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3 years ago

11-(3x+1) = 7(x-6)+2

Mathematics

2 answers:

Galina-37 [17]3 years ago

4 0

Hello!

$\large\boxed{x = 5}$

11 - (3x + 1) = 7(x - 6) + 2

Distribute the coefficients outside of the parenthesis:

11 - (3x) - (1) = 7(x) + 7(-6) + 2

Simplify:

11 - 3x - 1 = 7x - 42 + 2

Combine like terms:

10 - 3x = 7x - 40

Add 3x to both sides to isolate x:

10 = 10x - 40

Add 40 to both sides:

50 = 10x

Divide both sides by 10:

x = 5

Misha Larkins [42]3 years ago

4 0

Answer:

11-3x-1=7x-42+2

Put all like terms together

10+40=10x

x=50

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Find the area of the region enclosed by f(x) and the x axis for the given function over the specified u reevaluate f(x)=x^2+3x+4

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Step-by-step explanation:

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The piece-wise function f(x) is defined over an interval as follows:

f(x) = { x^2+3x+4 , x < 3

f(x) = { x^2+3x+4 , x≥3

Domain : [ -3 , 4 ]

Find:-

Find the area of the region enclosed by f(x) and the x axis

Solution:-

- The best way to tackle problems relating to piece-wise functions is to solve for each part individually and then combine the results.

- The first portion of function is valid over the interval [ -3 , 3 ]:

$f(x) = x^2+3x+4$

- The area "A1" bounded by f(x) is given as:

$A1 = \int\limits^a_b {f(x)} \, dx$

Where, The interval of the function { -3 , 3 ] = [ a , b ]:

$A1 = \int\limits^a_b {x^2+3x+4} \, dx\\\\A1 = \frac{x^3}{3} + \frac{3x^2}{2} + 4x |\limits_-_3^3 \\\\A1 = \frac{3^3}{3} + \frac{3*3^2}{2} + 4*3 - \frac{-3^3}{3} - \frac{3(-3)^2}{2} - 4(-3)\\\\A1 = 9 + 13.5 +12 + 9-13.5+12\\\\A1 =42 unit^2$

- Similarly for the other portion of piece-wise function covering the interval [3 , 4] :

$f(x) = 4x+10$

- The area "A2" bounded by f(x) is given as:

$A2 = \int\limits^a_b {f(x)} \, dx$

Where, The interval of the function { 3 , 4 ] = [ a , b ]:

$A2 = \int\limits^a_b {4x+10} \, dx\\\\A2 = 2x^2 + 10x |\limits_3^4 \\\\A2 = 2*(4)^2 + 10*4 - 2*(3)^2 - 10*3\\\\A2 = 32 + 40 - 18-30\\\\A2 =26 unit^2$

- The total area "A" bounded by the piece-wise function over the entire domain [ -3 , 4 ] is given:

A = A1 + A2

A = 42 + 26

A = 68 unit^2

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