By theme we have:

a = 2b = 3c = 4d = 6e

and because a,b,c,d,e are the ages of 5 people, them are bigger than 0

\(\Rightarrow a⋮2,3,4,6\) and a is  smallest

=> a is least common multiple

\(LCM\left(2,3,4,6\right)=12\)

So a is 12

=> \(\left\{{}\begin{matrix}b=6\\c=4\\d=3\\e=2\end{matrix}\right.\Rightarrow a+b+c+d+e=12+6+4+3+2=27\)

So the smallest possible value of a+b+c+d+e is 27

There are \(5\cdot3\cdot2\cdot4=120\) different uniforms can he wear to school.

Answer : 120 ways.

\(4x-12y=-19\Leftrightarrow12y=4x+19\Leftrightarrow y=\dfrac{1}{3}x+\dfrac{19}{12}\)

The x-coordinates of the intersection points of the graphs satisfy :

\(x^2-3x+3=\dfrac{1}{3}x+\dfrac{19}{12}\Leftrightarrow x^2-\dfrac{10}{3}x+\dfrac{17}{12}=0\)

Since there are 2 intersection points, we can apply the Vieta's formulas. The answer is \(\dfrac{10}{3}\)

Call the percent increase is x (%)

Because the number of participants increase each year study.

We have equation : 

\(\left\{{}\begin{matrix}P=40+40\cdot x\%\\P+P\cdot x\%=90\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}P=40+40\cdot x\%\\40+40\cdot x\%+\left(40+40\cdot x\%\right)\cdot x\%=90\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}P=40+40\cdot x\%\\x\%=50\%\end{matrix}\right.\)

So \(P=40+40\cdot50\%=60\)

Answer P = 60.

Call the percent increase is x (%)

Because the number of participants increase each year study.

We have equation : 

So 

Answer P = 60

Call the percent increase is x (%)

Because the number of participants increase each year study.

We have equation : 

{P=40+40⋅x%P+P⋅x%=90

⇔{P=40+40⋅x%40+40⋅x%+(40+40⋅x%)⋅x%=90

⇒{P=40+40⋅x%x%=50%

So P=40+40⋅50%=60

Answer P = 60.

Let x (mi/h) be the average speed driving from starting location to the delivery location.

\(\Rightarrow\) The average speed driving from delivery location(DL) to the starting location(SL) is x - 20 (mi/h)

It took her 180/x (hours) to travel from SL to DL and 180/(x - 20) (hours) to travel from DL to SL, which means: 180/x + 180/(x - 20) = 7,5

\(\Rightarrow\) x = 60 

So her average driving from SL to DL is 60 mi/h

3 kg

3 kg

tk nhé

Let x, y, z be the weights of three pumpkins :

\(x\le y\le z\)

So we have x + y = 8 ; x + z = 9 ; y + z = 11

=> ( x + z ) - ( x + y ) = 9 - 8

=> z - y = 1

=> z = ( 11 + 1 ) : 2 = 6

y = z - 1 = 5

x = 8 - y = 8 - 5 = 3

So the answer is 3 kg.