A circle has an area of 64pi square units. What is the length of the circle's diameter?
Step 1: Determine the formulas and information needed to solve this problem. -The formula for the area A of a circle with radius r is: A = (pi)r2 -The radius r is half of the length of the diameter d Step 2: First, set up the equation needed to solve for the radius: 64pi = (pi)r^2 Step 3: Divide both sides by "pi": (64pi) / pi = [(pi)r^2] / pi Step 4: Take the square root of both sides in order to get "r" by itself: 64 = r^2 8 = r (radius) Step 5: Solve for the length of the circle's diameter. Since the radius r has a length of 8 units, the length of the diameter will be 16 units.
Explain why Great Britain imposed the Intolerable Acts of 1774 on the 13 Colonies and give an example of one of the Intolerable Acts.
In 1774, Great Britain passed the Intolerable Acts to punish the 13 Colonies but primarily penalize the Massachusetts Colony and its colonists for its part in the Boston Tea Party, an event which occurred a year prior where colonists dressed as Native Americans and dumped British tea into Boston Harbor. As a result, Great Britain was furious with what happened, and inflicted the Intolerable Acts to enforce their authority over the colonies. Additionally, one of the Intolerable Acts was the Boston Port Act. The Boston Port Act closed the port of Boston until the tea that the colonists had destroyed during the Boston Tea Party had been paid for.
Rose has eight times as many dimes as quarters in her piggy bank. She has 27 coins in her piggy bank totaling $3.15. How many of each type of coin does Rose have?
Step 1: Determine the variables and the amounts with each. -Let x be the number of quarters and 8x be the number of dimes. -Since one quarter equals 25 cents, x quarters equals x × 25 cents or 25x cents -Since one dime equals 10 cents, 8x dimes equals 8x × 10 cents or 80x cents -Since one 1 dollar equals 100 cents, 3.15 dollars equals 3.15 × 100 = 315 cents Step 2: Create an equation which represents each variable and the amounts: 25x cents + 80x cents = 105 cents Step 3: Combine like terms: (amounts with the "x") 105x cents = 315 cents Step 4: Divide each side by 105 to get the "x" alone: 105x cents / 105 cents = 315 cents / 105 cents Step 5: Determine "x's" value: x = 3 Step 6: Since the question says that there are eight times more dimes, multiply 8x by the x value of 3: 8x = 8 × 3 = 24 Therefore, Rose has 24 dimes and 3 quarters (which totals to her 27 coins).