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(number of hours) x (wage rate)  =  (gross earnings)

       hours              x     10.62       =       127.40

                                      hours      =        127.40 / 10.62    =  12 hours  (approximately)

4x + ay  =  -8   --->     4x + ay  =  -8

2x - 3y  =  b     --->     4x - 6y   =  2b

Choose a = -6  and  b  =  -4

Then, you have two equivalent equations:  4x - 6y  =  -8

                                                                     4x - 6y  =  -8

t₁  =  2/3

t₉  =  t₁ + 8d     --->     -4/5  =  2/3 + 8d     --->     -22/15  =  8d     --->     d  =  -11/60

t₅  =  t₁ + 4d     --->     t₅  =  2/3 + 4(-11/60)  =  -1/15  

1*2*3*2*3 = 36 posibilities.

But if he gets it right on the first try then he doesn't need to try any more.  

Luna used 3/5 of her money to buy 10 earphones.

Rest of the money is (1 - 3/5) = 2/5.
Let, Luna buy x earphones with the

rest of her ,only.

So, 10/3/5 = x/2/5

=> 50/3 = 5x/2

=> x = 29/3 = 6

So, Luna can buy almost 6 earphones with the rest of her money.

Find the fraction

Hello Guest!

Why easy when it can be cumber.

\(0.72\overline 6 + 0.02\overline 3=\frac{109}{150}+\frac{7}{300}=\frac{218+7}{300}=\frac{225}{300}=\color{blue}\frac{3}{4}\)

  !

So we have that

[Bx  - 11 ] / [ x^2 -7x + 10]   =  A / [ x -2 ] + 3 / [x - 5]

Using partial fractions we can simplify this as

Bx  - 11   =  A[x - 5] + 3 [ x - 2]       simplify more

Bx  - 11  =  Ax - 5A  + 3x  - 6

Bx  - 11  = [ A + 3 ] x + [ -5A - 6 ]     equate coefficients

B  =  A +  3      

-11  = -5A - 6   ⇒  -5  =  -5A  ⇒    A  = 1

So....B  = 1 + 3   =  4

So....A + B  =   1  +  4  = 5

🎅🎅🎅🎅🎅

🥳🥳🥳🥳🥳

floor (r)  +  r  =  12.2  - r

floor (r)  +  2r   =   12.2

Note if  r = 4.1    we  have

floor (4.1)  + 2(4.1)  =  

4  +  8.2  =  

12.2

🎅🎅🎅🎅🎅

🥳🥳🥳🥳🥳

The four angles are   a,   a + d,   a + 2d,   a + 3d

--->     (a)  +  (a + d)  +  (a + 2d)  +  (a + 3d)  =  180

--->                                                   4a + 6d  =  360

--->                                                   2a + 3d  =  180

Also:  a + 3d  =  126     --->     3d  =  126 - a

Combining:         2a + 3d  =  180     and     3d  =  126 - a     --->     2a + (126 - a)  =  180

                                                                                                                  a + 126  =  180

                                                                                                                             a  =  54

The angles are:  54,  78,  102,  and  126.

log_4^a (8^b)  =  x     --->     [ 4^a ]^x  =  8^b     --->     [ (2²)^a ]^x  =  (2³)^b     --->     2^2ax  =  2^3b   

                                                                                                         --->     2ax  =  3b

                                                                                                         --->         x  =  (3b) / (2a) 

f(x) is a linear equation with slope = -0.5 and y-intercept = 2     --->     f(x)  =  -0.5x + 2

g(x) is a linear equation with slope = 1 and y-intercept = 0     --->     g(x)  =  x

g(1)  =  1     --->     f( g(1) )  =  -0.5(1) + 2  =  1.5

f(1)  =  -0.5(1) + 2  =  1.5     --->     g( f(1) )  =  g(1.5)  =  1.5

f( g(1) )  ·  g( f(1) )  = 1.5 · 1.5  =  2.25

If the function is:  f(x)  =  1 / (x - 64)  +  1 / (x² - 64)  +  1 / (x³ - 64)

The real solution of  x - 64  is  64

The real solutions of  x² - 64  are  8  and  -8

The real solution of  x³ - 64  is  4                       (there are also two complex solutions)

Thus, there are 4 real numbers not in the domain of this function.

A + B + C  =  180

(x + 2y) + (6x - 5y)+ (8x + 3y)  =  180

                                         15x  =  180

                                             x  =  12^o

The answer for x is independent from the value for y; y can have any value ...

x² - 2x + 5  =  0

Using the quadratic formula: 

x₁  =  [ 2 + sqrt( (-2)² - 4(1)(5) ) ]  /  [ (2)(1) ]  =  [ 2 + sqrt( 4 - 20) ]  / 2  =  [ 2 + sqrt(-16) ]  / 2  =  ( 2 + 4i ) / 2  =  1 + 2i

x₂  =  [ 2 - sqrt( (-2)² - 4(1)(5) ) ]  /  [ (2)(1) ]  =  [ 2 - sqrt( 4 - 20) ]  / 2  =  [ 2 - sqrt(-16) ]  / 2  =  ( 2 - 4i ) / 2  =  1 - 2i

a  =  1 / ( 1 + 2i )

b  =  1 / ( 1 - 2i )

a·b  =  [ 1 / ( 1 + 2i ) ]  ·  [ 1 / ( 1 - 2i ) ]  =  1 / ( 1² - (2i)² )  =  1 / ( 1 + 4 )  =  1 / 5

2x² - 5x - 4  =  2x + 3     --->     2x² - 7x - 7  =  0

Using the quadratic formula with  a = 7  b = -7  and  c = -7:

x  =  [ - -7  +/-  sqrt( (-7)² - 4(2)(-7) ) ]  /  [ (2)(2)

x  =  [ 7  +/-  sqrt(105) ]  /  4 

    0.7266666666...

+  0.0233333333...

=  0.7499999999...

=  0.75

=  3/4

I checked with a quick sketch and it is reasonably clear that that is correct.

0.0909090909 ...

100*0.0909090909 ... = 9.09090909 ...

1 *0.0909090909 ...    = 0.0909090909 ...

subract

99*0.0909090909 ...=9

0.0909090909 ...=9/99 = 1/11

yes that is right.

So

\(\frac{16}{LN}=\frac{2}{3}\)

Oh, I get it...       sinN = 16 / LN

(x - y)^2 = x^2 - 2xy + y^2 => 2xy = x^2 + y^2 - (x - y)^2 => 2xy = 24 - 6^2 = -12 => xy = -6

x^3 - y^3 = (x - y) (x^2 + x y + y^2) = 6( 24 - 6 ) = 108

What is the least possible value of the sum | x - 1 | + | x - 1.5 | + | x - 2 | + | x - 2.5 | + | x - 3 |?

Let x = 0.5 => 0.5 + 1.0 + 1.5 + 2.0 + 2.5 = 7.5

Let x = 1.0 => 0 + 0.5 + 1.0 + 1.5 + 2.0    = 5.0

Let x = 1.5 => 0.5 + 0 + 0.5 + 1.0 + 1.5    = 3.5

Let x = 2.0 => 1.0 + 0.5 + 0 + 0.5 + 1.0    = 3.0 (Least Possible Value)

Let x = 2.5 => 1.5 + 1.0 + 0.5 + 0 + 0.5    = 3.5

Let x = 3.0 =>  2.0 + 1.5 + 1.0 + 0.5 + 0   = 5.0

Let x = 3.5 => 2.5 + 2.0 + 1.5 + 1.0 + 0.5 = 7.5

Roll 2 fair dice = 36 outcomes. Outcomes with both dice showing prime number = {(2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5)}

P(both dice showing a prime number) = 9/36 = 1/4.

Circle centre O with r = 2, angle subtended between A and B, B and C, C and D, D and E, E and A with centre O = 360⁰ / 5 = 72⁰

Area of triangle ABO = (1/2)(2*2*sin 72⁰) = 1.902 sq units

[ABCDE] = There are 5 triangles of equal area = (1.902 sq units)5 = 9.51 sq units.

I expect this diagram comes with more information.

From what I have read:

This is a skin disease that can be inherited from either parent.

If it comes from both parents it will be more severe.