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3 years ago

12(x-2) +3x= 1/2(x+6)+2

Mathematics

2 answers:

ratelena [41]3 years ago

8 0

Answer: x=2

explanation: just right

Rus_ich [418]3 years ago

6 0

Answer:

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

12*(x-2)+3*x-((1)/(2)*(x+6)+2)=0

Simplify 1/2

((12•(x-2))+3x)-((—•(x+6))+2) = 0

((12 • (x - 2)) + 3x) - (——————— + 2) = 0

Adding a whole to a fraction

Rewrite the whole as a fraction using 2 as the denominator :

2=2/1= 2 . 2 / 2

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

(X+6) + 2 . 2 / 2 = X+10 / 2

(x + 10)

((12 • (x - 2)) + 3x) - ———————— = 0

(x + 10)

(12 • (x - 2) + 3x) - ———————— = 0

Subtracting a fraction from a whole

Rewrite the whole as a fraction using 2 as the denominator :

15x - 24 (15x - 24) • 2

15x - 24 = ———————— = ——————————————

1 2

Pull out like factors :

15x - 24 = 3 • (5x - 8)

Adding up the two equivalent fractions

3 • (5x-8) • 2 - ((x+10))/2 = 29x - 58/2

Pull out like factors :

29x - 58 = 29 • (x - 2)

29 • (x - 2)/2 =0

When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

29•(x-2)

———————— • 2 = 0 • 2

Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

29 • (x-2) = 0

Equation which are never true

Solve : 29 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a single variable equation

Solve : x-2 = 0

Add 2 to both sides of the equation :

x = 2

PLease Mark Brainliest!

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Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by

11111nata11111 [884]

Answer:

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is $V=l\times b\times h$

$V=(11-2x)\times (7-2x)\times x$

$V=4x^3-36x^2+77x$

Derivate w.r.t x,

$V'(x)=4(3x^2)-2(36x)+77$

$V'(x)=12x^2-72x+77$

The critical point when V'(x)=0

$12x^2-72x+77=0$

Solve by quadratic formula,

$x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}$

$x=4.607,1.392$

Derivate again w.r.t x,

$V''(x)=24x-72$

Now, $V''(4.607)=24(4.607)-72=38.568>0$ (+ve)

$V''(1.392)=24(1.392)-72=-38.592$ (-ve)

So, there is maximum at x=1.392.

The length of the box is $l=11-2x$

$l=11-2(1.392)=8.216$

The breadth of the box is $b=7-2x$

$b=7-2(1.392)=4.216$

The height of the box is h=1.392.

The dimension of the open rectangular box is $8.216\times 4.216\times 1.392$ .

The volume of the box is $V=l\times b\times h$

$V=8.216\times 4.216\times 1.392$

$V=48.217\ in.^3$

The volume of the box is 8.217 cubic inches.

5 0

3 years ago

30 POINTS TO WHOEVER HELPS WITH THIS I NEED IT ASAP PLEASE HELP

Mekhanik [1.2K]

Answer:

4a ) Difference ⇒ $ 63.24,

4b ) 4 children

Step-by-step explanation:

4a ) If the number of children is represented by the value of x, let us substitute a family of 2 children as value of x into this equation we are given;

y = 21.08 * ( 2 ) + 85.15 ⇒ Multiply 21.08 by 2,

y = 42.16 + 85.15 ⇒ Combine like terms,

y = 127.31

If y ⇒ amount spent on grocery's, let us solve for the amount spent on 5 children, and subtract from this amount;

y = 21.08 * ( 5 ) + 85.15 ⇒ Multiply 21.08 by 5,

y = 105.4 + 85.15 ⇒ Combine like terms,

y = 190.55

Difference; 190.55 - 127.31 = 63.24,

Solution; Difference ⇒ $ 63.24

4b ) If the amount is $ 169.47, let us plug it into our given equation provided amount spent on groceries ⇒ y;

169.47 = 21.08x + 85.15 ⇒ Subtract 85.15 from either side of equation,

21.08x = 84.32 ⇒ Divide either side 21.08,

x = 4 children

Solution; 4 children

5 0

3 years ago

X(x+7)=0 solve whatever this id

Anit [1.1K]

Step-by-step explanation:

x(x + 7) = 0

By Zero Product rule,

either x = 0 or (x + 7) = 0.

=> x = 0 or x = -7.

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3 years ago

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Answer: 3x^2 - 3x - 1

Explanation:

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-Dominant- [34]

Answer:

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Trapezoid - 65 units

Step-by-step explanation:

Because this triangle and trapezoid are reflections of each other when split in half, remove the highlighted parts to make them a rectangle. When made into a rectangle, you can use the formula length * width to find the area of either shape (trapezoid or triangle).
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3 years ago

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