All Answers 358514 Answers

9 l 9 - 8x l  = 2x + 3

We have two equations here

9 (9- 8x)   =   2x + 3                 and              9 (9 - 8x)  = -[ 2x + 3]

                    simplify

81  - 72x   = 2x + 3                                  and                                                      81 - 72x  =  -2x  - 3

add 72 x  to both sides, subtract 3 from both sides                      add 72 x  to both sides, add 3 to both sides

78   =  74x                            and                  84  = 70x

divide both sides by 74                                divide both sides by 70

78/ 74 = x                                                       84 / 70  = x

                                    reduce

39 / 37  = x                                                   6 / 5    = x

Real world situation...let's suppose that a bus will hold 50 people and the number of people on it = 35

So......the number of additional people, x, that the bus will hold can be modeled by

35  + x  ≤  50

3.14 x 10^-3 

  [ write two "0s" in front  and move the decimal point 3 places to the left ]

.00314

Thank you!!

l  -4b  - 8 l  +   l  -1  - b² l + 2b³, b  = -2

So we have

l  -4 (-2) - 8 l   +  [  -1 - (-2)² l  + 2 (-2)³   =

l  8 - 8  l   +  l  -1 - 4 l  + 2 (-8)  =

l 0 l   +  l  -5 l   -  16  =

0  +  5   - 16  =

5 - 16

-11

 CORRECTED ANSWER  !!!!!

Let the number of pounds of copper to be added  =  C

Note.....that  if the final mixture is 10% zinc.....then  the final mixture must contain 90% copper

So

[amt of copper present + amt of copper added]  / [ whole mixture ]    =  90% copper

Note that the whole mixture amt  =  150 + amt of copper to be added

So

[ 100 + C ]  / [ 150 + C]   = .90    multiply both sides by   150 + C

100 + C  = .90 [ 150 + C]  simplify

100 + C  = 135 + .90C        subtract  100, .90C from both sides

.1C  =  35                      divide both sides by .1

C  = 350 lbs of copper are  to be added

Proof

[350 + 100] / [ 150 + 350 ]  =  .90  = 90%

42x  = 5x + 15      subtract 5x from  both sides

37x  = 15             divide both sides by 37

x  = 15/37

0.5/0.75^2=

0.8888888888888889

Hope this helps!!

Division is a fraction

For example, if my fraction was 3 over 4 (3/4) 

I would put 3 divided by 4

In this calculator, this turns into a fraction

I hope this helped!! 

You can do this with the web 2.0calc on the home page.

Just type in 

factor(111111) and press equal

factor(111111)= = (((3*7)*11)*13)*37

I probably cannot help you but what do you think your username is?

I'll see if I can find it, maybe you are spelling it a little differently or not puting in capitals where they belong...

Factor of a polynomial with complex number

Factor the polynomial z^2 + zi + 6

z^2 + zi + 6 = (z - 2 i) (z + 3 i)

It is 0.87 miles from your house to school. You walk 4 miles per hour.

If you leave your house at 7:10am,

what time will you arrive at school?

\(\begin{array}{|rcll|} \hline && 0.87\, \text{miles} \times \frac{1\, \text{hour}} {4\, \text{miles}} \times \frac{60\, \text{min}} {1\, \text{hour} } \\ &=& \frac{0.87\times 60}{4}\, \text{min} \\ &=& 13.05\, \text{min} \\ \hline \end{array} \)

What time will you arrive at school?

\(7:10\,am + 13\, min = 7:23\,am\)

If the sum of four consecutive numbers is n, what is the first one?

Hello Guest!

The first one is x.

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

\(x = \frac{n-6}{4}\)

If the sum of z consecutive numbers is n, what is the first one?

\(x+(x+1)+(x+2)\ +\ ...\ +\ (x+z-1)=n\)

\(\frac{(x+(x+z-1)}{2}\times z=n\\ \frac{2x+z-1}{2}\times z=n\\ 2x+z-1=\frac{2n}{z}\\ 2x=\frac{2n}{z}-z+1\\ \color{blue}x=(\frac{2n}{z}-z+1)/2\\ \color{blue}general\ formula\)   

sample

4+5+6+7+8+9   z=6   n=39    x=4

\(x=(\frac{2n}{z}-z+1)/2=(\frac{2\cdot39}{6}-6+1)/2=4\).

  !

a cylinder has a volume of 3meters cubed and a radius of 0.8meters what is the height ?

Let r = radius
Let V = volume
Let h = height

\(\begin{array}{|rcll|} \hline V &=& \pi r^2 h \\ 3 &=& \pi \cdot (0.8)^2 \cdot h \\ 4.6875 &=& \pi h \quad & | \quad : \pi \\ \frac{4.6875}{\pi} &=& h \quad & | \quad \pi = 3.14159265359 \\ \frac{4.6875}{3.14159265359} &=& h \\ \mathbf {1.49207759149} &\mathbf {=} & \mathbf {h} \\ \hline \end{array}\)

         
The height of the cylinder is \(\mathbf{ \approx 1.5\ m}\)

If x, y, and z are real numbers for which

\(\begin{align*} \mathbf{x+y-z} &\mathbf{= -8,} \\ \mathbf{x-y+z} &\mathbf{= 18,\text{ and}} \\ \mathbf{-x+y+z} &\mathbf{= 30,} \\ \end{align*} \)

then what is xyz?

\(\begin{array}{|lrcl|} \hline (1) & x+y-z &=& -8 \\ (2) & x-y+z &=& 18 \\ (3) & -x+y+z&=& 30 \\ \\ \hline (1)+(2): & x+y-z + (x-y+z) &=& -8 + 18 \\ & 2x &=& 10 \\ & \mathbf{x} &\mathbf{=}& \mathbf{5} \\\\ \hline (1)+(3): & x+y-z + (-x+y+z) &=& -8 + 30 \\ & 2y &=& 22 \\ & \mathbf{y} &\mathbf{=}& \mathbf{11} \\\\ \hline (2)+(3): & x-y+z + (-x+y+z) &=& 18 + 30 \\ & 2z &=& 48 \\ & \mathbf{z} &\mathbf{=}& \mathbf{24} \\\\ \hline &xyz &=& 5\cdot 11 \cdot 24 \\ & \mathbf{xyz} &\mathbf{=}& \mathbf{1320} \\ \hline \end{array}\)

1. Let x and y be real numbers whose absolute values are different and that satisfy

\(\begin{align*} \mathbf{ x^3 }&\mathbf{ = 20x + 7y } \\ \mathbf{ y^3 }&\mathbf{ = 7x + 20y } \end{align*} \)

Find xy.

\(\begin{array}{lrcl|c|c|} &&&& I. & II.\\ \hline (1) & x^3 &=& 20x + 7y \\ &&&& + & - \\ (2) & y^3 &=& 7x + 20y \\ \end{array} \)

\(\begin{array}{|rcll|} \hline (I.) & x^3+y^3 &=& 20x + 7y +7x + 20y \\ & x^3+y^3 &=& 27x + 27y \\ & x^3+y^3 &=& 27(x+y) \\ &&& x^3+y^3 = (x+y)(x^2-xy+y^2) \\ & (x+y)(x^2-xy+y^2) &=& 27(x+y) \\ & \mathbf{x^2-xy+y^2} &\mathbf{=}& \mathbf{27} \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline (II.) & x^3-y^3 &=& 20x + 7y -(7x + 20y) \\ & x^3-y^3 &=& 13x -13y \\ & x^3-y^3 &=& 13(x-y) \\ &&& x^3-y^3 = (x-y)(x^2+xy+y^2) \\ & (x-y)(x^2+xy+y^2) &=& 13(x-y) \\ & \mathbf{x^2+xy+y^2} &\mathbf{=}& \mathbf{13} \\ \hline \end{array}\)

\(\begin{array}{|lrcll|} \hline (1) & \mathbf{x^2-xy+y^2} &\mathbf{=}& \mathbf{27} \\ (2) & \mathbf{x^2+xy+y^2} &\mathbf{=}& \mathbf{13} \\ \hline (2)-(1): & x^2+xy+y^2 -(x^2-xy+y^2) &=& 13 - 27 \\ & x^2+xy+y^2 -x^2+xy-y^2 &=& -14 \\ & xy +xy &=& -14 \\ & 2xy &=& -14 \\ & \mathbf{xy} &\mathbf{=}& \mathbf{-7} \\ \hline \end{array}\)

(x^(3/2))^(1/6)

___________

(x^(2/3))^(1/6)

simplify and use only positive exponents

\(\begin{array}{|rcll|} \hline && \dfrac{ (x^{\frac{3}{2}} )^{ \frac{1}{6} } } { (x^{\frac{2}{3}})^{ \frac{1}{6} } } \\ &=& \left(\dfrac{ x^{\frac{3}{2}} } { x^{\frac{2}{3}} } \right)^{ \frac{1}{6} } \\ &=& \left(x^{\frac{3}{2}} \cdot x^{-\frac{2}{3}} \right)^{ \frac{1}{6} } \\ &=& \left(x^{\frac{3}{2}-\frac{2}{3}} \right)^{ \frac{1}{6} } \\ &=& \left(x^{\frac{9-4}{6}} \right)^{ \frac{1}{6} } \\ &=& \left(x^{\frac{5}{6}} \right)^{ \frac{1}{6} } \\ &=& x^{\frac{5}{6}\cdot\frac{1}{6} } \\ &=& x^{\frac{5}{36}} \\ \hline \end{array} \)

what 5 differnt group of numbers multiply will be 111111

3×7×11×13×37 = 111111

thats only for prisms.

that's alot of numbers

Multiply the area of the base with the height

104.3076923076923077

(x^(3/2))^(1/6)

___________

(x^(2/3))^(1/6)

simplify and use only positive exponents

\((x^\frac{3}{2})^\frac{1}{6}/(x^\frac{2}{3})^\frac{1}{6} \)

\(=x^\frac{1}{4}/x^\frac{1}{9}\\ =x^{\frac{1}{4}-\frac{1}{9}}\\ \color{blue}=x^{\frac{5}{36}}\) 

  !

There are 2 3s, a 5, and 3 qs.

3*3=3^2

q*q*q=q^3

We get 3^2*5*q^3, so simplifying, we get 45q^3.