Mathematics Unit 2 Quiz

Explanation
The given equation states that 5 divided by x is equal to 10. In order to find the value of x, we need to determine what number when divided by 5 will result in 10. The only option that satisfies this condition is x = 0.5, as 5 divided by 0.5 does indeed equal 10. Therefore, x = 0.5 is the correct answer.

Explanation
The equation 2x + 1 = 5 can be solved by subtracting 1 from both sides to isolate the term with x. This gives us 2x = 4. Then, dividing both sides by 2, we find that x = 2.

Explanation
The equation given is (x + 6) / 3 = 2. To solve for x, we can multiply both sides of the equation by 3 to eliminate the fraction. This gives us x + 6 = 6. Then, we can subtract 6 from both sides of the equation to isolate x. This gives us x = 0. Therefore, the correct answer is x = 0.

Explanation
The given equation is 3/(x+2) = 3/4. To solve this equation, we can cross-multiply to get 4 * 3 = 3 * (x + 2). Simplifying further, we have 12 = 3x + 6. By subtracting 6 from both sides, we get 6 = 3x. Finally, dividing both sides by 3, we find that x = 2. Therefore, the correct answer is x = 2.

Explanation
The correct answer is x = 8 because when we substitute x = 8 into the equation x / 4 + x / 2 = 6, we get 8 / 4 + 8 / 2 = 2 + 4 = 6, which satisfies the equation.

Explanation
The given equation is a simple linear equation with one variable. To solve it, we need to isolate the variable x. By subtracting 2x from both sides of the equation, we get x + 1 = 5. Then, by subtracting 1 from both sides, we obtain x = 4. Therefore, the correct answer is x = 4.

Explanation
To solve the equation 3(x + 2) = 18, we need to simplify the expression on the left side. Distributing the 3, we get 3x + 6 = 18. Next, we isolate the variable by subtracting 6 from both sides, resulting in 3x = 12. Finally, we divide both sides by 3 to solve for x, giving us x = 4. Therefore, the correct answer is x = 4.

Explanation
The perimeter of a square is equal to the sum of all its sides. In this case, the perimeter is given as 20 cm. Since all sides of a square are equal, we can divide the perimeter by 4 to find the length of each side. 20 cm divided by 4 equals 5 cm. Therefore, the side length of the square is 5 cm.

Explanation
The perimeter of a rectangle is equal to twice the sum of its length and width. Let's assume the width of the rectangle is W cm. According to the given information, the length of the rectangle is less than the width by 2 cm, so the length would be (W - 2) cm. The perimeter is given as 24 cm, so we can set up the equation 2(W + (W - 2)) = 24. Simplifying this equation gives us 4W - 4 = 24, which further simplifies to 4W = 28. Dividing both sides by 4 gives us W = 7. Substituting this value back into the equation for the length, we find that the length is (7 - 2) = 5 cm. Therefore, the correct answer is L = 5 cm.