 \times 6}{8} \: , 4 + \frac{2 \times 6}{8}\right)} = \left (8 \:,5.5\right) [/tex]

Coordinates of point I are;

[tex]\mathbf{\left (2 + \frac{8 \times 7}{8} \: , 4 + \frac{2 \times 7}{8}\right)} = \left (9 \:,5.75\right) [/tex]

Which gives;

[tex]D→\left (4 \:,4.5\right) [/tex]

[tex]E→\left (5 \:,4.75\right) [/tex]

[tex]H→\left (8 \:,5.5\right) [/tex]

[tex]I →\left (9 \:,5.75\right) [/tex]

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Both triangles are congruent by either ASA or AAS Congruence Theorem. hence, the right answer is A: Yes, they are congruent by either ASA or AAS.

The ASA Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent included sides.

The AAS Congruence Theorem states that the two triangles are congruent if they have two pairs of congruent angles and a pair of congruent non-included sides.

Triangle LMQ is shown in the figure attached below.

Thus, Proving

Triangle MNL ≅ triangle QNL (ASA)

Triangle MNL and triangle QNL have two pairs of congruent angles:

<LNM ≅ LNQ and <MLN and <QLN

Also, they have a common side: side LN (included side).

Therefore, Triangle MNL and triangle QNL are congruent by ASA.

Triangle MNL ≅ triangle QNL ( by AAS)

Triangle MNL and triangle QNL have two pairs of congruent angles:

<LNM ≅ LNQ and <NML and <NQL

Also, they have a common side: side LN (non-included side).

Thus, Triangle MNL and triangle QNL are congruent by ASA.

Hence, the right answer is: A: Yes, they are congruent by either ASA or AAS.

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Answer: option A

Step-by-step explanation:

The list is known as the sampling frame.

To conduct a survey on current social work majors, a researcher gets a list of all students who have declared a social work major from the registrar from which a sample will be drawn.

This list is known as a sampling frame.

The sampling frame is the list from which units are drawn for the sample.

Hence, the list is known as the sampling frame.

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The value of n that satisfies the inequality is 6.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

4n − 12 < 2n + 2

For n= 6

4(6) - 12 = 12

2(6) + 2 = 14

Thus, n=6 satisfies

For n= 7

4(7) - 12 = 16

2(7) + 2 = 16

Thus, n=7 not satisfies

For n=8

4(8) - 12 = 20

2(8) + 2 = 18

Thus, n=8 not satisfies.

For n= 9

4(9) - 12 = 24

2(9) + 2 = 20

Thus, n=9 not satisfies.

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The sample space neeeded for the experiment to find the face cards is 52.

Given there is a standard deck of cards.

We have to finf the sample space needed for the experiment of finding the probability of face cards.

Probability is the chance  of happening an event among all the events that are possible. It lies between 0 and 1. The probability is the number of items divided by the total items.

Sample is a part of population. It is studied when the study of whole population is difficult to do.

Cards in a deck=52

Number of face cards is 12.

When we  draw a card from the deck then it might be a face card or not. So we have to draw all the cards of a standard deck because it might possible that face card is present at the end of deck.

Hence the sample size needed in the experiment is 52.

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Answer:

2.7930 × [tex]10^{4}[/tex]

Step-by-step explanation:

1.9 × 105 × 140 = 27,930

Scientific notation: 2.7930 × [tex]10^{4}[/tex]

Answer:

the slope of a line is parallel to the line is (3,-2)

(0,2)

Answer: 6

Step-by-step explanation:

The slope of ST is

[tex]\frac{-5-0}{0-(-6)}=-\frac{5}{6}[/tex]

The slope of UV is

[tex]\frac{y-1}{-9-(-3)}=\frac{y-1}{-6}[/tex]
Since parallel segments have the same slope,

[tex]-\frac{5}{6}=-\frac{y-1}{6}\\\\5=y-1\\\\y=6[/tex]

The orthographic projection based on the information given is illustrated below.

It should be noted that orthographic projection is a common method that's used for representing three-dimensional objects where each of the object is viewed along parallel lines that are perpendicular to the plane of the drawing.

In this case, it is a form of parallel projection, where all the projection lines are orthogonal to the projection plane which then results in every plane of the scene appearing in affine transformation on the viewing surface.

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The chances that two people would have matching DNA fingerprints for these three locations is 1/1,000,000  

According to statement

In location A the chance that two people have four repeats is  1 in 100.

In location B the chance that two people have eight repeats is  1 in 50.

In location C the chance that two people have three repeats is  1 in 200.

So, to find the probability that two people would have matching DNA fingerprints for these three locations

Multiply the all chances in these locations:

1/100 x 1/50 x 1/200 = 1/1,000,000    

So, The chances that two people would have matching DNA fingerprints for these three locations is 1/1,000,000  

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Answer:

32468.41 yards

Step-by-step explanation:

11,405.59 + 12,048.82 + 9,014 = 32468.41

32468.41 yards

René Descartes provided the first systematic link between Euclidean geometry and algebra.

This branch of mathematics involves the study of object shape, their spatial relationship and that of their surrounding space.

René Descartes is referred to as the father of analytic geometry due to him establishing the relationship between Euclidean geometry and algebra.

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Answer:

(2,3),(4,3),(-2,-3),(-4,-3)

Step-by-step explanation:

A function is defined as a relation in which each domain element (x-value) is paired with exactly one range element (y-value).

This means that each value we input for x must have only one possible output. If the same x-value yields more than one y-value, it is not a function.

The correct answer, as shown above, meets the criteria of a function, as each x-value is shown to produce exactly one y-value. In this set of ordered pairs, if x = 2, then y = 3, and if x = -2, then x = -3.

A set of ordered pairs is not a function if there are ordered pairs with the same x-values but different y-values.

In the other sets of ordered pairs, one x-value has more than one possible y-value. Let's use the last set as an example:

(5,1),(5,2),(5,3),(5,4)

Inputting 5 as x produces four different y values; there is no one y value for the x-value. y could equal 1, 2, 3, or 4.

The correct option is D:

the curves do not intersect, so there is no solution

The area of the rectangle is given by:

f(x) = (x + 7)*(5x - 3)

f(x) = 5x² -3x + 35x - 21

f(x) = 5x² + 32x - 21

For the circle, the area is:

g(x) = 2*pi*(x + 6)^2

g(x) = 2pi*x^2  + 12pi*x + 72pi

The solution is given g(x) = f(x).

By graphing both functions (the green curve is the area of the rectangle, the orange one is the area of the circle). The two curves never do intercept, so the correct option is D.

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The incorrect statement is the typical number for customers in store A is greater than that of store B.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The end of the first line represents the minimum number and the end of the second line represents the maximum number.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Spread of store A = 88 - 50 = 38

Spread of store B = 90 - 48 = 42

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Answer:

2c+2b

Step-by-step explanation:

this is because standard form only applies to no. from 10 and above , furthermore, they are unlike terms

In the give diagram, the value of f is 6.0

From the question, we are to determine the value of f

Using the law of sines, we can write that

[tex]\frac{f}{sinF} =\frac{e}{sinE}[/tex]

From the given information,

F = 27°

e = 13

E = 98°

Putting the parameters into the equation, we get

[tex]\frac{f}{sin(27)} =\frac{13}{sin(98)}[/tex]

[tex]\frac{f}{0.4540} =\frac{13}{0.9903}[/tex]

[tex]f=\frac{13 \times 0.4540}{0.9903}[/tex]

f = 5.9598

f ≅ 6.0

Hence, the value of f is 6.0

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The equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c

The given parameters are:

Number of uniform = 8

Cost of each = $14

The cost of the uniforms and the shorts is then calculated as:

Cost = Number of uniforms * (Cost of uniform + Cost of short)

This gives

Cost= 8 * (14 + c)

Expand

Cost = 112 + 8c

Hence, the equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c

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Answer:

(x+1)²+(y-2)²= 20

Step-by-step explanation:

P = (-3,-2)

Q = (1, 6)

Center (h, k)

C = ((-3+1)/2 , (-2+6)/2)

C = (-2/2 , 4/2)

C = (-1 , 2)

Radius = Distance from the center to point Q

R = √((1-(-1))² + (6-(2))²)

R = √((2)² + (4)²)

R = √(4+ 16)

R = √20

Equation

(x-h)²+(y-k)²= R²

(x-(-1))²+(y-2)²= (√20)²

(x+1)²+(y-2)²= 20