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belka [17]
3 years ago
11

Express b+1/3b-2 with “b” as the subject

Mathematics
1 answer:
lara [203]3 years ago
4 0

Answer:

b = \frac{1+2a}{3a-1}

Step-by-step explanation:

Given

a = \frac{b+1}{3b-2} ( multiply both sides by 3b - 2 )

a(3b - 2) = b + 1 ← distribute left side

3ab - 2a = b + 1 ( subtract b from both sides )

3ab - b - 2a = 1 ( add 2a to both sides )

3ab - b = 1 + 2a ← factor out b from each term on the left side

b(3a - 1) = 1 + 2a ( divide both sides by 3a - 1 )

b = \frac{1+2a}{3a-1}

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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
avanturin [10]

The correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".

The given inequality is -3(2x - 5) < 5(2 - x)

We need to simplify the inequality.

<h3>What is inequality?</h3>

In mathematics, inequality is a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.

Consider LHS and simplify -3(2x - 5) = -3(2x)-5(-3)

⇒ -3(2x - 5) = - 6x + 15 [∵(-)(-) = (+)]

Consider RHS and simplify 5(2 - x) = 5(2) + 5(-x)

⇒5(2 - x) = 10 - 5x [∵(+)(-) = (-)]

Now, - 6x + 15 < 10 - 5x

By subtracting 15 from both sides, we get

- 6x < -5 - 5x

By adding 5x to both sides, we get - x < - 5

The coefficient of x is -1. So, divide both sides by -1

Then we get x > 5

Hence, the correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".

To learn more about inequalities visit:

brainly.com/question/20383699.

#SPJ1

5 0
1 year ago
I need help on this.
andrew11 [14]

To find the midpoint, add x1 and x2 then divide by 2, then add y1 and y2 and divide by 2.


Midpoint = (2a +2b /2 , 0 + 2c /2)


Midpoint = a+b, c


3 0
2 years ago
Write the equation in slope-intercept form:<br> 3y = 2x +15
Sergeu [11.5K]

Answer:

y = 2/3x + 5

Step-by-step explanation:

Hope this helps! :)

3 0
2 years ago
PLEASE HELP 20+ POINTS!! What is the cosine equation of the function shown?
noname [10]

Answer:   \bold{y=7\ \cos\bigg(x-\dfrac{\pi}{4}\bigg)-4}

<u>Step-by-step explanation:</u>

y = A cos (Bx - C) + D

  • A (amplitude) = max - D
  • B = Period/2π  --->   Period is the distance from max to next max
  • C = B · Phase Shift  ---> Phase shift is distance from y-axis to max
  • D (vertical shift) = (max + min)/2

D = (max + min)/2     =     (3 - 11)/3      =  -4

A = max - D               =     3 - (-4)         = 7

Period = 9π/4 - π/4   =    8π/4            = 2π

B = Period/2π           =    2π/2π          = 1

Phase Shift = π/4 - 0 =     π/4

C = B · Phase Shift    =  1 · π/4            = π/4

Equation:

           y = 7 cos (1·x - π/4) + (-4)

               

8 0
3 years ago
What is the 5th term in the geometric sequence described by this explicit
Studentka2010 [4]

Answer:

C

Step-by-step explanation:

Using the explicit formula, then

a₅ = 50 × (-2)^{4} = 50 × 16 = 800 → C

4 0
3 years ago
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