All Answers 358087 Answers

Solve for x:
2 x^2+3 x-5 = 0

The left hand side factors into a product with two terms:
(x-1) (2 x+5) = 0

Split into two equations:
x-1 = 0 or 2 x+5 = 0

Add 1 to both sides:
x = 1 or 2 x+5 = 0

Subtract 5 from both sides:
x = 1 or 2 x = -5

Divide both sides by 2:
Answer: |  x = 1                     or                 x = -5/2

Not sure I know what 'Algebra Tiles' are ...but:

-4x + 8 = -8

Subtract 8 from both sides

-4x = -16    Divide both sides by -4

x = 4

-4x= -8+8

x= -8=8/4

x= 0/4

614.36

Do you mean:     y = 15 , 418  e ^(-0.929x)    ???         you'll need more info to calculate 'y' or 'x'     

Use Pythag theo to get length     8.3^2  + L^2 = 43.6^2      L= 42.8

Sq Ft of wall =   8.3 x 42.8 = 355.26

Each can covers 21.5 sq ft

355.26/21.5 =   16.524 cans ~  17 cans 

Nitrous oxide is N2O   Molecular weight is 14(2) + 16  = 44 gm/mole

STP = Standard Temp and Pressure     0 degrees C   and one atm pressure

One mole of gas occupies 22.4 liters of space at STP

1kg of N2O   is   1000/44 moles  =   22.727 moles

22.727 moles x 22.4 l / mole =  509 liters          A cubic meter is 1000 liters      509/1000= .509 m^3   for 1 kg N20 @ STP     (about a half of a cubic meter)

any number raised to 0 is 1 except for 0

any number raised to 0 is 1 except for 0

You can watch this video and a mathematicians explains how to resolve it:

https://www.youtube.com/watch?v=u7Z9UnWOJNY

You'll have to be given the numbers the pie sections represent       and the total pie number       

then   pi r^2 = area        each section then will be   (pie section number)/(total pie  number)  x pi r^2

10 x 12 +12=132 inches

132 x 23 =3,036 square inches.

1 Square foot=12 x 12 =144 sq.inches

3,036 / 144 =21 1/12 square feet

10'12" = 11'

11' (12 in/ft)  x 23"  = 3036 in^2  

3036/144 = 21.0833 ft^2

This is called "Zeno's Paradox", or a version of it. Google it and you will get some answers.

I honestly have no Idea, because when you add it up, it is going to take forever, and with no more clues, it will remain impossible :( unless I am wrong, please correct me

72X3 is 216

In general      \(\tan{(a + b)}=\frac{\tan a+\tan b}{1-\tan a\times \tan b}\)

Also  \(\tan{\frac{\pi}{4}}=1\)

So  \(\tan{(\frac{\pi}{4}+3t)}=\frac{1+\tan{3t}}{1-1\times\tan{3t}}\rightarrow \frac{1+\tan{3t}}{1-\tan{3t}}\)

.

.

[112/16] - [119/17] + [3 x 19] =

     7      -       7       +     57    = 57

Here is a step by step explanation! But, prepare yourself, it is very lengthy!!:
Verify the following identity:
(1+tan(3 t))/(1-tan(3 t))  =  tan(pi/4+3 t)

Multiply both sides by 1-tan(3 t):
1+tan(3 t)  =  ^?tan(pi/4+3 t) (1-tan(3 t))

Write tangent as sine/cosine:
1+(sin(3 t))/(cos(3 t))  =  ^?(1-(sin(3 t))/(cos(3 t))) (sin(pi/4+3 t))/(cos(pi/4+3 t))

(1-((sin(3 t))/(cos(3 t)))) ((sin(pi/4+3 t))/(cos(pi/4+3 t))) = ((1-(sin(3 t))/(cos(3 t))) sin(pi/4+3 t))/(cos(pi/4+3 t)):
1+(sin(3 t))/(cos(3 t))  =  ^?(sin(pi/4+3 t) (1-(sin(3 t))/(cos(3 t))))/(cos(pi/4+3 t))

Put 1+(sin(3 t))/(cos(3 t)) over the common denominator cos(3 t): 1+(sin(3 t))/(cos(3 t))  =  (cos(3 t)+sin(3 t))/(cos(3 t)):
(cos(3 t)+sin(3 t))/(cos(3 t))  =  ^?(sin(pi/4+3 t) (1-(sin(3 t))/(cos(3 t))))/(cos(pi/4+3 t))

Put 1-(sin(3 t))/(cos(3 t)) over the common denominator cos(3 t): 1-(sin(3 t))/(cos(3 t))  =  (cos(3 t)-sin(3 t))/(cos(3 t)):
(cos(3 t)+sin(3 t))/(cos(3 t))  =  ^?((cos(3 t)-sin(3 t))/(cos(3 t)) sin(pi/4+3 t))/(cos(pi/4+3 t))

Cross multiply:
cos(3 t) cos(pi/4+3 t) (cos(3 t)+sin(3 t))  =  ^?cos(3 t) sin(pi/4+3 t) (cos(3 t)-sin(3 t))

Divide both sides by cos(3 t):
cos(pi/4+3 t) (cos(3 t)+sin(3 t))  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

cos(pi/4+3 t) = cos(pi/4) cos(3 t)-sin(pi/4) sin(3 t):
cos(pi/4) cos(3 t)-sin(pi/4) sin(3 t) (cos(3 t)+sin(3 t))  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

cos(pi/4) = 1/sqrt(2):
(1/sqrt(2) cos(3 t)-sin(pi/4) sin(3 t)) (cos(3 t)+sin(3 t))  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

sin(pi/4) = 1/sqrt(2):
((1 cos(3 t))/sqrt(2)-1/sqrt(2) sin(3 t)) (cos(3 t)+sin(3 t))  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

((1 cos(3 t))/sqrt(2)-(1 sin(3 t))/sqrt(2)) (cos(3 t)+sin(3 t)) = cos(3 t)^2/sqrt(2)-sin(3 t)^2/sqrt(2):
cos(3 t)^2/sqrt(2)-sin(3 t)^2/sqrt(2)  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

cos(3 t)^2 = 1/2 (1+cos(6 t)):
1/sqrt(2) (1+cos(6 t))/2-sin(3 t)^2/sqrt(2)  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

(1+cos(6 t))/2 = 1/2+1/2 cos(6 t):
1/sqrt(2) 1/2+(cos(6 t))/2-sin(3 t)^2/sqrt(2)  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

sin(3 t)^2 = 1/2 (1-cos(6 t)):
(1 (1/2+(cos(6 t))/2))/(sqrt(2))-1/sqrt(2) (1-cos(6 t))/2  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

(1-cos(6 t))/2 = 1/2-1/2 cos(6 t):
(1 (1/2+(cos(6 t))/2))/(sqrt(2))-1/sqrt(2) 1/2-(cos(6 t))/(2)  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

(1 (1/2+(cos(6 t))/2))/(sqrt(2)) = 1/(2 sqrt(2))+(cos(6 t))/(2 sqrt(2)):
(1)/(2 sqrt(2))+(1)/(2 sqrt(2)) cos(6 t)-(1 (1/2-(cos(6 t))/(2)))/(sqrt(2))  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

-(1 (1/2-(cos(6 t))/(2)))/(sqrt(2)) = (cos(6 t))/(2 sqrt(2))-1/(2 sqrt(2)):
(1)/(2 sqrt(2))+(1)/(2 sqrt(2)) cos(6 t)+(cos(6 t))/(2 sqrt(2))-(1)/(2 sqrt(2))  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

(1)/(2 sqrt(2))+cos(6 t) (1)/(2 sqrt(2))-(1)/(2 sqrt(2))+cos(6 t) (1)/(2 sqrt(2)) = (cos(6 t))/sqrt(2):
(cos(6 t))/sqrt(2)  =  ^?sin(pi/4+3 t) (cos(3 t)-sin(3 t))

sin(pi/4+3 t) = cos(3 t) sin(pi/4)+cos(pi/4) sin(3 t):
(cos(6 t))/sqrt(2)  =  ^?cos(3 t) sin(pi/4)+cos(pi/4) sin(3 t) (cos(3 t)-sin(3 t))

sin(pi/4) = 1/sqrt(2):
(cos(6 t))/sqrt(2)  =  ^?(cos(3 t)-sin(3 t)) (1/sqrt(2) cos(3 t)+cos(pi/4) sin(3 t))

cos(pi/4) = 1/sqrt(2):
(cos(6 t))/sqrt(2)  =  ^?(cos(3 t)-sin(3 t)) ((1 cos(3 t))/sqrt(2)+1/sqrt(2) sin(3 t))

(cos(3 t)-sin(3 t)) ((cos(3 t) 1)/sqrt(2)+(1 sin(3 t))/sqrt(2)) = cos(3 t)^2/sqrt(2)-sin(3 t)^2/sqrt(2):
(cos(6 t))/sqrt(2)  =  ^?cos(3 t)^2/sqrt(2)-sin(3 t)^2/sqrt(2)

cos(3 t)^2 = 1/2 (1+cos(6 t)):
(cos(6 t))/sqrt(2)  =  ^?1/sqrt(2) (1+cos(6 t))/2-sin(3 t)^2/sqrt(2)

(1+cos(6 t))/2 = 1/2+1/2 cos(6 t):
(cos(6 t))/sqrt(2)  =  ^?1/sqrt(2) 1/2+(cos(6 t))/2-sin(3 t)^2/sqrt(2)

sin(3 t)^2 = 1/2 (1-cos(6 t)):
(cos(6 t))/sqrt(2)  =  ^?(1 (1/2+(cos(6 t))/2))/(sqrt(2))-1/sqrt(2) (1-cos(6 t))/2

(1-cos(6 t))/2 = 1/2-1/2 cos(6 t):
(cos(6 t))/sqrt(2)  =  ^?(1 (1/2+(cos(6 t))/2))/(sqrt(2))-1/sqrt(2) 1/2-(cos(6 t))/(2)

(1 (1/2+(cos(6 t))/2))/(sqrt(2)) = 1/(2 sqrt(2))+(cos(6 t))/(2 sqrt(2)):
(cos(6 t))/sqrt(2)  =  ^?(1)/(2 sqrt(2))+(1)/(2 sqrt(2)) cos(6 t)-(1 (1/2-(cos(6 t))/(2)))/(sqrt(2))

-(1 (1/2-(cos(6 t))/(2)))/(sqrt(2)) = (cos(6 t))/(2 sqrt(2))-1/(2 sqrt(2)):
(cos(6 t))/sqrt(2)  =  ^?(1)/(2 sqrt(2))+(1)/(2 sqrt(2)) cos(6 t)+(cos(6 t))/(2 sqrt(2))-(1)/(2 sqrt(2))

(1)/(2 sqrt(2))+cos(6 t) (1)/(2 sqrt(2))-(1)/(2 sqrt(2))+cos(6 t) (1)/(2 sqrt(2)) = (cos(6 t))/sqrt(2):
(cos(6 t))/sqrt(2)  =  ^?(cos(6 t))/sqrt(2)

The left hand side and right hand side are identical:
Answer: |  (identity has been verified)

Circumference = pi*D  where D is Diameter,  so here:  D = 4/pi feet

Cross-sectional Area, A = pi*(D/2)^2   so  A = pi*(2/pi)^2 →  A = 4/pi  ft^2

Volume, V, is A*Length  so  V = (4/pi)*20 or  V = 80/pi ft^3

.

x/x - 7=y
(x-7x)/x = y
x - 7x = xy
x(1 - 7) = xy divide both sides by (1 - 7)
x =xy / (1 - 7)

Assuming this is \(\frac{x}{x-7}=y\)

Multiply both sides by x - 7:  \(x = y(x-7)\)

Distribute the y over the bracketed terms;   \(x=yx-7y\)

Subtract yx from both sides:  \(x-yx=-7y\)

Factor the left-hand side;  \(x(1-y)=-7y\)

Divide both sides by 1 - y:  \(x=\frac{-7y}{1-y}\)

Alternatively, we could write this as:  \(x=\frac{7y}{y-1}\)

.

What is 3 to the 4th power=3^4=3 x 3 x 3 x 3=81