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3 years ago

4x−3/2 − 5−2x/3 − 3x−4/3 =5

Mathematics

1 answer:

Rina8888 [55]3 years ago

7 0

Answer:

x = 77/2

Step-by-step explanation:

Solve for x:

4 x - (2 x)/3 - 3 x - 5 - 3/2 - 4/3 = 5

Put each term in 4 x - (2 x)/3 - 3 x - 5 - 3/2 - 4/3 over the common denominator 6: 4 x - (2 x)/3 - 3 x - 5 - 3/2 - 4/3 = (24 x)/6 - (4 x)/6 - (18 x)/6 - 30/6 - 9/6 - 8/6:

(24 x)/6 - (4 x)/6 - (18 x)/6 - 30/6 - 9/6 - 8/6 = 5

(24 x)/6 - (4 x)/6 - (18 x)/6 - 30/6 - 9/6 - 8/6 = (24 x - 4 x - 18 x - 30 - 9 - 8)/6:

(24 x - 4 x - 18 x - 30 - 9 - 8)/6 = 5

Grouping like terms, 24 x - 4 x - 18 x - 30 - 9 - 8 = (24 x - 4 x - 18 x) + (-9 - 30 - 8):

((24 x - 4 x - 18 x) + (-9 - 30 - 8))/6 = 5

24 x - 4 x - 18 x = 2 x:

(2 x + (-9 - 30 - 8))/6 = 5

-9 - 30 - 8 = -47:

(2 x + -47)/6 = 5

Multiply both sides of (2 x - 47)/6 = 5 by 6:

(6 (2 x - 47))/6 = 6×5

(6 (2 x - 47))/6 = 6/6×(2 x - 47) = 2 x - 47:

2 x - 47 = 6×5

6×5 = 30:

2 x - 47 = 30

Add 47 to both sides:

2 x + (47 - 47) = 47 + 30

47 - 47 = 0:

2 x = 30 + 47

30 + 47 = 77:

2 x = 77

Divide both sides of 2 x = 77 by 2:

(2 x)/2 = 77/2

2/2 = 1:

Answer: x = 77/2

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19) Albert says that the two systems of equations shown have the same solutions.

k0ka [10]

Answer:

option A) Agree, because the solutions are the same is correct.

Step-by-step explanation:

FIRST SYSTEM

$6x + y= 2$

$-x-y=-3$

solving the system

$\begin{bmatrix}6x+y=2\\ -x-y=-3\end{bmatrix}$

$\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}6\:\mathrm{:}\:\quad \:-6x-6y=-18$

$\begin{bmatrix}6x+y=2\\ -6x-6y=-18\end{bmatrix}$

adding the equation

$-6x-6y=-18$

$+$

$\underline{6x+y=2}$

$-5y=-16$

so the system becomes

$\begin{bmatrix}6x+y=2\\ -5y=-16\end{bmatrix}$

solve -5y for y

$-5y=-16$

Divide both sides by -5

$\frac{-5y}{-5}=\frac{-16}{-5}$

simplify

$y=\frac{16}{5}$

$\mathrm{For\:}6x+y=2\mathrm{\:plug\:in\:}y=\frac{16}{5}$

$6x+\frac{16}{5}=2$

subtract 16/5 from both sides

$6x+\frac{16}{5}-\frac{16}{5}=2-\frac{16}{5}$

$6x=-\frac{6}{5}$

Divide both sides by 6

$\frac{6x}{6}=\frac{-\frac{6}{5}}{6}$

$x=-\frac{1}{5}$

Therefore, the solution to the FIRST SYSTEM is:

$x=-\frac{1}{5},\:y=\frac{16}{5}$

SECOND SYSTEM

$2x-3y = -10$

$-x-y=-3$

solving the system

$\begin{bmatrix}2x-3y=-10\\ -x-y=-3\end{bmatrix}$

$\mathrm{Multiply\:}-x-y=-3\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-2x-2y=-6$

$\begin{bmatrix}2x-3y=-10\\ -2x-2y=-6\end{bmatrix}$

$-2x-2y=-6$

$+$

$\underline{2x-3y=-10}$

$-5y=-16$

so the system of equations becomes

$\begin{bmatrix}2x-3y=-10\\ -5y=-16\end{bmatrix}$

solve -5y for y

$-5y=-16$

Divide both sides by -5

$\frac{-5y}{-5}=\frac{-16}{-5}$

Simplify

$y=\frac{16}{5}$

$\mathrm{For\:}2x-3y=-10\mathrm{\:plug\:in\:}y=\frac{16}{5}$

$2x-3\cdot \frac{16}{5}=-10$

$2x=-\frac{2}{5}$

Divide both sides by 2

$\frac{2x}{2}=\frac{-\frac{2}{5}}{2}$

Simplify

$x=-\frac{1}{5}$

Therefore, the solution to the SECOND SYSTEM is:

$x=-\frac{1}{5},\:y=\frac{16}{5}$

Conclusion:

As both systems of equations have the same solution.

Therefore, we conclude that Albert is right when says that the two systems of equations shown have the same solutions.

Hence, option A) Agree, because the solutions are the same is correct.

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Answer:

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Step-by-step explanation:

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3 years ago

The value of 100-30÷5 with parentheses can have a value of 1l4 or 49. EXPLAIN.

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A taxi charges a base fee plus $0.75/km.

Naily [24]

a) The rate of change in this situation is 0.75 dollars/km

b) The equation for the cost of hiring a taxi in terms of length of the

trip is y = 0.75 x + b

c) The initial value represents in this situation is $1.2

Step-by-step explanation:

The given is:

A taxi charges a base fee plus $0.75/km.
A 10-km trip costs $8.70

∵ A rate of change is a rate that describes how one quantity

changes in relation to another quantity

∵ The unit cost of a taxi is 0.75 dollars for each 1 kilometer

∴ The rate of change = 0.75 dollars/km

a) The rate of change in this situation is 0.75 dollars/km

Assume that the cost of hiring a taxi is $y for length of a trip x km

and a base fee of $b

∵ The length of the trip = x km

∵ The cost per km = $0.75

∵ The base fee = $b

∵ The cost of hiring a taxi = $y

- Write an equation for the the cost of hiring a taxi

∴ y = 0.75 x + b

b) The equation for the cost of hiring a taxi in terms of length

of the trip is y = 0.75 x + b

∵ The length of the trip is 10 km

∴ x = 10

∵ The cost of the hiring a taxi is $8.70

∴ y = 8.70

- Substitute these values in the equation of part (b)

∵ y = 0.75 x + b

∴ 8.70 = 0.75(10) + b

∴ 8.70 = 7.5 + b

- Subtract 7.5 from both sides

∴ 1.2 = b

∵ b is the base fee

∴ b is the initial value

∴ The initial value = $1.2

c) The initial value represents in this situation is $1.2

Learn more:

You can learn more about word problems in brainly.com/question/3950386

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