Consider the two triangles shown below. Which of the triangle congruence theorems could be used to prove the triangles congruent without establishing any additional information?
A: SAS
B: SSA
C: SSS
D: HL

Answer:2.5:1

Step-by-step explanation:

Using matrices the value of y is calculated to be -2

A determinant is a square array of numbers or variables surrounded by vertical lines.

This method is applied by first solving the determinant of the problem

D = 2 * 6 - 2 * 7

D = 12 - 14

D = -2

Solving for y

Replace the second column with the column at the right side of the equality sign. Solve the determinant in this condition and divide with the first determinant D = -2

Δ = (2 * 6) - (2 * 4) = 12 - 8 = 4

y = Δ / D

y = 4 / -2

y = -2

hence y = -2

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a) The formula to represent the relationship is y = 0.50x + 15

b) On a coordinate plane the graph will be a straight line because it is a linear function

c) the slope is 0.50 and y intercept is 15

2.(a) The slope of the line is calculated to be 2/5

b) In one minute, Kailee will run 0.4 laps

c) In 24 minutes, she will run 9.6 laps

The slope, m of the linear function is calculated using the points on the graph (5.5, 2.2) and  (11, 4.4)

m = (y₀ - y₁) / (x₀ - x₁)

m = (2.2 - 4.4) / (5.5 - 11)

m = (-2.2) / (-5.5)

m = 2/5

The equation is y = mx where m = 2/5 = 0.4

in one minute, x = 1,

y = 2/5 * 1 = 2/5 laps

in 24 minutes, x = 24

y = 2/5 * 24 = 9.6 laps

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By taking the quotient between consecutive terms we can see that it is constant, thus, the sequence is geometric.

A geometric sequence is a sequence where, to get the next term, we need to multiply the previous term by a constant number.

The general recursive formula for a geometric sequence is:

Aₙ = c*Aₙ₋₁

Where c is a constant.

The given sequence is:

500, 100, 20

If we take the quotient between two consecutive terms, we will get:

100/500 = 1/5

20/100 = 1/5

We got the same denominator in both equations, then we can write:

100 = 500*(1/5)

20 = 100*(1/5)

So we have the previous term times a constant, which s 1/5, so this is a geometric sequence.

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Line PQ is parallel to EF in the triangle DEF. So, ABC, DPQ, etc. Thus, we can state that A = D, B = P, and C = Q, indicating that the triangle ABC is comparable to the triangle DEF.

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Step-by-step explanation:

f(x) = x² + 5 g(x) = x + 4

for f(g(x)) or (f○g)(x) we take the expression of g and place it everywhere in the expression of f where x is mentioned.

so, (x + 4) goes into (x² + 5) giving us

((x + 4)² + 5) = x² + 8x + 16 + 5 = x² + 8x + 21

so, (2) is the correct answer.

8.

the same principle

f(x) = 2x + 9 g(x) = (x - 9)/2

just here we take f and put it into g :

g(f(x)) = ((2x + 9) - 9)/2 = 2x/2 = x

so,

(a) g(f(15)) = 15

(b) g(f(-3)) = -3

(c) g(f(x)) = x

to verify e.g. (a) we use x = 15 in f(x)

f(15) = 2×15 + 9 = 30 + 9 = 39

and then we use this result as new x = 39 in g :

g(39) = (39 - 9)/2 = 30/2 = 15

correct.

the total number of deer in the park can be expected to be less than two years old 360.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, Park rangers tagged 80 deer in a park they found that 24 of the deer were less than two years old.

The number of deer that are less than two years old:

=> 1200 * 24/80

Since the ratio of the deer is 24/80

=> 1200*3/10

=> 360

Therefore, 360 is the total number of deer in the park can be expected to be less than two years old.

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The train covers 150 kilometers in one and a half hours.

To calculate the distance a train travels in one and a half hours at an average speed of 100 kilometers per hour, you can use the formula:

Distance = Speed x Time

In this case, the distance the train travels in 1.5 hours is:

Distance = 100 km/h x 1.5 hours = 150 kilometers

So the train would cover a distance of 150 kilometers in 1.5 hours.

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Answer: 5148 can be expressed as a product of prime factors using power notation. To find the prime factorization of 5148, we can divide it by the smallest prime number that divides it until the quotient is a prime number.

5148 = 2 * 2574

2574 = 2 * 1287

1287 = 3 * 429

429 = 3 * 143

143 = 11 * 13

So the prime factorization of 5148 is:

5148 = 2^2 * 3^3 * 11 * 13

Therefore, 5148 can be expressed as a product of prime factors using power notation as 2^2 * 3^3 * 11 * 13.

Step-by-step explanation:

Answer:2² x 3² x 11 x 13

Step-by-step explanation:

5148 - This is divisible by 9 as the sum of digits is 18 which a multiple of 9.

5148/9 = 572

572 is divisible by 4 as the sum of last two digits is a multiple of 4.

572/4 = 143  

143 is divisible by 11 and 13.

So, the factors are 4 x 9 x 11 x 13 or 2² x 3² x 11 x 13

Cheers

Answer:

7 × (6 - 2)

Step-by-step explanation:

difference of 6 and 2: 6 - 2

difference of 6 and 2 multiplied by 7: 7 × (6 - 2)

Answer: 7*(6-2)

Step by Step Explanation: Change the words into math signs

The possible dimensions of the rectangular garden are 8ft by 12ft, 6ft by 16ft, and 4ft by 24ft

In this problem, Misaki used five sections of fencing, two 4 ft sections, two 6 ft sections, and one 8 ft section to build a rectangular garden without cutting any. To find the possible dimensions of the garden, we can use the lengths of the fencing sections to make different combinations of the length and width of the garden.

Here are a few possible combinations for the rectangle shaped garden.

A garden that is 8 ft by 12 ft: This would use the two 4 ft sections as the width and the two 6 ft sections as the length.

A garden that is 6 ft by 16 ft: This would use the two 4 ft sections as the width and the one 8 ft section and two 6 ft sections as the length.

A garden that is 4 ft by 24 ft: This would use the two 6 ft sections as the width and the one 8 ft section and two 4 ft sections as the length.

It's important to notice that there are no other possibilities with the given lengths of fencing. Misaki can't have different dimensions because all the lengths are given, and if the width and length are swapped, we will get a different rectangular garden.

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Answer: 4/12

Step-by-step explanation:

Simplify each fraction by dividing or multiplying. Then you’ll get the answer

Answer:

4/12

Step-by-step explanation:

you simpify 4/12 and get 1/3 and that is what is being shown in the picture.

Answer:

The missing length is:

[tex]\sqrt{50}[/tex]

or

[tex]5\sqrt{2}[/tex]

Step-by-step explanation:

To solve for a length in a right triangle, we have to use the Pythagorean Theorem which states:

[tex]a^{2} +b^{2} =c^{2}[/tex]

Where a and b are sides and c is the hypotenuse.

[tex]7^{2} +1^{2} =c^{2}[/tex]

[tex]49+1=c^{2}[/tex]

[tex]c^{2} =50[/tex]

[tex]c=\sqrt{50}[/tex]

[tex]c=5\sqrt{2}[/tex]

42

Step-by-step explanation:

Answer: The complementary event for choosing a red marble is choosing a blue or purple. The total number of marbles is 5. The probability of choosing a red marble is 1/5, and the complement would be 4/5.

By :- Utsav Xettri

The number of games the team is projected to win is 56 games.

four times the difference of thirty-nine and five times the difference of eighteen and thirteen games

4{39 - 5(18 - 13)}

open parenthesis

= 4{39 - 5(5)}

= 4{39 - 25)

= 4(14)

= 56 games

Hence, based on the given statement, it is predicted that the team will win 56 games.

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Answer:78

Step-by-step explanation:

very simple

acb is an enlargment of fdc

39/18=2 3/18

2 3/18x36=78

The time she expects to finish is 4:14 PM

What does division of fractions mean?

A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.

5 9/10 = 5.9 hours = 5 hours (0.9*60)  minutes=  5 hours 54 minutes

Count 5 hours from 10:20 am, it is 3:20 pm

Add 54 minutes, 3 hour 74 minutes

60 minutes = 1 hour

it will be 4 pm remaining minutes = 74-60= 14

So, the time she expects to finish is 4:14 PM

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Answer:

The mean is affected by outliers that do not influence the mean. Therefore, when the distribution of data is skewed to the left, the mean is often less than the median.

Step-by-step explanation:

MAKE SURE TO REPHRASE

Answer:

38

Step-by-step explanation:

Just took the test

A function is an equation that has a single solution for each value of y.

When two functions f and g share a domain and a codomain, and f(a)=g is true for each an in the domain, we say that the two functions are equal (a).

A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x).

If two functions share the same domain and codomain as well as the same values across the board, then they are considered to be equal.

In spite of how the elements are arranged in the sets, two sets are said to be equal when all of their components are present in both. Afterward, the sets are referred to as equal sets. When all of one set's elements are absent from the other, two sets are said to be unequal.

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Answer: 23 percent

23 percent of attendees supported the home team.

The percentage of people supporting the home team is 22.98%.

Percentage is a way to express a fraction or proportion as a relative quantity out of 100. It is often denoted by the "%" symbol. It's used to compare and represent quantities, such as discounts, proportions, or rates, in a more easily understandable form. To find the percentage of people who supported the home team, we need to divide the number of people supporting the home team by the total number of people attending the game and then multiply by 100.

Therefore,

Calculating the percentage of people supporting the home team -

= (Number of people supporting the home team / Total number of people attending) x 100%

Substituting the values -

= (667 / 2900) x 100%

= 667/29

= 22.98

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Hi there! So already noticeable, there are some given parts and pieces.  AD is unknown, and BC it seems is also unknown, since they are both congruent to each other.  Segment AB is twice the length of AD, and AB is parallel to BC.  DC is 4 cm longer than AB.  

If you've done proofs, here's one thing that can help: Angle ADC and BCD are congruent to each other by same-side interior angles theorem.

If you haven't done proofs, I'm just going to keep this a little bit more understandable.  I don't want to overload you with a million formulas/theorems.

AD = BC
AB = 2(AD)
AB || BC
DC = AB + 4

Wait a minute... :)

AD x 2 = AB.  AB is 4 units shorter than DC.  

Try making an equation.  AD can be x, AB can be y, and DC can be z.

2x = y
y + 4 = z, z - 4 = y

2x = z - 4

So try substituting in some things that can work.  The length of AB has to be 2 times the length of AD.  DC is AD + 4.  AD can be 2, AB can be 4, and DC can be 8.  

2(2) = (8 - 4)
4 = 4 :)

Looks like it works! You should probably ask your teacher/parents for help with this one, it looks a little odd.  But that's the best I can do for you.  :)

Answer:

Step-by-step explanation: i need help too hope u find ur problem

:o

The complete table for the given quadratic equations is:

                   a                 b               c                d

1.                  1                -3                1                5

2.                 1                -2                1                5

3.                 3                6                3                1

When the middle term of a quadratic equation is split, we must rewrite the expression as the sum or difference of the two parts. We must split the middle phrase into two halves in order to determine the sum or difference of the words.

1. x² + 2x - 15

Split the middle term

= x² + 5x - 3x - 15

= x(x + 5) - 3(x + 5)

= (x - 3)(x + 5)

So, a = 1, b = -3, c = 1, d = 5

2. 2x³ + 6x² - 20x

= 2x(x² + 3x - 10)

= 2x(x² + 5x - 2x -10)

= 2x(x(x + 5) - 2(x + 5))

= 2x(x - 2)(x + 5)

So, a = 1, b = -2, c = 1, d = 5

3. 9x² + 21x + 6

= 3(3x² + 7x + 2)

Use splitting middle term method

= 3(3x² + 6x + x + 2)

= 3(3x(x + 2) + 1(x + 2))

= 3(x + 2)( 3x + 1)

= (3x + 6)(3x + 1)

So, a = 3, b = 6, c = 3, d = 1

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The best statement is F(x) is a linear function because x and f(x) are both increasing.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

x  f(x)

-1    1

0    5

2    13

4    21

8    37

Now, the rate of change is

= (5-1)/ (0+1)

= 4

and, the rate of change is

= (13-5)/ (2-0)

= 8/2

= 4

and, rate of change

= (21- 13) / (4-2)

= 8/2

= 4

Hence, F(x) is a linear function.

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Answer:Factor 3x^2-27. Step 1. Factor out of . Tap for more steps... Step 1.1. Factor out of . Step 1.2. Factor out of . Step 1.3. Factor out of . Step 2. Rewrite as . Step 3. Factor. Tap for

Step-by-step explanation:

The z-score for the data is Z= -2.83.

The standard score in statistics is the number of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.

The formula for calculating the z-score is :

Mean = 33000

μ = 34000

n = 200

σ = 5000

Putting all values,

[tex]Z = \dfrac{\bar x-\mu}{\sigma}\\Z = \dfrac{33000 - 34000}{\dfrac{5000}{\sqrt{200}}}\\Z = -2.83[/tex]

Hence, the value of the z-score will be Z= -2.83.

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The solution of the equation y = 3x + 2 at point (1, 5 ) is true.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression is y = 3x + 2, and the point is ( 1,5). The solution for the expression will be written as,

y = 3x + 2

5 = ( 3 x 1 ) + 2

5 = 3 + 2

5 = 5

Hence, the correct solution for the equation is point ( 1, 5).

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The required value of t is equal to 1/√13

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields, and weight.

Given here: The vector A=    [tex]t\left[\begin{array}{ccc}2\\3\\\end{array}\right][/tex] and we are required to find or simply normalize this vector A by multiplying a scalar t

On Multiplying the scalar t we get the matrix A= [tex]\left[\begin{array}{ccc}2t\\3t\\\end{array}\right][/tex]

Now normalizing the vector A we get ||A|| as

[tex]\sqrt{4t^2+9t^2} \\=\sqrt{13t^2} \\=\sqrt{13}.t[/tex]

If t=1/√13 we get  ||A||  as equal to 1

Thus for t=1/√13 we get the length of the vector as equal to one.

Hence, The required value of t is equal to 1/√13

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The value of cos(45°) is 1√2. The solution is obtained using properties of a right angled-triangle.

What is a right angled-triangle?

A right angled-triangle is a type of triangle whose one angle is 90° and the remaining two angles add up to 90°, thus, making the sum of the angles equal to 180°. The prolonged side of the triangle is known as hypotenuse.

The right triangle's three sides are connected to one another. The Pythagorean Theorem explains how these two things are related.

Base^2 + Perpendicular^2 = Hypotenuse^2

We are given length of one side equal to 6.

We know that sin 45°= Opposite side/Hypotenuse= 1/√2

Therefore, the hypotenuse will be 6√2.

Using Pythagoras theorem, we get

(6√2)^2= 6^2+ Perpendicular^2

72-36= Perpendicular^2

Perpendicular= 6  

We know that for cosine, it is adjacent side/hypotenuse.

Since, the adjacent side is 6 and the hypotenuse is 6√2,

Cos(45°)= 6/6√2 = 1√2

Hence, the value of cos(45°) is 1√2.

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