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To solve a geometric sequence, identify the first term and the common ratio. Use the formula a_n = a_1 * r^(n-1) to find any term in the sequence.
Exponential depreciation occurs when an asset loses value at a consistent percentage each year. For example, if a bakery's equipment originally worth $80,000 depreciates at 6% annually, it retains 94% of its value each year, leading to the correct formula: $a_n = 80,000(0.94)^{n-1}$.
Fractions represent parts of a whole, consisting of a numerator (top number) and a denominator (bottom number). For example, in the fraction 1/4, 1 is the part you have, and 4 is the total number of equal parts in the whole.
To find the y-intercept of a function, substitute 0 for x in the equation and solve for y. The resulting value of y is the y-intercept, where the graph crosses the y-axis.
To find the maximum height of a quadratic function like -x² + 14x - 40, use the vertex formula x = -b/2a. Substituting values gives a maximum height of 9 feet.
To calculate 2000 x 45, you can break it down into simpler parts. First, multiply 2 by 45 to get 90, then add the three zeros from 1000, resulting in 90,000.
Not all decimals that go on forever are irrational. Repeating decimals, like 2.333... or 4.686868..., are rational since they can be expressed as fractions, while non-repeating decimals, like π, are irrational.
To solve the equation x² - x = 144, first rearrange it to x² - x - 144 = 0. Then, you can use factoring or the quadratic formula to find the values of x.
To analyze the path of a rocket modeled by a quadratic function, first find the vertex to determine the maximum height, and then find the x-intercepts to see when the rocket is on the ground.
To determine the rule for generating terms in a number sequence, identify the common difference between consecutive terms. For example, in the sequence 23, 19.5, 16, 12.5, the common difference is -3.5, meaning you subtract 3.5 from each term to find the next.
$30 is approximately 22.2% of 135. To find this, divide 30 by 135 and convert the result to a percentage.
Yes, Desmos can help you visualize parabolas and separate variables in motion problems. By entering the equation into Desmos, you can easily find the vertex, which represents the maximum height of the parabola.
Your current checking account balance is $216.04, which is less than your original balance of $250.00 due to various transactions that decreased the total.
To find out how much 47 hotdogs cost, multiply the price of one hotdog by 47. For example, if each hotdog costs 10 rupees, then 47 hotdogs would cost 470 rupees.
No, a negative sign in front of a variable does not change the process of finding its derivative. The derivative of -3x is simply -3, as the negative sign remains with the coefficient.
To calculate compound interest, use the formula A = P(1 + r/n)^(nt). For a principal of $3500 at 7.5% interest compounded semiannually, the interest earned in the first year is calculated in parts, yielding a total balance of $3,812.50 at year-end.
To solve long division problems, set them up correctly, divide step by step, and bring down digits as needed. For example, in 5,129 ÷ 23, start by dividing the first two digits and continue the process.
To find the probability of a baseball fly ball traveling fewer than a certain distance, use the z-score formula. For example, for a distance of 234 feet, the probability can be calculated by standardizing the value and using normal distribution tables or a calculator.
To solve 3000 * 4000 - 10 + 2345, first multiply 3000 by 4000, then subtract 10 and add 2345. The final answer is 11,989,990.
Domain refers to the set of all possible x-values in a function, while range refers to the possible y-values. Understanding these concepts is crucial for mastering graph interpretation.
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