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80 is the answer

courage

x = shortest piece

x-3  = next piece

x +4 = last piece                summed they equal 84 inches

x      +     x-3      +      x+4    = 84

3x + 1 = 84

3x = 83

x = 83/3  inches           now you should be able to find the other two lengths....

9≤17−4x      add 4x to both sides

4x + 9 <= 17      subtract 9 from each side

4x <= 8              divide by 4

x <= 2

x     +        x+4   <= 14       where x = neighbors age

2x+4<=14

2x<=10

x<=5

Look under your original post

Look under the original post.

Let the number of big vases ==B
Let the number of small vases ==S

B + S ==837....................(1)
0.9B ==Big vases left after 1/10 got broken.
S + 47 - total of small vases.
[S + 47] ==1/3 * 0.9B.......(2), solve for B, S

B==680 - Big vases that he started with.
S==157 - Small vases that he started with.

680  -  157 ==523 difference between Big and Small vases

Peter spent: $1.20 * 15 ==$18 spent in 15 days.
$1.20 * 1 2/3 ==$2 - what Cindy spent daily

a)  2D ==18 + 1.20D + 11.60, solve for D
2D - 1.20D ==29.60
0.8D == 29.60
D==29.60 / 0.8 ==37 days it took Cindy to spend all her money.

b) Peter spent: $1.20 * [37 + 15] days==$1.20 x 52 days ==$62.40 in total

Check: Cindy spent:$2 * 37 days==$74
$74 - $62.40 ==$11.60 that Cindy spent more than Peter.

ACTUALLY.....   your 'answer' of 48 is the marbles that Theodore has.....    not the total of the two friends.....

48 is the answer

courage

a/t = 2/3        a = 2/3 t

(a-2 )/(t+2) = 3/5

a-2 = 3/5 (t+2)        sub in the red equation

2/3t -2  = 3/5 (t+2)    solve for t     then you can solve for   a = 2/3 t     then add them together for the total

x= 1st piece

3x = 2nd

4x = 3rd piece        totalled, they equal 40 inches

x  + 3x   +   4x   = 40

8x= 40

x=5 inches

Let the amount of money that Antwan has==A

Then, Joe has ==1/3A

A - 15 ==3/5 * [1/3A + 15]

A - 15==1/5A + 9

A - 1/5A ==9 + 15

4/5A ==24

4A ==24 * 5 ==120

A ==120 / 4 ==$30 what Antwan started with

1/3 * 30 ==$10 what Joe started with

Fourth is -2,2

Sum of convex decagon interior angles = 1440                 ( that is (10-2  * 180)   )

(5 *2 + 8*2 + 9*6) y = 1440

80y = 1440     solve for y

Let the number of roses at AF==A
Let the number of roses at BF==B

2/7A==3/4B
[A - 84] / [B + 58] ==3/2, solve for A, B

Use substitution to get:

A==399 roses - what Angel Florist started with
B==152 roses - what Beauty Florist started with.

What is the question?

Factors of 36 are 1,2,3,4,6,9,12,18,36

If there are five ones then other must be 36

If there are four ones then we can have    2,18    3,12    4,9     6,6

If there are 3 ones then  2,2,9    2,3,6     3,3,4     

If there are 2 ones then   2,2,3,3  

If there is only one 1 then there are no possibilities.

So I get  1+ 4 + 3+1 = 9

But i have not checked it.

how about 1 1 1 1 1 36

there is no mention that these integer have to be single digit.

How many ways can three types of animals be arranged in a line.  That is easy. 3! = 6 ways.

It looks like it can be written in 6 different ways:

11149 , 11166 , 11229 , 11236 , 11334 , 12233 , Total =  6 different ways.

(3^100) mod (23*3)==3 the remainder

(2^70 + 3^70)  mod (13*5)==13 the remainder.

P = 4 + √8

What is a + b^2?

Hello Guest!

\(x^2 + 5x + 8 = -14\\ x_{1,2}= \frac{1}{2}(-5\pm 3\sqrt{7}i)\\ x_1=a+b_1i=-\frac{5}{2}+\frac{3\sqrt{7}i}{2}\\ {\color{blue}a+b_1^2}=-\frac{5}{2}+\frac{63}{4}\color{blue}=\dfrac{53}{4}\)

\(x_2=a+b_2i=-\frac{5}{2}-\frac{3\sqrt{7}i}{2}\\ {\color{blue}a+b_2^2}=-\frac{5}{2}+\frac{63}{4}\color{blue}=\dfrac{53}{4}\)

  !