Algebra
Solve for x: 2x + 5 = 17
Subtract 5 from both sides, 2x = 12, then divide by 2, x = 6.
Calculate the area of a rectangle with length 8 cm and width 5 cm.
Area = length * width = 8 cm * 5 cm = 40 cm²
Evaluate the expression: 5 + 2 * 3
5 + 2 * 3 = 5 + 6 = 11
Simplify the fraction: 24/36
The fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, GCD(24, 36) = 12. Divide both by 12 to get 2/3
Calculate the mean of the following numbers: 10, 12, 15, 18, 20.
Mean = (10 + 12 + 15 + 18 + 20) / 5 = 75 / 5 = 15
Solve the equation for y: 3y - 7 = 8
Add 7 to both sides, 3y = 15, then divide by 3, y = 5
Find the perimeter of a square with each side measuring 9 meters.
Perimeter = 4 * side length = 4 * 9 m = 36 meters
Simplify the expression: 5 * (7 - 2) + 4.
Start with the parentheses, 7 - 2 = 5. Then, perform the multiplication, 5 * 5 = 25. Finally, add 25 + 4 = 29.
Add the fractions: 1/4 + 3/8
To add fractions, find a common denominator, which is 8 in this case. Convert both fractions, 1/4 = 2/8, then add: 2/8 + 3/8 = 5/8
A school bus travels at an average speed of 40 km/h. How long does it take to travel 120 km?
Time = Distance / Speed = 120 km / 40 km/h = 3 hours
Solve for z: 5z - 3 = 32
Add 3 to both sides, 5z = 35. Finally, divide by 5 on both sides, z = 7
What is the volume of a cube with edges measuring 6 cm?
Volume = edge length^3 = 6 cm^3 = 216 cm³
Simplify the expression: 2 + 3 * (8 - 4) ÷ 2
Start with the parentheses, 8 - 4 = 4. Then, perform the multiplication, 3 * 4 = 12. Next, do the division, 12 ÷ 2 = 6. Finally, add 2 + 6 = 8
Subtract the fractions: 5/6 - 2/3
Find a common denominator, which is 6 in this case. Convert both fractions, 5/6 = 5/6, then subtract: 5/6 - 2/3 = 4/6 = 1/6
What three numbers, when added together, give the same result as when multiplied together?
The numbers are 1, 2, and 3. 1 + 2 + 3 = 6, and 1 * 2 * 3 = 6
Simplify the expression: 3(4x + 2) - 2(3x - 5).
Distribute the multiplication, 12x + 6 - 6x + 10. Combine like terms, 12x - 6x + 6 + 10 = 6x + 16. Simplify, 2(3x+8).
What is the sum of the interior angles of a triangle?
The sum of the interior angles of a triangle is always 180 degrees
Simplify the expression: 12 - (4 + 2) * 3 / 6
Begin with the parentheses, 4 + 2 = 6. Then, perform the multiplication, 6 * 3 = 18. Next, do the division, 18 / 6 = 3. Finally, subtract 12 - 3 = 9
Multiply the fractions: 2/5 * 3/4
To multiply fractions, simply multiply the numerators and denominators: (2 * 3) / (5 * 4) = 6/20 = 3/10
If two cats can catch two mice in two minutes, how many cats are needed to catch 100 mice in 100 minutes?
The number of cats needed remains the same – two cats. The problem states that two cats can catch two mice in two minutes. Therefore, the rate at which they catch mice is 1 mouse per cat per minute. So, two cats will catch 100 mice in 100 minutes.
Solve the equation: 3(x - 2) = 4x + 5.
Distribute the multiplication, 3x - 6 = 4x + 5. Move the variable terms to one side, 3x - 4x = 5 + 6, which simplifies to -x = 11. Finally, multiply by -1 to isolate x, x = -11
The Area of a Triangle is 100. The Height is 10. What is the base?
Area of Triangle: 1/2BH
1/2 B(10)=100. First, Divide 10/2 =5. Then divide by 5 on both sides. Base = 20
Simplify the expression: 15 - 2 * 3^2 + 8 ÷ 4
First, perform the exponentiation, 3^2 = 9. Then, do the multiplication, 2 * 9 = 18. Next, perform the division, 8 ÷ 4 = 2. Finally, perform the addition and subtraction, 15 - 18 + 2 = -1
Divide the fractions: (7/25) / (6/19)
First K.C.I. Keep the first fraction, change the division to multiply and flip the last fraction = (7/25)/(19/6). Multiply the fractions (133/150)
What is the next number in the sequence: 1, 1, 2, 3, 5, 8, 13, ...?
This is the Fibonacci sequence. The next number is found by adding the two previous numbers: 13 + 8 = 21. So, the next number is 21.