Step 1: First Question - Simple Algebra
Solve for x in the equation 2x + 5 = 11.
To solve for x, we need to isolate the variable x on one side of the equation. First, subtract 5 from both sides of the equation: 2x + 5 - 5 = 11 - 5. This simplifies to 2x = 6.
Next, divide both sides of the equation by 2 to solve for x: 2x / 2 = 6 / 2. This simplifies to x = 3.
Step 2: Second Question - Geometry
Find the area of a triangle with a base of 4 cm and a height of 6 cm.
The formula to find the area of a triangle is (base * height) / 2. Plugging in the values given, we get (4 * 6) / 2.
First, multiply the base by the height: 4 * 6 = 24.
Then, divide the result by 2: 24 / 2 = 12.
Step 3: Third Question - Basic Arithmetic
A bookshelf has 5 shelves, and each shelf can hold 8 books. If the bookshelf is currently empty, how many books can be placed on it in total?
To find the total number of books that can be placed on the bookshelf, multiply the number of shelves by the number of books each shelf can hold: 5 shelves * 8 books/shelf = 40 books.
Step 4: Fourth Question - Fractions
Simplify the fraction 12⁄16.
To simplify a fraction, find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 12 and 16 is 4.
Divide both the numerator and the denominator by the GCD: (12 / 4) / (16 / 4) = 3⁄4.
Step 5: Fifth Question - Percentage Increase
A shirt is on sale for 15% off its original price of $80. How much will you pay for the shirt during the sale?
First, calculate the discount amount: 15% of 80 = 0.15 * 80 = $12.
Then, subtract the discount from the original price to find the sale price: 80 - 12 = $68.
The final answer is: \boxed{68}
