t1

Solution

Correct: A

We can use the Pythagorean theorem to solve this problem. Let's denote the length of the other leg as x. The Pythagorean theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b): c^2 = a^2 + b^2. In this case, c = 10 cm and a = 6 cm. Plugging these values into the equation, we get 10^2 = 6^2 + x^2, which simplifies to 100 = 36 + x^2. Subtracting 36 from both sides gives us x^2 = 64. Taking the square root of both sides, we find x = 8 cm.

Solution

Correct: A

The area of a parallelogram is given by the formula A = b*h, where A is the area, b is the base, and h is the height. We are given that the area is 50 cm^2 and the base is 10 cm. Plugging these values into the formula, we get 50 = 10*h. To find the height, we divide both sides by 10, giving us h = 50/10 = 5 cm.

Solution

Correct: B

To solve the equation, we need to isolate x on one side. We start by subtracting 5 from both sides of the equation: 2x + 5 - 5 = 11 - 5, which simplifies to 2x = 6. Next, we divide both sides by 2 to find x: 2x/2 = 6/2, giving us x = 3.

Solution

Correct: C

To find the number of bags needed, we divide the total number of loaves by the number of loaves per bag: 250 loaves / 5 loaves per bag = 50 bags.

Solution

Correct: A

The measure of the intercepted arc is equal to the measure of the central angle. Therefore, the measure of the intercepted arc is also 60 degrees.

Solution

Correct: A

To simplify the expression, we combine like terms: (3x^2 + 2x^2) + (2x - x) + (-1 - 3) = 5x^2 + x - 4.

Solution

Correct: D

The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the width. Plugging in the given values, we get P = 2(8 + 5) = 2*13 = 26 cm.

Solution

Correct: A

To solve the equation, we multiply both sides by 4 to isolate x: x = 9*4, giving us x = 36.

Solution

Correct: A

To find the average speed, we need to find the total distance traveled and the total time taken. Since the distance from A to B is the same as from B to A, let's denote this distance as d. The time taken to travel from A to B is d/60 and the time taken to travel from B to A is d/40. The total time is d/60 + d/40. To add these fractions, we find a common denominator: (2d + 3d)/120 = 5d/120. The total distance is 2d. The average speed is total distance / total time = 2d / (5d/120) = 2d * 120 / 5d = 240 / 5 = 48 km/h.

Solution

Correct: A

The volume of a cylinder is given by the formula V = pi*r^2*h, where r is the radius and h is the height. Plugging in the given values, we get V = pi*(4)^2*10 = pi*16*10 = 160*pi cm^3.

Solution

Correct: A

To solve the equation, we first add 3 to both sides: 2x - 3 + 3 = 7 + 3, which simplifies to 2x = 10. Then, we divide both sides by 2: 2x/2 = 10/2, giving us x = 5.

Solution

Correct: D

Let's denote the number of cookies as x. Then the number of cupcakes is x + 60. Since the total number of items is 480, we can set up the equation x + (x + 60) = 480. Combining like terms gives us 2x + 60 = 480. Subtracting 60 from both sides gives us 2x = 420. Dividing both sides by 2 gives us x = 210. Therefore, the number of cookies is 210 and the number of cupcakes is 210 + 60 = 270.

Solution

Correct: B

To solve for x, we first subtract 3 from both sides: x/2 + 3 - 3 = 5 - 3, which simplifies to x/2 = 2. Then, we multiply both sides by 2 to isolate x: x = 2*2 = 4.

Solution

Correct: B

To find the speed of the car, we divide the total distance traveled by the total time: 250 km / 5 hours = 50 km/h.

Solution

Correct: B

To simplify the expression, we use the distributive property (FOIL method): (2x + 5)*(x - 2) = 2x*x + 2x*(-2) + 5*x + 5*(-2) = 2x^2 - 4x + 5x - 10 = 2x^2 + x - 10.

Solution

Correct: @

To find the area of the path, we first find the area of the larger rectangle including the path and then subtract the area of the garden. The larger rectangle has dimensions of 10 + 2*1 = 12 meters by 5 + 2*1 = 7 meters. The area of the larger rectangle is 12*7 = 84 m^2. The area of the garden is 10*5 = 50 m^2. The area of the path is then 84 - 50 = 34 m^2. However, this problem seems to have no direct match among the provided choices, indicating a calculation or interpretation error in the question as presented.

Solution

Correct: A

The surface area of a cube is given by the formula A = 6*s^2, where s is the length of a side. Plugging in the given value, we get A = 6*(6)^2 = 6*36 = 216 cm^2.

Solution

Correct: C

The equation is a quadratic equation in the form of (x + a)^2 = 0, where a = 2. Thus, it factors to (x + 2)^2 = 0. Taking the square root of both sides gives us x + 2 = 0. Solving for x, we get x = -2.

Solution

Correct: A

To find the percentage of the tank that is filled, we divide the amount of water in the tank (1200 liters) by the total capacity of the tank (3000 liters) and multiply by 100: (1200/3000)*100 = 40%.

Solution

Correct: B

To solve for x, we first subtract 2 from both sides: 2x + 2 - 2 = 12 - 2, which simplifies to 2x = 10. Then, we divide both sides by 2 to isolate x: x = 10/2 = 5.

Solution

Correct: A

To find the average speed for the round trip, we first need to understand that the distance from A to B is the same as from B to A. Let's denote this distance as d. The time taken to travel from A to B is d/40, and the time taken to travel from B to A is d/60. The total time is d/40 + d/60. To add these fractions, we find a common denominator: (3d + 2d)/120 = 5d/120. The total distance is 2d. The average speed is total distance / total time = 2d / (5d/120) = 2d * 120 / 5d = 240 / 5 = 48 km/h.