1/2 (3x + 5) = 7 anyone can someone explain this problem to me so I can understand it better.

kompoz [17]

In the equation

$3^x = 3\cdot 2^x$

divide both sides by $2^x$ to get

$\dfrac{3^x}{2^x} = 3 \cdot \dfrac{2^x}{2^x} \\\\ \implies \left(\dfrac32\right)^x = 3$

Take the base-3/2 logarithm of both sides:

$\log_{3/2}\left(\dfrac32\right)^x = \log_{3/2}(3) \\\\ \implies x \log_{3/2}\left(\dfrac 32\right) = \log_{3/2}(3) \\\\ \implies \boxed{x = \log_{3/2}(3)}$

Alternatively, you can divide both sides by $3^x$ :

$\dfrac{3^x}{3^x} = \dfrac{3\cdot 2^x}{3^x} \\\\ \implies 1 = 3 \cdot\left(\dfrac23\right)^x \\\\ \implies \left(\dfrac23\right)^x = \dfrac13$

Then take the base-2/3 logarith of both sides to get

$\log_{2/3}\left(2/3\right)^x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x \log_{2/3}\left(\dfrac23\right) = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(\dfrac13\right) \\\\ \implies x = \log_{2/3}\left(3^{-1}\right) \\\\ \implies \boxed{x = -\log_{2/3}(3)}$

(Both answers are equivalent)

8 0

2 years ago

Question 6 Express this decimal as a fraction. ? 1.21 = ^ it has a line over the 21.

saul85 [17]

Answer: 40/33

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

Determine whether each equation below does or does not represent a proportional relationship. support your answer using either a

Triss [41]

Answer:

As the ratio for all the points on the equation y = x is same. Hence, the equation y = x REPRESENTS a proportional relationship.
As the ratio for all the points on the equation y = x+2 is not same. Hence, the equation y = x + 2 DOES NOT REPRESENT a proportional relationship.

Step-by-step explanation:

Solving equation A: y = x 

Let us consider the given equation A:

y = x

Putting x = 1 in y = x

y = x

y = 1 ∵ x = 1

Hence, (1, 1) is the ordered pair of y = x

Putting x = 2 in y = x

y = x

y = 2 ∵ x = 2

Hence, (2, 2) is the ordered pair of y = x

Putting x = 3 in y = x

y = x

y = 3 ∵ x = 3

Hence, (3, 3) is the ordered pair of y = x

Putting x = 4 in y = x

y = x

y = 4 ∵ x = 4

Hence, (4, 4) is the ordered pair of y = x

Putting x = 5 in y = x

y = x

y = 5 ∵ x = 5

Hence, (5, 5) is the ordered pair of y = x

Lets us consider all the ordered pairs i.e. (1, 1), (2, 2), (3, 3), (4, 4) and (5, 5) to make a table for y = x.

y x

1 1

2 2

3 3

4 4

5 5

As from the table, lets take the ratio of every point i.e. y/x

For (1, 1), the ratio will be y/x ⇒ 1/1 = 1
For (2, 2), the ratio will be y/x ⇒ 2/2 = 1
For (3, 3), the ratio will be y/x ⇒ 3/3 = 1
For (4, 4), the ratio will be y/x ⇒ 4/4 = 1
For (5, 5), the ratio will be y/x ⇒ 5/5 = 1

Hence, the ratio for all the points on the equation y = x is same. Hence, the equation y = x REPRESENTS a proportional relationship. Please also check the graph in attached figure a.

Solving equation A: y = x +2

Let us consider the given equation A:

y = x + 2

Putting x = 1 in y = x + 2

y = x + 2

y = 1 + 2 ⇒ 3 ∵ x = 1

Hence, (1, 3) is the ordered pair of y = x + 2

Putting x = 2 in y = x + 2

y = x + 2

y = 2 +2 ⇒ 4 ∵ x = 2

Hence, (2, 4) is the ordered pair of y = x + 2

Putting x = 3 in y = x + 2

y = x + 2

y = 3 + 2 ⇒ 5 ∵ x = 3

Hence, (3, 5) is the ordered pair of y = x + 2

Putting x = 4 in y = x + 2

y = x + 2

y = 4 + 2 ⇒ 6 ∵ x = 4

Hence, (4, 6) is the ordered pair of y = x + 2

Putting x = 5 in y = x + 2

y = x + 2

y = 5 +2 ⇒ 7 ∵ x = 5

Hence, (5, 7) is the ordered pair of y = x + 2

Lets us consider all the ordered pairs i.e. (1, 3), (2, 4), (3, 5), (4, 6) and (5, 7) to make a table for y = x + 2.

y x + 2

1 3

2 4

3 5

4 6

5 7

As from the table, lets take the ratio of every point i.e. y/x

For (1, 3), the ratio will be y/x ⇒ 3/1 = 3
For (2, 4), the ratio will be y/x ⇒ 4/2 = 2
For (3, 5), the ratio will be y/x ⇒ 5/3 = 5/3
For (4, 6), the ratio will be y/x ⇒ 6/4 = 3/2
For (5, 7), the ratio will be y/x ⇒ 7/5 = 7/5

Hence, the ratio for all the points on the equation y = x+2 is not same. Hence, the equation y = x + 2 DOES NOT REPRESENT a proportional relationship. Please also check the graph in attached figure a.

Keywords: equation, graph

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6 0

3 years ago

SOMEONE PLEASE HELP ASAP!!!!!

Margaret [11]

Answer:

x = 1

y = 1

Step-by-step explanation:

System of Equations

We are given the system of equations:

2x + y = 3

x = 2y - 1

Substituting x in the first equation:

2(2y - 1) + y = 3

Operating:

4y - 2 + y = 3

5y = 3 + 2

y = 5/5 = 1

y = 1

Since:

x = 2y - 1

Then:

x = 2(1) - 1

x = 1

Solution:

x = 1

y = 1

7 0

3 years ago

What is the area of the square adjacent to the third side of the triangle?

Naddik [55]

Answer:

85 units^2 = Area of Blue Square

and

x = 5 units

Step-by-step explanation:

To do this we use the Pythagorean theorem (a^2 + b^2 = c^2). a and b represent the legs of the triangle whereas c represents the longest side of the triangle, or the hypotenuse.

Since we know the area of a square is the side length multiplied by itself (or the side length squared), $\sqrt{35}$ is the side length of the pink square and $\sqrt{50}$ is the side length of the green square.