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Artist 52 [7]
2 years ago
10

Given the system of linear equations:

Mathematics
1 answer:
Andre45 [30]2 years ago
8 0

The equations y=−5 and y=3x−2 make up the system of linear equations

The solution to the system is (-1,-5)

<h3>The graph of the system</h3>

The system of equation

y=−5

y=3x−2

See attachment for the graph of the system

<h3>The solution to the system</h3>

This is the point where the lines of the equation intersect.

From the graph in (a), the lines intersect at point (-1,-5)

Hence, the solution to the system is (-1,-5)

<h3>How to verify the solution</h3>

In (b), we have:

(x,y) = (-1,-5)

Substitute (x,y) = (-1,-5) in the system of equations.

So, we have:

-5 =−5

-5=3(-1)−2 -> -5 = -5

The above shows that the system of equations is true, for the solution

Read more about system of equations at:

brainly.com/question/14323743

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xeze [42]

Answer:

40

Step-by-step explanation

34 divided by 85 times 100 equals 40

plz mark me as brainliest :)

6 0
3 years ago
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In a rhombus MPKN with an obtuse angle K the diagonals intersect each other at point E. The measure of one of the angles of a ∆P
allsm [11]
The rhombus has a couple of very interesting properties. The first is that the diagonals meet at 90o angles.

The second is that all the sides are congruent. That's actually the key to the problem (or one of them.

The third is that the diagonals are line segments that bisect the angles where the vertex of the angle is. 

So just to make sure you understand what that last statement means <PKM  =  <NKM
K is the vertex of angle PKN 

Now the really heavy duty stuff about your question.
Given
K is obtuse. Therefore <PKM can't be 16o because MKN would also have to be 16 degrees and together they don't add up to anything over 90o.
So the 16o angle is at <EPK

Remember that the diagonals meet at right angles. <PEK = 90o

Finally all triangles have 180o
< PKE = 180 - 16 - 90 = 74. So to review
<PKE = 74o
<EPK = 16o
<PEK = 90o That's one half the problem.

Moving on to triangle PMN
By the properties of parallel lines and a rhombus  and isosceles triangles, that since PKN is bisected (rhombus property) Then PKN = 2* PKM =2*74 = 148o
The angle opposite <PKN is equal to <PKN so <PMN = <PKN
Since PKN = 148 then PMN = 148
Since KPN = 16o then PMN = 16o
Since triangle <PMN is isosceles <PNM = 16o

Summing up 
PMN = 148o
MPN = 16o
MNP = 16o

That's both triangles solved. This is a really nice little problem. If you google properties of a rhombus, you will find all the properties I have used proven. 
 
5 0
3 years ago
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14 ft ? 4 yd is &lt;,&gt;,or =
zubka84 [21]
14 feet is larger because 1 yard is 3 feet. so 4*3=12 ft, and 12ft is less than 14 ft
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3 years ago
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Solve this thing pls<br> <img src="https://tex.z-dn.net/?f=3%5Cleft%28q-7%5Cright%29%3D27" id="TexFormula1" title="3\left(q-7\ri
evablogger [386]

Answer:

  • Solution of equation ( q ) = <u>1</u><u>6</u>

Step-by-step explanation:

In this question we have given an equation that is <u>3 </u><u>(</u><u> </u><u>q </u><u>-</u><u> </u><u>7</u><u> </u><u>)</u><u> </u><u>=</u><u> </u><u>2</u><u>7</u><u> </u>and we have asked to solve this equation that means to find the value of <u> </u><u>q</u><u> </u><u>.</u>

<u>Solution : -</u>

\quad \: \longmapsto \:  3(q - 7) = 27

<u>Step </u><u>1</u><u> </u><u>:</u> Solving parenthesis :

\quad \: \longmapsto \:3q - 21 = 27

<u>Step </u><u>2</u><u> </u><u>:</u> Adding 21 on both sides :

\quad \: \longmapsto \:3q -  \cancel{ 21} +  \cancel{21} = 27  +  21

On further calculations we get :

\quad \: \longmapsto \:3q = 48

<u>Step </u><u>3 </u><u>:</u> Dividing by 3 from both sides :

\quad \: \longmapsto \: \frac{ \cancel{3}q}{ \cancel{3}}  =  \cancel {\frac{48}{3} }

On further calculations we get :

\quad \: \longmapsto \:   \pink{\boxed{\frak{q = 16}}}

  • <u>Therefore</u><u>,</u><u> </u><u>solution</u><u> </u><u>of </u><u>equation</u><u> </u><u>(</u><u> </u><u>q </u><u>)</u><u> </u><u>is </u><u>1</u><u>6</u><u> </u><u>.</u>

<u>Verifying</u><u> </u><u>:</u><u> </u><u>-</u>

Now we are very our answer by substituting value of q in the given equation . So ,

  • 3 ( q - 7 ) = 27

  • 3 ( 16 - 7 ) = 27

  • 3 ( 9 ) = 27

  • 27 = 27

  • L.H.S = R.H.S

  • Hence, Verified.

<u>Therefore</u><u>,</u><u> </u><u>our </u><u>solution</u><u> </u><u>is </u><u>correct</u><u> </u><u>.</u>

<h2><u>#</u><u>K</u><u>e</u><u>e</u><u>p</u><u> </u><u>Learning</u></h2>
3 0
2 years ago
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41. Which system is represented by the graph?
nekit [7.7K]

Answer:

the answer is the first choice please mark me brainliest

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