a triangle had sides with lengths 5, 12, and 13.
verify this is a pythagorean triple

Taking into account the definition of a system of linear equations, the number of adults attended the Saturday matinee showing is 29 and the number of children attended the Saturday matinee showing is 16.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

The tickets to gone with the wind, at the classic movie house, cost $4.50 for adults and $2 for children.

45 people attended the Saturday matinee showing and the Classic movie House sold $162.50 worth of tickets.

So, the system of equations to be solved is

[tex]\left \{ {{x+y=45} \atop {4.50x+2y=162.5}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "x" from the first equation you get:

x=45 - y

Then, substituting the expression in the second equation you get:

4.50×(45 - y) +2y=162.5

Solving:

4.50×45 - 4.50y +2y=162.5

4.50×45 - 4.50y +2y=162.5

202.5 -2.5y= 162.5

-2.5y= 162.5 -202.5

-2.5y= -40

y= (-40)÷ (-2.5)

y=16

Now, replacing in the expression x=45 - y you get:

x=45 -y

x= 45-16

x= 29

Finally, the number of adults attended the Saturday matinee showing is 29 and the number of children attended the Saturday matinee showing is 16.

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[tex]\cfrac{2}{x+4}~~ + ~~\cfrac{x}{x-3}\implies \cfrac{(x-3)2~~ + ~~(x+4)x}{\underset{\textit{using this LCD}}{(x+4)(x-3)}} \\\\\\ \cfrac{2x-6+x^2+4x}{(x+4)(x-3)} \implies \cfrac{x^2+6x-6}{(x+4)(x-3)}\qquad x\ne -4,3[/tex]

why can't it be -4 or 3? for if it ever does become -4 or 3, the denominator will turn to 0, giving an undefined fraction.

Answer:

put the line on y= -2

Step-by-step explanation:

The figure ABC is reflected along the line y = -2 and the new coordinated will be A(-2, -4), B (3, 0), and C (-2, -7).

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.

Given:

The coordinates of the figure of ABC is given as A(-2, 0), C(-2, 3), and B(3, -4),

The new coordinates of A'B'C' are A(-2, -4), B(3, 0), and C(-2, -7),

If the given figure is reflected as y = -x,

Then, the coordination will change like (-y, -x),

Thus, the new coordinates of ABC will be A(-2, -4), B (3, 0), and C (-2, -7).

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Using a system of equations, it is found that Teresa's password in the 7th day of the month is of 98.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The rule for her password is defined as follows: A whole number that is equal to four times the fourth power of the day of the month divided by two times the square day of the month. Hence, considering n as the day of the month, the equation is given by:

[tex]P = \frac{4n^4}{2n^2} = 2n^2[/tex]

Hence, for the 7th day, the password is given by:

P = 2 x 7² = 98.

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Answer:

30

Step-by-step explanation:

let unknown angle = x

cos = adjacent / hypotenuse

adjacent of ? = 13

hypotenuse = 15

cos(x) = (13/15)

==> take inverse cos of both sides

x = 30 (rounded)

Note : hypotenuse = longest side and adjacent = side thats not the hypotenuse or opposite

Answer:

it's not reasonable because the t-shirts alone cost 30 and the shoes cost 20 so it would cost 50 altogether.

Answer:

[tex]let \: \alpha \: be \: the \: 45 \\ \tan( \alpha ) = \frac{p}{b} \\ \tan(45) = \frac{x}{3 \sqrt{2} } \\ 1 = \frac{x}{3 \sqrt{2} } \\ x = 3 \sqrt{2} \\ by \: using \: pythagoras \: therom \\ {y}^{2} = {3 \sqrt{2} }^{2} + {3 \sqrt{2} }^{2} \\ {y}^{2} = 18 + 18 \\ y = \sqrt{36} \\ y = 6[/tex]

Step-by-step explanation:

hope this will help you

9%

I need 20 letters so I'm just typing this but it is 9%

The coordinates of vertex B' are (-1,3)

Reflection is a mathematical transformation in which a image of an object is formed by flipping it over a reflection line a distance equal to the distance of the object from the reflection line.

Analysis:

When an object is reflected along the y-axis, only the the x-coordinate changes , if reflected along the x-axis, only the y-coordinate changes.

So vertex B' is a reflected vertex along the y- axis since it is at x=2

The distance of the x-coordinate of vertex B from the mirror line is 5-2 = 3

so the x-coordinate of vertex B' is going 3 units away from the mirror line which is at -1.

So the coordinates of vertex B' are (-1,3)

In conclusion, the coordinates of vertex B' reflected over the line X= 2 are (-1,3)

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Answer:

[tex]\left( fg\right) \left( x\right) =2x^3\sqrt[3]{x}\\\\\left( \frac{f}{g} \right) \left( x\right) =\frac{2x^{3}}{\sqrt[3]{x} }[/tex]

Step-by-step explanation:

The range of f as shown in the graph is -6 ≤ f(x) ≤ 5. The correct option is A. -6 ≤ f(x) ≤ 5

From the question, we are to determine the range of f.

The range of a function is the set of its possible output values.

The graph of the function, f, is shown in the diagram.

From the graph,

The minimum value of f on the x-axis is -6. That is, f(x) ≥ -6

and

The maximum value of f on the x-axis is 5. That is, f(x) ≤ 5

Combining the two expressions, we get

f(x) ≥ -6 and f(x) ≤ 5

That is,

-6 ≤ f(x) and f(x) ≤ 5

∴ -6 ≤ f(x) ≤ 5

Hence, the range of f as shown in the graph is -6 ≤ f(x) ≤ 5. The correct option is A. -6 ≤ f(x) ≤ 5

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Answer:

Explanitory

Response

Step-by-step explanation:

edge

Answer:

[tex]\frac{4}{12}[/tex] or [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{1}{4} + \frac{1}{12} = \frac{3}{12} + \frac{1}{12} = \frac{4}{12}[/tex]

Answer:

The answer to this question is -2.

Step-by-step explanation:

First, multiply one of the equations by something that can cancel out the other variable.

3x+2y=20

3(x+4y=0)

3x+2y=20

3x+12y=0

Now, subtract both equations.

-10y=20

Now, divide both sides by -10.

y=-2

Hope this helps!

Answer: Population: all the ham meat; Sample: four random places in the ham

Step-by-step explanation: I just took the test and got it right

Answer:

Centre (5,-9) and radius is 14

Step-by-step explanation:

The circle equation is of form,

[tex] = > {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} [/tex]

where centre is (a,b) and radius is 'r'.

Answer:

D) 8

Step-by-step explanation:

Use the Intersecting Chords Theorem to find the value of x:

[tex]x*x=16*4\\\\x^2=64\\\\x=8[/tex]

Answer:

I think its B

Step-by-step explanation:

Answer:

ai = 190.0

Step-by-step explanation:

I'll presume the sequence is arithmetic, simply because assuming the series is mathematical, there is more than one solution.

Assuming the series is comprised of numbers in an arithmetic progression, you will have...  (see attachment for better explanation and step by step.)

The constant of proportionality between y and x in the graph is 3/2 option third is correct.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

We have a graph shown in the picture.

As we can see, the given graph shows a line, which passes through (0, 0)

y = ax

a is the constant of proportionality.

We have two points (0, 0) and (6, 9) (from the graph)

From the above two points, we can find the equation of a line.

y = (9/6)x

y = (3/2)x

The value of the constant of proportionality is 3/2

Thus, the constant of proportionality between y and x in the graph is 3/2 option third is correct.

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Answer:

Step-by-step explanation:

1.169

Answer:

8^2−38+85+3√8 =111+6√2

(Decimal: 119.485281)

Answer:

I think none are solutions

Answer:

[tex]\cos^{-1}( \cos 43^{\circ}) = 43^{\circ}[/tex]

Step-by-step explanation:

The correct answer of the given function [tex]cos^{-1}[/tex] (cos 43°) will be 43°.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

It will be possible to comprehend the graphs, domains, differentiation, and integration of the four quadrants' trigonometric functions.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

We know that the inverse trigonometric function of any function will vanish.

[tex]cos^{-1}[/tex]  (cos 43°)  = 43° cos inverse has vanished with cos and thus 43° is coming out to be the answer.

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Answer:

Step-by-step explanation:

A set of random numbers can be used for simulating a situation by defining how the numbers will be used to represent the possible outcomes. Trials are repeated using newly-generated random numbers until there are a sufficient number of trials to give a reasonable prediction of the probability of interest.

__

We can simulate the situation as follows:

Here are our trials and results.

48 09 52 47 65 05 60 44 64 97 -- 3 of 10

11 96 69 33 54 86 43 13 47 31 -- 5 of 10

56 52 16 97 22 26 29 57 94 23 -- 5 of 10

42 66 97 09 62 17 35 52 98 26 -- 5 of 10

53 44 26 82 41 88 38 32 64 31 -- 6 of 10

73 43 45 30 41 29 59 15 81 66 -- 5 of 10

23 54 46 11 32 12 95 52 28 34 -- 6 of 10

41 59 26 41 19 53 14 73 32 05 -- 7 of 10

82 87 37 09 67 70 03 44 78 21 -- 5 of 10

11 15 30 29 89 37 97 79 34 25 -- 7 of 10

__

Of these 10 trials, 4 showed the result that at least 6 of the next 10 students will choose a computer course. That is, the probability is estimated to be about 4/10 = 40%.

_____

Additional comment

Here, we can only predict the probability of interest as some multiple of 10%, since we have numbers sufficient for only 10 trials.

We could arrange the random numbers a different way and reuse them, but we choose not to for the purpose of this answer. For that to make sense, we need to have assurance that these numbers are truly random.

The number of repeated values among these 100 pairs of digits suggests that this is a poor set of numbers to be using. 26 and 41 each show up 4 times, for example. The probability of that happening by chance in a truly random set of numbers is about 0.03%. A chance event is considered to be unlikely if its probability is less than 1%.

Answer:50%

Step-by-step explanation:believe me it is 50%. 40% isn’t even a option. 50% is the correct answer.

Answer:

60.

Step-by-step explanation:

P = 2( 17 + 13)

= 2 * 30

= 60

Answer:

1,514,919

Step-by-step explanation:

I just used a calculator cuz in 6th you can use one but here's the answer

Answer:

If the couple purchases a house and they made all their payments, their total cost of the house would be $1,541,919.

Explanation:

$256,000
$443,504
$513,765
$328,650 +
------------------

$1,541,919

The solution to the given quadratic expression using the completing the square is  x = ±√10 +8

This is a method of factoring quadratic expression. Given the quadratic function.

x^2 − 16x + 54 = 0

Subtract 54 from both sides

x^2 − 16x = -54

Complete the square

x^2 -16x +8^2 = -54 + 64

(x-8)² = 10
x - 8 = ±√10
x = ±√10 +8

Hence the solution to the given quadratic expression using the completing the square is  x = ±√10 +8

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