Geometry Question, Need Help. I will give brainliest!

By applying Cramer's rule as solution method, the solution of the linear system 3 · x + 2 · y = 5 and x + 3 · y = 4 is equal to the set (x, y) = (1, 1).

Determinants are constructions studied in linear algebra and related to matrices, one of the most common applications of determinants is the solution of linear equations, whose simplest form is known as the Cramer's rule.

Now we proceed to use this rule to get the solution of the linear system:  

[tex]x = \frac{\left|\begin{array}{cc}5&2\\4&3\end{array}\right| }{\left|\begin{array}{cc}3&2\\1&3\end{array}\right|}[/tex]

[tex]x = \frac{(5)\cdot (3)-(4)\cdot (2)}{(3)\cdot (3) -(1)\cdot (2)}[/tex]

x = 1

[tex]y = \frac{\left|\begin{array}{cc}3&5\\1&4\end{array}\right| }{\left|\begin{array}{cc}3&2\\1&3\end{array}\right|}[/tex]

[tex]y = \frac{(3)\cdot (4) - (5)\cdot (1)}{(3)\cdot (3) - (1)\cdot (2)}[/tex]

y = 1

By applying Cramer's rule as solution method, the solution of the linear system 3 · x + 2 · y = 5 and x + 3 · y = 4 is equal to the set (x, y) = (1, 1).

To learn more on Cramer's rule: https://brainly.com/question/12682009

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Answer:

Step-by-step explanation:

We have

Find the  measure of angle x:

Bearing of the flight from Elgin to Canton is:

Answer:

235°

Step-by-step explanation:

Bearing: The angle (in degrees) measured clockwise from north.

The given scenario can be modeled as a triangle.

Given sides of the triangle:

As due north is at a right angle to due west, the angle in the right corner of the triangle is:

⇒ 90° - 44° = 46°

Use the Sine Rule to find angle y marked on the attached diagram (the angle opposite side b).

Sine Rule

[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

[tex]\implies \sf \dfrac{\sin 46^{\circ}}{680}=\dfrac{\sin y}{545}[/tex]

[tex]\implies \sf \sin y= \dfrac{545\sin 46^{\circ}}{680}[/tex]

[tex]\implies \sf y= \sin^{-1} \left(\dfrac{545\sin 46^{\circ}}{680}\right)[/tex]

[tex]\implies \sf y=35.20682806...^{\circ}[/tex]

Interior angles of a triangle sum to 180°

⇒ x° + y° + 46° = 180°

⇒ x° + 35.2068...° + 46° = 180°

⇒ x° = 98.79317194...°

Consecutive Interior Angles Theorem

When a straight line intersects two parallel straight lines, the consecutive interior angles formed sum to 180°.  Therefore the angle between due north and side a of the triangle is:

⇒ 180° - 44° = 136°

To find the bearing of the flight from Elgin to Canton, find the angle labelled green on the attached diagram:

[tex]\implies \sf Bearing =136^{\circ}+ 98.79317194...^{\circ}[/tex]

[tex]\implies \sf Bearing = 234.7931719...^{\circ}[/tex]

[tex]\implies \sf Bearing = 235^{\circ}[/tex]

As bearings are usually given as a three-figure bearings, the bearing of the flight from Elgin to Canton is 235°.

Learn more about bearings here:

https://brainly.com/question/27928951

Answer: Find the measures of an exterior angle and an interior angle given the number of sides of each regular polygon. Round to the nearest tenth, if necessary. 24 b 15, 345 24, 156 7.5, 172.5 15, 165​

Step-by-step explanation:  sum, S, of the measure of the interior angles of a polygon with n sides is: ... The sum of the interior angles of a 24 -gon is 3960. ... angles of a polygon is (n−2)⋅180 , where n is the number of sides. ... Each exterior angle measures 36024=15 . ... The sum of the 24 interior angles is then 24⋅165=3960 .

Answer:

(-5, -1)

General Formulas and Concepts:

Algebra I

Functions

Graphing

Solving systems of equations by graphing

Step-by-step explanation:

Where the 2 equations intersect is the solution to the systems of equations.

Answer:6722.8(sorry if i'm wrong)

Step-by-step explanation:

Answer:

a-8x+21y-10=19

b-3(x-6y)=6

c-(15-12)=4

Step-by-step explanation:

Answer:

4 roses were red.

Step-by-step explanation:

(2/3)*6=4

Answer:

THE ANSWER IS B BECAUSE I AM  BIG BRAIN

Step-by-step explanation:

Answer:

NK = 42

Step-by-step explanation:

Scale factor of dilating KLMN to form K'L'M'N' = ⅔. This fraction implies there was a reduction of the original shape to form the new image/shape.

NK corresponds to N'K'

N'K' = 28

To get the NK, divide 28 by the scale factor.

28 ÷ ⅔ = 28*³/2 = 42

NK = 42

Answer:

225 square feet

Step-by-step explanation:

If one side = 15 ft, and it's a square, you do 15 x 15 = 225 square feet

Hope that helps!

Answer:

2

Step-by-step explanation:

Rearrange to same form:

2y = -5x + 10

y = -5/2x + 10

ay = -5x + 4

Parallel lines have no intersection and solution, thus a = 2

Answer:

Step-by-step explanation:

For there to be no solution the lines must be parallel and have different y intercepts. To be parallel they must have the same slope.

Solving each for y

y=(10-5x)/2 and y=(4-x)/a

So the slopes are

-5/2 and -1/a, if they are equal

-5/2=-1/a

-5a=-2

a=2/5

Answer:

A U B= 1,2,3,4,6,10,11

Step-by-step explanation:

because A union B is all number from set A and set B together without repeating

Answer:

200,000

Step-by-step explanation:

100000 + 100000

Answer:

The beam of light is moving along the shoreline at a velocity of approximately 196 kilometers per second.

Step-by-step explanation:

The statement is described geometrically in the image attached below by means of a right triangle. All variables are described below:

[tex]OP[/tex] - Minimum distance between lighthouse and the straight shoreline, in kilometers.

[tex]PP'[/tex] - Distance along the straight shoreline, in kilometers.

[tex]\theta[/tex] - Angle of rotation of the lighthouse, in sexagesimal degrees.

To find the rate of change of distance along the straight shoreline ([tex]\frac{dPP'}{dt}[/tex]), in kilometers per minute, we use the following trigonometric relationship:

[tex]PP' = OP \cdot \tan \theta[/tex] (1)

Then, we differentiate this expression in time:

[tex]\frac{dPP'}{dt} = OP\cdot \dot \theta \cdot \sec^{2}\theta[/tex] (2)

Where [tex]\dot \theta[/tex] is the rate of change of the angle of rotation of the lighthouse, in radians per minute.

The angle at the given instant is calculated by (1): [tex]OP = 5\,km[/tex], [tex]PP' = 1\,km[/tex]

[tex]\theta = \tan^{-1} \left(\frac{PP'}{OP} \right)[/tex]

[tex]\theta \approx 11.310^{\circ}[/tex]

If we know that [tex]\dot \theta = 37.699\,\frac{rad}{min}[/tex], [tex]\theta \approx 11.310^{\circ}[/tex] and [tex]OP = 5\,km[/tex], then the rate of change is:

[tex]\frac{dPP'}{dt} \approx 196,035\,\frac{km}{min}[/tex]

The beam of light is moving along the shoreline at a velocity of approximately 196 kilometers per second.

Answer:

D 12rad2 12rad2 24

Step-by-step explanation:

Answer:

£268.8

Step-by-step explanation:

192 = 100%

19.2= 10%

19.2 x 4 = 76.8

76.8 = 10%

76.8 + 192 = 268.8

I hope this helped :)

Answer:

AAS postulate

Step-by-step explanation:

Answer:

i hope it help u:))

Step-by-step explanation:

i think that it will be ASA postulate

Answer:

A right triangle contains a right angle, so it must have two sides that are perpendicular. If the slopes of two sides can be shown to be negative reciprocals of each other, then it can be concluded that a right angle is formed. If a triangle contains a right angle, then it is a right triangle

Step-by-step explanation:

to determine if a triangle is a right triangle using slopes, you have to understand perpendicular slopes/negative reciprocals.

You can calculate the slope of all 3 sides of the triangle and if two of the slopes are negative reciprocals, then those two lines intersect creating a right angle/right triangle.

Let's say there's triangle ABC.

If the slope of AB is 1/2

and the slope of BC is 2/5

and the slope of CA is -2/1

then AB and CA intersect resulting in a right angle (triangle).

Answer:

There are 16 buses

Step-by-step explanation:

HOPE THIS IS HELPFUL!!!

Answer:

[tex](f\circ g )(x) = -4[/tex]

Step-by-step explanation:

We have

[tex](f\circ g )(x) := f(g(x))[/tex]

Therefore,

[tex]f(x)=x+1 \implies f(x)=g(x)+1[/tex]

So,

[tex](f\circ g )(x) = 5x + 1[/tex]

For [tex]x = -1:[/tex]

[tex](f\circ g )(x) = 5(-1) + 1 = -5+1=-4[/tex]

Answer:

Simplify 3log3(-5) = undefined?

Step-by-step explanation:

Answer:

5 ^7

Step-by-step explanation:

Answer:

hhffuutxu da ruzrxtoxotx suzs txyfyfxkfzfjzrzjrzurzi f2f jfizeyUrYsU

Step-by-step explanation:

that boi sus fo real nfcgxjfxiffxdkhdkydkgzxd lux kygksktskgxkhxyzjrztjztkxlyslyskt

Answer:

45%

Step-by-step explanation:

let's say 20 is 100%

10 is 50%

then 10 divided by 5 (to get 10%) is 2

so 1 is 5%

then we wanna get 9 so we do 10-1 which equals the percentages 50-5 to get 45%

Answer:

96

Step-by-step explanation:

24*4=96

Answer:

sir u can try looking up on internet, we do not do homeworks/assignemnts for people

Step-by-step explanation:

Answer:

220m

Step-by-step explanation:

2 pie r=2*22/7*3.5=220 m