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Tems11 [23]
3 years ago
10

What is the solution this system of equations? 2/3x+y=6 and -2/3x-y=2

Mathematics
1 answer:
liraira [26]3 years ago
3 0

\bf \begin{cases}
\cfrac{2}{3}x+y=6\\[0.8em]
-\cfrac{2}{3}x-y=2
\end{cases}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
\stackrel{\textit{using the first equation}}{\cfrac{2}{3}x+y=6}\implies y=6-\cfrac{2x}{3}
\\\\[-0.35em]
~\dotfill


\bf \stackrel{\textit{using the found \underline{y} in the second equation}}{-\cfrac{2x}{3}-\left( 6-\cfrac{2x}{3} \right)=2}\implies -\cfrac{2x}{3}-6+\cfrac{2x}{3}=2
\\\\\\
\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{-2x-18+2x=6}\implies -18\ne 6\impliedby \stackrel{\textit{system is inconsistent}}{\textit{no solutions}}


if you set both equations to a y = mx+b, you'll notice the slope is the same, meaning the lines are parallel to each other, thus they never meet.

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4 years ago
Write the slope intercept equation of a line which is parallel to y=3x+5 passing through (-6,3). Can anyone please explain with
Eduardwww [97]

Remember that the slope intercept formula is:

y = mx + b

m is the slope

b is the y-intercept

If lines are parallel then they have the same slope (m)

This means that the slope of the line will be 3 :

y = 3x + b

Now we must find b

To do that you must plug in the point the line goes through in the x and y of the equation.

(-6, 3)

3 = 3(-6) + b

3 = -18 + b

21 = b

y = 3x + 21

Hope this helped!

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15) It is given that the charge of the waffle cone = $1.85

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C = 1.85 + 0.6x

16) To find the cost for 6 scoops of ice cream, put x = 6 in the above expression and simplify.

C = 1.85 + 0.6(6)

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Hence, cost of 6 scoops of ice cream = $5.45.                                                                                

7 0
4 years ago
(f + h)(x) <br> given f(x)= 3x-2x+4, g(x)= 8x-2, h(x)= 3x +2
zheka24 [161]

Answer:

To find the answers, all I have to do is apply the operations (plus, minus, times, and divide) that they tell me to, in the order that they tell me to.

(f + g)(x) = f (x) + g(x)

= [3x + 2] + [4 – 5x]

= 3x + 2 + 4 – 5x

= 3x – 5x + 2 + 4

= –2x + 6

(f – g)(x) = f (x) – g(x)

= [3x + 2] – [4 – 5x]

= 3x + 2 – 4 + 5x

= 3x + 5x + 2 – 4

= 8x – 2

(f  × g)(x) = [f (x)][g(x)]

= (3x + 2)(4 – 5x)

= 12x + 8 – 15x2 – 10x

= –15x2 + 2x + 8

\left(\small{\dfrac{f}{g}}\right)(x) = \small{\dfrac{f(x)}{g(x)}}(  

g

f

​  

)(x)=  

g(x)

f(x)

​  

 

= \small{\dfrac{3x+2}{4-5x}}=  

4−5x

3x+2

​  

 

My answer is the neat listing of each of my results, clearly labelled as to which is which.

( f + g ) (x) = –2x + 6

( f – g ) (x) = 8x – 2

( f  × g ) (x) = –15x2 + 2x + 8

\mathbf{\color{purple}{ \left(\small{\dfrac{\mathit{f}}{\mathit{g}}}\right)(\mathit{x}) = \small{\dfrac{3\mathit{x} + 2}{4 - 5\mathit{x}}} }}(  

g

f

​  

)(x)=  

4−5x

3x+2

​

Step-by-step explanation:

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lys-0071 [83]

Answer:

the answer is a

Step-by-step explanation:

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