Simplify 7/56

Problem:

Simplify $ \frac{7}{56} $

Solution:

$ \frac{1}{8} $

312 is 65% of what number

Problem:

312 is 65% of what number?

Solution:

480

$ \frac{2x^2}{7} \times \frac{3}{4x^2} $

Problem:

$ \frac{2x^2}{7} \times \frac{3}{4x^2} $

Solution:

$ \frac{3}{14} $

Simplify

Problem:

$ (\frac{a^3}{m})^{-4} $

Solution:

$ (\frac{a^3}{m})^{-4} = \frac{m^4}{a^{12}} $

(x-3)(x-2)

Problem:

(x-3)(x-2)

Solution:

x = 3 or x = 2

Expanding give $ x^2 - 5x + 6 $

Solve for x

Problem:

Solution:

x = 11

The angle is 74, the top angle is 32

0 = b squared - 4 a c = 3^2 - 4(1)-3

Problem:

The problem is only this equation

0 = b squared - 4 a c = 3^2 - 4(1)-3

Solution:

This is incorrect, first or all, if you multiply a negative number, you cannot just write the number at the end like -3, this is minus 3, not multiply negative 3, you need to add a bracket there.

Alright, assume the bracket is there, the equation is still not right, 3^2 - 4(1)(-3) = 21 is not zero.

Alright, ignoring the 0 part, it means we have B = 3, A = 1, C = -3, then the answer is given by

$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-3 \pm \sqrt{21}}{2} $.

Equation

Problem:

2(3x - 4) = 3x + 1

Solution:

x = 3

Evaluate

Problem:

$ \frac{6}{\sqrt{5} + 4} $

Solution:

$ \frac{6}{\sqrt{5} + 4} = 0.96214474... $

Ordering numbers

Problem:

Order the numbers:

$ \sqrt{8}, -3.75, 3, \frac{9}{4} $

Solution:

$ -3.75 < \frac{9}{4} < \sqrt{8} < 3 $

x + 5 = 10x

Problem:

$ x + 5 = 10x $

Solution:

$ x = \frac{5}{9} $

Complete ratio table

Solution:

72	36	24	12
126	63	42	21

29 . 16 . 8 . 25

Problem:

29 . 16 . 8 . 25

Solution:

92800

Rectangle

Problem:

The length of the rectangle is 4 times it width, the rectangle's width is 8m.

What is the area of the rectangle..

Solution:

Length = 32 meter, Area =  256 meter squared

Simplify

Problem:

$ \frac{x^{-1/3}y^{-3/4}x^{-7/4}}{(y^{-2/3})^{4/3}} $

Answer:

$ \frac{y^{5/36}}{x^{25/12}} $

6(2x-6)=-3(-4x-3)-5

Problem:

6(2x-6)=-3(-4x-3)-5

Solution:

There is something wrong with the problem, it simplifies to

12x - 36 = 12x + 4

There is no x that can make this equation true, in another words, the answer is no solution.

1/5 - 2/15 + 9/10

$ \frac{1}{5} - \frac{2}{15} + \frac{9}{10} = \frac{29}{30} $

p + 8 = 14.1

p = 6.1

675 ÷ (6 + 9 ÷ 3)

675 ÷ (6 + 9 ÷ 3) =75

Opposites

To move three units from -7, we can do it either to the left or to the right

Let start with moving to the right, we start at -7

-11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1  0
                  *

-11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1  0
                      * 

-11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1  0
                          * 

-11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1  0
                              *

Then we move the other way, we get

-11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1  0
                  *

-11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1  0
              *

-11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1  0
          *

-11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1  0
      * 

So the answer is -4 and -10

Graphing f(x)/2

Problem:

Graphing, $ y = \frac{1}{2}f(x) $

Solution:

Without a specific $ f(x) $ given, I just used a random $ f(x) = (x - 2)(x - 4)(x - 6) $.

Here is a graph with both $ f(x) $ and $ \frac{1}{2}f(x) $.

Problem: 4(5n-7)=10n+2

 Problem: 4(5n-7)=10n+2

The solution is n = 3

Problem: How do I write 11 <= m <= 19 as an absolute inequality?

Answer: |m - 15| <= 4