All Answers 358468 Answers

So Anson buys 2x
kingsley buys 4-3x
jacky bought 2+5=x
annie bought 3=x
 

Thank you so much Melody! 😊

Yes, i believe that is correct.

Joy buys some slices.  I don't know how many. So I will let the unknown number be represented by the letter X

Joy buys X slices.

How many does Ansan buy (answer in terms of X)

Then work your way through the other purchases.

Make an equation then solve it.

Give it a go and show us your logic so we can help you more  if you need it.

To other answerers: Please let asker guest answer this.

Let ABCDEFGH be a cube of side length 5, as shown. Let P and Q be points on line AB and line AE, respectively, such that AP = 3 and AQ = 1. The plane through C, P, and Q intersects line DH at R. Find DR.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

∠CPQ ≈ 68.199º

∠DCR ≅ ∠APQ = 18.43494881º

DR = tan(∠DCR) * CD = 1.66666667    or     5/3

Thank you so much CPhill, :)

x  = number he ate on Monday

x + 4 =  Wed

3(x + 4)   = Fri

x  +  (x + 4)  + 3(x + 4)   =  26

x +  x  + 4  + 3x + 12 =   26

5x  + 16  =  26  

5x  = 26 - 16

5x   =  10

x =    2         on  Mon

x + 4  =     6   on Wed

3(6)  = 18  on Fri

a(a + 2b)  = 104/3

a^2  + 2ab    = 104/3      add b^2  to both sides and factor the  left side

a^2  + 2ab  + b^2 =    104/3  + b^2

(a + b)^2  =  104/3 + 7/9

( a + b)^2  =  313/9

sqrt [  (a + b)^2  ]  =   l a + b l

sqrt  [ 313/9 ]  =  l a + b l  =  sqrt (313) / 3

CORRECTIONS:

The perimeter of triangle A₃B₃C₃ is 14 times the perimeter of triangle ABC, and the triangle is turned upside-down.

P = 224 units

A (0, 0)      B (3, 4)        C (6, 0) 

A₁ (5.76, - 7.68)        B₁ (4, - 3)         C₁ (0, - 6)   

A₂ (13.76, - 7.68)           B₂ (12, - 3)          C₂ (8, - 6)   

A₃ (-192.64, 107.52)           B₃ (-168, 42)            C₃ (-112, 84)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Question: Why am I not able to edit my own post???!! It's weird... makes me 

First Term = 3 / 49

a. The value of r==13 / 49

b. The ratio test tells you that series converges to = 1 / 12

(a)

 5

 Σ C(5,n)  * (2x^5)^(5-n) *  [ (-1/9)y^4 ] ^(n)

n = 0

(b)

C(5, 2)  * (2x^5)^3  *  [ (-1/9)y^4]^2   =    10 * 8x^15  * (1/81)*y^8   =   80 x^15  y^8  / 81

a. 96 / 160 ==6/10 common ratio

b. 160 *  (6/10)^7 =69,984 / 15,625 - the 8th term

a(n) = a(n - 1) * 6 / 10 - Explicit Formula.

c. 160, 96, 288/5, 864/25, 2592/125, 7776/625, 23328/3125, 69984/15625==6145024 / 15625 - Total sum.

12^(1/4) part  is correct

Angles  should  be 90° apart   = pi/2

Calculation of  angle,   θ  =    arctan  (6sqrt (3) / 6)   =  arctan  ( sqrt (3)) = pi/3

1st  angle = (  θ/4)  =   (pi/3)/4  =  pi/12

2nd angle=  pi/12  + pi/2 =  7pi/12

3rd angle  =  7pi/12  + pi/2 =  13pi/12

4th angle =  13pi/12  +  pi/2  =  19pi/12

THX....!!!!

Look at the graph here :  https://www.desmos.com/calculator/fgiku8nsic

This triangle  will have a base of 6

The  apex of the  triangle is   (1.8, 3.4)

The distance  between this  point and the  y axis is the  altitude of the  triangle and  is  just  1.8  units

So.....the area is 

(1/2) ( 6) (1.8)  = 

3 * 1.8   =

5.4 units^2

Omg CHPIll I am big fan of you, actually respect you

We have  10 * 4 * 6 =   240 cubes

Number of cubes  with no wax on them  = 

(10 - 2)  ( 4 - 2)  ( 6 - 2)   =

8  *   2   *   4     =

64

Given that a(a + 2b) = 104/3 and b^2 = 7/9 then find |a + b|.

b^2 =7/9

b =sqrt(7/9)

a(a + 2*sqrt(7/9) =104/3, solve for a

a^2 + 2*sqrt(7/9)a =104/3

Solve for a:
a^2 + (2 sqrt(7) a)/3 = 104/3

Add 7/9 to both sides:
a^2 + (2 sqrt(7) a)/3 + 7/9 = 319/9

Write the left hand side as a square:
(a + sqrt(7)/3)^2 = 319/9

Take the square root of both sides:
a + sqrt(7)/3 = sqrt(319)/3 or a + sqrt(7)/3 = -sqrt(319)/3

Subtract sqrt(7)/3 from both sides:
a = sqrt(319)/3 - sqrt(7)/3 or a + sqrt(7)/3 = -sqrt(319)/3

Subtract sqrt(7)/3 from both sides:
 
a = sqrt(319)/3 - sqrt(7)/3      or        a = -sqrt(7)/3 - sqrt(319)/3

Abs[a + b] =sqrt(319) / 3

I'm assuming a regular triangular pyramid

The sides of  the triangle  cannot be  18, 18  and 41   because  this violates  the  triangular inequality

So....the sides  must  be  41,41  and 18  where  41 is the  slant height and 18 a base  edge

Sum of edge lengths =  3 ( 18 + 41)   = 3 ( 59)  =  177

Answered here :

https://web2.0calc.com/questions/fractions-decimals_1

Midpoint  =

[  ( 1 + 1)/2 , (4 + 10) / 2  ]  =  [ 2/2, 14/2 ] =   (1 , 7)     

You should be able to  finish this....

thank you

Mmmm....I don't  know, either.....that's the best I can do....

Your questions seem to  be  truncating, but I can answer this one.....

Using the distance  formula....

sqrt  [ (2a - 4)^2   + (a - 4 - (-1) )^2  ] =  2sqrt (10)        square both sides

(2a - 4)^2  +  ( a - 3)^2  =  40    simplify

4a^2 - 16a + 16  + a^2 - 6a + 9 =  40

5a^2 -22a  -15  =  0       factor

(5a  - 3) ( a  + 5)  =  0

So

5a - 3  =  0           a +  5   =0

5a   = 3                 a  = -5

a = 3/5

Product of all possible values of a =  (3/5) (-5)  =   -3