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Although I do not hold an administrative position here at this site, I believe it is impossible to delete a question one posts to this forum. Post caerfully! 

1 ounce = 28.35 grams

$950 / $73 =13.0137 ounces of saffron.

13.0137 x 28.35 =368.94 grams of saffron.

368.94 / 1,000 =0.36894 kg of saffron.

MaxWong

Let's define a few terms. 

Integer: The whole numbers and their opposites

Whole numbers: The set of all positive numbers and 0.

Rational Number: A number in which its decimal expansion either terminates or repeats. Some people also know that a rational number can always be expressed as \(\frac{a}{b}\) such that \(a,b\in\mathbb{Z}\hspace{1mm}\text{and}\hspace{1mm}GCF(a,b)=1\).

Irrational Number: A number in which its decimal expansion neither terminates nor repeats. Some people also know that an irrational number canot be expressed as \(\frac{a}{b}\) such that \(a,b\in\mathbb{Z}\).

Now that we have defined these terms, let's figure out the classification of all these numbers using a table!
 

\(\frac{1}{x(x-4)}+\frac{5-2x}{x^2-3x-4}=\frac{5}{x(x+1)}\)

Factor the  x² - 3x - 4 . What two numbers add to  -3  and multiply to  -4 ?       +1  and  -4  .

\(\frac{1}{x(x-4)}+\frac{5-2x}{(x+1)(x-4)}=\frac{5}{x(x+1)}\)

                                                                      Multiply the first fraction by  \(\frac{x+1}{x+1}\) .

\(\frac{1(x+1)}{x(x-4)(x+1)}+\frac{5-2x}{(x+1)(x-4)}=\frac{5}{x(x+1)}\)

                                                                      Multiply the middle fraction by  \(\frac{x}{x}\) .

\(\frac{1(x+1)}{x(x-4)(x+1)}+\frac{(5-2x)x}{(x+1)(x-4)x}=\frac{5}{x(x+1)}\)

                                                                      Multiply the last fraction by  \(\frac{x-4}{x-4}\) .

\(\frac{1(x+1)}{x(x-4)(x+1)}+\frac{(5-2x)x}{(x+1)(x-4)x}=\frac{5(x-4)}{x(x+1)(x-4)}\)

Now we have a common denominator. Let's multiply both sides by this denominator...but first we must say that   x ≠ 0 ,  x ≠ 4 ,  and  x ≠ -1 , because these values cause a zero in the denominator of the original equation.

1(x + 1) + (5 - 2x)x  =  5(x - 4)          When    x ≠ 0 ,  x ≠ 4 ,  and  x ≠ -1  .

                                                             Multiply out the parenthesees and simplify.

x + 1 + 5x - 2x²  =  5x - 20

-2x² + x + 21  =  0

                                                             Solve for  x  with the quadratic formula.

\(x = {-1 \pm \sqrt{1^2-4(-2)(21)} \over 2(-2)} \\~\\ x = {-1 \pm 13\over -4} \\~\\ x=-\frac{12}{4}=-3\qquad\text{ or }\qquad x=\frac{-14}{-4}=\frac{7}{2}\)

\(44𝑥 = 𝑙 \)

To solve for x, divide both sides by 44.

\(x={𝑙\over 44}\)

\(a-c = d-r\)

To solve for a, add c to both sides.

\(a=c+d-r\)

\(9e+4=14+8e\)

Subtract 8e from both sides.

\(e+4=14\)

Subtract 4 from both sides.

\(e=10\)

\(5c+16.5=13.5+10c\)

Subtract 10c from both sides.

\(-5c+16.5=13.5\)

Subtract 16.5 from both sides.

\(-5c=-3\)

Divide both sides by -5.

\(c={-3\over -5}\)

The negatives cancel out.

\(c={3\over 5}=0.6\)

Solve for x:
1/(x (x - 4)) + (5 - 2 x)/(x^2 - 3 x - 4) = 5/(x (x + 1))

Hint: | Write the left hand side as a single fraction.
Bring 1/((x - 4) x) + (5 - 2 x)/(x^2 - 3 x - 4) together using the common denominator x (x - 4) (x + 1):
(-2 x^2 + 6 x + 1)/(x (x - 4) (x + 1)) = 5/(x (x + 1))

Hint: | Multiply both sides by a polynomial to clear fractions.
Cross multiply:
x (x + 1) (-2 x^2 + 6 x + 1) = 5 x (x - 4) (x + 1)

Hint: | Write the quartic polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
-2 x^4 + 4 x^3 + 7 x^2 + x = 5 x (x - 4) (x + 1)

Hint: | Write the cubic polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
-2 x^4 + 4 x^3 + 7 x^2 + x = 5 x^3 - 15 x^2 - 20 x

Hint: | Move everything to the left hand side.
Subtract 5 x^3 - 15 x^2 - 20 x from both sides:
-2 x^4 - x^3 + 22 x^2 + 21 x = 0

Hint: | Factor the left hand side.
The left hand side factors into a product with five terms:
-x (x + 1) (x + 3) (2 x - 7) = 0

Hint: | Multiply both sides by a constant to simplify the equation.
Multiply both sides by -1:
x (x + 1) (x + 3) (2 x - 7) = 0

Hint: | Find the roots of each term in the product separately.
Split into four equations:
x = 0 or x + 1 = 0 or x + 3 = 0 or 2 x - 7 = 0

Hint: | Look at the second equation: Solve for x.
Subtract 1 from both sides:
x = 0 or x = -1 or x + 3 = 0 or 2 x - 7 = 0

Hint: | Look at the third equation: Solve for x.
Subtract 3 from both sides:
x = 0 or x = -1 or x = -3 or 2 x - 7 = 0

Hint: | Look at the fourth equation: Isolate terms with x to the left hand side.
Add 7 to both sides:
x = 0 or x = -1 or x = -3 or 2 x = 7

Hint: | Solve for x.
Divide both sides by 2:
x = 0 or x = -1 or x = -3 or x = 7/2

Hint: | Now test that these solutions are correct by substituting into the original equation.
Check the solution x = -3.
1/((x - 4) x) + (5 - 2 x)/(x^2 - 3 x - 4) ⇒ (5 - 2 (-3))/(-4 - 3 (-3) + (-3)^2) + 1/((-4 - 3) (-3)) = 5/6
5/(x (x + 1)) ⇒ -5/(3 (1 - 3)) = 5/6:
So this solution is correct

Hint: | Check the solution x = -1.
1/((x - 4) x) + (5 - 2 x)/(x^2 - 3 x - 4) ⇒ (5 - 2 (-1))/(-4 - 3 (-1) + (-1)^2) + 1/((-4 - 1) (-1)) = ∞^~
5/(x (x + 1)) ⇒ -5/(1 - 1) = ∞^~:
So this solution is incorrect

Hint: | Check the solution x = 0.
1/((x - 4) x) + (5 - 2 x)/(x^2 - 3 x - 4) ⇒ 1/((0 - 4) 0) + (5 - 2 0)/(-4 - 3 0 + 0^2) = ∞^~
5/(x (x + 1)) ⇒ 5/(0 (1 + 0)) = ∞^~:
So this solution is incorrect

Hint: | Check the solution x = 7/2.
1/((x - 4) x) + (5 - 2 x)/(x^2 - 3 x - 4) ⇒ 1/(1/2 (7/2 - 4) 7) + (5 - (2 7)/2)/(-4 - (3 7)/2 + (7/2)^2) = 20/63
5/(x (x + 1)) ⇒ 5/(7/2 (1 + 7/2)) = 20/63:
So this solution is correct

Hint: | Gather any correct solutions.
The solutions are:
x = -3          or          x = 7/2

It took me a long time to spot the error in your calculation, but I finally found it! By the way, alignment is always a tricky subject, but you did very well!

However, here is where your error was made. Now, my alignment skills are not up to par either, so bare with me please:
 

\(-0.25r-0.125=0.5\)

                -0.125     -0.125

--------------------------------------

\(-0.25r=\hspace{1cm}0.375\)

However, this is incorrect. It should be the following!

\(-0.25r-0.125=0.5\)

                +0.125     +0.125

--------------------------------------

\(-0.25r=\textcolor{red}{0.625}\)

Now, when you solve from here, you will get that \(r=-2.5\).

\(\frac{53541}{100}\) is an improper fraction--not a mixed number. 

\(535\frac{41}{100}\), however, is a mixed number that is the equivalent of 535.41

28 + 30 + 32 + .... + 86

Note....that we can pair the terms as follows

[ 28 + 86 ] + [ 30 + 84] + [ 32 + 82 ] +......+ [56 + 58]

Each pair sums to 114

And the number of pairs is given by   [56 - 28] / 2 + 1  = 15 pairs

So...the sum is   15 * [ 114 ]  =    1710

 (6/13)𝑥 = 51     multiply both sides by  13/6

x  = 51 (13/6)   =  663 / 6

45.1 + 21.5𝑥 =  125.6      multiplly through by 10 to clear the decimals

451  + 215x  = 1256       subtract 451 from both sides

805  = 215x                  divide both sides by 215

805 / 215  = x  = 161 / 43

Matt wants to walk his dog around the block. The block has a rectangle shape. The dimensions of the block is 3 miles long and 2450 yards wide. How many feet would Matt walk if he walked his dog around the block two times? Write an equation and solve for x.

There really isn't any "x"  to solve for....we  just need to convert miles and yards to feet

1 mile  = 5280 ft....so   3 miles   = 3 * 5280 =  15840 ft

1 yard  = 3 ft.......so 2450 yards  = 2450 * 3  = 7350 ft

One complete trip comprises the perimeter of a rectangle that is   15840 x 7350

So......one trip around the block is equal to the perimeter of this rectangle  = 2 [ 15840 + 7350 ]  = 46380 ft

So....two trips is twice as far   = 2 * 46380  = 92760 ft

A number to the second power is 7 less, than the quotient of forty-two over 8. Write an equation to represent the problem.

Let N be the number.....so we have that

N^2  +   7  =  42 / 8

134x+(-100)= 112, Solve for x

Add 100 to both sides

134x  = 212      divide both sides by 134

x  = 212 / 134  =    106 / 67

(x+2)(x+2)=x^2+4x+4

 5 - (2x + 3)  =

5 - 2x  - 3   =

2 - 2x

-2x^2 - 5x = -50       multiply through by -1

2x^2  + 5x  = 50      complete the square on x

2 [x ^2  +  (5/2)x ]  = 50       divide both sides by 2

x^2  +  (5/2)x     = 25         take (1/2)  of (5/2)  = 5/4.....square this = 25/16,  and add to both sides 

x^2  + (5/2)x  + 25/16  =   25  +  25/16         factor the left side and simplify the right

[ x +  5/4 ] ^2   =   [ 400 + 25]  / 16          take both roots

x + 5/4  =  ±√ [ 425]  / 4

x + 5/4  =   ±5√17 / 4       subtract 5/4 from both sides

x  = ±5√17 / 4  - 5/4  =  [  -5  ± 5√17 ] / 4  

If you have a square whose side is 12 inches long,then the area of the square is   12   X   12  square inches  which is

144   square inches.    That's the simplest shape, you can of course have others.

5-2x -3 

2x=5+3

2x=8

x=8:2 

x=4

-2x²-5x=-50? 

 0.3939   this is a rational number because it can be expressed as the ratio  3939 / 10000

√ 45  =   3√5        any  number that has a square root remaining after we simplify it is irrational

9      is  rational [ can be expressed as a ratio such as 18/2, etc.]......also an integer    ....also a whole number [ a "counting number" or  0]

-2  is rational  [ can be expressed as the ratio such as   -4/2 , etc] ......also an integer ...it is not a whole number because it is not a "counting" number or 0

Thanks so much!!

Perimeter  =  2 (W + H)

So....we have this

2 ( W + H)  < 180       sub in for the width

2 ( 26  + H)  < 180        divide both sides by 2

26 +  H  <   90               subtract 26 from both sides

H <  64 in

So....for the perimeter to be less that 180 in, the height must be less than  64 in

Let  x be the number of $50  software programs that should be produced

Let y be the number of $35 video games that should be produced

And we have these two constraints

x ≤ 200     and  y ≤ 300

Also....we have the constraint that

x + y   ≤  425

And we want to  maximize this :   50x  + 35y

Look at the folowing graph of these  constrraints :  https://www.desmos.com/calculator/2gpyq2qxwl

The  possible solutions  occur at the corner points of the intersections  of the three constraints

These occur at  ( x, y)   = (125 , 300)  and  (200 , 225)

Putting these  into       50x  +  35y

(125, 300)  =   50(125) + 35(300)   =  $16750

And

(200, 225)  =  50(200) + 35(225)  = $17875

So......producing 200 software programs and  225 video games will maximize the profit

[-5/2] (3x+4) < 6-3x          multiply both sides by 2

-5 (3x + 4)   <  12 - 6x         distribute the  -5 over the terms in parentheses

-15x - 20  <  12 - 6x            add 15x to both sides, subtract 12 from both sides

-32 <  9x                      divide both sides by 9

-32 / 9 < x         which means the same as     x > -32 / 9

T   =   3U / E      

Multiply both sides by  E

ET  =  3U

Divide both sides by 3

ET / 3    =   U

0.032