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3 years ago

How many solutions exist for the system of equations below? 3x+y=18 3x+y=16

2 answers:

7 0

A) 3x+y=18
B) 3x+y=16

These equations are inconsistent and have no solutions. If these equations were graphed, it would be two parallel lines.

emmainna [20.7K]3 years ago

6 0

we have

$3x+y=18$ -------> equation $1$

solve for y

$y=-3x+18$

The slope $m=-3$

$3x+y=16$ -------> equation $2$

solve for y

$y=-3x+6$

The slope $m=-3$

The two slopes are the same, so the lines are parallel.

therefore

It's an inconsistent system of equations that has no solution.

the answer is

The system has no solution

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alekssr [168]

The similarity ratio of ΔABC to ΔDEF = 2 : 1.

Solution:

The image attached below.

Given ΔABC to ΔDEF are similar.

To find the ratio of similarity triangle ABC and triangle DEF.

In ΔABC: AC = 4 and CB = 5

In ΔDEF: DF = 2, EF = ?

Let us first find the length of EF.

We know that, If two triangles are similar, then the corresponding sides are proportional.

⇒ $\frac{AC}{DF} =\frac{BC}{EF}$

⇒ $\frac{4}{2} =\frac{5}{EF}$

⇒ $4EF=5\times2$

⇒ $EF=\frac{5\times 2}{4}$

⇒ $EF=\frac{5}{2}$

Ratio of ΔABC to ΔDEF = $\frac{AC}{DF} =\frac{4}{2}=\frac{2}{1}$

Similarly, ratio of ΔABC to ΔDEF = $\frac{BC}{EF} =\frac{5}{\frac{5}{2}}=\frac{2}{1}$

Hence, the similarity ratio of ΔABC to ΔDEF = 2 : 1.

6 0

3 years ago

Determine if the lines are parallel, perpendicular, or neither 10x+5y=-5 and y=-2x+6

Ksenya-84 [330]

If they are parallel they will have the same slope , m

So in y = mx + c, if there are two equations which both have the same m value they will be parallel.
If the lines are perpendicular they'll have slopes like this: 1/2 to -2/1 - where they flip and a negative gets added.

In the equations: 10x + 5y = -5 , and y = -2x + 6
We can rearrange 10x + 5y = -5 to be in the form y = mx + c
10x + 5y = -5
5y = -5 - 10x
y = -1 - 2x
y = -2x - 1

Since y = -2x - 1 and y = -2x + 6 both have the same slope of -2 they are parallel!

7 0

4 years ago

Cos ( α ) = √ 6/ 6 and sin ( β ) = √ 2/4 . Find tan ( α − β )

Zina [86]

Answer:

$\purple{ \bold{ \tan( \alpha - \beta ) = 1.00701798}}$

Step-by-step explanation:

$\cos( \alpha ) = \frac{ \sqrt{6} }{6} = \frac{1}{ \sqrt{6} } \\ \\ \therefore \: \sin( \alpha ) = \sqrt{1 - { \cos}^{2} ( \alpha ) } \\ \\ = \sqrt{1 - \bigg( {\frac{1}{ \sqrt{6} } \bigg )}^{2} } \\ \\ = \sqrt{1 - {\frac{1}{ {6} }}} \\ \\ = \sqrt{ {\frac{6 - 1}{ {6} }}} \\ \\ \red{\sin( \alpha ) = \sqrt{ { \frac{5}{ {6} }}} } \\ \\ \tan( \alpha ) = \frac{\sin( \alpha ) }{\cos( \alpha ) } = \sqrt{5} \\ \\ \sin( \beta ) = \frac{ \sqrt{2} }{4} \\ \\ \implies \: \cos( \beta ) = \sqrt{ \frac{7}{8} } \\ \\ \tan( \beta ) = \frac{\sin( \beta ) }{\cos( \beta ) } = \frac{1}{ \sqrt{7} } \\ \\ \tan( \alpha - \beta ) = \frac{ \tan \alpha - \tan \beta }{1 + \tan \alpha . \tan \beta} \\ \\ = \frac{ \sqrt{5} - \frac{1}{ \sqrt{7} } }{1 + \sqrt{5} . \frac{1}{ \sqrt{7} } } \\ \\ = \frac{ \sqrt{35} - 1 }{ \sqrt{7} + \sqrt{5} } \\ \\ \purple{ \bold{ \tan( \alpha - \beta ) = 1.00701798}}$

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3 years ago

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nignag [31]

The answer is irrational

4 0

3 years ago

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