All Answers 356005 Answers

Let the number of apples Mr Leon buy

Given the number of pears was 1/3 the 

apples.

The number of pears = 1/3x.

Given the number of apples was twice the number of

Mangoes.

Number of mangoes = x/2.

Mr Leon spent $60 on some apples, mangoes and 

pears in the ratio 3:5:2.

It means he spent $3y on apples, $5y on mangoes

and $2y on pears .

=> $3y + $5y + $2y = $60

=> $10y = $60

=>    y = 6

He spend $18 on apples, $30 on mangoes 

and $12 on pears.

Given mangoes were of 3 for $5

In $30 he can by 6*3=18 mangoes.

It means the number of mangoes he bought = 18.

Since, the number of mangoes = x/2

           => x/2 = 18         => x = 36

It means the number of apples he bought = 36

The number of pears he bought = 36/3 = 12

The total number of fruit he bought = 18 + 36 + 12

                                              = 66.

He bought 66 fruits altogether.

Rhombus diagonals bisect each other at right angles

Use pythagorean theorem to find   1/2   of the other diagonal = sqrt 2072      TOTAL diagonal length = 2 sqrt (2072) = 91.04 units

            x + 12 = 1/2 (y-12)

=>      2x + 24 = y - 12

=>      2x - y = -36

          3x = 171

            x = 57

            y = 150

Christo had 57 marbles and Aris had 150 marbles at first.

=>     Aris had 150 marbles at first.

y = 5x^2-20x+1357+x^2-4x =

y = 6x^2 - 24x + 1357               will have a minimum value (y) at th4e 'x' value given by   -b /2a    = 24/12 = 2

Use this value of x in the equation to find the minimum value = 1333

9x^2 - 30x - 42 - x^2 - 2x  =

8x^2 - 32x - 42  = 0     

8 (x^2 - 4x)        - 42   = 0          'Complete the square'  for 'x'  

8 ( x-2)²    - 32    -42    = 0

8 (x-2)² - 74   = 0                           <====== Now you can see a    b   and   c   to finish

Area = 42pi square units

The volume of CFAH = (4 * 5 * 6) - (4 * 20)

amount spent on apples --- $ 3x
amount spent on mangoes -- $ 5x
amount spent on pears ---$ 2x
3x+5x+2x = 60
x = 6

"The mangoes were at 3 for $5", but he spent 5x or $30 on mangoes
at 3 for $5, there must have been 18 mangoes. 

number of
apples : pears : mangoes = 2y : 2y/3 : y 
= 6y : 2y : 3y

But we know the number of mangoes is 18
so 3y = 18, y = 6
so we have 36 apples, 12 pears and 18 mangoes

check:
twice as many apples as mangoes ?? Yes
The number of pears was 1/3 the number of apples ?? , YES
 

The interior angle sum to   ( n-2) * 180 = 1440

36x + 1188 = 1440

x = 7                                      so the two angles with 'x' in them are 147^o     105^o        so the smallest angle is 105^o

Kinda messy, but here is my solution

w = width

s = side

Sum of edges =  4 w   +   8 s   = 60

                              w +      2s = 15

                                   w = 15 - 2s

Surface area =  s*s    + s*s   + w*s  + w*s + w*s + w*s   =  2s^2 + 4 ws = 56   

                                                                                             s^2 + 2ws = 28        sub in the red equation for w

                                   s^2 +2s (15-2s) = 28

                                  s^2 + 30s - 4s^2  - 28 = 0

                                    -3s^2 + 30s-28 = 0               Quadratic formula show s = 1.04189    or  8.95811 (throw out ....too big)

                                                                                                             then w = 15-2s = 12.91622

Now we have the dimensions of the 3-d solid      diagonal = sqrt ( s^2 + s^2 + w^2) =~~ 13 units

Wrong

252% increase,as 6.3 is 2.52 times bigger

The length of the diagonal is 10*sqrt(2).

There are 7 possible lengths for the third side.

The possible values of AC are 26, 27, 28, 29, 30, for a total of $\boxed{5}$ values.

Rhombus sides are all equal    148 / 4 = 37 per side

   the diagonals of a rhombus intersect at right angles (see image below)  and bisect each other

        using pythag theorem you can find 1/2 of the other diagonal to be sqrt 1173  for total digonal length 2 * sqrt 1173

Area of a rhombus = diagonal 1  * diagonal 2   / 2        = 28 * 2 sqrt1173 / 2   units²     <====== I trust you can finish

removing 1/9 from A   leaves 8/9 A   left in A
 

8/9 A  / (B + 1/9 A)   = 4/7            Then   given that   B+ 1/9 A  =  42 + 8/9 A     sub this in for  ( B +  1/9 A)

8/9 A / (42 +8/9 A) = 4/7               

8/9 A = 4/7 ( 42 + 8/9 A)                         reults in A = 63    then because  B+ 1/9 A  =  42 + 8/9 A        B = 91 marbles originally

(6.3 - 2.5) / 2.5    * 100% = _________  percent increase

There was a total of 41 pupils in a class. Each girl made 35 bookmarks while each boy made 20 bookmarks for a fundraising project. The total number of bookmarks made by all the pupils was 1165. How many girls were there in the class?  

Let G represent the number of girls  

Let B represent the number of boys  

G + B = 41                    (equation 1)  

35G + 20B = 1165        (equation 2)  

Multiply eq 1 by 20              20G + 20B = 820     (equation 3)    

Subtract eq 3 from eq 2       35G + 20B = 1165  

                                            20G + 20B =   820

                                             15G           =  345  

                                                 G           =    23 girls  

You can substitute 23 into equation 1 to find the number of boys,

but the problem didn't ask for the number of boys.  

Have you even gone as far as graphing the given points?