We see that, if x satisfies the equation above => 

\(-8< 3x+4< -32\) and \(8< 3x+4< 32\)

So we have \(28\cdot2=56\) possible values of x.

Solve each equations we will have the exact values of x.

\(\sqrt{2+4+6+x}\) (Condition \(-12\le x< 8\)).

\(\Leftrightarrow\sqrt{12+x}=n\left(n\in N\right)\)

So x will satisfy \(x=\left\{-12;-11;-8;-3;4\right\}\)

The sum of \(x=-12-11-8-3+4=-30\)

Answer : - 30.

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.

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Call the number is a.

We have \(a\cdot x=a:0,125\)

\(\Leftrightarrow a\cdot x=a:\dfrac{1}{8}\)

\(\Leftrightarrow a\cdot x=a\cdot8\Rightarrow x=8\)

So the value of x is 8.

Answer : 8.

The shape must be placed in the shaded space is triangle :

Answer : Triangle \(\Delta\)

When Samir completes a ten-day job with the second ways, we have the total amounts he can earn:

\(1+2+4+8+16+32+64+128+256+512=1023\)

So the positive difference of the total amounts Samir can be paid :

\(1023-1000=23\)

Answer : 23.

The degree  measure of an interior angle of a regular pentagon is :

\(\left(5-2\right)\cdot\dfrac{180}{5}=3\cdot36=108^o\)

Answer : \(108^o\)

We have : y = x + a.

See : 5 = 2 + a => a = 3.

6 = 3 + a => a = 3.

7 = 4 + a => a = 3.

So the value of a is 3.

Answer : 3.

The first odd number is 21.

The last odd number is 157.

So there will be \(\dfrac{157-21}{2}+1=69\) (odd numbers) between 20 and 158.

Answer : 69 odd numbers.

We know that all the sides of a square are equal.

So we have : \(x-2=3\)

\(\Rightarrow x=5\)

So the value of x is 5.

Answer : 5.

The number of red grapes : \(50\cdot20\%=10\left(grapes\right)\)

So there will be \(50-10=40\left(grapes\right)\) are not red.

Answer : 40 grapes.

Area of the 120 mm2 triangle: 
Area = 1/2 x height x base 
120mm² = 1/2 x 10 x base 
Find out the base: 
120mm² = 5 x base 
base = 120/5 
=> base = 24mm. 

We know that two triangles that are similar will have same increase in height and base dimensions. 
Since height is doubled, then base is doubled. 

So :

height is 20mm 
base is 48mm 
The area of a similar triangle with a height of 20 mm is :

\(\dfrac{1}{2}\cdot20\cdot48=480\left(mm^2\right)\)

Answer : 480 mm2.

We have : \(Side=2\cdot Radius\)

So one side of the square is \(2\cdot4=8\left(ft\right)\)

The area of the square : \(8\cdot8=64\left(ft^2\right)\)

Answer : 64.

The sum of books : 6 + 3 + 7 = 16 (books)

The number of math books is : \(3+7=10\left(books\right)\)

The probability is : \(\dfrac{10}{16}=\dfrac{5}{8}\)

Answer : \(\dfrac{5}{8}\)

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

Answer : 120 ways.

We have :

1 year : 12 month.

35 years : x month

So \(x=12\cdot35=420\left(months\right)\)

Answer : 420 months.

We have the formula :

Volume = Length x Width x Height.

So \(120=5\cdot4\cdot height\)

So the value of the height is \(\dfrac{120}{5\cdot4}=6\left(in\right)\)

Answer : 6 in.

\(FACT\left(96\right)=2^5\cdot3\)

The greatest prime factor of 96 is 3.

Answer : 3.