Algebra Flashcards

Where x is 4 and y is -2.35, calculate 1.12x + 21.5y + 13.22.

Answer: -32.785

To solve this, substitute the given values of x=4 and y=-2.35 into the expression 1.12x + 21.5y + 13.22. This yields (1.12 * 4) + (21.5 * -2.35) + 13.22. Calculating these parts gives 4.48 - 50.525 + 13.22, which sums up to -32.785.

Samuel is contrasting the costs of two brands of paper towels, A and B. The cheaper per roll price is Brand B, at $1.74. Brand B comes in packs of 12, but Brand A comes in packs of 8. The cost to buy a pack of Brand B is the same as the cost to buy a pack of Brand A. How much does Brand A cost each roll?

Answer: $2.61

First, calculate the cost of a pack of Brand B: $1.74/roll * 12 rolls/pack = $20.88 per pack. Since a pack of Brand A costs the same, a pack of Brand A also costs $20.88. To find the cost per roll for Brand A, divide the pack cost by the number of rolls: $20.88 / 8 rolls = $2.61 per roll.

The same kind of vacuum cleaner costs $115 to be purchased by both a veteran of war and an elderly person. They are each going to use their coupons, which state, respectively, "Senior discount $50!" and "veterans enjoy 20% off all store items!" Who is offered a better deal?

Answer: The senior citizen

The original price is $115. The senior citizen gets a $50 discount, so their price is $115 - $50 = $65. The veteran gets a 20% discount, which is 0.20 * $115 = $23, making their price $115 - $23 = $92. Comparing the two, $65 for the senior citizen is less than $92 for the veteran, meaning the senior citizen receives a better deal.

For x, solve 5 (x+3) = 3 (x-5)

Answer: x = -15

First, distribute the numbers outside the parentheses: 5x + 15 = 3x - 15. Next, gather the x terms on one side by subtracting 3x from both sides, resulting in 2x + 15 = -15. Finally, subtract 15 from both sides to isolate 2x, giving 2x = -30, and then divide by 2 to find x = -15.

Solve for the following variables: 3x - (2x + 3)2 = 5

Answer: x = -11

The equation is 3x - (2x + 3)2 = 5. First, distribute the 2 into the parentheses: 3x - (4x + 6) = 5. Then, distribute the negative sign: 3x - 4x - 6 = 5. Combine like terms: -x - 6 = 5. Add 6 to both sides: -x = 11. Finally, multiply by -1 to solve for x: x = -11.

Someone's unattended luggage drops from a helicopter's open hatchway at 30,000 feet in the air. How long before the luggage hits the ground can a rescue team attempt to catch it? If the luggage is falling at its terminal speed of 145 feet per second, this is an assumption.

Answer: 3 minutes and 27 seconds

To find the time it takes for the luggage to hit the ground, divide the total distance by the terminal speed: 30,000 feet / 145 feet per second ≈ 206.896 seconds. To convert this to minutes and seconds, divide by 60: 206.896 / 60 ≈ 3.448 minutes. This equates to 3 minutes and approximately 0.448 * 60 = 26.88 seconds, which rounds to 3 minutes and 27 seconds.

Is the following series arithmetic or geometric? 0, 2, 4, 6, 8

Answer: Arithmetic

An arithmetic series is defined by a constant difference between consecutive terms. In the given series (0, 2, 4, 6, 8), the difference between each term and the preceding one is consistently 2 (e.g., 2-0=2, 4-2=2). This constant common difference confirms that the series is arithmetic.