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3 years ago

2(3/5n +3) - (2/3n-1)

Mathematics

2 answers:

Leokris [45]3 years ago

6 0

Hey there!

In order to solve this equation we have to distribute the negative symbols

So the subtraction symbol in the center of the equation becomes a addition symbol but the 1 is a negative

$2(\frac{3}{5} n +3 ) + -1 (\frac{2}{3}n-1) \\ \\ 2(\frac{3}{5} n+3)-1(\frac{2}{3}n) + -1(-1 ) \\ \\ 2(\frac{3}{5}n +3) + \frac{-2}{3} +1$

We can distribute in the normal method now!

$2(\frac{3}{5} n) +2(3)+ \frac{-2}{3}n+` \\ \\ \\ 2(\frac{3}{5} n) = \frac{6}{5}n \\ \\ \\ 2(3) = 6 \\ \\ \\ = \frac{6}{5}n + 6 + \frac{-2}{3} + 1$

Next, combine your like values (like terms)

$\frac{6}{5} n +6 + \frac{-2}{3}n +1 \\ \\ \\ \\ \frac{6}{5}n + \frac{-2}{3}n + (6 +1)$

Solving for our result

$\frac{6}{5}n + \frac{-2}{3} n = \frac{8}{15} \\ \\ \\ \\ \\ 6 + 1 = 7$

Therefore your answer would most likely be: $\frac{8}{15} + 7$

Good luck on your assignment and enjoy your day!

~ $LoveYourselfFirst:)$

borishaifa [10]3 years ago

4 0

Hey there! :)

2(3/5n + 3) - (2/3n - 1)

Simplify.

(2 * 3/5n) + (2 * 3) - (2/3n -1)

Simplify.

6/5n + 6 - 2/3n + 1

Add like terms.

(6/5n - 2/3n) + (6 + 1)

Make the fractions have the same denominator by multiplying fraction 1 (6/5n) by 3/3 and fraction 2 (-2/3n) by 5/5.

6/5n * 3/3 = 18/15n

-2/3n * 5/5 = -10/15n

So, our new equation looks like this : (18/15n - 10/15n) + (6 + 1)

Simplify.

8/15n + 6 —> final answer.

Hope this helped! :)

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Answer:

(a) x=2, y=-1

(b) x=2, y=2

(c) $\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) x=-2, y=-7

Step-by-step explanation:

Cramer's Rule

It's a predetermined sequence of steps to solve a system of equations. It's a preferred technique to be implemented in automatic digital solutions because it's easy to structure and generalize.

It uses the concept of determinants, as explained below. Suppose we have a 2x2 system of equations like:

$\displaystyle \left \{ {{ax+by=p} \atop {cx+dy=q}} \right.$

We call the determinant of the system

$\Delta=\begin{vmatrix}a &b \\c &d \end{vmatrix}$

We also define:

$\Delta_x=\begin{vmatrix}p &b \\q &d \end{vmatrix}$

And

$\Delta_y=\begin{vmatrix}a &p \\c &q \end{vmatrix}$

The solution for x and y is

$\displaystyle x=\frac{\Delta_x}{\Delta}$

$\displaystyle y=\frac{\Delta_y}{\Delta}$

(a) The system to solve is

$\displaystyle \left \{ {{x+y=1} \atop {x-2y=4}} \right.$

Calculating:

$\Delta=\begin{vmatrix}1 &1 \\1 &-2 \end{vmatrix}=-2-1=-3$

$\Delta_x=\begin{vmatrix}1 &1 \\4 &-2 \end{vmatrix}=-2-4=-6$

$\Delta_y=\begin{vmatrix}1 &1 \\1 &4 \end{vmatrix}=4-3=3$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{3}{-3}=-1$

The solution is x=2, y=-1

(b) The system to solve is

$\displaystyle \left \{ {{4x-y=6} \atop {x-y=0}} \right.$

Calculating:

$\Delta=\begin{vmatrix}4 &-1 \\1 &-1 \end{vmatrix}=-4+1=-3$

$\Delta_x=\begin{vmatrix}6 &-1 \\0 &-1 \end{vmatrix}=-6-0=-6$

$\Delta_y=\begin{vmatrix}4 &6 \\1 &0 \end{vmatrix}=0-6=-6$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-6}{-3}=2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-6}{-3}=2$

The solution is x=2, y=2

$\displaystyle \left \{ {{-x+2y=0} \atop {x+2y=5}} \right.$

Calculating:

$\Delta=\begin{vmatrix}-1 &2 \\1 &2 \end{vmatrix}=-2-2=-4$

$\Delta_x=\begin{vmatrix}0 &2 \\5 &2 \end{vmatrix}=0-10=-10$

$\Delta_y=\begin{vmatrix}-1 &0 \\1 &5 \end{vmatrix}=-5-0=-5$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{-10}{-4}=\frac{5}{2}$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{-5}{-4}=\frac{5}{4}$

The solution is

$\displaystyle x=\frac{5}{2}, y=\frac{5}{4}$

(d) The system to solve is

$\displaystyle \left \{ {{6x-y=-5} \atop {4x-2y=6}} \right.$

Calculating:

$\Delta=\begin{vmatrix}6 &-1 \\4 &-2 \end{vmatrix}=-12+4=-8$

$\Delta_x=\begin{vmatrix}-5 &-1 \\6 &-2 \end{vmatrix}=10+6=16$

$\Delta_y=\begin{vmatrix}6 &-5 \\4 &6 \end{vmatrix}=36+20=56$

$\displaystyle x=\frac{\Delta_x}{\Delta}=\frac{16}{-8}=-2$

$\displaystyle y=\frac{\Delta_y}{\Delta}=\frac{56}{-8}=-7$

The solution is x=-2, y=-7

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3 years ago

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MaRussiya [10]

The speed of one car is 'S'. The speed of the other car is (S + 10).

In 5 hours, the first car travels (5S) miles, and the other car travels 5(S + 10) miles.

Since they're going in opposite directions, the distance between them at any time
is the sum of the distance that each one has traveled.

500 = (5S) + 5(S + 10)

500 = 5S + 5S + 50

500 = 10S + 50

Subtract 50 from each side:

450 = 10S

Divide each side by 10

S = 45

S + 10 = 55

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4 years ago

What is the simplest form of the expression 6x(x − 4) − 16x2 − (9x − 1)

Sedbober [7]

Use distributie property which is
a(b+c)=ab+ac
therefor
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distribute the negative 1 infroont of the (9x-1)
-1(9x-1)=-9x+1
now we have

6x^2-24x-16x^2-9x+1
gropu like terms
6x^2-16x^2-24x-9x+1
add like terms
-10x^2-33x+1 is simplest form

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3 years ago